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Inverse Design of Tetracene Polymorphs with Enhanced Singlet Fission Performance by Property-Based Genetic Algorithm Optimization
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  • Rithwik Tom
    Rithwik Tom
    Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania15213, United States
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  • Siyu Gao
    Siyu Gao
    Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania15213, United States
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  • Yi Yang
    Yi Yang
    Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania15213, United States
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    Orcidhttps://orcid.org/0000-0001-9905-126X
  • Kaiji Zhao
    Kaiji Zhao
    Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania15213, United States
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  • Imanuel Bier
    Imanuel Bier
    Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania15213, United States
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    Orcidhttps://orcid.org/0000-0003-1084-770X
  • Eric A. Buchanan
    Eric A. Buchanan
    Department of Chemistry, University of Colorado, Boulder, Colorado80309, United States
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  • Alexandr Zaykov
    Alexandr Zaykov
    Institute of Organic Chemistry and Biochemistry, Czech Academy of Sciences, 16610Prague 6, Czech Republic
    Department of Physical Chemistry, University of Chemistry and Technology, 166 28Prague 6, Czech Republic
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  • Zdeněk Havlas
    Zdeněk Havlas
    Institute of Organic Chemistry and Biochemistry, Czech Academy of Sciences, 16610Prague 6, Czech Republic
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  • Josef Michl
    Josef Michl
    Department of Chemistry, University of Colorado, Boulder, Colorado80309, United States
    Institute of Organic Chemistry and Biochemistry, Czech Academy of Sciences, 16610Prague 6, Czech Republic
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  • Noa Marom*
    Noa Marom
    Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania15213, United States
    Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania15213, United States
    Department of Chemistry, Carnegie Mellon University, Pittsburgh, Pennsylvania15213, United States
    *[email protected]
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    Orcidhttps://orcid.org/0000-0002-1508-1312
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Chemistry of Materials

Cite this: Chem. Mater. 2023, 35, 3, 1373–1386
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https://doi.org/10.1021/acs.chemmater.2c03444
Published January 21, 2023

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Abstract

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The efficiency of solar cells may be improved by using singlet fission (SF), in which one singlet exciton splits into two triplet excitons. SF occurs in molecular crystals. A molecule may crystallize in more than one form, a phenomenon known as polymorphism. Crystal structure may affect SF performance. In the common form of tetracene, SF is experimentally known to be slightly endoergic. A second, metastable polymorph of tetracene has been found to exhibit better SF performance. Here, we conduct inverse design of the crystal packing of tetracene using a genetic algorithm (GA) with a fitness function tailored to simultaneously optimize the SF rate and the lattice energy. The property-based GA successfully generates more structures predicted to have higher SF rates and provides insight into packing motifs associated with improved SF performance. We find a putative polymorph predicted to have superior SF performance to the two forms of tetracene, whose structures have been determined experimentally. The putative structure has a lattice energy within 1.5 kJ/mol of the most stable common form of tetracene.

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Introduction

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The maximum efficiency of a single-junction solar cell is given by the Shockley–Queisser limit, (1) which assumes that one photon is converted into one charge carrier. Under ambient conditions, the resulting conversion efficiency is approximately 33%. One of the main reasons for performance degradation is the energy loss when high-energy excitons relax to the band edge, wasting the excess energy of high-energy photons as heat. This may be overcome by multiexciton generation methods in which a high-energy photon can be split into lower-energy excitons that are efficiently harvested. (2) Thus, the limit of efficiency of a solar cell may be enhanced to nearly 47%. (3)
Singlet fission (SF) is a multiexciton generation phenomenon observed in molecular crystals, where a singlet-state exciton is converted into two triplet-state excitons. (4−6) SF was discovered as early as 1965 in crystalline anthracene. (7) To date, certain materials have been observed to undergo SF in the solid state, including acenes, (4,5,8−11) rylenes, (12−15) diphenylisobenzofuran, (16,17) carotenoids, (18−20) and thiophenes. (21−24) For a material to undergo SF, the adiabatic singlet exciton energy should be greater than twice the adiabatic triplet exciton energy. A singlet exciton with more electron delocalization on neighboring molecules can potentially improve the coupling between singlet and triplet states. (25−28) Thus, a higher degree of charge transfer character (%CT) in the lowest singlet excited state is considered beneficial to SF. (4,6,29) In addition to efficient SF, practical applications in solar cells require several desirable properties such as photostability, conductivity, and exciton diffusibility. (29,30) This has motivated the search for new classes of SF materials that are commercially viable. Recently, several experimental (31,32) and computational (28,33−38) studies have focused on identifying new candidate materials for SF.
The electronic and optical properties of a molecular crystal depend on how the molecules are packed and the resulting electronic coupling between them. Polymorphs, i.e., different crystal structures of the same molecule, can have significantly different properties. (35,39,40) Understanding the effect of crystal packing on singlet fission (SF) has been of recent interest. (5,6,35,41−45) Tetracene, one of the earliest known SF materials, has been reported to exhibit polymorphism. (46−48) The SF in the common form of tetracene has been found to be slightly endoergic. (49) This means that modifying the crystal packing may potentially shift the singlet and triplet excitation energies to make SF more or less favorable. Two unique crystal structures of tetracene are available in the Cambridge Structural Database (CSD). (46,50−53) The T1 crystal structure, shown in Figure 1a, is the commonly occurring bulk phase of tetracene. (54) T2, shown in Figure 1b, is a polymorph found predominantly in thin films. (55,56) Both forms of tetracene contain two molecules per unit cell. As shown in panels b and c of Figure 1, the molecule pair of the T1 crystal structure (gray) is slipped relative to that of T2 (green). A detailed account of the differences in the structure of these polymorphs and their experimental synthesis and characterization can be found in ref (55). SF in a thin film form of tetracene was experimentally found to be significantly faster than in the stable T1 polymorph. (57) The crystal structure therein was not fully solved to determine the atomic positions; however, it is assumed by the authors to be T2 on the basis of the lattice parameters. The transfer of triplet excitons was also found to be more efficient for T2, potentially making it a better candidate than T1 for SF-sensitized silicon cells. (58) This demonstrates that the specific crystal packing of tetracene is crucial for its SF performance.

Figure 1

Figure 1. Two experimentally observed forms of tetracene: (a) the common T1 polymorph (54) and (b) the second form, T2, (55) viewed along the c-axis with the molecules colored green and the T1 molecules colored black, overlaid using the Cambridge Crystallographic Data Centre (CCDC) packing similarity tool. (59) (c) Overlay of the molecules of the T1 form in gray and the T2 form in green.

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In addition to the thermodynamic driving force, which results from the energy balance between the singlet and triplet excited states, kinetic considerations affect the SF performance of a molecular crystal. To elucidate the effect of crystal packing on SF rates, Michl and Havlas developed a dimer-based model, (60) implemented in the “Simple” code. (61) Simple was not designed to predict absolute SF rates but to identify geometrical factors affecting SF for a given material. Thus, Simple may be helpful in the identification of optimal dimers for a specific molecule. The Simple model has been applied to dimers of ethylene, (61) tetracene, (62) 1,3-diphenylisobenzofuran, (43) and other molecules. (63,64) The results of these studies suggest that the SF rate is sensitive to slight changes in geometry, validating experimental observations. These studies have analyzed millions of chromophore orientations within a dimer and have provided useful guidance for optimal packing. However, the dimers found to be optimal are not those seen in the experimentally observed crystal structures. In particular, the dimer extracted from the T1 form of tetracene is close to only the 10th most optimal dimer found by Simple. (62) It is thus challenging to realize a crystal with optimal dimer geometry for SF in practice. To find molecular packing arrangements that are experimentally synthesizable, it is important to consider the space of potential polymorphs, i.e., the local minima of the potential energy surface (PES) that are within a range of approximately 4 kJ/mol (65) of the global minimum. For this purpose, tools for molecular crystal structure prediction (CSP) can be utilized.
CSP is the fundamental problem of predicting the crystal structure of a molecule using computer simulations. (66−69) CSP is a notoriously challenging problem because it requires searching a high-dimensional space with high accuracy. (70,71) A typical CSP workflow starts by generating putative crystal structures using random or quasi-random methods to adequately sample the configurational space. (72−75) A variety of global optimization algorithms are used to explore the PES. (68,69,76,77) These optimization schemes are coupled with hierarchical energy evaluations and geometry relaxations that employ increasingly more accurate and computationally expensive methods for reducing the number of candidates to be considered further. Dispersion-inclusive density functional theory (DFT) has become the method of choice for ranking candidate structures. (71,78) The effect of temperature on ranking can be accounted for by applying vibrational corrections via the harmonic or quasi-harmonic approximation methods. (79,80) Recently, CSP has been used in conjunction with experiments to discover potential polymorphs. (81,82)
While traditional CSP is focused on searching for the structures with the lowest energy, we are interested in structures with optimal SF performance. The search for a structure with a target property is known as inverse design. (83,84) To this end, we use a property-based genetic algorithm (GA). A GA generates new offspring by performing crossover and mutation operations on the structural genes of parent structures. Structures are selected for mating on the basis of a fitness function, which assigns a higher probability of selection to fitter structures. This propagates desirable features in the population. The cycle of fitness evaluation, selection, and mating repeats until no better structures are found. For CSP, structures with lower energies (i.e., higher stability) have a higher fitness. An advantage of a GA over other methods is that the fitness function can be formulated to optimize any property of interest. GAs with tailor-made fitness functions have been used, for example, to optimize the electronic, (85) optical, (86) and excitonic (87) properties of materials, as well as transport properties of organic semiconductor molecules. (88) Unlike the global minimum search of traditional CSP, a property-based GA does not necessarily yield one optimum but a set of solutions with the target property and stability within an acceptable range. Once putative structures predicted to possess desirable properties are found, experimental synthesis may be pursued. It is possible to synthesize metastable molecular crystal polymorphs by a variety of experimental techniques. (89) For example, changing the solvent and crystallization conditions (temperature, pressure, etc.), (90−92) tailor-made additives, (93,94) solution shearing, (95,96) epitaxial templating, (97) and nanoscale confinement (98−101) can produce different polymorphs.
We have developed the GAtor GA code for molecular crystal structure prediction. (102−104) To perform inverse design of crystal structures with enhanced SF performance, we have implemented in GAtor a property-based fitness function, tailored to simultaneously minimize the energy and maximize the SF rate. SF rates are evaluated by using Simple for dimers extracted from the crystal structures because this is a descriptor that is computationally efficient to evaluate within the GA. Our inverse design strategy is then applied to tetracene because its known polymorphs have been experimentally observed to display significantly different SF performance. The SF+energy-based fitness function successfully biases the GA to generate structures predicted to have higher SF rates. The resulting structures provide insight into what packing motifs would be likely to lead to enhanced SF performance. The structures found within the polymorph energy range are further evaluated by using many-body perturbation theory. We identify a structure with a thermodynamic driving force for SF higher than those of both known forms of tetracene and a singlet exciton with a high degree of charge transfer character. Furthermore, the lattice energy of this structure is only 1.5 kJ/mol higher than that of the most stable T1 structure of tetracene, and therefore it is likely to be experimentally synthesizable.

Methods

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Approach

Workflow Overview

Figure 2 shows an overview of the inverse design workflow. The first step (panel a) is generating a pool of random structures using Genarris. (73) Genarris randomly creates structures in all possible space groups consistent with the symmetry of the molecule and the requested number of molecules in the unit cell. Unit cells are generated with a distribution around a predicted volume. (105) Fast, hierarchical structure checks are conducted to remove crystals with unphysically close intermolecular contact distances. An initial set of random structures undergo down-selection based on structural diversity and stability. Structural similarity is evaluated on the basis of a radial symmetry function (RSF) descriptor, (106) and the affinity propagation (AP) machine learning algorithm is utilized for clustering. (107) A final set of structures are fully relaxed with dispersion-inclusive DFT. This is used as the initial population to seed GAtor runs.

Figure 2

Figure 2. Overview of the inverse design workflow for finding putative molecular crystal polymorphs with improved SF performance. (a) Initial pool generation with Genarris. (b) GAtor runs are conducted using the traditional energy-based fitness function, the niching fitness function, and the SF+energy based fitness function. (c) Workflow of GAtor with the SF+energy based fitness function. (d) Postprocessing.

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The next step (panel b) is conducting GA runs. GAtor has the following unique features. First, a massive parallelization scheme enables the efficient utilization of high-performance computing resources by running several GA replicas in parallel. The GA replicas pick parent crystals for mating, generate offspring, and relax them with DFT independently, and interact only through a shared population of structures. (87,102) Second, several crossover and mutation schemes, designed for molecular crystals, are implemented in GAtor, which achieve a balance between exploration and exploitation by breaking or preserving space group symmetries. Third, in addition to the traditional energy-based fitness function, evolutionary niching has been implemented in GAtor to prevent the GA from being trapped in local minima and force it to explore structurally diverse basins. (103) This helps overcome initial pool biases and selection biases, known as genetic drift.
To perform inverse design, we have implemented in GAtor a fitness function based on a combination of a high SF rate and a low energy. This adds to the GAtor workflow a step of calculating the SF rates of the structures in the population using Simple (panel c). Simple uses a dimer model to compute SF rates. The singlet exciton on the excited chromophore couples into a singlet biexciton, which then decomposes into two triplet excitons. Simple computes the rate of biexciton formation using the Fermi golden rule. The SF electronic matrix elements are computed on the basis of a frontier orbital model using only the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of the two molecules. To evaluate the SF rate of a molecular crystal using Simple, dimers are extracted from the crystal structure and the highest result obtained is taken as the SF rate of that structure. (33) The computational efficiency of Simple is advantageous for fast evaluations within the GA. GAtor runs are conducted using the traditional energy-based fitness function, the niching fitness function, and the SF-based fitness function. With each fitness function, two runs are conducted with different crossover versus mutation rates. Our recommended best practice for CSP is to perform several GAtor runs with different settings. (102−104)
The best structures produced by GAtor undergo postprocessing (panel d). First, the structures are re-relaxed and re-ranked using increasingly accurate dispersion-inclusive DFT methods. Initially, the structures are relaxed and ranked using the computationally efficient Perdew–Burke–Ernzerhof (PBE) (108) semilocal functional with the Tkatchenko–Scheffler (TS) (109) pairwise dispersion method. Pairwise methods add the dispersion contribution to the DFT total energy by summing over the interactions between pairs of atoms. In the TS method, the parameters of the correction are derived from the DFT charge density in a first-principles manner. Next, the structures are re-relaxed and re-ranked using PBE with the many-body dispersion (MBD) method. (110,111) The MBD method considers the non-additive many-body contributions to the dispersion energy, as well as the effect of dielectric screening on the atomic polarizabilities. Finally, only the structures within the polymorph range are re-ranked by single-point energy evaluation using the more accurate but computationally expensive PBE-based hybrid functional (PBE0), (112) which contains a fraction of exact (Fock) exchange in addition to the semilocal exchange and correlation. PBE0+MBD has been shown to provide accurate ranking of molecular crystal polymorphs. (79,113−115) Here, we consider the energy range for viable polymorphs as 4 kJ/mol, based on the observation that nonconformational polymorphs are typically within 4 kJ/mol of each other. (65) Larger energy differences, of up to10 kJ/mol, have been observed in some cases, in particular for conformational polymorphs; (65,116) however, because tetracene is a very rigid molecule, we consider larger energy differences unlikely.
For the sake of simplicity and speed, Simple uses a variety of approximations. In particular, delocalization of the singlet state beyond two molecules, which can occur in molecular crystals, (25,27,28,34,35) is neglected. Therefore, the prospective SF performance of all structures within the polymorph energy range of 4 kJ/mol is further assessed using many-body perturbation theory (MBPT), which describes excited-state properties in the solid state with periodic boundary conditions. Within MBPT, band structures are computed within the GW approximation, where G is the one-particle Green’s function and W is the screened Coulomb interaction. (117−119) The GW approximation accounts for the renormalization of the electron energies due to the polarization response to the addition or removal of an electron. (120) The optical properties, including singlet and triplet excitation energies, optical absorption spectra, and exciton wave functions, are subsequently calculated by solving the Bethe–Salpeter equation (BSE), using the GW quasiparticle energies as input. The BSE accounts for the electron–hole interaction and resulting exciton binding energy. (119,121,122)

GA Fitness Functions

To perform traditional CSP, GAtor uses an energy-based fitness function, in which structures with lower energies are assigned a higher fitness value. To evaluate the energy-based fitness function, the energy of the ith crystal relative to the GA pool, ϵi, is computed using
ϵi=Emax−EiEmax−Emin
(1)
where Emax and Emin are the maximal and minimal total energy values in the population, respectively, and Ei is the energy of structure i. The energy-based fitness, fienergy, (102) is then computed as
fienergy=ϵi∑jϵj
(2)
To steer the GA to explore undersampled low-energy regions of the potential energy surface, evolutionary niching has been implemented in GAtor by using a cluster-based fitness function. AP is used to cluster the population on the basis of structural similarity with respect to an RSF descriptor. The fitness of each cluster is divided by its number of members, such that oversampled basins are penalized. The population is re-clustered, and fitness is re-evaluated after the addition of each new structure to the pool. The cluster-based fitness function, finiching, (103) is given by
finiching=f¯if¯max
(3)
with
f¯i=fienergymi
(4)
where mi is the niche count, i.e., the number of members in the cluster, to which the ith structure belongs.
Here, we have implemented a new fitness function to perform inverse design of the crystal packing to enhance the SF performance. To compute the SF-based fitness, the relative performance for the ith crystal, σi, is defined as
σi=Si−SminSmax−Smin
(5)
where Smin and Smax are the minimum and maximum values, respectively, in the pool of the logarithm of the SF rate computed using Simple, as shown in Figure 2c. To simultaneously maximize the SF performance and minimize the lattice energy, we define the combined fitness as
fiSF=f~i∑jf~j
(6)
with
f~i=wϵi+(1−w)σi
(7)
where w is a weight factor that controls the relative importance of lattice energy and SF rate and ϵi is the relative energy, as defined in eq 1. Here, we use a w of 0.5.

Computational Details

Genarris

An initial population of structures for GAtor was generated using the Robust Workflow implemented within Genarris, (73) as shown in Figure 2a. The initial “raw” pool contained approximately 10,000 random structures with two molecules per unit cell (Z = 2). To prevent the generation of structures with unphysically close intermolecular contact distances, Genarris uses a specific radius proportion (sr). If atoms A and B with van der Waals radii rA and rB, respectively, belong to two distinct molecules and are closer to each other than sr(rA + rB), then the structure is rejected. For structure generation, we used an sr of 0.85. Genarris predicted the unit cell volume to be 606 Å3, which differs from the experimental values of 580 Å3 for T1 and 573 Å3 for T2 by only a few percent. Next, the RSF descriptor was computed for all of the structures, and diversity-based selection was performed by clustering the structures using AP and selecting 1000 structures from the cluster centers (exemplars). Then, single-point energy evaluations were performed for the remaining structures using the PBE (108) functional with the TS (109) pairwise dispersion correction with thelower-level settings described in Section 2.2.4. AP clustering was performed again into 100 clusters, and the lowest-energy structure from each cluster was selected. Finally, the geometry of the remaining structures was optimized using PBE+TS with lower-level settings. Duplicate structures were removed from the pool using the Pymatgen Structure Matcher tool (123) with the default tolerances, leaving 50 structures in the pool. Statistical analysis of the population of structures throughout the workflow of Genarris is provided in the Supporting Information.

GAtor

All GAtor runs were seeded using the same set of initial structures generated by Genarris. Six GAtor runs were conducted, as shown in Figure 2b, using the energy-based fitness function, the niching fitness function, and the SF-based fitness function. For each fitness function, two runs were performed using crossover to mutation probabilities of 25% and 75% and tournament selection with a tournament size of 10. (102) “Standard mutation” and “standard crossover” schemes were used for mutation and crossover. The intermolecular closeness checks used an sr of 0.8. Local optimizations and energy evaluations within GAtor were performed using PBE+TS with lower-level settings. Each run generated at least 60 structures. Energy convergence plots are provided in the Supporting Information. All of the runs together generated ∼400 structures, approximately half of which were found to be duplicates. The 100 lowest-energy structures were reoptimized and re-ranked using PBE+TS and PBE+MBD (110) with thehigher-level settings, described in Section 2.2.4. The crystal structures within the polymorph energy range were re-ranked again with PBE0+MBD and higher-level settings by single-point energy evaluations using the PBE+MBD geometries. The version of GAtor used for this work (GAtor 1.2) is freely available for download from https://www.noamarom.com/software/download/.

Simple

To assess SF rates, we used the Simple (61) program for dimers extracted from the generated crystal structures of tetracene. All dimers with an intermolecular center of mass distance of <10 Å were considered. In Simple, the HOMO and LUMO are expanded using a natural atomic orbital (NAO) basis for computation. If hA, lA, hB, and lB denote the HOMO and LUMO of molecules A and B, respectively, then the first singlet state is represented by 1(hA → lA) and 1(hB → lB). The charge transfer states, where an electron is transferred, are given by 1(hB → lA) and 1(hA → lB), and the final biexciton is represented by 3(hA → lA) and 3(hB → lB), which couples into an overall singlet state. Natural atomic orbitals were computed using the natural bond orbital (NBO) analysis version 3.1 code within the Gaussian 16 package. (124) The reorganization energy for computing SF rates was set to 0.3 eV. (62) A Python script was used to create input files for Simple from NBO analysis and automate the calculation for all dimer geometries within a crystal. The logarithm of the highest SF rate among all of the dimers (si) was used as a measure of the SF performance of a given crystal.

DFT

Genarris and GAtor interface with the FHI-aims (125) code for geometry optimization and energy evaluation of crystal structures. The lower-level settings used within GAtor and Genarris correspond to the light numerical settings and tier 1 basis sets of FHI-aims. The higher-level settings used for re-ranking correspond to the tight numerical settings and tier 2 basis sets of FHI-aims. All calculations (except the interaction chain analysis provided in the Supporting Information) used a k-point mesh of 3 × 3 × 3.

GW+BSE

GW+BSE, as implemented in the BerkeleyGW code, (126) was used here to evaluate the excited-state properties of putative tetracene polymorphs. To obtain the input wave functions for GW+BSE calculations, mean field DFT calculations using the PBE functional were performed with the Quantum ESPRESSO code. (127) A coarse k-grid of 4 × 4 × 2 was used in the mean field calculations. We used Troullier–Martins norm-conserving pseudopotentials. (128) The kinetic energy cutoff was set to 50 Ry. The RPA dielectric matrix and the electron self-energy within the GW approximation used the coarse grid wave functions as input. 548 unoccupied bands were included in the GW calculation. The BSE was solved within the Tamm–Dancoff approximation (TDA). Forty valence bands and 40 conduction bands were included in the BSE calculation. Taking the full dielectric matrix as input to screen the attraction between the electron (e) and hole (h), we constructed the e–h interaction kernel on the coarse k-point grid. To construct the Bethe–Salpeter Hamiltonian, the GW quasiparticle energies and e–h interaction kernel calculated with coarse k-point settings were interpolated onto the fine k-point grid of 8 × 8 × 4. The subsequent diagonalization yielded the excitation energies and wave functions. The exciton wave functions of the tetracene polymorphs were converged using supercells of 8 × 8 × 4, based on the criterion proposed in ref (34). Then, the degree of SF charge transfer character (%CT) of the singlet exciton was calculated by double-Bader analysis (DBA). (28,34) DBA is an extension of the Bader charge partitioning scheme to exciton wave functions with two spatial variables. %CT is calculated by performing nested sums over the electron distributions obtained for different positions of the hole within a molecule. Absorption spectra were calculated for light polarized along the three crystal axes and averaged.

Results and Discussion

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GA Performance

Figure 3a shows the minimum energy of the GA population as a function of GA iteration, where each addition of a new structure to the population is considered as an iteration. (102) All GA runs converge to the common form of tetracene, T1, which is the lowest-energy structure. We note that the GA run using the SF+energy fitness function with a 75% crossover probability generates the T1 structure with a slightly distorted geometry, which is ∼0.25 kJ/mol higher in energy. The reason for this is that geometry relaxations are performed within GAtor with computationally efficient and less stringent lower-level settings. This structure is identified as a duplicate of the relaxed T1 structure by GAtor’s duplicate check and subsequently relaxes to the T1 structure in postprocessing with PBE+MBD and higher-level settings (we note that once the distorted T1 structure is generated GAtor’s duplicate checks prevent the addition of new T1 forms to the pool because of the presence of this structure). The GA runs using the SF+energy fitness function are the quickest to generate the T1 structure, within 6 and 10 iterations for crossover probabilities of 25% and 75%, respectively. The GA runs using the energy-based fitness functions find the T1 structure within 29 and 26 iterations for crossover probabilities of 25% and 75%, respectively. The runs using evolutionary niching are the slowest to generate the T1 structure within 60 and 41 iterations for crossover probabilities of 25% and 75%, respectively. The T2 structure is generated quickly by all GA runs. All runs generate it within five iterations, except the run using evolutionary niching with a crossover probability of 75%, which finds T2 within eight iterations.

Figure 3

Figure 3. (a) The minimum energy and (b) the maximum SF rate in the pool after each GAtor iteration for different fitness functions and crossover to mutation probabilities. The energy-based fitness does not improve the SF rate of the pool with GA iterations. The cross marks the (distorted) T1 structure.

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Each GA run follows its own unique path to reach the experimental structures. Figures 4 and 5 show the different evolutionary routes traversed by GAtor runs using different fitness functions and crossover to mutation probabilities. The T1 structure is generally reached by complex routes, typically consisting of more than one step. Most routes involve only mutation operations, in particular the strain mutation. In contrast, the routes for generating T2 involve only one step of either mutation or crossover from the initial pool. This explains why the T2 structure is generated fast by all GA runs. For T2, both types of breeding operators, crossover and mutations, are equally beneficial. For both the T1 and T2 structures, the initial pool ancestors have higher space group symmetries that are broken by the GA breeding operators.

Figure 4

Figure 4. Evolutionary routes that produced the T1 experimental structure of tetracene in GA runs using different fitness functions and crossover probabilities. All routes start from initial pool structures. The packing motifs and space groups of all structures are also shown. The a-, b-, and c-axes are colored red, green, and blue, respectively.

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Figure 5

Figure 5. Evolutionary routes that produced the T2 experimental structure of tetracene in GA runs using different fitness functions and crossover probabilities. All routes start from initial pool structures. The packing motifs and space groups of all structures are also shown. The a-, b-, and c-axes are colored red, green, and blue, respectively.

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Figure 3b shows the maximum SF rate in the population as a function of GA iteration. As explained in Methods, the SF rate of a given crystal structure is taken as the logarithm of the highest SF rate computed by Simple out of all of the dimers extracted from that structure. For the GA runs using the energy-based fitness function, the maximum SF rate does not improve relative to the initial pool. In contrast, both GA runs using the SF+energy-based fitness function generate packing motifs comprising dimers that yield higher SF rates. This is because higher fitness is assigned to structures that have desirable dimers. Consequently, these structures are selected more often for breeding and pass their structural genes to offspring via the mutation and crossover operations. This improves the average SF rate of the population resulting in more optimal structures for SF. The GA runs using evolutionary niching produce mixed results. The run using a crossover probability of 25% does not generate structures with SF rates that are higher than those in the initial population, whereas the run using a crossover probability of 75% does. While the niching fitness function is not specifically tailored to search for structures with higher SF rates, it is designed to perform more exploration of undersampled regions of the PES. Thus, it may fortuitously stumble upon structures with higher SF rates.
Figure 6 shows the SF rate computed by Simple as a function of the relative energy of the crystal structures generated by the GAtor runs using a crossover probability of 25% with different fitness functions. Plots for the runs using a crossover probability of 75% are provided in the Supporting Information. The T1 and T2 forms are indicated by red and blue crosses, respectively. We note that the relative energies presented here are as computed during the GAtor runs using PBE+TS with lower-level settings. SF rates of dimers computed using Simple are known to be highly sensitive to the geometry. (62) Therefore, slight differences in the relaxed geometries at this level of theory produce somewhat different energies and SF rates for the T1 and T2 structures generated in different GA runs. This emphasizes the need to re-relax the GA-generated structures with higher-level numerical settings during postprocessing to obtain more accurate and reliable geometries for final energy ranking, as discussed below (see additional analysis of the dependence of the Simple rate on the geometry in the Supporting Information). Compared to the runs using the energy-based fitness function and evolutionary niching, the run using the SF+energy fitness function generates a significantly larger number of structures with a SF rate higher than that of the structures found in the initial population. However, most of the structures with particularly high SF rates are outside of the polymorph range of 4 kJ/mol, indicated by the red line. This is likely because the packing motifs that comprise dimers with a high SF rate are not energetically favorable. A similar behavior is evident in the runs using 75% crossover probability, as shown in the Supporting Information.

Figure 6

Figure 6. SF rates as a function of relative energy for the structures generated by GAtor runs with a crossover probability of 25% using (a) the energy-based fitness function, (b) evolutionary niching, and (c) the SF+energy-based fitness function. The red line denotes the polymorph range of 4 kJ/mol. The T1 and T2 polymorphs of tetracene are indicated by red and blue crosses, respectively. The relative energies presented here are as computed during the GAtor runs using PBE+TS with lower-level settings. Slight differences in the relaxed geometries at this level of theory produce somewhat different SF rates for the T1 and T2 structures generated in different GA runs.

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Figure 7 shows the lattice parameter distributions of the structures generated by the GA runs using different fitness functions with a 25% crossover probability. The lattice parameter distributions for the runs with a 75% crossover probability are shown in the Supporting Information. The T1 and T2 structures are marked by red and blue crosses, respectively. The structures are colored based on the basis of the logarithm of their Simple SF rates and their PBE+TS energy relative to the T1 structure in the top and bottom rows, respectively. The T1 and T2 structures are located in the same basin of the lattice parameter space. Overall, the lattice parameter space has a single low-energy basin, in which all of the potential polymorphs of tetracene reside. In contrast, there are multiple high-SF rate regions outside of the low-energy cluster. As shown in panels a and b, the GA run using the energy-based fitness function mainly explores the main low-energy basin. The GA runs using evolutionary niching and the SF-based fitness function both explore more outside of the main low-energy basin. However, the regions they explore differ. The niching run heavily explores a region on the left side of the lattice parameter plot with small a parameters, which turns out to be unproductive because it does not contain structures with a particularly low energy or high SF rate. This explains why the niching run is the slowest to generate the experimental structures. In the case of tetracene, the main low-energy basin also coincides with relatively high SF rates. This is why the run using the energy+SF-based fitness function succeeds in finding both experimentally known structures relatively fast. This run also explores a region on the bottom right of the lattice parameter plot, characterized by several clusters with relatively high SF rates. The exploration of these regions of the configuration space explains why the GA run using the SF+energy-based fitness function succeeds in generating more structures with relatively high SF rates. As shown in the Supporting Information, the runs with a crossover probability of 75% also show a similar trend. We note that the structure of the PES, namely, the number of low-energy basins and whether they coincide with high-SF rate regions, is dependent on the material. Therefore, for materials other than tetracene, the different fitness functions and GA operations may perform differently in terms of the speed of finding the known structure(s) and other putative polymorphs with enhanced SF performance.

Figure 7

Figure 7. Lattice parameter distributions of the structures generated by GAtor runs with different fitness functions and 25% crossover to mutation probability. Panels a and b present the SF rate and relative energy, respectively, as a function of lattice parameters for the GA run using the energy-based fitness function. Panels c and d present the SF rate and relative energy, respectively, as a function of lattice parameters for the GA run using evolutionary niching. Panels e and f present the SF rate and relative energy, respectively, as a function of lattice parameters for the GA run using the SF+energy-based fitness function. The T1 and T2 polymorphs of tetracene are marked by red and blue crosses, respectively.

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Figure 8 shows a comparison between dimers extracted from the structure with the highest overall Simple SF rate and from the T2 and T1 forms. The best overall dimer, colored lime green in Figure 8, has a slip-stacked structure with the molecular planes facing each other. This dimer belongs to a crystal structure that has a π-stacked packing motif with a slip in the direction of the in-plane short axis. This packing arrangement is not energetically favorable for tetracene, with the energy of this structure being over 20 kJ/mol above the global minimum energy, as shown in Figure 6c. Therefore, it is unlikely to be experimentally synthesizable. In the dimers extracted from the T1 and T2 structures, the molecules are positioned at an angle, with no cofacial interactions. This is a result of the herringbone packing of these structures.

Figure 8

Figure 8. Comparison of the highest SF dimers of different crystal structures viewed along directions of: (a) the in-plane long axis and (b) the in-plane short axis of the tetracene molecule. T1 is colored red. T2 is colored blue. The structure with the overall highest-rate SF dimer in the GA pool is colored lime green.

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Previously, the best dimers of tetracene have been identified and ranked using a grid search approach with Simple. (62) Therein, the dimers were isolated, not a part of a crystal structure, and their relative stability was not considered. The dimer with the highest SF rate generated by GAtor resembles the fifth best tetracene dimer found in ref (62). The best dimer extracted from the T1 and T2 structures ranks as the 10th best dimer in ref (62). In most of the best SF dimers found in the GA population, the molecules have their long axes parallel to each other. In contrast, in the best isolated dimers found in ref (62), the molecules are rotated along the out-of-plane axis, such that their long axes are non-parallel. Such configurations are uncommon among the low-energy crystal structures of tetracene, presumeably because they are less stable.
On the basis of the results shown in Figures 3–8, the SF+energy fitness function successfully biases the GA toward generating dimers with higher SF rates that are also energetically stable within a crystal structure. Structure–property relations can be derived by examining the structures predicted to have high SF rates. Although some of the packing motifs with dimer configurations that produce high SF rates are not energetically favorable for tetracene, valuable insight is still gleaned as to what packing arrangements should be sought. It may be possible to achieve such packing arrangements by chemical modification of the tetracene backbone. For example, it has been shown that adding side groups can help stabilize different packing motifs. (45,129−131)

Putative Polymorphs

After combining the structures generated by all GAtor runs, re-relaxing them with higher-level numerical settings, and performing duplicate checks, about 160 unique structures remain. These structures undergo postprocessing, as described in Methods. Figure 9 shows the energy ranking of the structures in the polymorph range of 4 kJ/mol using increasingly accurate exchange-correlation functionals and dispersion methods. The experimentally stable form, T1, is consistently ranked as the lowest in energy by all three methods. The ranking of the T2 form changes significantly upon switching from the TS pairwise dispersion method to the MBD method. With PBE+TS, the T2 structure is found ∼2.5 kJ/mol above the T1 structure, whereas PBE+MBD ranks T1, T2, and P1 as nearly degenerate within an energy range of 0.2 kJ/mol. Switching from the semilocal PBE functional to the PBE0 hybrid functional destabilizes the T2 structure and shifts it to ∼0.75 kJ/mol above the T1 form. To further investigate the differences between DFT functionals and dispersion methods, we performed interaction chain analysis, as described in ref (104), for the T1 and T2 structures. A full account is provided in the Supporting Information. We find that side-to-face and face-to-face interactions, which are present in both the T1 and T2 structures, are overstabilized by PBE+TS and understabilized by PBE+MBD, compared to PBE0+MBD. Edge-to-edge interactions, which are present only in the T2 structure (along the c-axis), are overstabilized by both PBE+TS and PBE+MBD, compared to PBE0+MBD. Whether a certain structure is understabilized or overstabilized compared to another depends on the overall balance of different interactions. As shown in the Supporting Information, for tetracene, stability is loosely correlated with density. Several putative structures are as dense but significantly less stable than the structures in the polymorph range.

Figure 9

Figure 9. Re-ranking of tetracene structures generated by GAtor using increasingly accurate DFT functionals and dispersion methods. Relative energies are referenced to the lowest-energy structure with each method. The experimental structures and some low-energy putative structures are also shown.

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Because of its computational efficiency, Simple is a practical choice for evaluating the SF performance of putative crystal structures within the GA. However, as explained above, the dimer model implemented in Simple does not consider the extended nature of excitons in molecular crystals, which may be delocalized over several molecules, as is the case for tetracene. (57) For tetracene, the best dimer extracted from the T1 structure is predicted to yield a SF rate higher than that of the T2 structure (see Figure 6), contrary to experimental observations. (57) We note that in the future Simple may be replaced by more advanced models that go beyond the dimer approximations and/or by machine learning models (36) for the evaluation of the SF-based fitness function. The GW+BSE method can capture the many-body effects in a molecular crystal with periodic boundary conditions. We proceed to evaluate the prospective SF performance of structures by using GW+BSE to calculate the singlet and triplet excitation energies and the corresponding exciton wave functions. The GW+BSE calculations were performed only on structures in the polymorph range due to their high computational cost.
In Figure 10, the structures in the polymorph range are compared to the two known forms of tetracene with respect to a two-dimensional descriptor for SF performance, evaluated using GW+BSE. (27,28,33,34) The primary descriptor, plotted on the x-axis, is the thermodynamic driving force for SF, i.e., the energy difference between the singlet exciton energy and twice the triplet exciton energy, ES – 2ET. We note that the singlet and triplet excitation energies obtained with GW+BSE are vertical values, neglecting geometry relaxation in the excited state. Vibrational effects and entropic effects are also not considered here. Because GW+BSE systematically underestimates the SF driving force, (27,28,33−35) we restrict the discussion to a comparative assessment of the putative polymorphs. A high driving force indicates that a material is likely to undergo SF with a high rate. However, an overly high driving force increases the energy loss in the SF process and may be beneficial to other processes competing with SF. In the T1 structure of tetracene, SF is slightly endoergic, which leads to a relatively slow fission rate. (8,132,133) Therefore, a driving force somewhat higher than that of the T1 structure of tetracene would be ideal. (5)

Figure 10

Figure 10. (a) Putative polymorphs of tetracene compared to the T1 and T2 structures based on a two-dimensional descriptor calculated with GW+BSE. The thermodynamic driving force for SF, ES – 2ET, is displayed on the x-axis, and the singlet exciton charge transfer character, %CT, is displayed on the y-axis. The error bars represent the range of %CT values obtained using double-Bader analysis with the hole located at different sites. Exciton wave functions for (b) T1, (c) T2, and (d) P3 are also shown. The electron distribution is colored yellow with respect to the hole position colored in red.

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The singlet exciton wave functions of T1 and T2, computed using GW+BSE, are shown in Figure 10. Exciton wave functions have two spatial variables corresponding to the electron and hole probability distributions. Here, the electron probability distribution is visualized in yellow with respect to a fixed hole position, colored in red. Excitons in molecular crystals may be classified on the basis of the localization of the electron distribution with respect to the hole position. (6) In a Frenkel exciton, the electron distribution is concentrated on the same molecule as the hole. In a charge transfer (CT) exciton, the electron is distributed on other molecules. Typically, excitons are not purely one or the other but have a degree of charge transfer character (%CT). The degree of CT character of the singlet exciton wave function is the secondary descriptor displayed on the y-axis in Figure 10. This descriptor is motivated by the growing body of experimental evidence for the involvement of a virtual charge transfer state in the SF process. (29,134−137) A singlet exciton with a high degree of CT character, i.e., with the hole and the electron probability distributions centered on different molecules, is thought to be favorable for SF. (6,9,25,29,138,139) For the singlet exciton of T1, there is some probability of finding the electron on the same molecule as the hole. In comparison, for T2 and P3 there is virtually no electron probability on the molecule with the hole.
Crystal packing affects both the SF driving force and the character of the singlet exciton. The T2 structure has both a higher driving force and a singlet exciton with a higher degree of charge transfer character than the T1 structure. Hence, on the basis of the two-dimensional (2D) descriptor, the SF performance of the T2 structure is expected to be better than that of the T1 structure, which is consistent with experimental observations. Of the other structures in the polymorph range, P1 and P2 have a lower SF driving force than T1 and %CT values similar to that of T1. P4 and P6 have a driving force and a %CT similar to those of T1. P5 has a driving force higher than those of T1 and T2 but a %CT lower than that of T1. Only P3 has a higher driving force than both T1 and T2, as well as a high %CT, similar to that of T2. Thus, P3 is identified as the most promising polymorphic form of tetracene based on the 2D descriptor. In Figure 11, the absorption spectrum of the P3 structure, calculated with GW+BSE, is compared with the T1 and T2 structures. The optical gaps of all three structures are within a narrow range of 2.29–2.38 eV. However, the absorption characteristics near 2.5 eV are slightly different. T2 and P3 have a sharper absorption peak relative to T1. On this basis, the absorption behavior of the P3 structure is similar to that of the T2 structure and well-suited for SF-based solar cells. Moreover, the PBE0+MBD relative energy of P3 is only 1.5 kJ/mol above the T1 form, making it a potentially realizable structure.

Figure 11

Figure 11. Absorption spectra of the T1, T2, and P3 structures computed using GW+BSE. The spectrum of T1 is compared with experimental data, adapted with permission from ref (140), Copyright 2008 John Wiley and Sons. The vertical lines denote the optical gap, which is equal to the lowest singlet excitation energy. The solar spectral energy distribution is also shown.

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Conclusion

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In summary, we have conducted inverse design of the crystal packing of tetracene to enhance its singlet fission performance. This was achieved by implementing a fitness function based on the SF rate and stability in the GAtor genetic algorithm package. For fast evaluation of SF rates within the GA, we used a dimer model implemented in the Simple code. We have demonstrated that the property-based genetic algorithm succeeds in generating structures predicted to have higher SF rates. Analysis of these structures reveals structure–property relations and provides insight into packing motifs associated with high SF rates. The structures found within the polymorph energy range of 4 kJ/mol above the common form of tetracene, which is the global minimum, were further assessed using many-body perturbation theory. We have identified a putative polymorph predicted to have a thermodynamic driving force for SF higher than those of both known forms of tetracene, and a singlet exciton with a high degree of charge transfer character. This structure is only 1.5 kJ/mol higher in energy than the common form of tetracene, well within the viable polymorph range. Therefore, it may be experimentally synthesizable.
Because of the versatility of the genetic algorithm, different fitness functions can be easily implemented. The SF-based fitness function may be improved in the future by using more advanced models that go beyond the dimer approximation and/or machine learning models. (36) Furthermore, GA fitness functions may be tailored to search for any property or combination of properties of interest. The results of property-based GAs can help guide experimental synthesis efforts in promising directions. If metastable structures are found that are predicted to have desirable properties and be relatively close in energy to the global minimum, it may be possible to synthesize them. Specifically for molecular crystals, a variety of experimental techniques exist for growing metastable polymorphs, (89) including changing the solvent and crystallization conditions (temperature, pressure, etc.), (90−92) tailor-made additives, (93,94) solution shearing, (95,96) epitaxial templating, (97) and nanoscale confinement. (98−101) If packing motifs correlated with desirable properties are predicted to be too high in energy to be synthesizable for a parent compound, they may be achieved by chemical modifications, such as functionalization with side groups. (45,129−131,141) We note, however, that CSP often produces more putative structures than are realized experimentally. (142) This is mainly because crystallization conditions and kinetics are not considered in CSP, including the energy barriers for solid-state transformations. (143) In conclusion, inverse design by property-based genetic algorithms is a highly useful strategy for discovery of materials with enhanced properties for various applications.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.chemmater.2c03444.

  • Statistical analysis of the population of structures throughout the Genarris workflow, additional analysis of GAtor runs, GW band structures and BSE absorption spectra of structures within the polymorph energy range, interaction chain analysis of the T1 and T2 structures, comparison of Simple rates before and after postprocessing (PDF)

  • Structures of the putative polymorphs found up to 10 kJ/mol above the global minimum in the form of FHI-aims geometry (ZIP)

Terms & Conditions

Most electronic Supporting Information files are available without a subscription to ACS Web Editions. Such files may be downloaded by article for research use (if there is a public use license linked to the relevant article, that license may permit other uses). Permission may be obtained from ACS for other uses through requests via the RightsLink permission system: http://pubs.acs.org/page/copyright/permissions.html.

Author Information

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  • Corresponding Author
    • Noa Marom - Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania15213, United States;  Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania15213, United States;  Department of Chemistry, Carnegie Mellon University, Pittsburgh, Pennsylvania15213, United States;  Orcidhttps://orcid.org/0000-0002-1508-1312;  Email: [email protected]
  • Authors
    • Rithwik Tom - Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania15213, United States
    • Siyu Gao - Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania15213, United States
    • Yi Yang - Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania15213, United States;  Orcidhttps://orcid.org/0000-0001-9905-126X
    • Kaiji Zhao - Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania15213, United States
    • Imanuel Bier - Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania15213, United States;  Orcidhttps://orcid.org/0000-0003-1084-770X
    • Eric A. Buchanan - Department of Chemistry, University of Colorado, Boulder, Colorado80309, United States
    • Alexandr Zaykov - Institute of Organic Chemistry and Biochemistry, Czech Academy of Sciences, 16610Prague 6, Czech Republic;  Department of Physical Chemistry, University of Chemistry and Technology, 166 28Prague 6, Czech Republic
    • Zdeněk Havlas - Institute of Organic Chemistry and Biochemistry, Czech Academy of Sciences, 16610Prague 6, Czech Republic
    • Josef Michl - Department of Chemistry, University of Colorado, Boulder, Colorado80309, United States;  Institute of Organic Chemistry and Biochemistry, Czech Academy of Sciences, 16610Prague 6, Czech Republic
  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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The authors thank Justin Johnson from the National Renewable Energy Laboratory (NREL) for sharing information about the tetracene polymorph obtained in ref (57). Research at Carnegie Mellon University was supported by the National Science Foundation (NSF) Division of Materials Research (DMR) through Grant DMR-2131944. Work in Prague was supported by the Institute of Organic Chemistry and Biochemistry (RVO: 61388963) and the Ministry of Education, Youth and Sports of the Czech Republic through e-INFRA CZ (ID: 90140). Work in Boulder was supported by the U.S. Department of Energy (DOE), Office of Basic Energy Sciences, Division of Chemical Sciences, Biosciences, and Geosciences, under Grant DE-SC0007004. This research used resources of the National Energy Research Scientific Computing Center (NERSC), a DOE Office of Science User Facility supported by the Office of Science of the DOE, under Contract DE-AC02-05CH11231, the Argonne Leadership Computing Facility (ALCF), which is a DOE Office of Science User Facility supported under Contract DE-AC02-06CH11357, and the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation Grant ACI-1548562.

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    Laser generation of excitons and fluorescence in anthracene crystals
    Singh, S.; Jones, W. J.; Siebrand, W.; Stoicheff, B. P.; Schneider, W. G.
    Journal of Chemical Physics (1965), 42 (1), 330-42CODEN: JCPSA6; ISSN:0021-9606.
    Exptl. and theoretical studies are reported of the short-lived and delayed fluorescence of anthracene single crystals, excited by single- and double-proton absorption. A giant-pulse ruby laser provides the primary source of radiation of 14,400 cm.-1 (up to 1027 photons/cm.2 sec.) and is also used to generate 2nd-harmonic radiation from adenosine 5'-diphosphate, as well as stimulated Raman radiation of 12,800 and 17,500 cm.-1 from liquid O. The time dependence of the fluorescence intensity is studied as a function of laser intensity, crystal temp., and excitation wavelength. The very intense fast fluorescence with a half-life of 30 nsec. at 300°K., characteristic of singlet exciton decay, and the relatively weak delayed fluorescence which involves intermediate triplet states, are sepd. by using sectored disks. The triplet state at 14,750 cm.-1 can be populated (1) by direct absorption of laser photons, involving an activation energy of 350 cm.-1; (2) via 2-photon absorption, presumably leading to a vibrationally excited state of the 1B2u exciton, followed by intersystem crossing; (3) via 1-photon (2nd-harmonic) excitation from levels ≥700 cm.-1 into the singlet absorption band, followed by conversion of the singlet exciton into a triplet pair. The latter process is suggested by the observed activation energy of 700 cm.-1 In agreement with these interpretations, the delayed fluorescence intensity varies with the 2nd to 4th power of the laser intensity, depending on the exptl. conditions. Also, light of 17,500 cm.-1 leads exclusively to process (1), light of 12,800 cm.-1 exclusively to (2). Triplet lifetimes from 2-17 msec. are obtained, depending on crystal purity, which indicates that unimol. triplet decay is an extrinsic, radiationless process. A singlet-triplet intersystem crossing rate const. of ∼3 × 10-5 sec.-1 is estd. The triplet-triplet annihilation rate const. is ∼5 × 10-11 cm.3 sec.-1 This value, considered together with the triplet-pair creation process, suggests a triplet exchange rate ⪆1013 sec.-1 and a triplet diffusion const. ⪆5 × 10-4 cm.2/sec.
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  8. 8
    Wilson, M. W.; Rao, A.; Johnson, K.; Gélinas, S.; Di Pietro, R.; Clark, J.; Friend, R. H. Temperature-independent singlet exciton fission in tetracene. J. Am. Chem. Soc. 2013, 135, 16680– 16688,  DOI: 10.1021/ja408854u
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    8
    Temperature-Independent Singlet Exciton Fission in Tetracene
    Wilson, Mark W. B.; Rao, Akshay; Johnson, Kerr; Gelinas, Simon; di Pietro, Riccardo; Clark, Jenny; Friend, Richard H.
    Journal of the American Chemical Society (2013), 135 (44), 16680-16688CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    The authors use transient absorption spectroscopy to demonstrate that the dynamics of singlet exciton fission in tetracene are independent of temp. (10-270 K). Low-intensity, broad-band measurements allow the identification of spectral features while minimizing bimol. recombination. Hence, by directly observing both species, the time const. for the conversion of singlets to triplet pairs is ∼90 ps. However, in contrast to pentacene, where fission is effectively unidirectional, the emissive singlet in tetracene is readily regenerated from spin-correlated geminate triplets following fission, leading to equil. dynamics. Although free triplets are efficiently generated at room temp., the interplay of superradiance and frustrated triplet diffusion contributes to a nearly 20-fold increase in the steady-state fluorescence as the sample is cooled. Together, these results require that singlets and triplet pairs in tetracene are effectively degenerate in energy, and begin to reconcile the temp. dependence of many macroscopic observables with a fission process which does not require thermal activation.
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  9. 9
    Broch, K.; Dieterle, J.; Branchi, F.; Hestand, N.; Olivier, Y.; Tamura, H.; Cruz, C.; Nichols, V.; Hinderhofer, A.; Beljonne, D. Robust singlet fission in pentacene thin films with tuned charge transfer interactions. Nat. Commun. 2018, 9, 954,  DOI: 10.1038/s41467-018-03300-1
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    9
    Robust singlet fission in pentacene thin films with tuned charge transfer interactions
    Broch K; Dieterle J; Hinderhofer A; Schreiber F; Broch K; Branchi F; Cerullo G; Hestand N J; Spano F C; Olivier Y; Beljonne D; Tamura H; Cruz C; Nichols V M; Bardeen C J; Beljonne D
    Nature communications (2018), 9 (1), 954 ISSN:.
    Singlet fission, the spin-allowed photophysical process converting an excited singlet state into two triplet states, has attracted significant attention for device applications. Research so far has focused mainly on the understanding of singlet fission in pure materials, yet blends offer the promise of a controlled tuning of intermolecular interactions, impacting singlet fission efficiencies. Here we report a study of singlet fission in mixtures of pentacene with weakly interacting spacer molecules. Comparison of experimentally determined stationary optical properties and theoretical calculations indicates a reduction of charge-transfer interactions between pentacene molecules with increasing spacer molecule fraction. Theory predicts that the reduced interactions slow down singlet fission in these blends, but surprisingly we find that singlet fission occurs on a timescale comparable to that in pure crystalline pentacene. We explain the observed robustness of singlet fission in such mixed films by a mechanism of exciton diffusion to hot spots with closer intermolecular spacings.
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  10. 10
    Sanders, S. N.; Kumarasamy, E.; Fallon, K. J.; Sfeir, M. Y.; Campos, L. M. Singlet fission in a hexacene dimer: energetics dictate dynamics. Chem. Sci. 2020, 11, 1079– 1084,  DOI: 10.1039/C9SC05066C
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    10
    Singlet fission in a hexacene dimer: energetics dictate dynamics
    Sanders, Samuel N.; Kumarasamy, Elango; Fallon, Kealan J.; Sfeir, Matthew Y.; Campos, Luis M.
    Chemical Science (2020), 11 (4), 1079-1084CODEN: CSHCCN; ISSN:2041-6520. (Royal Society of Chemistry)
    Singlet fission (SF) is an exciton multiplication process with the potential to raise the efficiency limit of single junction solar cells from 33% to up to 45%. Most chromophores generally undergo SF as solid-state crystals. However, when such mols. are covalently coupled, the dimers can be used as model systems to study fundamental photophys. dynamics where a singlet exciton splits into two triplet excitons within individual mols. Here we report the synthesis and photophys. characterization of singlet fission of a hexacene dimer. Comparing the hexacene dimer to analogous tetracene and pentacene dimers reveals that excess exoergicity slows down singlet fission, similar to what is obsd. in mol. crystals. Conversely, the lower triplet energy of hexacene results in an increase in the rate of triplet pair recombination, following the energy gap law for radiationless transitions. These results point to design rules for singlet fission chromophores: the energy gap between singlet and triplet pair should be minimal, and the gap between triplet pair and ground state should be large.
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  11. 11
    Sun, D.; Deng, G.-H.; Xu, B.; Xu, E.; Li, X.; Wu, Y.; Qian, Y.; Zhong, Y.; Nuckolls, C.; Harutyunyan, A. R. Anisotropic singlet fission in single crystalline hexacene. Iscience 2019, 19, 1079– 1089,  DOI: 10.1016/j.isci.2019.08.053
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    11
    Anisotropic Singlet Fission in Single Crystalline Hexacene
    Sun, Dezheng; Deng, Gang-Hua; Xu, Bolei; Xu, Enshi; Li, Xia; Wu, Yajing; Qian, Yuqin; Zhong, Yu; Nuckolls, Colin; Harutyunyan, Avetik R.; Dai, Hai-Lung; Chen, Gugang; Chen, Hanning; Rao, Yi
    iScience (2019), 19 (), 1079-1089CODEN: ISCICE; ISSN:2589-0042. (Elsevier B.V.)
    Singlet fission is known to improve solar energy utilization by circumventing the Shockley-Queisser limit. The two essential steps of singlet fission are the formation of a correlated triplet pair and its subsequent quantum decoherence. However, the mechanisms of the triplet pair formation and decoherence still remain elusive. Here we examd. both essential steps in single cryst. hexacene and discovered remarkable anisotropy of the overall singlet fission rate along different crystal axes. Since the triplet pair formation emerges on the same timescale along both crystal axes, the quantum decoherence is likely responsible for the directional anisotropy. The distinct quantum decoherence rates are ascribed to the notable difference on their assocd. energy loss according to the Redfield quantum dissipation theory. Our hybrid exptl./theor. framework will not only further our understanding of singlet fission, but also shed light on the systematic design of new materials for the third-generation solar cells.
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  12. 12
    Albrecht, W.; Michel-Beyerle, M.; Yakhot, V. Exciton fission in excimer forming crystal. Dynamics of an excimer build-up in α-perylene. Chem. Phys. 1978, 35, 193– 200,  DOI: 10.1016/0301-0104(78)85205-7
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    12
    Exciton fission in excimer forming crystal. Dynamics of an excimer build-up in α-perylene
    Albrecht, W. G.; Michel-Beyerle, M. E.; Yakhot, V.
    Chemical Physics (1978), 35 (1-2), 193-200CODEN: CMPHC2; ISSN:0301-0104.
    The optically induced fission of singlet states in both α- and β-perylene crystals is investigated at room temp. In the monomeric β-perylene the fission threshold coincides with the energy of two triplet excitons whereas it is blue-shifted by ≈3500 cm-1 in the excimer forming α-crystal. This indicates that the excimer is formed prior to fission, emerging from the initially excited monomer state, and it implies that the rate of excimer formation kexc > 1012 s-1. Theor. ests. led to kexc ≈1013 s-1. Two adjacent perylene mols. in the α-crystal, each of them in the T1 electronic state, are bound with a binding energy B2T1 ≈350 cm-1.
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  13. 13
    Eaton, S. W.; Shoer, L. E.; Karlen, S. D.; Dyar, S. M.; Margulies, E. A.; Veldkamp, B. S.; Ramanan, C.; Hartzler, D. A.; Savikhin, S.; Marks, T. J. Singlet exciton fission in polycrystalline thin films of a slip-stacked perylenediimide. J. Am. Chem. Soc. 2013, 135, 14701– 14712,  DOI: 10.1021/ja4053174
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    13
    Singlet exciton fission in polycrystalline thin films of a slip-stacked perylenediimide
    Eaton, Samuel W.; Shoer, Leah E.; Karlen, Steven D.; Dyar, Scott M.; Margulies, Eric A.; Veldkamp, Brad S.; Ramanan, Charusheela; Hartzler, Daniel A.; Savikhin, Sergei; Marks, Tobin J.; Wasielewski, Michael R.
    Journal of the American Chemical Society (2013), 135 (39), 14701-14712CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    The crystal structure of N,N-bis-(n-octyl)-2,5,8,11-tetraphenylperylene-3,4:9,10-bis-(dicarboximide), 1, obtained by X-ray diffraction reveals that 1 has a nearly planar perylene core and π-π stacks at a 3.5 Å interplanar distance in well-sepd. slip-stacked columns. Theory predicts that slip-stacked, π-π-stacked structures should enhance interchromophore electronic coupling and thus favor singlet exciton fission. Photoexcitation of vapor-deposited polycryst. 188 nm thick films of 1 results in a 140 ± 20% yield of triplet excitons (3*1) in τSF = 180 ± 10 ps. These results illustrate a design strategy for producing perylenediimide and related perylene derivs. that have the optimized interchromophore electronic interactions which promote high-yield singlet exciton fission for potentially enhancing org. solar cell performance and charge sepn. in systems for artificial photosynthesis.
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  14. 14
    Aulin, Y. V.; Felter, K. M.; Günbas, D. D.; Dubey, R. K.; Jager, W. F.; Grozema, F. C. Morphology-Independent Efficient Singlet Exciton Fission in Perylene Diimide Thin Films. ChemPlusChem. 2018, 83, 230– 238,  DOI: 10.1002/cplu.201700449
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    14
    Morphology-Independent Efficient Singlet Exciton Fission in Perylene Diimide Thin Films
    Aulin, Yaroslav V.; Felter, Kevin M.; Guenbas, D. Deniz; Dubey, Rajeev K.; Jager, Wolter F.; Grozema, Ferdinand C.
    ChemPlusChem (2018), 83 (4), 230-238CODEN: CHEMM5; ISSN:2192-6506. (Wiley-VCH Verlag GmbH & Co. KGaA)
    Perylene diimides are conjugated chromophores that are of considerable interest owing to their ability to transform a singlet excited state into two triplets by singlet fission. Although singlet fission has previously been reported for certain perylene diimide derivs., there is some uncertainty about the rates and yield of the process in these materials. In this report, ultrafast transient absorption spectroscopy is used to demonstrate that singlet fission in perylene diimides can occur on a sub-picosecond timescale with quantum yields approaching the theor. limit of 200 %.
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  15. 15
    Hall, C. L.; Andrusenko, I.; Potticary, J.; Gao, S.; Liu, X.; Schmidt, W.; Marom, N.; Mugnaioli, E.; Gemmi, M.; Hall, S. R. 3D electron diffraction structure determination of terrylene, a promising candidate for intermolecular singlet fission. ChemPhysChem 2021, 22, 1631– 1637,  DOI: 10.1002/cphc.202100320
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    15
    3D Electron Diffraction Structure Determination of Terrylene, a Promising Candidate for Intermolecular Singlet Fission
    Hall, Charlie L.; Andrusenko, Iryna; Potticary, Jason; Gao, Siyu; Liu, Xingyu; Schmidt, Werner; Marom, Noa; Mugnaioli, Enrico; Gemmi, Mauro; Hall, Simon R.
    ChemPhysChem (2021), 22 (15), 1631-1637CODEN: CPCHFT; ISSN:1439-4235. (Wiley-VCH Verlag GmbH & Co. KGaA)
    Herein we demonstrate the prowess of the 3D electron diffraction approach by unveiling the structure of terrylene, the third member in the series of peri-condensed naphthalene analogs, which has eluded structure detn. for 65 years. The structure was detd. by direct methods using electron diffraction data and corroborated by dispersion-inclusive d. functional theory optimizations. Terrylene crystalizes in the monoclinic space group P21/a, arranging in a sandwich-herringbone packing motif, similar to analogous compds. Having solved the crystal structure, we use many-body perturbation theory to evaluate the excited-state properties of terrylene in the solid-state. We find that terrylene is a promising candidate for intermol. singlet fission, comparable to tetracene and rubrene.
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  16. 16
    Johnson, J. C.; Nozik, A. J.; Michl, J. High triplet yield from singlet fission in a thin film of 1, 3-diphenylisobenzofuran. J. Am. Chem. Soc. 2010, 132, 16302– 16303,  DOI: 10.1021/ja104123r
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    16
    High Triplet Yield from Singlet Fission in a Thin Film of 1,3-Diphenylisobenzofuran
    Johnson, Justin C.; Nozik, Arthur J.; Michl, Josef
    Journal of the American Chemical Society (2010), 132 (46), 16302-16303CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    Direct observation of triplet absorption and ground-state depletion upon pulsed excitation of a polycryst. thin solid film of 1,3-diphenylisobenzofuran at 77 K revealed a 200 ± 30% triplet yield, which was attributed to singlet fission.
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  17. 17
    Ryerson, J. L.; Schrauben, J. N.; Ferguson, A. J.; Sahoo, S. C.; Naumov, P.; Havlas, Z.; Michl, J.; Nozik, A. J.; Johnson, J. C. Two thin film polymorphs of the singlet fission compound 1, 3-diphenylisobenzofuran. J. Phys. Chem. C 2014, 118, 12121– 12132,  DOI: 10.1021/jp502122d
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    17
    Two Thin Film Polymorphs of the Singlet Fission Compound 1,3-Diphenylisobenzofuran
    Ryerson, Joseph L.; Schrauben, Joel N.; Ferguson, Andrew J.; Sahoo, Subash Chandra; Naumov, Pance; Havlas, Zdenek; Michl, Josef; Nozik, Arthur J.; Johnson, Justin C.
    Journal of Physical Chemistry C (2014), 118 (23), 12121-12132CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
    Polycryst. thin films of 1,3-diphenylisobenzofuran (1) with a morphol. referred to here as α exhibit highly efficient singlet fission, producing two triplet states for every absorbed photon at 77 K, and about 1.4 triplet states per absorbed photon at room temp. However, the triplet yield depends strongly on the specific cryst. form of 1, and for the morphol. referred to as β the triplet yields are roughly an order of magnitude smaller. In this study, α, β, and mixed α/β films of 1 are prepd. by thermal evapn. and soln. drop-casting, and the structural and photophys. differences that may account for the very different triplet quantum yields are explored. The crystallites of 1 in thin films have been identified with two bulk crystal polymorphs grown from soln. and structurally characterized. Anal. of absorption spectra of the films reveals a 600 cm-1 blue shift in the onset and a unique spectral profile for the form α crystallites as compared to form β. Intermol. interactions between columns of slip-stacked mols. are different in the two polymorphs, and this likely gives rise to the much smaller triplet quantum yield for β-1.
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  18. 18
    Gradinaru, C. C.; Kennis, J. T.; Papagiannakis, E.; Van Stokkum, I. H.; Cogdell, R. J.; Fleming, G. R.; Niederman, R. A.; Van Grondelle, R. An unusual pathway of excitation energy deactivation in carotenoids: singlet-to-triplet conversion on an ultrafast timescale in a photosynthetic antenna. Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 2364– 2369,  DOI: 10.1073/pnas.051501298
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    18
    An unusual pathway of excitation energy deactivation in carotenoids: singlet-to-triplet conversion on an ultrafast timescale in a photosynthetic antenna
    Gradinaru, Claudiu C.; Kennis, John T. M.; Papagiannakis, Emmanouil; Van Stokkum, Ivo H. M.; Cogdell, Richard J.; Fleming, Graham R.; Niederman, Robert A.; Van Grondelle, Rienk
    Proceedings of the National Academy of Sciences of the United States of America (2001), 98 (5), 2364-2369CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
    Carotenoids are important biomols. that are ubiquitous in nature and find widespread application in medicine. In photosynthesis, they have a large role in light harvesting (LH) and photoprotection. They exert their LH function by donating their excited singlet state to nearby (bacterio)chlorophyll mols. In photosynthetic bacteria, the efficiency of this energy transfer process can be as low as 30%. Here, evidence is presented that an unusual pathway of excited state relaxation in carotenoids underlies this poor LH function, by which carotenoid triplet states are generated directly from carotenoid singlet states. This pathway, operative on a femtosecond and picosecond timescale, involves an intermediate state, which was identified as a new, hitherto uncharacterized carotenoid singlet excited state. In LH complex-bound carotenoids, this state is the precursor on the reaction pathway to the triplet state, whereas in extd. carotenoids in soln., this state returns to the singlet ground state without forming any triplets. The authors discuss the possible identity of this excited state and argue that fission of the singlet state into a pair of triplet states on individual carotenoid mols. constitutes the mechanism by which the triplets are generated. This is, to our knowledge, the first ever direct observation of a singlet-to-triplet conversion process on an ultrafast timescale in a photosynthetic antenna.
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  19. 19
    Manawadu, D.; Valentine, D. J.; Marcus, M.; Barford, W. Singlet triplet-pair production and possible singlet-fission in carotenoids. J. Phys. Chem. Lett. 2022, 13, 1344– 1349,  DOI: 10.1021/acs.jpclett.1c03812
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    19
    Singlet Triplet-Pair Production and Possible Singlet-Fission in Carotenoids
    Manawadu, Dilhan; Valentine, Darren J.; Marcus, Max; Barford, William
    Journal of Physical Chemistry Letters (2022), 13 (5), 1344-1349CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
    Internal conversion from the photoexcited state to a correlated singlet triplet-pair state is believed to be the precursor of singlet fission in carotenoids. We present numerical simulations of this process using a π-electron model that fully accounts for electron-electron interactions and electron-nuclear coupling. The time-evolution of the electrons is detd. rigorously using the time-dependent d. matrix renormalization group method, while the nuclei are evolved via the Ehrenfest equations of motion. We apply this to zeaxanthin, a carotenoid chain with 18 fully conjugated carbon atoms. We show that the internal conversion of the primary photoexcited state, S2, to the singlet triplet-pair state occurs adiabatically via an avoided crossing within ~ 50 fs with a yield of ~ 60%. We further discuss whether this singlet triplet-pair state will undergo exothermic vs. endothermic intra- or interchain singlet fission.
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    Musser, A. J.; Maiuri, M.; Brida, D.; Cerullo, G.; Friend, R. H.; Clark, J. The nature of singlet exciton fission in carotenoid aggregates. J. Am. Chem. Soc. 2015, 137, 5130– 5139,  DOI: 10.1021/jacs.5b01130
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    20
    The Nature of Singlet Exciton Fission in Carotenoid Aggregates
    Musser, Andrew J.; Maiuri, Margherita; Brida, Daniele; Cerullo, Giulio; Friend, Richard H.; Clark, Jenny
    Journal of the American Chemical Society (2015), 137 (15), 5130-5139CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    Singlet exciton fission allows the fast and efficient generation of two spin triplet states from one photoexcited singlet. It has the potential to improve org. photovoltaics, enabling efficient coupling to the blue to UV region of the solar spectrum to capture the energy generally lost as waste heat. However, many questions remain about the underlying fission mechanism. The relation between intermol. geometry and singlet fission rate and yield is poorly understood and remains one of the most significant barriers to the design of new singlet fission sensitizers. Here the authors explore the structure-property relation and examine the mechanism of singlet fission in aggregates of astaxanthin, a small polyene. The authors isolate five distinct supramol. structures of astaxanthin generated through self-assembly in soln. Each is capable of undergoing intermol. singlet fission, with rates of triplet generation and annihilation that can be correlated with intermol. coupling strength. In contrast with the conventional model of singlet fission in linear mols., no intermediate states are involved in the triplet formation: instead, singlet fission occurs directly from the initial 1Bu photoexcited state on ultrafast time scales. This result demands a reevaluation of current theories of polyene photophysics and highlights the robustness of carotenoid singlet fission.
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    Beljonne, D.; Cornil, J.; Friend, R.; Janssen, R.; Brédas, J.-L. Influence of chain length and derivatization on the lowest singlet and triplet states and intersystem crossing in oligothiophenes. J. Am. Chem. Soc. 1996, 118, 6453– 6461,  DOI: 10.1021/ja9531135
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    Influence of Chain Length and Derivatization on the Lowest Singlet and Triplet States and Intersystem Crossing in Oligothiophenes
    Beljonne, D.; Cornil, J.; Friend, R. H.; Janssen, R. A. J.; Bredas, J. L.
    Journal of the American Chemical Society (1996), 118 (27), 6453-6461CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    On the basis of CI calcns., we first describe the nature of the lowest singlet and triplet excited states in oligothiophenes ranging in size from two to six rings. We calc. the vertical excitation energies from the singlet ground state S0 to the first one-photon allowed singlet excited state S1 as well as the energy difference between the ground state and the lowest triplet state T1. The computed transition energies are in very good agreement with the measured values and indicate a strong confinement of the lowest triplet. We also uncover the nature of the higher-lying triplet excited state Tn that is coupled via a large oscillator strength to T1. The evolution with chain length of the T1-Tn excitation energies compares well with the exptl. evolution based on photoinduced absorption data. Next, we investigate the geometry relaxation phenomena occurring in the S1 and T1 states; more pronounced and localized bond-length deformations are calcd. in the triplet state than in the singlet, confirming the more localized character of T1. We also analyze the influence on the lowest excited states of grafting electroactive end-groups on the conjugated path of terthiophene. Finally, the various mechanisms involved in the nonradiative decay of the singlet excitations are discussed, and results are presented as a guide toward the optimization of light emission efficiency in conjugated systems.
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    Busby, E.; Xia, J.; Low, J. Z.; Wu, Q.; Hoy, J.; Campos, L. M.; Sfeir, M. Y. Fast singlet exciton decay in push-pull molecules containing oxidized thiophenes. J. Phys. Chem. B 2015, 119, 7644– 7650,  DOI: 10.1021/jp511704r
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    22
    Fast Singlet Exciton Decay in Push-Pull Molecules Containing Oxidized Thiophenes
    Busby, Erik; Xia, Jianlong; Low, Jonathan Z.; Wu, Qin; Hoy, Jessica; Campos, Luis M.; Sfeir, Matthew Y.
    Journal of Physical Chemistry B (2015), 119 (24), 7644-7650CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
    A common synthetic strategy used to design low-bandgap org. semiconductors employs the use of push-pull building blocks, where electron -rich and electron-deficient monomers are alternated along the π-conjugated backbone of a mol. or polymer. Incorporating strong pull units with high electron affinity is a means to further decrease the optical gap for IR optoelectronics or to develop n-type semiconducting materials. The use of thiophene-1,1-dioxide as a strong acceptor in push-pull oligomers affects the electronic structure and carrier dynamics in unexpected ways. Critically, the overall excited-state lifetime is reduced by several orders of magnitude relative to unoxidized analogs due to the introduction of low-energy optically dark states and low-energy triplet states that allow for fast internal conversion and intramol. singlet fission. The electronic structure and excited-state lifetime are strongly dependent on the no. of sequential thiophene-1,1-dioxide units. Probably both the static and dynamical optical properties are highly tunable via small changes in chem. structure that have drastic effects on the optoelectronic properties, which can impact the types of applications that involve these materials.
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  23. 23
    Dean, J. C.; Zhang, R.; Hallani, R. K.; Pensack, R. D.; Sanders, S. N.; Oblinsky, D. G.; Parkin, S. R.; Campos, L. M.; Anthony, J. E.; Scholes, G. D. Photophysical characterization and time-resolved spectroscopy of a anthradithiophene dimer: exploring the role of conformation in singlet fission. Phys. Chem. Chem. Phys. 2017, 19, 23162– 23175,  DOI: 10.1039/C7CP03774K
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    23
    Photophysical characterization and time-resolved spectroscopy of a anthradithiophene dimer: exploring the role of conformation in singlet fission
    Dean, Jacob C.; Zhang, Ruomeng; Hallani, Rawad K.; Pensack, Ryan D.; Sanders, Samuel N.; Oblinsky, Daniel G.; Parkin, Sean R.; Campos, Luis M.; Anthony, John E.; Scholes, Gregory D.
    Physical Chemistry Chemical Physics (2017), 19 (34), 23162-23175CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
    Quant. singlet fission has been obsd. for a variety of acene derivs. such as tetracene and pentacene, and efforts to extend the library of singlet fission compds. is of current interest. Preliminary calcns. suggest anthradithiophenes exhibit significant exothermicity between the first optically-allowed singlet state, S1, and 2 × T1 with an energy difference of >5000 cm-1. Given the fulfillment of this ingredient for singlet fission, here we investigate the singlet fission capability of a difluorinated anthradithiophene dimer (2ADT) covalently linked by a (dimethylsilyl)ethane bridge and derivatized by triisobutylsilylethynyl (TIBS) groups. Photophys. characterization of 2ADT and the single functionalized ADT monomer were carried out in toluene and acetone soln. via absorption and fluorescence spectroscopy, and their photo-initiated dynamics were investigated with time-resolved fluorescence (TRF) and transient absorption (TA) spectroscopy. In accordance with computational predictions, two conformers of 2ADT were obsd. via fluorescence spectroscopy and were assigned to structures with the ADT cores trans or cis to one another about the covalent bridge. The two conformers exhibited markedly different excited state deactivation mechanisms, with the minor trans population being representative of the ADT monomer showing primarily radiative decay, while the dominant cis population underwent relaxation into an excimer geometry before internally converting to the ground state. The excimer formation kinetics were found to be solvent dependent, yielding time consts. of ∼1.75 ns in toluene, and ∼600 ps in acetone. While the difference in rates elicits a role for the solvent in stabilizing the excimer structure, the rate is still decidedly long compared to most singlet fission rates of analogous dimers, suggesting that the excimer is neither a kinetic nor a thermodn. trap, yet singlet fission was still not obsd. The result highlights the sensitivity of the electronic coupling element between the singlet and correlated triplet pair states, to the dimer conformation in dictating singlet fission efficiency even when the energetic requirements are met.
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    Zhao, T.; Kloc, C.; Ni, W.; Sun, L.; Gurzadyan, G. G. Revealing ultrafast relaxation dynamics in six-thiophene thin film and single crystal. J. Photochem. Photobiol. A: Chem. 2021, 404, 112920,  DOI: 10.1016/j.jphotochem.2020.112920
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    Revealing ultrafast relaxation dynamics in six-thiophene thin film and single crystal
    Zhao, Tongyu; Kloc, Christian; Ni, Wenjun; Sun, Licheng; Gurzadyan, Gagik G.
    Journal of Photochemistry and Photobiology, A: Chemistry (2021), 404 (), 112920CODEN: JPPCEJ; ISSN:1010-6030. (Elsevier B.V.)
    The excited state dynamics of six-thiophene (6T) thin film and single crystal was studied by time-resolved fluorescence and femtosecond transient absorption techniques under different excitation conditions. The dominant process in 6T system is the generation of ion pairs, dissocd. to polarons staying for up to 130-3700 ns in film and 1 ms in crystal. Singlet fission (SF) was directly obsd. from the upper vibrational levels of the first excited singlet state S1 in 6T thin film/single crystal within 30 fs, which competes with intramol. vibrational relaxation. Triplet state lifetime is dramatically shortened from 6T single crystal (1 ms) to thin film (4 ns) due to triplet-triplet annihilation, which is influenced by structural defects in amorphous regions of 6T film. Compared with 6T crystal, the partially ordered semicryst. morphol. of 6T film suggests the impact of well-structured crystallinity and mol. packing on the photocarriers transport dynamics and lifetime of triplet state. Moreover, excitation to upper excited singlet state (4.96 eV) leads to a higher yield of polarons (factor of 4), while SF in film/crystal is fully suppressed. Existence of long-lived photogenerated polarons may count π-conjugated oligomers as promising materials for developing org.-mol.-based optoelectronic devices.
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    Sharifzadeh, S.; Darancet, P.; Kronik, L.; Neaton, J. B. Low-energy charge-transfer excitons in organic solids from first-principles: The case of pentacene. J. Phys. Chem. Lett. 2013, 4, 2197– 2201,  DOI: 10.1021/jz401069f
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    Low-Energy Charge-Transfer Excitons in Organic Solids from First-Principles: The Case of Pentacene
    Sharifzadeh, Sahar; Darancet, Pierre; Kronik, Leeor; Neaton, Jeffrey B.
    Journal of Physical Chemistry Letters (2013), 4 (13), 2197-2201CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
    The nature of low energy optical excitations, or excitons, in org. solids is of central relevance to many optoelectronic applications, including solar energy conversion. Excitons in solid pentacene, a prototypical org. semiconductor, have been the subject of many exptl. and theor. studies, with differing conclusions as to the degree of their charge-transfer character. Using first-principles calcns. based on d. functional theory and many-body perturbation theory, the authors compute the av. electron-hole distance and quantify the degree of charge-transfer character within optical excitations in solid-state pentacene. The authors show that several low-energy singlet excitations are characterized by a weak overlap between electron and hole and an av. electron-hole distance greater than 6 Å. Addnl., the authors show that the character of the lowest-lying singlet and triplet excitons is well-described with a simple analytic envelope function of the electron-hole distance.
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    Beljonne, D.; Yamagata, H.; Brédas, J.-L.; Spano, F.; Olivier, Y. Charge-transfer excitations steer the Davydov splitting and mediate singlet exciton fission in pentacene. Phys. Rev. Lett. 2013, 110, 226402,  DOI: 10.1103/PhysRevLett.110.226402
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    Charge-transfer excitations steer the Davydov splitting and mediate singlet exciton fission in pentacene
    Beljonne, D.; Yamagata, H.; Bredas, J. L.; Spano, F. C.; Olivier, Y.
    Physical Review Letters (2013), 110 (22), 226402/1-226402/5CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    Quantum-chem. calcns. are combined to a model Frenkel-Holstein Hamiltonian to assess the nature of the lowest electronic excitations in the pentacene crystal. We show that an admixt. of charge-transfer excitations into the lowest singlet excited states form the origin of the Davydov splitting and mediate instantaneous singlet exciton fission by direct optical excitation of coherently coupled single and double exciton states, in agreement with recent expts.
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    Wang, X.; Liu, X.; Tom, R.; Cook, C.; Schatschneider, B.; Marom, N. Phenylated acene derivatives as candidates for intermolecular singlet fission. J. Phys. Chem. C 2019, 123, 5890– 5899,  DOI: 10.1021/acs.jpcc.8b12549
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    Phenylated Acene Derivatives as Candidates for Intermolecular Singlet Fission
    Wang, Xiaopeng; Liu, Xingyu; Tom, Rithwik; Cook, Cameron; Schatschneider, Bohdan; Marom, Noa
    Journal of Physical Chemistry C (2019), 123 (10), 5890-5899CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
    Singlet fission (SF), a spin-conserving process where one singlet exciton is converted into two triplet excitons, may improve the efficiency of org. photovoltaics. Only a few materials have been exptl. obsd. to undergo intermol. SF, most of which are acenes and their derivs. Using many-body perturbation theory in the GW approxn. and the Bethe-Salpeter equation, we systematically investigate the electronic and excitonic properties of tetracene, pentacene, and their phenylated derivs. in the gas phase and solid state. Their potential for SF is evaluated with respect to the thermodn. driving force and the singlet exciton charge-transfer character. In both the gas phase and solid state, pentacene and its derivs. are more promising than tetracene analogs. Within a family of mols. contg. the same acene backbone, increasing the no. of Ph side groups is detrimental for the SF driving force in the gas phase. However, in the solid state, the SF driving force and the exciton character are modulated by intermol. interactions present within different packing arrangements. Mols. with a higher no. of Ph side groups often form crystals with less cofacial interactions between the acene backbones. These crystals are found to exhibit a higher SF driving force and a higher degree of singlet exciton charge-transfer character. In particular, 5,7,12,14-tetraphenylpentacene, 1,4,6,8,11,13-hexaphenylpentacene, and 1,2,3,4,6,8,9,10,11,13-decaphenylpentacene emerge as promising candidates for intermol. SF in the solid state.
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    Wang, X.; Liu, X.; Cook, C.; Schatschneider, B.; Marom, N. On the possibility of singlet fission in crystalline quaterrylene. J. Chem. Phys. 2018, 148, 184101,  DOI: 10.1063/1.5027553
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    On the possibility of singlet fission in crystalline quaterrylene
    Wang, Xiaopeng; Liu, Xingyu; Cook, Cameron; Schatschneider, Bohdan; Marom, Noa
    Journal of Chemical Physics (2018), 148 (18), 184101/1-184101/10CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    Singlet fission (SF), the spontaneous down-conversion of a singlet exciton into two triplet excitons residing on neighboring mols., is a promising route to improve org. photovoltaic (OPV) device efficiencies by harvesting two charge carriers from one photon. However, only a few materials have been discovered that exhibit intermol. SF in the solid state, most of which are acene derivs. Recently, there has been a growing interest in rylenes as potential SF materials. We use many-body perturbation theory in the GW approxn. and the Bethe-Salpeter equation to investigate the possibility of intermol. SF in cryst. perylene and quaterrylene. A new method is presented for detg. the percent charge transfer (%CT) character of an exciton wave-function from double-Bader anal. This enables relating exciton probability distributions to crystal packing. Based on comparison to known and predicted SF materials with respect to the energy conservation criterion (ES-2ET) and %CT, cryst. quaterrylene is a promising candidate for intermol. SF. Furthermore, quaterrylene is attractive for OPV applications, thanks to its high stability and narrow optical gap. Perylene is not expected to exhibit SF; however, it is a promising candidate for harvesting sub-gap photons by triplet-triplet annihilation. (c) 2018 American Institute of Physics.
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    Monahan, N.; Zhu, X.-Y. Charge transfer–mediated singlet fission. Annu. Rev. Phys. Chem. 2015, 66, 601– 618,  DOI: 10.1146/annurev-physchem-040214-121235
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    Charge transfer-mediated singlet fission
    Monahan, N.; Zhu, X.-Y.
    Annual Review of Physical Chemistry (2015), 66 (), 601-618CODEN: ARPLAP; ISSN:0066-426X. (Annual Reviews)
    Singlet fission, the splitting of a singlet exciton into two triplet excitons in mol. materials, is interesting not only as a model many-electron problem, but also as a process with potential applications in solar energy conversion. Here we discuss limitations of the conventional four-electron and mol. dimer model in describing singlet fission in cryst. org. semiconductors, such as pentacene and tetracene. We emphasize the need to consider electronic delocalization, which is responsible for the decisive role played by the Mott-Wannier exciton, also called the charge transfer (CT) exciton, in mediating singlet fission. At the strong electronic coupling limit, the initial excitation creates a quantum superposition of singlet, CT, and triplet-pair states, and we present exptl. evidence for this interpretation. We also discuss the most recent attempts at translating this mechanistic understanding into design principles for CT state-mediated intramol. singlet fission in oligomers and polymers.
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    Rao, A.; Friend, R. H. Harnessing singlet exciton fission to break the Shockley–Queisser limit. Nat. Rev. Mater. 2017, 2, 17063,  DOI: 10.1038/natrevmats.2017.63
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    Harnessing singlet exciton fission to break the Shockley-Queisser limit
    Rao, Akshay; Friend, Richard H.
    Nature Reviews Materials (2017), 2 (11), 17063CODEN: NRMADL; ISSN:2058-8437. (Nature Research)
    A review. Singlet exciton fission is a carrier multiplication process in org. semiconductors that generates two electron-hole pairs for each photon absorbed. Singlet fission occurs on sub-100 fs timescales with yields of up to 200%, and photovoltaic devices based on singlet fission have achieved external quantum efficiencies above 100%. The major challenge for the field is to use singlet fission to improve the efficiency of conventional inorg. solar cells, such as silicon, and to break the Shockley-Queisser limit on the efficiency of single-junction photovoltaics. Achieving this goal requires a broader and more collaborative effort than the one used at present. Synthetic chemists, spectroscopists, theorists, materials scientists, device physicists and engineers will need to work together. In this Review, we critically assess the current status of the field, highlight the key results and identify the challenges ahead. In doing so, we seek to open the field to new expertise and ideas, which will in turn promote both fundamental science and device applications.
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    Lu, H.; Chen, X.; Anthony, J. E.; Johnson, J. C.; Beard, M. C. Sensitizing singlet fission with perovskite nanocrystals. J. Am. Chem. Soc. 2019, 141, 4919– 4927,  DOI: 10.1021/jacs.8b13562
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    Sensitizing singlet fission with perovskite nanocrystals
    Lu, Haipeng; Chen, Xihan; Anthony, John E.; Johnson, Justin C.; Beard, Matthew C.
    Journal of the American Chemical Society (2019), 141 (12), 4919-4927CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    The marriage of colloidal semiconductor nanocrystals and functional org. mols. has brought unique opportunities in emerging photonic and optoelectronic applications. Traditional semiconductor nanocrystals have been widely demonstrated to initiate efficient triplet energy transfer at the nanocrystal-acene interface. Herein, we report that unlike conventional semiconductor nanocrystals, lead halide perovskite nanocrystals promote an efficient Dexter-like singlet energy transfer to surface-anchored pentacene mols. rather than triplet energy transfer. Subsequently, mol. pentacene triplets are efficiently generated via singlet fission on the nanocrystal surface. Our demonstrated strategy not only unveils the obscure energy dynamics between perovskite nanocrystal and acenes, but also brings important perspectives of utilizing singlet fission throughout the solar spectrum.
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    Budden, P. J.; Weiss, L. R.; Müller, M.; Panjwani, N. A.; Dowland, S.; Allardice, J. R.; Ganschow, M.; Freudenberg, J.; Behrends, J.; Bunz, U. H. Singlet exciton fission in a modified acene with improved stability and high photoluminescence yield. Nat. Commun. 2021, 12, 1527,  DOI: 10.1038/s41467-021-21719-x
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    Singlet exciton fission in a modified acene with improved stability and high photoluminescence yield
    Budden, Peter J.; Weiss, Leah R.; Muller, Matthias; Panjwani, Naitik A.; Dowland, Simon; Allardice, Jesse R.; Ganschow, Michael; Freudenberg, Jan; Behrends, Jan; Bunz, Uwe H. F.; Friend, Richard H.
    Nature Communications (2021), 12 (1), 1527CODEN: NCAOBW; ISSN:2041-1723. (Nature Research)
    We report a fully efficient singlet exciton fission material with high ambient chem. stability. 10,21-Bis(triisopropylsilylethynyl)tetrabenzo[a,c,l,n]pentacene (TTBP) combines an acene core with triphenylene wings that protect the formal pentacene from chem. degrdn. The electronic energy levels position singlet exciton fission to be endothermic, similar to tetracene despite the triphenylenes. TTBP exhibits rapid early time singlet fission with quant. yield of triplet pairs within 100 ps followed by thermally activated sepn. to free triplet excitons over 65 ns. TTBP exhibits high photoluminescence quantum efficiency, close to 100% when dil. and 20% for solid films, arising from triplet-triplet annihilation. In using such a system for exciton multiplication in a solar cell, max. thermodn. performance requires radiative decay of the triplet population, obsd. here as emission from the singlet formed by recombination of triplet pairs. Combining chem. stabilization with efficient endothermic fission provides a promising avenue towards singlet fission materials for use in photovoltaics.
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    Liu, X.; Tom, R.; Gao, S.; Marom, N. Assessing zethrene derivatives as singlet fission candidates based on multiple descriptors. J. Phys. Chem. C 2020, 124, 26134– 26143,  DOI: 10.1021/acs.jpcc.0c08160
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    Assessing Zethrene Derivatives as Singlet Fission Candidates Based on Multiple Descriptors
    Liu, Xingyu; Tom, Rithwik; Gao, Siyu; Marom, Noa
    Journal of Physical Chemistry C (2020), 124 (48), 26134-26143CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
    Singlet fission (SF) is a process where one singlet exciton splits into two triplet excitons. Utilizing SF may potentially increase the efficiency of solar cells beyond the Shockley-Queisser limit. To discover new SF materials, predictive descriptors for SF performance are needed. We consider multiple descriptors to assess several zethrene derivs. as candidate materials for intermol. SF in the solid state. The descriptors include single mol. multiradical characters, many-body perturbation theory calcns. of the thermodn. driving force for SF and the singlet exciton charge transfer character in crystals, and a kinetic model based on mol. dimers extd. from the crystal structures. The zethrenes are compared to acenes known to exhibit SF with respect to these descriptors. The results indicate that all zethrene and heptazethrene derivs. studied here may exhibit SF. In particular, 7,14-bis(2,4,6-trimethylphenyl)dibenzo[de,mn]naphthacene (Z-T) emerges as a promising candidate. Its SF driving force is higher than tetracene, whose fission process is slightly endoergic, but lower than pentacene. Its singlet exciton charge transfer character is close to pentacene, and its crystal packing leads to a higher SF rate than other zethrene derivs. Therefore, it may undergo fast SF with high energy efficiency. The approach of considering multiple descriptors may be useful for evaluating addnl. candidate materials for SF.
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    Liu, X.; Tom, R.; Wang, X.; Cook, C.; Schatschneider, B.; Marom, N. Pyrene-stabilized acenes as intermolecular singlet fission candidates: importance of exciton wave-function convergence. J. Phys.: Condens. Matter 2020, 32, 184001,  DOI: 10.1088/1361-648X/ab699e
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    Pyrene-stabilized acenes as intermolecular singlet fission candidates: importance of exciton wave-function convergence
    Liu, Xingyu; Tom, Rithwik; Wang, Xiaopeng; Cook, Cameron; Schatschneider, Bohdan; Marom, Noa
    Journal of Physics: Condensed Matter (2020), 32 (18), 184001CODEN: JCOMEL; ISSN:0953-8984. (IOP Publishing Ltd.)
    Singlet fission (SF) is a photophys. process considered as a possible scheme to bypass the Shockley-Queisser limit by generating two triplet-state excitons from one high-energy photon. Polyacene crystals, such as tetracene and pentacene, have shown outstanding SF performance both theor. and exptl. However, their instability prevents them from being utilized in SF-based photovoltaic devices. In search of practical SF chromophores, we use many-body perturbation theory within the GW approxn. and Bethe-Salpeter equation to study the excitonic properties of a family of pyrene-stabilized acenes. We propose a criterion to define the convergence of exciton wave-functions with respect to the fine k-point grid used in the BerkeleyGW code. An open-source Python code is presented to perform exciton wave-function convergence checks and streamline the double Bader anal. of exciton character. We find that the singlet excitons in pyrene-stabilized acenes have a higher degree of charge transfer character than in the corresponding acenes. The pyrene-fused tetracene and pentacene derivs. exhibit comparable excitation energies to their corresponding acenes, making them potential SF candidates. The pyrene-stabilized anthracene deriv. is considered as a possible candidate for triplet-triplet annihilation because it yields a lower SF driving force than anthracene.
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    Wang, X.; Garcia, T.; Monaco, S.; Schatschneider, B.; Marom, N. Effect of crystal packing on the excitonic properties of rubrene polymorphs. CrystEngComm 2016, 18, 7353– 7362,  DOI: 10.1039/C6CE00873A
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    Effect of crystal packing on the excitonic properties of rubrene polymorphs
    Wang, Xiaopeng; Garcia, Taylor; Monaco, Stephen; Schatschneider, Bohdan; Marom, Noa
    CrystEngComm (2016), 18 (38), 7353-7362CODEN: CRECF4; ISSN:1466-8033. (Royal Society of Chemistry)
    Singlet fission (SF), the conversion of one singlet exciton into two triplet excitons, may lead to the realization of high efficiency org. photovoltaics by generating two carriers from one photon. Recently, SF has been obsd. in mol. crystals of rubrene. While the orthorhombic form of rubrene is most often obsd. under ambient conditions, metastable monoclinic and triclinic polymorphs are known. Here, dispersion-inclusive d. functional theory (DFT) is used to investigate the relative stability of all three phases. Many-body perturbation theory is then employed to study the effect of crystal structure on the electronic and excitonic properties. Band structures are calcd. within the GW approxn. and optical properties are calcd. by solving the Bethe-Salpeter equation (BSE). We find that crystal packing significantly affects the electronic and excitonic properties of rubrene. Based on our calcns., the triclinic and esp. the monoclinic forms of rubrene are expected to exhibit higher SF efficiencies than the orthorhombic form.
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    Liu, X.; Wang, X.; Gao, S.; Chang, V.; Tom, R.; Yu, M.; Ghiringhelli, L. M.; Marom, N. Finding predictive models for singlet fission by machine learning. npj Comput. Mater. 2022, 8, 70,  DOI: 10.1038/s41524-022-00758-y
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    Minami, T.; Nakano, M. Diradical character view of singlet fission. J. Phys. Chem. Lett. 2012, 3, 145– 150,  DOI: 10.1021/jz2015346
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    Diradical Character View of Singlet Fission
    Minami, Takuya; Nakano, Masayoshi
    Journal of Physical Chemistry Letters (2012), 3 (2), 145-150CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
    The feasibility conditions of singlet fission on the excitation energy differences are revealed as functions of the multiple diradical characters yi [defined by the occupation nos. of the LUNO (= Lowest Unoccupied Natural Orbital) + i (i = 0, 1, ...), where 0 ≤ yi ≤ 1 and yi ≥ yj (i > j)] using the linear H4 full CI model. The diradical characters suited for singlet fission are found to lie in the region with y0 > 0.10 except for y0 ∼ y1, though its energy efficiency is better in case of smaller y0, to which diradical and multiradical compds. with low/intermediate diradical characters such as open-shell singlet polycyclic arom. hydrocarbons belong. These findings indicate that the multiple diradical character is an effective indicator for exploring mol. systems for efficient singlet fission.
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    Padula, D.; Omar, Ö. H.; Nematiaram, T.; Troisi, A. Singlet fission molecules among known compounds: finding a few needles in a haystack. Energy Environ. Sci. 2019, 12, 2412– 2416,  DOI: 10.1039/C9EE01508F
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    Nogueira, B. A.; Castiglioni, C.; Fausto, R. Color polymorphism in organic crystals. Commun. Chem. 2020, 3, 34,  DOI: 10.1038/s42004-020-0279-0
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    Color polymorphism in organic crystals
    Nogueira Bernardo A; Fausto Rui; Nogueira Bernardo A; Castiglioni Chiara; Fausto Rui
    Communications chemistry (2020), 3 (1), 34 ISSN:.
    Color polymorphism is an interesting property of chemical systems which present crystal polymorphs of different colors. It is a rare phenomenon, with only a few examples reported in the literature hitherto. Nevertheless, systems exhibiting color polymorphism have many potential applications in different domains, such as pigment, sensor, and technology industries. Here, known representative chemical systems showing color polymorphism are reviewed, and the reasons for them to present such property discussed. Also, since some of the concepts related to color polymorphism have been frequently used imprecisely in the scientific literature, this article provides concise, systematic definitions for these concepts.
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  40. 40
    Moliterni, A.; Altamura, D.; Lassandro, R.; Olieric, V.; Ferri, G.; Cardarelli, F.; Camposeo, A.; Pisignano, D.; Anthony, J. E.; Giannini, C. Synthesis, crystal structure, polymorphism and microscopic luminescence properties of anthracene derivative compounds. Acta. Crystallogr. B Struct. Sci. Cryst. Eng. Mater. 2020, 76, 427– 435,  DOI: 10.1107/S2052520620004424
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    Synthesis, crystal structure, polymorphism and microscopic luminescence properties of anthracene derivative compounds
    Moliterni, Anna; Altamura, Davide; Lassandro, Rocco; Olieric, Vincent; Ferri, Gianmarco; Cardarelli, Francesco; Camposeo, Andrea; Pisignano, Dario; Anthony, John E.; Giannini, Cinzia
    Acta Crystallographica, Section B: Structural Science, Crystal Engineering and Materials (2020), 76 (3), 427-435CODEN: ACSBDA; ISSN:2052-5206. (International Union of Crystallography)
    Anthracene deriv. compds. are currently investigated because of their unique phys. properties (e.g. bright luminescence and emission tunability), which make them ideal candidates for advanced optoelectronic devices. Intermol. interactions are the basis of the tunability of the optical and electronic properties of these compds., whose prediction and exploitation benefit from knowledge of the crystal structure and the packing architecture. Polymorphism can occur due to the weak intermol. interactions, requiring detailed structural anal. to clarify the origin of obsd. material property modifications. Addnl., laser confocal microscopy and fluorescence lifetime imaging microscopy confirm the results obtained by the X-ray diffraction characterization, i.e. shifting the substituents towards the external benzene rings of the anthracene unit favors π-π interactions, impacting on both the morphol. and the microscopic optical properties of the crystals. The compds. with more isolated anthracene units feature shorter lifetime and emission spectra, more similar to those of isolated mols. The crystallog. study, supported by the optical investigation, sheds light on the influence of non-covalent interactions on the crystal packing and luminescence properties of anthracene derivs., providing a further step towards their efficient use as building blocks in active components of light sources and photonic networks.
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    Bhattacharyya, K.; Datta, A. Polymorphism controlled singlet fission in tips-anthracene: role of stacking orientation. J. Phys. Chem. C 2017, 121, 1412– 1420,  DOI: 10.1021/acs.jpcc.6b10075
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    Polymorphism Controlled Singlet Fission in TIPS-Anthracene: Role of Stacking Orientation
    Bhattacharyya, Kalishankar; Datta, Ayan
    Journal of Physical Chemistry C (2017), 121 (3), 1412-1420CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
    Generation of multiple triplet excitons from one singlet exciton (singlet fission, SF) has been reported in several org. mols. recently. The overall SF yield in such mol. materials, however, is controlled by polymorphism in org. semiconductors through noncovalent interactions like van der Waals and weak electrostatic interactions. In this article, we demonstrate how SF is strongly perturbed by even small variations in mol. packing for polymorphic crystals of triisopropylsilyethnyl-anthracene derivs., TIPS-Ant (PI and PII). Based on quantum chem. calcns., SF dynamics have been computed for both PI and PII polymorphs. PI and PII differ in their intermol. π···π stacking patterns, which eventually control their electronic properties. Using the incoherent hopping model for the crystals, we computed SF rate through the Marcus electron transfer theory. For both PI and PII, the direct two-electron pathway predominates over the charge-transfer (CT) mediated mechanism. PII has higher triplet yield (∼196%) compared to PI (∼178%). Both time-dependent DFT as well as Weller equation reveal that the charge transfer (CT) state is a high energy state, and hence, CT mediated SF barely influences triplet yield. Interplay of the local excitation (LE), multiple excitation (ME), and correlated triplet (T1T1) energy levels controlled the overall exciton dynamics/diffusion in TIPS-Ant polymorphs. Polymorphism is shown to be a key factor for the rational design of optimal SF in polyarom. hydrocarbons (PAH).
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    Mayonado, G.; Vogt, K. T.; Van Schenck, J. D.; Zhu, L.; Fregoso, G.; Anthony, J.; Ostroverkhova, O.; Graham, M. W. High-symmetry anthradithiophene molecular packing motifs promote thermally activated singlet fission. J. Phys. Chem. C 2022, 126, 4433– 4445,  DOI: 10.1021/acs.jpcc.1c10977
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    High-Symmetry Anthradithiophene Molecular Packing Motifs Promote Thermally Activated Singlet Fission
    Mayonado, Gina; Vogt, Kyle T.; Van Schenck, Jonathan D. B.; Zhu, Liangdong; Fregoso, Garrett; Anthony, John; Ostroverkhova, Oksana; Graham, Matt W.
    Journal of Physical Chemistry C (2022), 126 (9), 4433-4445CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
    When considering the optimal mol. packing to realize charge multiplication in org. photovoltaic materials, subtle changes in intermol. charge transfer (CT) coupling can strongly modulate singlet fission. To understand why certain packing arrangements are more conducive to charge multiplication by triplet pair (TT) formation, we measure the diffraction-limited transient absorption (TA) response from four single-crystal functionalized derivs. of fluorinated anthradithiophene: diF R-ADT (R = TES, TSBS, TDMS, TBDMS). diF TES-ADT and diF TDMS-ADT both exhibit 2D brickwork packing structures, diF TSBS-ADT adopts a 1D sandwich-herringbone packing structure, and diF TBDMS-ADT exhibits a 1D twisted-columnar packing structure. When brickwork or twisted-columnar single crystals are resonantly probed parallel to their charge transfer (CT)-axis projections, the TA signal is dominated by a rising component on the picosecond time scale (rate kTT), attributed to TT state population. When probed orthogonal to the CT-axis, we instead recover the falling TA kinetics of singlet state depletion at rate kA. The rising to falling rate ratio ests. the TT formation efficiency, εTT = kTT/kA relative to exciton self-trapping. εTT ranged from near 100% in diF TES-ADT to 84% in diF TDMS-ADT. Interestingly, diF TSBS-ADT crystals only manifest falling kinetics of CT-mediated self-trapping and singlet state depletion. Singlet fission is prohibitive in diF TSBS-ADT crystals owing to its lower symmetry sandwich-herringbone packing that leads to S1 to CT-state energy sepn. that is ~ 3x larger than in other packings. Collectively, these results highlight optimal packing configurations that either enhance or completely suppress CT-mediated TT formation.
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    Buchanan, E. A.; Michl, J. Optimal arrangements of 1, 3-diphenylisobenzofuran molecule pairs for fast singlet fission. Photochem. Photobiol. Sci. 2019, 18, 2112– 2124,  DOI: 10.1039/c9pp00283a
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    Optimal arrangements of 1,3-diphenylisobenzofuran molecule pairs for fast singlet fission
    Buchanan, Eric A.; Michl, Josef
    Photochemical & Photobiological Sciences (2019), 18 (9), 2112-2124CODEN: PPSHCB; ISSN:1474-905X. (Royal Society of Chemistry)
    A simplified version of the frontier orbital model has been applied to pairs of C2, C2v, Cs, and C1 symmetry 1,3-diphenylisobenzofuran rotamers to det. their best packing for fast singlet fission (SF). For each rotamer the square of the electronic matrix element for SF was calcd. at 2.2 x 109 pair geometries and a few thousand most significant phys. accessible local maxima were identified in the six-dimensional space of mutual arrangements. At these pair geometries, SF energy balance was evaluated, relative SF rate consts. were approximated using Marcus theory, and the SF rate const. kSF was maximized by further optimization of the geometry of the mol. pair. The process resulted in 142, 67, 214, and 291 unique geometries for the C2, C2v, Cs, and C1 symmetry mol. pairs, resp., predicted to be superior to the C2 symmetrized known crystal pair structure. These optimized pair geometries and their triplet biexciton binding energies are reported as targets for crystal engineering and/or covalent dimer synthesis, and as possible starting points for high-level pair geometry optimizations.
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    Piland, G. B.; Bardeen, C. J. How morphology affects singlet fission in crystalline tetracene. J. Phys. Chem. Lett. 2015, 6, 1841– 1846,  DOI: 10.1021/acs.jpclett.5b00569
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    How Morphology Affects Singlet Fission in Crystalline Tetracene
    Piland, Geoffrey B.; Bardeen, Christopher J.
    Journal of Physical Chemistry Letters (2015), 6 (10), 1841-1846CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
    The dependence of exciton dynamics on the cryst. morphol. of tetracene is studied using time-resolved photoluminescence. Single crystals exhibit relatively slow singlet decays with times that range from 130 to 300 ps depending on the sample. This decay has an activation energy of ∼450 cm-1 at 200-400 K. Single-crystal samples also exhibit more pronounced quantum beats due to the triplet pair spin coherences. Polycryst. thin films grown by thermal evapn. have singlet decay times ∼70-90 ps with a much weaker temp. dependence. Many thin-film samples also exhibit a red-shifted excimer-like emission. When a polycryst. thin film is thermally annealed to produce larger crystal domains, single-crystal behavior is recovered. The authors hypothesize that the different dynamics arise from the ability of singlet excitons in the thin films to sample regions with defects or packing motifs that accelerate singlet fission.
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    Buchanan, E. A.; Kaleta, J.; Wen, J.; Lapidus, S. H.; Císařová, I.; Havlas, Z.; Johnson, J. C.; Michl, J. Molecular packing and singlet fission: the parent and three fluorinated 1, 3-diphenylisobenzofurans. J. Phys. Chem. Lett. 2019, 10, 1947– 1953,  DOI: 10.1021/acs.jpclett.8b03875
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    Molecular Packing and Singlet Fission: The Parent and Three Fluorinated 1,3-Diphenylisobenzofurans
    Buchanan, Eric A.; Kaleta, Jiri; Wen, Jin; Lapidus, Saul H.; Cisarova, Ivana; Havlas, Zdenek; Johnson, Justin C.; Michl, Josef
    Journal of Physical Chemistry Letters (2019), 10 (8), 1947-1953CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
    Crystal structures, singlet fission (SF) rate consts., and other photophys. properties are reported for three fluorinated derivs. of 1,3-diphenylisobenzofuran and compared with those of the two crystal forms of the parent. The results place constraints on the notion that the effects of mol. packing on SF rates could be studied sep. from effects of chromophore structural changes by examg. groups of chromophores related by weakly perturbing substitution if their crystal structures are different. The results further provide exptl. evidence that dimer-based models of SF are not sufficiently general and that trimer- and possibly even higher oligomer-based or many-body models need to be formulated.
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    Sondermann, U.; Kutoglu, A.; Bassler, H. X-ray diffraction study of the phase transition in crystalline tetracene. J. Phys. Chem. 1985, 89, 1735– 1741,  DOI: 10.1021/j100255a039
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    X-ray diffraction study of the phase transition in crystalline tetracene
    Sondermann, U.; Kutoglu, A.; Bassler, H.
    Journal of Physical Chemistry (1985), 89 (9), 1735-41CODEN: JPCHAX; ISSN:0022-3654.
    Cryst. tetracene undergoes a structural transition to a 2nd triclinic phase at <200 K. The transition temp. depends on external parameters, such as the strength of mech. coupling of the crystal to a supporting surface, and is subject to a hysteresis effect. The parameters of the new phase were detd. and a structure proposed on the basis of lattice energy calcns. The transition involves a rotation of the mol. at 1/2,1/2,0 around the axis normal to the mol. plane. Translational displacement of the face-centered mol., equiv. to a redn. of crystal symmetry from P‾1 to P1, stabilizes the new phase.
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    Venuti, E.; Della Valle, R. G.; Farina, L.; Brillante, A.; Masino, M.; Girlando, A. Phonons and structures of tetracene polymorphs at low temperature and high pressure. Phys. Rev. B 2004, 70, 104106,  DOI: 10.1103/PhysRevB.70.104106
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    Phonons and structures of tetracene polymorphs at low temperature and high pressure
    Venuti, Elisabetta; Della Valle, Raffaele Guido; Farina, Luca; Brillante, Aldo; Masino, Matteo; Girlando, Alberto
    Physical Review B: Condensed Matter and Materials Physics (2004), 70 (10), 104106/1-104106/8CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
    Crystals of tetracene were studied by lattice phonon Raman spectroscopy as a function of temp. and pressure. Two different phases (polymorphs I and II) were obtained, depending on sample prepn. and history. Polymorph I is the most frequently grown phase, stable at ambient conditions. Application of pressure >1 GPa yields polymorph II, which is also obtained by cooling the sample <140 K. However, the conditions for inducing the phase transitions depend on sample prepn. and history, and polymorph II can also be maintained at ambient conditions. The authors have calcd. the crystallog. structures and phonon frequencies as a function of temp., starting from the configurations of the energy min. found by exploring the potential energy surface of cryst. tetracene. The spectra calcd. for the 1st and 2nd deepest min. match satisfactorily those measured for polymorphs I and II, resp. The temp. dependence of the spectra is described correctly. All published x-ray structures, once assigned to the appropriate polymorph, are also reproduced.
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    Della Valle, R. G.; Venuti, E.; Brillante, A.; Girlando, A. Inherent structures of crystalline tetracene. J. Phys. Chem. A 2006, 110, 10858– 10862,  DOI: 10.1021/jp0611020
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    Inherent Structures of Crystalline Tetracene
    Della Valle, Raffaele Guido; Venuti, Elisabetta; Brillante, Aldo; Girlando, Alberto
    Journal of Physical Chemistry A (2006), 110 (37), 10858-10862CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
    The authors have systematically sampled the potential energy surface of cryst. tetracene to identify its local min. These min. represent all possible stable configurations and constitute the inherent structures of the system. The crystal is described in terms of rigid mols. with Coulombic and atom-atom interactions. Hundreds of distinct min. are identified, mostly belonging to the space groups P‾1 (triclinic) and P21/c (monoclinic), with a variety of structural arrangements. The deepest min. corresponds to the high temp.-low pressure polymorph. This is the only polymorph with a completely described x-ray structure, which is satisfactorily described by the calcns. The next deep min. is likely to correspond to the low temp.-high pressure polymorph, which was exptl. identified but not yet fully described.
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    Groff, R.; Avakian, P.; Merrifield, R. Coexistence of exciton fission and fusion in tetracene crystals. Phys. Rev. B 1970, 1, 815,  DOI: 10.1103/PhysRevB.1.815
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    Groom, C. R.; Bruno, I. J.; Lightfoot, M. P.; Ward, S. C. The Cambridge structural database. Acta Crystallographica Section B: Structural Science, Crystal Engineering and Materials 2016, 72, 171– 179,  DOI: 10.1107/S2052520616003954
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    The Cambridge Structural Database
    Groom, Colin R.; Bruno, Ian J.; Lightfoot, Matthew P.; Ward, Suzanna C.
    Acta Crystallographica, Section B: Structural Science, Crystal Engineering and Materials (2016), 72 (2), 171-179CODEN: ACSBDA; ISSN:2052-5206. (International Union of Crystallography)
    The Cambridge Structural Database (CSD) contains a complete record of all published org. and metal-org. small-mol. crystal structures. The database has been in operation for over 50 years and continues to be the primary means of sharing structural chem. data and knowledge across disciplines. As well as structures that are made public to support scientific articles, it includes many structures published directly as CSD Communications. All structures are processed both computationally and by expert structural chem. editors prior to entering the database. A key component of this processing is the reliable assocn. of the chem. identity of the structure studied with the exptl. data. This important step helps ensure that data is widely discoverable and readily reusable. Content is further enriched through selective inclusion of addnl. exptl. data. Entries are available to anyone through free CSD community web services. Linking services developed and maintained by the CCDC, combined with the use of std. identifiers, facilitate discovery from other resources. Data can also be accessed through CCDC and third party software applications and through an application programming interface.
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    Campbell, R.; Robertson, J. M.; Trotter, J. The crystal structure of hexacene, and a revision of the crystallographic data for tetracene. Acta crystallogr. 1962, 15, 289– 290,  DOI: 10.1107/S0365110X62000699
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    The crystal structure of hexacene, and a revision of the crystallographic data for tetracene and pentacene
    Campbell, R. B.; Robertson, J. Monteath; Trotter, J.
    Acta Crystallographica (1962), 15 (), 289-90CODEN: ACCRA9; ISSN:0365-110X.
    cf. Robertson, et al., CA 55, 21745d. A redetn. of the crystal structures of tetracene and pentacene yielded slightly different triclinic unit cell consts. which now are: for tetracene, a 7.90, b 6.03, c 13.53 A., α 100.3°, β 113.2°, γ 86.3°, Z = 2, and space group P‾1; for pentacene, a 7.90, b 6.06, c 16.01 A., α 101.9°, β 112.6°, γ 85.8°, Z = 2, and space group P‾1. New data for the orientation of the mols. in the unit cell are given, but they lead to insignificant changes in bond lengths and angles. Hexacene has a structure very similar to the lower benzologues, with a 7.9, b 6.1, c 18.4, α 102.7°, β 112.3°, γ 83.6°, Z = 2, and space group P‾1. Although insufficient data were observed for a detn. of at. parameters, the similarity of diffraction-intensity distribution indicates a mol. arrangement in the unit cell similar to the other members of the series.
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    Rang, Z.; Haraldsson, A.; Kim, D. M.; Ruden, P. P.; Nathan, M. I.; Chesterfield, R. J.; Frisbie, C. D. Hydrostatic-pressure dependence of the photoconductivity of single-crystal pentacene and tetracene. Appl. Phys. Lett. 2001, 79, 2731– 2733,  DOI: 10.1063/1.1410878
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    Hydrostatic-pressure dependence of the photoconductivity of single-crystal pentacene and tetracene
    Rang, Zhenlin; Haraldsson, Anders; Kim, Dong M.; Ruden, P. Paul; Nathan, Marshall I.; Chesterfield, Reid J.; Frisbie, C. Daniel
    Applied Physics Letters (2001), 79 (17), 2731-2733CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)
    Pentacene and tetracene show readily observable photocond. when illuminated with light in the blue part of the visible spectrum. The authors measured the change of photocond. with hydrostatic pressure in single-crystal samples of both materials. Possible mechanisms for the obsd. increase in photocond. with pressure are discussed. The authors conclude that a carrier-mobility increase under pressure is most likely to cause the increase in photocond. in the case of pentacene. For tetracene, changes in the absorption spectrum in the range of the excitation wavelengths may also be significant. The authors also observe a phase transition near 0.3 GPa in tetracene, in agreement with previous results.
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    Vaubel, G.; Baessler, H. Temperature dependence of width and position of the lowest singlet-singlet transition in crystalline tetracene. Mol. Cryst. Liq. Cryst. 1970, 12, 39– 45,  DOI: 10.1080/15421407008082758
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    Temperature dependence of width and position of the lowest singlet-singlet transition in crystalline tetracene
    Vaubel, Gert; Baessler, Heinz
    Molecular Crystals and Liquid Crystals (1970), 12 (1), 39-45CODEN: MCLCA5; ISSN:0026-8941.
    Linewidth and position of the lowest singlet-singlet transition in cryst. tetracene were investigated at 130°K to room-temp. Below 200°K the linewidth is temp. independent. The values for both Davydov components are 450 ± 50 cm-1 (‖b) a nd 300 ± 50 cm-1 (.SCRIPTL.b), i.e., at least twice as much as for cryst. an - thracene. Upon slow cooling the redshift of the absorption peaks, which is reported to occur below 70°K, occurs almost continuously in the temp. range 300-18 0°K. This raises doubts whether it results from a lst order phase transition of the crystal lattice.
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    Holmes, D.; Kumaraswamy, S.; Matzger, A. J.; Vollhardt, K. P. C. On the nature of nonplanarity in the [N] Phenylenes. Chem. - Eur. J. 1999, 5, 3399– 3412,  DOI: 10.1002/(SICI)1521-3765(19991105)5:11<3399::AID-CHEM3399>3.0.CO;2-V
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    On the nature of nonplanarity in the [N]phenylenes
    Holmes, Daniel; Kumaraswamy, Sriram; Matzger, Adam J.; Vollhardt, K. Peter C.
    Chemistry - A European Journal (1999), 5 (11), 3399-3412CODEN: CEUJED; ISSN:0947-6539. (Wiley-VCH Verlag GmbH)
    The [N]phenylenes display marked deformation from planarity in the cryst. state. In order to probe the generality of this phenomenon, several derivs. were synthesized and their single-crystal X-ray structures were obtained. All new compds. displayed some degree of nonplanarity. Thus, for example, the parent triangular [4]phenylene (4b = I with R = H) has a median bend angle at the ring junction of 1.5° and a range of 0.3° to 3.5°, whereas hexakis[triisopropylsilyl(ethynyl)] triangular [4]phenylene (4c = I with R = iso-Pr3SiC≡C) possesses the bulkiest appendages and the largest median bend angle and range (3.8° and 1.7° - 5.6°, resp.). A detailed anal. of the bending and twisting angles at the ring junctions, however, revealed that the magnitude of deformations were independent of topol., mol. size, and substituent type. In contrast to the phenylenes, a Cambridge Structural Database (CSD) search of unsubstituted and non-peri-substituted naphthalenes and anthracenes shows these mols. to be virtually planar in the solid state. A comparison of the single-point energies (HF/6-31G*) of the phenylenes with the acenes calcd. for mols. possessing a fixed bend angle at the ring fusion of 3°, 6°, 9°, and 12° reveals the former to be 26% to 45% easier to deform than the latter. Based on these results, the nonplanarity seen for the phenylenes is most likely a consequence of crystal-packing forces deforming particularly flexible mols.
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    Pithan, L.; Nabok, D.; Cocchi, C.; Beyer, P.; Duva, G.; Simbrunner, J.; Rawle, J.; Nicklin, C.; Schäfer, P.; Draxl, C. Molecular structure of the substrate-induced thin-film phase of tetracene. J. Chem. Phys. 2018, 149, 144701,  DOI: 10.1063/1.5043379
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    Molecular structure of the substrate-induced thin-film phase of tetracene
    Pithan, Linus; Nabok, Dmitrii; Cocchi, Caterina; Beyer, Paul; Duva, Giuliano; Simbrunner, Joseph; Rawle, Jonathan; Nicklin, Chris; Schaefer, Peter; Draxl, Claudia; Schreiber, Frank; Kowarik, Stefan
    Journal of Chemical Physics (2018), 149 (14), 144701/1-144701/5CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    We present a combined exptl. and theor. study to solve the unit-cell and mol. arrangement of the tetracene thin film (TF) phase. TF phases, also known as substrate induced phases (SIPs), are polymorphs that exist at interfaces and decisively impact the functionality of org. thin films, e.g., in a transistor channel, but also change the optical spectra due to the different mol. packing. As SIPs only exist in textured ultrathin films, their structure detn. remains challenging compared to bulk materials. Here, we use grazing incidence X-ray diffraction and atomistic simulations to ext. the TF unit-cell parameters of tetracene together with the at. positions within the unit-cell. (c) 2018 American Institute of Physics.
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    Nahm, R.; Engstrom, J. Who’s on first? Tracking in real time the growth of multiple crystalline phases of an organic semiconductor: tetracene on SiO2. J. Chem. Phys. 2017, 146, 052815,  DOI: 10.1063/1.4971288
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    Who's on first? Tracking in real time the growth of multiple crystalline phases of an organic semiconductor: Tetracene on SiO2
    Nahm, R. K.; Engstrom, J. R.
    Journal of Chemical Physics (2017), 146 (5), 052815/1-052815/8CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    The authors have examd. the effect of growth rate on the evolution of 2 polymorphs of thin films of tetracene on SiO2 using synchrotron x-ray radiation and mol. beam techniques. Ex situ x-ray reflectivity shows that tetracene forms 2 phases on SiO2: a thin-film phase and a bulk phase. The authors used in situ, real-time grazing incidence diffraction during growth to reveal the nature of growth concerning these 2 phases. There is initially growth of only the thin-film phase, up to a thickness of several monolayers. This is followed by the nucleation of the bulk phase, growth of both phases, and finally growth of only the bulk phase. The deposited thickness when the bulk phase nucleates increases with increasing growth rate. Similarly, the deposited thickness at which the thin-film phase sats. also increases with increasing growth rate. These apparent dependencies on growth rate are actually a consequence of the local coverage, which depends on growth rate, particularly for the former effect. At low growth rates, there is 3D growth resulting from the upward transport of tetracene at island edges, resulting in tall features where mols. escape the influence of the substrate and form into the bulk phase. Increasing the growth rate leads to growth that is more 2D and uniform in coverage, delaying the formation of the bulk phase. (c) 2017 American Institute of Physics.
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    Arias, D. H.; Ryerson, J. L.; Cook, J. D.; Damrauer, N. H.; Johnson, J. C. Polymorphism influences singlet fission rates in tetracene thin films. Chem. Sci. 2016, 7, 1185– 1191,  DOI: 10.1039/C5SC03535J
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    Polymorphism influences singlet fission rates in tetracene thin films
    Arias, Dylan H.; Ryerson, Joseph L.; Cook, Jasper D.; Damrauer, Niels H.; Johnson, Justin C.
    Chemical Science (2016), 7 (2), 1185-1191CODEN: CSHCCN; ISSN:2041-6520. (Royal Society of Chemistry)
    We report the effect of crystal structure and crystallite grain size on singlet fission (SF) in polycryst. tetracene, one of the most widely studied SF and org. semiconductor materials. SF has been comprehensively studied in one polymoprh (Tc I), but not in the other, less stable polymorph (Tc II). Using carefully controlled thermal evapn. deposition conditions and high sensitivity ultrafast transient absorption spectroscopy, we found that for large crystallite size samples, SF in nearly pure Tc II films is significantly faster than SF in Tc I films. We also discovered that crystallite size has a minimal impact on the SF rate in Tc II films, but a significant influence in Tc I films. Large crystallites exhibit SF times of 125 ps and 22 ps in Tc I and Tc II, resp., whereas small crystallites have SF times of 31 ps and 33 ps. Our results demonstrate first, that attention must be paid to polymorphism in obtaining a self-consistent rate picture for SF in tetracene and second, that control of polymorphism can play a significant role towards achieving a mechanistic understanding of SF in polycryst. systems. In this latter context we show that conventional theory based on non-covalent tetracene couplings is insufficient, thus highlighting the need for models that capture the delocalized and highly mobile nature of excited states in elucidating the full photophys. picture.
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  58. 58
    Daiber, B.; Maiti, S.; Ferro, S. M.; Bodin, J.; Van Den Boom, A. F.; Luxembourg, S. L.; Kinge, S.; Pujari, S. P.; Zuilhof, H.; Siebbeles, L. D.; Ehrler, B. Change in Tetracene Polymorphism Facilitates Triplet Transfer in Singlet Fission-Sensitized Silicon Solar Cells. J. Phys. Chem. Lett. 2020, 11, 8703– 8709,  DOI: 10.1021/acs.jpclett.0c02163
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    Change in Tetracene Polymorphism Facilitates Triplet Transfer in Singlet Fission-Sensitized Silicon Solar Cells
    Daiber, Benjamin; Maiti, Sourav; Ferro, Silvia M.; Bodin, Joris; van den Boom, Alyssa F. J.; Luxembourg, Stefan L.; Kinge, Sachin; Pujari, Sidharam P.; Zuilhof, Han; Siebbeles, Laurens D. A.; Ehrler, Bruno
    Journal of Physical Chemistry Letters (2020), 11 (20), 8703-8709CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
    Singlet fission in tetracene generates two triplet excitons per absorbed photon. If these triplet excitons can be effectively transferred into silicon (Si), then addnl. photocurrent can be generated from photons above the bandgap of Si. This could alleviate the thermalization loss and increase the efficiency of conventional Si solar cells. Here, we show that a change in the polymorphism of tetracene deposited on Si due to air exposure facilitates triplet transfer from tetracene into Si. Magnetic field-dependent photocurrent measurements confirm that triplet excitons contribute to the photocurrent. The decay of tetracene delayed photoluminescence was used to det. a transfer efficiency of ~ 36% into Si. Our study suggests that control over the morphol. of tetracene during the deposition will be of great importance to boost the triplet transfer yield further.
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    Macrae, C. F.; Edgington, P. R.; McCabe, P.; Pidcock, E.; Shields, G. P.; Taylor, R.; Towler, M.; van de Streek, J. Mercury: visualization and analysis of crystal structures. J. Appl. Crystallogr. 2006, 39, 453– 457,  DOI: 10.1107/S002188980600731X
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    Mercury: visualization and analysis of crystal structures
    Macrae, Clare F.; Edgington, Paul R.; McCabe, Patrick; Pidcock, Elna; Shields, Greg P.; Taylor, Robin; Towler, Matthew; van de Streek, Jacco
    Journal of Applied Crystallography (2006), 39 (3), 453-457CODEN: JACGAR; ISSN:0021-8898. (Blackwell Publishing Ltd.)
    Since its original release, the popular crystal structure visualization program Mercury has undergone continuous further development. Comparisons between crystal structures are facilitated by the ability to display multiple structures simultaneously and to overlay them. Improvements were made to many aspects of the visual display, including the addn. of depth cueing, and highly customizable lighting and background effects. Textual and numeric data assocd. with structures can be shown in tables or spreadsheets, the latter opening up new ways of interacting with the visual display. At. displacement ellipsoids, calcd. powder diffraction patterns and predicted morphologies can now be shown. Some limited mol.-editing capabilities were added. The object-oriented nature of the C++ libraries underlying Mercury makes it easy to re-use the code in other applications, and this has facilitated three-dimensional visualization in several other programs produced by the Cambridge Crystallog. Data Center.
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    Havlas, Z.; Michl, J. Guidance for Mutual Disposition of Chromophores for Singlet Fission. Isr. J. Chem. 2016, 56, 96– 106,  DOI: 10.1002/ijch.201500054
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    Guidance for Mutual Disposition of Chromophores for Singlet Fission
    Havlas, Zdenek; Michl, Josef
    Israel Journal of Chemistry (2016), 56 (1), 96-106CODEN: ISJCAT; ISSN:0021-2148. (Wiley-VCH Verlag GmbH & Co. KGaA)
    The choice of chromophores and of their mutual geometrical arrangement for optimized singlet fission (SF) rates are considered. The electronic matrix element that enters the Fermi golden rule for the rate of SF is worked out algebraically for a simple model, but the d. of states factor is not analyzed here. The model treats only the highest occupied and lowest unoccupied orbitals of the partners. It provides an approx. formula that requires only the knowledge of the expansion coeffs. of these orbitals and of overlap integrals between AOs on the partners to obtain an est. of the electronic matrix element. An illustrative application to a pair of ethylene mols. suggests that favored geometries will be those in which one of the AOs on the first ethylene overlaps with both AOs on the second ethylene, while the other AO on the first ethylene overlaps with at least one, and preferably both, AOs of the second ethylene as little as possible.
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    Zaykov, A.; Felkel, P.; Buchanan, E. A.; Jovanovic, M.; Havenith, R. W.; Kathir, R. K.; Broer, R.; Havlas, Z.; Michl, J. Singlet Fission Rate: Optimized Packing of a Molecular Pair. Ethylene as a Model. J. Am. Chem. Soc. 2019, 141, 17729– 17743,  DOI: 10.1021/jacs.9b08173
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    Singlet Fission Rate: Optimized Packing of a Molecular Pair. Ethylene as a Model
    Zaykov, Alexandr; Felkel, Petr; Buchanan, Eric A.; Jovanovic, Milena; Havenith, Remco W. A.; Kathir, R. K.; Broer, Ria; Havlas, Zdenek; Michl, Josef
    Journal of the American Chemical Society (2019), 141 (44), 17729-17743CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    A procedure is described for unbiased identification of all π-electron chromophore pair geometry choices that locally maximize the rate of conversion of a singlet exciton into singlet biexciton (triplet pair), using a simplified version of the diabatic frontier orbital model of singlet fission (SF). The resulting approx. optimal geometries provide insight and are expected to represent useful starting points for searches by more advanced methods. The general procedure is illustrated on a pair of ethylenes as the simplest model of a π-electron system, but it is applicable to pairs of much larger mols., with dozens of nonhydrogen atoms, and not necessarily planar. The authors 1st examine the value of |TA|2, the square of the electronic matrix element for SF with initial excitation fully localized on partner A, on a grid of several billion geometries within the 6-dimensional space of phys. realizable possibilities. The optimized pair geometries follow the qual. guidance proposed earlier. In the neighborhood of each local max. of |TA|2, consideration of mixing with charge-transfer configurations and of excitonic interaction between partners A and B dets. the SF energy balance and yields squared matrix elements |T*|2 and |T**|2 for the lower and upper excitonic states S* and S**, resp. Assuming Boltzmann populations of these states, the geometry is further optimized to maximize k, the sum of the SF rates obtained from Marcus theory, and this reorders the suitable geometries substantially. At 87 pair geometries, the |T*|2 and |T**|2 values are compared with those obtained from high-level ab initio nonorthogonal CI calcns. and found to follow the same trend. Finally, the biexciton binding energy at the optimized geometries is calcd. Altogether 13 significant local maxima of SF rate for a pair of ethylenes are identified in the phys. relevant part of space that avoids mol. interpenetration in the hard spheres approxn. The 3 best geometries are twist-stacked, slip-stacked, and L-shaped. The maxima occur at the (5-dimensional) surfaces of 7 6-dimensional parent regions of space centered at phys. inaccessible geometries at which the calcd. SF rate is very large but the 2 ethylenes interpenetrate. The results are displayed in interactive graphics. The computer code (Simple) written for these calcns. is flexible in that it permits a choice of performing the search for local maxima in 6 dimensions on |TA|2, |T*|2, or k. It is available as freeware at https://cloud.uochb.cas.cz/simple.
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    Buchanan, E. A.; Havlas, Z.; Michl, J. Optimal arrangements of tetracene molecule pairs for fast singlet fission. Bull. Chem. Soc. Jpn. 2019, 92, 1960– 1971,  DOI: 10.1246/bcsj.20190229
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    Optimal Arrangements of Tetracene Molecule Pairs for Fast Singlet Fission
    Buchanan, Eric A.; Havlas, Zdenek; Michl, Josef
    Bulletin of the Chemical Society of Japan (2019), 92 (12), 1960-1971CODEN: BCSJA8; ISSN:0009-2673. (Chemical Society of Japan)
    In search for a qual. understanding of the effects of mol. packing on singlet fission (SF) rate, a simplified version of the frontier orbital model is described and illustrated on a pair of tetracene mols. To identify all favorable phys. accessible pair geometries, all significant local maxima of the square of the electronic matrix element for SF have been located within the six-dimensional space of possible arrangements of two rigid bodies, using a grid of over 4.7 x 108 pair geometries. Those at which the mols. interpenetrate were excluded using a hard-sphere model. The effects of intermol. interaction on the SF energy balance and thus its rate const. kSF were approximated using Marcus theory at each of the maxima using the same simplified version of the frontier orbital model. Starting at these local maxima, the pair geometries were optimized for max. kSF and the 21 best are reported along with their computed Davydov splitting and triplet biexciton binding energies. The optimal pair structures at the resulting maxima follow qual. rules published previously and further elaborated here.
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    Ryerson, J. L.; Zaykov, A.; Aguilar Suarez, L. E.; Havenith, R. W.; Stepp, B. R.; Dron, P. I.; Kaleta, J.; Akdag, A.; Teat, S. J.; Magnera, T. F. Structure and photophysics of indigoids for singlet fission: Cibalackrot. J. Chem. Phys. 2019, 151, 184903,  DOI: 10.1063/1.5121863
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    Structure and photophysics of indigoids for singlet fission: Cibalackrot
    Ryerson, Joseph L.; Zaykov, Alexandr; Aguilar Suarez, Luis E.; Havenith, Remco W. A.; Stepp, Brian R.; Dron, Paul I.; Kaleta, Jiri; Akdag, Akin; Teat, Simon J.; Magnera, Thomas F.; Miller, John R.; Havlas, Zdenek; Broer, Ria; Faraji, Shirin; Michl, Josef; Johnson, Justin C.
    Journal of Chemical Physics (2019), 151 (18), 184903/1-184903/16CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    We report an investigation of structure and photophysics of thin layers of cibalackrot, a sturdy dye derived from indigo by double annulation at the central double bond. Evapd. layers contain up to three phases, two cryst. and one amorphous. Relative amts. of all three have been detd. by a combination of X-ray diffraction and FT-IR reflectance spectroscopy. Initially, excited singlet state rapidly produces a high yield of a transient intermediate whose spectral properties are compatible with charge-transfer nature. This intermediate more slowly converts to a significant yield of triplet, which, however, does not exceed 100% and may well be produced by intersystem crossing rather than singlet fission. The yields were detd. by transient absorption spectroscopy and cor. for effects of partial sample alignment by a simple generally applicable procedure. Formation of excimers was also obsd. In order to obtain guidance for improving mol. packing by a minor structural modification, calcns. by a simplified frontier orbital method were used to find all local maxima of singlet fission rate as a function of geometry of a mol. pair. The method was tested at 48 maxima by comparison with the ab initio Frenkel-Davydov exciton model. (c) 2019 American Institute of Physics.
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    Rais, D. Singlet Fission in Thin Solid Films of Bis(thienyl)diketopyrrolopyrroles. ChemPlusChem. 2020, 85, 2689– 2703,  DOI: 10.1002/cplu.202000623
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    Singlet Fission in Thin Solid Films of Bis(thienyl)diketopyrrolopyrroles
    Rais, David; Toman, Petr; Pfleger, Jiri; Acharya, Udit; Panthi, Yadu R.; Mensik, Miroslav; Zhigunov, Alexander; Thottappali, Muhammed A.; Vala, Martin; Markova, Aneta; Stritesky, Stanislav; Weiter, Martin; Ciganek, Martin; Krajcovic, Jozef; Pauk, Karel; Imramovsky, Ales; Zaykov, Alexandr; Michl, Josef
    ChemPlusChem (2020), 85 (12), 2689-2703CODEN: CHEMM5; ISSN:2192-6506. (Wiley-VCH Verlag GmbH & Co. KGaA)
    The singlet fission (SF) process discovered in bis(thienyl)diketopyrrolopyrroles (TDPPs) can boost their potential for photovoltaics (PV). The crystal structures of TDPP analogs carrying n-hexyl, Bu, or 2-(adamant-1-yl)ethyl substituents are similar, but contain increasingly slipped stacked neighbor mols. The obsd. SF rate consts., kSF, (7±4), (9±3) and (5.6±1.9) ns-1 for thin films of the three compds., resp., are roughly equal, but the triplet quantum yields vary strongly: (120±40), (160±40) and (70±16), resp. The recent mol. pair model reproduces the near equality of all three kSF at the crystal geometries and identifies all possible pair arrangements in which SF is predicted to be faster, by up to two orders of magnitude. However, it is also clear that the presently non-existent ability to predict the rates of processes competing with SF is pivotal for providing a guide for efforts to optimize the materials for PV.
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    Cruz-Cabeza, A. J.; Reutzel-Edens, S. M.; Bernstein, J. Facts and fictions about polymorphism. Chem. Soc. Rev. 2015, 44, 8619– 8635,  DOI: 10.1039/C5CS00227C
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    Facts and fictions about polymorphism
    Cruz-Cabeza, Aurora J.; Reutzel-Edens, Susan M.; Bernstein, Joel
    Chemical Society Reviews (2015), 44 (23), 8619-8635CODEN: CSRVBR; ISSN:0306-0012. (Royal Society of Chemistry)
    A review. We present new facts about polymorphism based on (i) crystallog. data from the Cambridge Structural Database (CSD, a database built over 50 years of community effort), (ii) 229 solid form screens conducted at Hoffmann-La Roche and Eli Lilly and Company over the course of 8+ and 15+ years resp. and (iii) a dataset of 446 polymorphic crystals with energies and properties computed with modern DFT-d methods. We found that mol. flexibility or size has no correlation with the ability of a compd. to be polymorphic. Chiral mols., however, were found to be less prone to polymorphism than their achiral counterparts and compds. able to hydrogen bond exhibit only a slightly higher propensity to polymorphism than those which do not. While the energy difference between polymorphs is usually less than 1 kcal mol-1, conformational polymorphs are capable of differing by larger values (up to 2.5 kcal mol-1 in our dataset). As overall statistics, we found that one in three compds. in the CSD are polymorphic while at least one in two compds. from the Roche and Lilly set display polymorphism with a higher est. of up to three in four when compds. are screened intensively. While the statistics provide some guidance of expectations, each compd. constitutes a new challenge and prediction and realization of targeted polymorphism still remains a holy grail of materials sciences.
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    Thakur, T. S.; Dubey, R.; Desiraju, G. R. Crystal structure and prediction. Annu. Rev. Phys. Chem. 2015, 66, 21– 42,  DOI: 10.1146/annurev-physchem-040214-121452
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    Crystal structure and prediction
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    Annual Review of Physical Chemistry (2015), 66 (), 21-42CODEN: ARPLAP; ISSN:0066-426X. (Annual Reviews)
    A review. The notion of structure is central to the subject of chem. This review traces the development of the idea of crystal structure since the time when a crystal structure could be detd. from a three-dimensional diffraction pattern and assesses the feasibility of computationally predicting an unknown crystal structure of a given mol. Crystal structure prediction is of considerable fundamental and applied importance, and its successful execution is by no means a solved problem. The ease of crystal structure detn. today has resulted in the availability of large nos. of crystal structures of higher-energy polymorphs and pseudopolymorphs. These structural libraries lead to the concept of a crystal structure landscape. A crystal structure of a compd. may accordingly be taken as a data point in such a landscape.
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    Woodley, S. M.; Catlow, R. Crystal structure prediction from first principles. Nat. Mater. 2008, 7, 937– 946,  DOI: 10.1038/nmat2321
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    Crystal structure prediction from first principles
    Woodley, Scott M.; Catlow, Richard
    Nature Materials (2008), 7 (12), 937-946CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)
    A review. The prediction of structure at the at. level is 1 of the most fundamental challenges in condensed matter science. The current status of the field is surveyed, and recent developments in methodol. are considered, paying particular attention to approaches for surveying energy landscapes. The current state of the art in this field is illustrated with topical applications to inorg., esp. microporous solids, and to mol. crystals; and applications to nanoparticulate structures are discussed. Future directions and challenges in the field are considered.
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    Bowskill, D. H.; Sugden, I. J.; Konstantinopoulos, S.; Adjiman, C. S.; Pantelides, C. C. Crystal Structure Prediction Methods for Organic Molecules: State of the Art. Annu. Rev. Chem. Biomol. Eng. 2021, 12, 593– 623,  DOI: 10.1146/annurev-chembioeng-060718-030256
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    Crystal Structure Prediction Methods for Organic Molecules: State of the Art
    Bowskill, David H.; Sugden, Isaac J.; Konstantinopoulos, Stefanos; Adjiman, Claire S.; Pantelides, Constantinos C.
    Annual Review of Chemical and Biomolecular Engineering (2021), 12 (), 593-623CODEN: ARCBCY; ISSN:1947-5438. (Annual Reviews)
    A review. The prediction of the crystal structures that a given org. mol. is likely to form is an important theor. problem of significant interest for the pharmaceutical and agrochem. industries, among others. As evidenced by a series of six blind tests organized over the past 2 decades, methodologies for crystal structure prediction (CSP) have witnessed substantial progress and have now reached a stage of development where they can begin to be applied to systems of practical significance. This article reviews the state of the art in general-purpose methodologies for CSP, placing them within a common framework that highlights both their similarities and their differences. The review discusses specific areas that constitute the main focus of current research efforts toward improving the reliability and widening applicability of these methodologies, and offers some perspectives for the evolution of this technol. over the next decade.
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    Bardwell, D. A.; Adjiman, C. S.; Arnautova, Y. A.; Bartashevich, E.; Boerrigter, S. X.; Braun, D. E.; Cruz-Cabeza, A. J.; Day, G. M.; Della Valle, R. G.; Desiraju, G. R. Towards crystal structure prediction of complex organic compounds–a report on the fifth blind test. Acta. Crystallogr. B Struct. Sci. Cryst. Eng. Mater. 2011, 67, 535– 551,  DOI: 10.1107/S0108768111042868
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    Towards crystal structure prediction of complex organic compounds - a report on the fifth blind test
    Bardwell, David A.; Adjiman, Claire S.; Arnautova, Yelena A.; Bartashevich, Ekaterina; Boerrigter, Stephan X. M.; Braun, Doris E.; Cruz-Cabeza, Aurora J.; Day, Graeme M.; Della Valle, Raffaele G.; Desiraju, Gautam R.; van Eijck, Bouke P.; Facelli, Julio C.; Ferraro, Marta B.; Grillo, Damian; Habgood, Matthew; Hofmann, Detlef W. M.; Hofmann, Fridolin; Jose, K. V. Jovan; Karamertzanis, Panagiotis G.; Kazantsev, Andrei V.; Kendrick, John; Kuleshova, Liudmila N.; Leusen, Frank J. J.; Maleev, Andrey V.; Misquitta, Alston J.; Mohamed, Sharmarke; Needs, Richard J.; Neumann, Marcus A.; Nikylov, Denis; Orendt, Anita M.; Pal, Rumpa; Pantelides, Constantinos C.; Pickard, Chris J.; Price, Louise S.; Price, Sarah L.; Scheraga, Harold A.; van de Streek, Jacco; Thakur, Tejender S.; Tiwari, Siddharth; Venuti, Elisabetta; Zhitkov, Ilia K.
    Acta Crystallographica, Section B: Structural Science (2011), 67 (6), 535-551CODEN: ASBSDK; ISSN:0108-7681. (International Union of Crystallography)
    Following on from the success of the previous crystal structure prediction blind tests (CSP1999, CSP2001, CSP2004 and CSP2007), a 5th such collaborative project (CSP2010) was organized at the Cambridge Crystallog. Data Center. A range of methodologies was used by the participating groups to evaluate the ability of the current computational methods to predict the crystal structures of the six org. mols. chosen as targets for this blind test. The 1st four targets, two rigid mols., one semi-flexible mol. and a 1:1 salt, matched the criteria for the targets from CSP2007, while the last two targets belonged to two new challenging categories - a larger, much more flexible mol. and a hydrate with more than one polymorph. Each group submitted three predictions for each target it attempted. There was at least one successful prediction for each target, and two groups were able to successfully predict the structure of the large flexible mol. as their 1st place submission. While not as many groups successfully predicted the structures of the three smallest mols. as in CSP2007, there is now evidence that methodologies such as dispersion-cor. d. functional theory (DFT-D) are able to reliably do so. The results also highlight the many challenges posed by more complex systems and show that there are still issues to be overcome.
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  71. 71
    Reilly, A. M.; Cooper, R. I.; Adjiman, C. S.; Bhattacharya, S.; Boese, A. D.; Brandenburg, J. G.; Bygrave, P. J.; Bylsma, R.; Campbell, J. E.; Car, R. Report on the sixth blind test of organic crystal structure prediction methods. Acta. Crystallogr. B Struct. Sci. Cryst. Eng. Mater. 2016, 72, 439– 459,  DOI: 10.1107/S2052520616007447
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    71
    Report on the sixth blind test of organic crystal structure prediction methods
    Reilly, Anthony M.; Cooper, Richard I.; Adjiman, Claire S.; Bhattacharya, Saswata; Boese, A. Daniel; Brandenburg, Jan Gerit; Bygrave, Peter J.; Bylsma, Rita; Campbell, Josh E.; Car, Roberto; Case, David H.; Chadha, Renu; Cole, Jason C.; Cosburn, Katherine; Cuppen, Herma M.; Curtis, Farren; Day, Graeme M.; Di Stasio, Robert A., Jr.; Dzyabchenko, Alexander; van Eijck, Bouke P.; Elking, Dennis M.; van den Ende, Joost A.; Facelli, Julio C.; Ferraro, Marta B.; Fusti-Molnar, Laszlo; Gatsiou, Christina-Anna; Gee, Thomas S.; de Gelder, Rene; Ghiringhelli, Luca M.; Goto, Hitoshi; Grimme, Stefan; Guo, Rui; Hofmann, Detlef W. M.; Hoja, Johannes; Hylton, Rebecca K.; Iuzzolino, Luca; Jankiewicz, Wojciech; de Jong, Daniel T.; Kendrick, John; de Klerk, Niek J. J.; Ko, Hsin-Yu; Kuleshova, Liudmila N.; Li, Xiayue; Lohani, Sanjaya; Leusen, Frank J. J.; Lund, Albert M.; Lv, Jian; Ma, Yanming; Marom, Noa; Masunov, Artem E.; McCabe, Patrick; McMahon, David P.; Meekes, Hugo; Metz, Michael P.; Misquitta, Alston J.; Mohamed, Sharmarke; Monserrat, Bartomeu; Needs, Richard J.; Neumann, Marcus A.; Nyman, Jonas; Obata, Shigeaki; Oberhofer, Harald; Oganov, Artem R.; Orendt, Anita M.; Pagola, Gabriel I.; Pantelides, Constantinos C.; Pickard, Chris J.; Podeszwa, Rafal; Price, Louise S.; Price, Sarah L.; Pulido, Angeles; Read, Murray G.; Reuter, Karsten; Schneider, Elia; Schober, Christoph; Shields, Gregory P.; Singh, Pawanpreet; Sugden, Isaac J.; Szalewicz, Krzysztof; Taylor, Christopher R.; Tkatchenko, Alexandre; Tuckerman, Mark E.; Vacarro, Francesca; Vasileiadis, Manolis; Vazquez-Mayagoitia, Alvaro; Vogt, Leslie; Wang, Yanchao; Watson, Rona E.; de Wijs, Gilles A.; Yang, Jack; Zhu, Qiang; Groom, Colin R.
    Acta Crystallographica, Section B: Structural Science, Crystal Engineering and Materials (2016), 72 (4), 439-459CODEN: ACSBDA; ISSN:2052-5206. (International Union of Crystallography)
    The sixth blind test of org. crystal structure prediction (CSP) methods has been held, with five target systems: a small nearly rigid mol., a polymorphic former drug candidate, a chloride salt hydrate, a co-crystal and a bulky flexible mol. This blind test has seen substantial growth in the no. of participants, with the broad range of prediction methods giving a unique insight into the state of the art in the field. Significant progress has been seen in treating flexible mols., usage of hierarchical approaches to ranking structures, the application of d.-functional approxns., and the establishment of new workflows and 'best practices' for performing CSP calcns. All of the targets, apart from a single potentially disordered Z' = 2 polymorph of the drug candidate, were predicted by at least one submission. Despite many remaining challenges, it is clear that CSP methods are becoming more applicable to a wider range of real systems, including salts, hydrates and larger flexible mols. The results also highlight the potential for CSP calcns. to complement and augment exptl. studies of org. solid forms.
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    Li, X.; Curtis, F. S.; Rose, T.; Schober, C.; Vazquez-Mayagoitia, A.; Reuter, K.; Oberhofer, H.; Marom, N. Genarris: Random generation of molecular crystal structures and fast screening with a Harris approximation. J. Chem. Phys. 2018, 148, 241701,  DOI: 10.1063/1.5014038
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    Genarris: Random generation of molecular crystal structures and fast screening with a Harris approximation
    Li, Xiayue; Curtis, Farren S.; Rose, Timothy; Schober, Christoph; Vazquez-Mayagoitia, Alvaro; Reuter, Karsten; Oberhofer, Harald; Marom, Noa
    Journal of Chemical Physics (2018), 148 (24), 241701/1-241701/16CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    The authors present Genarris, a Python package that performs configuration space screening for mol. crystals of rigid mols. by random sampling with phys. constraints. For fast energy evaluations, Genarris employs a Harris approxn., whereby the total d. of a mol. crystal is constructed via superposition of single mol. densities. Dispersion-inclusive d. functional theory is then used for the Harris d. without performing a self-consistency cycle. Genarris uses machine learning for clustering, based on a relative coordinate descriptor developed specifically for mol. crystals, which is robust in identifying packing motif similarity. In addn. to random structure generation, Genarris offers 3 workflows based on different sequences of successive clustering and selection steps: the Rigorous workflow is an exhaustive exploration of the potential energy landscape, the Energy workflow produces a set of low energy structures, and the Diverse workflow produces a max. diverse set of structures. The latter is recommended for generating initial populations for genetic algorithms. The implementation of Genarris is reported and its application is demonstrated for 3 test cases. (c) 2018 American Institute of Physics.
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    Tom, R.; Rose, T.; Bier, I.; O’Brien, H.; Vázquez-Mayagoitia, Á.; Marom, N. Genarris 2.0: A random structure generator for molecular crystals. Comput. Phys. Commun. 2020, 250, 107170,  DOI: 10.1016/j.cpc.2020.107170
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    73
    Genarris 2.0: A random structure generator for molecular crystals
    Tom, Rithwik; Rose, Timothy; Bier, Imanuel; O'Brien, Harriet; Vazquez-Mayagoitia, Alvaro; Marom, Noa
    Computer Physics Communications (2020), 250 (), 107170CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier B.V.)
    A review. Genarris is an open source Python package for generating random mol. crystal structures with phys. constraints for seeding crystal structure prediction algorithms and training machine learning models. Here we present a new version of the code, contg. several major improvements. A MPI-based parallelization scheme has been implemented, which facilitates the seamless sequential execution of user-defined workflows. A new method for estg. the unit cell vol. based on the single mol. structure has been developed using a machine-learned model trained on exptl. structures. A new algorithm has been implemented for generating crystal structures with mols. occupying special Wyckoff positions. A new hierarchical structure check procedure has been developed to detect unphys. close contacts efficiently and accurately. New intermol. distance settings have been implemented for strong hydrogen bonds. To demonstrate these new features, we study two specific cases: benzene and glycine. Genarris finds the exptl. structures of the two polymorphs of benzene and the three polymorphs of glycine.Program Title: Genarris 2.0Program Files doi:http://dx.doi.org/10.17632/grx6mz4pjn.1Licensing provisions: BSD-3 ClauseProgramming language: Python, CExternal routines/libraries: Spglib, ASE, pymatgen, SciPy, mpi4py, scikit-learn, PyTorch, FHI-aims. Nature of problem: Mol. crystal structure prediction.Soln. method: Genarris 2.0 generates mol. crystal structures over the 230 space groups, on general and special Wyckoff positions, using phys. constraints. Down-sampling of the generated structures may be performed subsequently, based on mol. crystal packing descriptors and an unsupervised machine learning algorithm. Lastly, ab initio structure relaxation may be performed for the final pool. Depending on the user-defined workflow implemented, Genarris may be used to generate diverse mol. crystal datasets to seed evolutionary algorithms or to train machine learning algorithms or as a standalone crystal structure prediction method. Restrictions: For crystal structure generation, the mol. of interest must be semi-rigid with no bond rotational degrees of freedom.Unusual features: Genarris 2.0 is a highly distributed program, making use of MPI for Python parallelization. The user has the ability to design and implement workflows by executing a user-defined list of procedures. Genarris 2.0 offers new features including a machine learning model for estg. the mol. vol. in the solid state from the single mol. structure, structure generation in special Wyckoff positions of space groups, hierarchical structure checks including rigorous treatment of non-orthogonal structures, and clustering and down-selection workflows combining first principles simulations with machine learning.
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    Pickard, C. J.; Needs, R. Ab initio random structure searching. J. Phys.: Condens. Matter 2011, 23, 053201,  DOI: 10.1088/0953-8984/23/5/053201
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    Ab initio random structure searching
    Pickard, Chris J.; Needs, R. J.
    Journal of Physics: Condensed Matter (2011), 23 (5), 053201/1-053201/23CODEN: JCOMEL; ISSN:0953-8984. (Institute of Physics Publishing)
    A review. It is essential to know the arrangement of the atoms in a material in order to compute and understand its properties. Searching for stable structures of materials using first-principles electronic structure methods, such as d.-functional-theory (DFT), is a rapidly growing field. Here we describe our simple, elegant and powerful approach to searching for structures with DFT, which we call ab initio random structure searching (AIRSS). Applications to discovering the structures of solids, point defects, surfaces, and clusters are reviewed. New results for iron clusters on graphene, silicon clusters, polymeric nitrogen, hydrogen-rich lithium hydrides, and boron are presented.
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    Case, D. H.; Campbell, J. E.; Bygrave, P. J.; Day, G. M. Convergence properties of crystal structure prediction by quasi-random sampling. J. Chem. Theory Comput. 2016, 12, 910– 924,  DOI: 10.1021/acs.jctc.5b01112
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    Convergence Properties of Crystal Structure Prediction by Quasi-Random Sampling
    Case, David H.; Campbell, Josh E.; Bygrave, Peter J.; Day, Graeme M.
    Journal of Chemical Theory and Computation (2016), 12 (2), 910-924CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    Generating sets of trial structures that sample the configurational space of crystal packing possibilities is an essential step in the process of ab initio crystal structure prediction (CSP). One effective methodol. for performing such a search relies on low-discrepancy, quasi-random sampling, and implementation of such a search for mol. crystals is described. The authors restrict ourselves to rigid org. mols. and, by considering their geometric properties, build trial crystal packings as starting points for local lattice energy minimization. They also describe a method to match instances of the same structure, which they use to measure the convergence of the packing search toward completeness. The use of these tools is demonstrated for a set of mols. with diverse mol. characteristics and as representative of areas of application where CSP has been applied. An important finding is that the lowest energy crystal structures are typically located early and frequently during a quasi-random search of phase space. It is usually the complete sampling of higher energy structures that requires extended sampling. They show how the procedure can first be refined, through targeting the vol. of the generated crystal structures, and then extended across a range of space groups to make a full CSP search and locate exptl. obsd. and lists of hypothetical polymorphs. As the described method has also been created to lie at the base of more involved approaches to CSP, which are being developed within the Global Lattice Energy Explorer (GLEE) software, a few of these extensions are briefly discussed.
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    Price, S. L. Predicting crystal structures of organic compounds. Chem. Soc. Rev. 2014, 43, 2098– 2111,  DOI: 10.1039/C3CS60279F
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    Predicting crystal structures of organic compounds
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    Chemical Society Reviews (2014), 43 (7), 2098-2111CODEN: CSRVBR; ISSN:0306-0012. (Royal Society of Chemistry)
    A review. Currently, org. crystal structure prediction (CSP) methods are based on searching for the most thermodynamically stable crystal structure, making various approxns. in evaluating the crystal energy. The most stable (global min.) structure provides a prediction of an exptl. crystal structure. However, depending on the specific mol., there may be other structures which are very close in energy. In this case, the other structures on the crystal energy landscape may be polymorphs, components of static or dynamic disorder in obsd. structures, or there may be no route to nucleating and growing these structures. A major reason for performing CSP studies is as a complement to solid form screening to see which alternative packings to the known polymorphs are thermodynamically feasible.
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    Oganov, A. R.; Pickard, C. J.; Zhu, Q.; Needs, R. J. Structure prediction drives materials discovery. Nat. Rev. Mater. 2019, 4, 331– 348,  DOI: 10.1038/s41578-019-0101-8
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    Moellmann, J.; Grimme, S. DFT-D3 study of some molecular crystals. J. Phys. Chem. C 2014, 118, 7615– 7621,  DOI: 10.1021/jp501237c
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    DFT-D3 Study of Some Molecular Crystals
    Moellmann, Jonas; Grimme, Stefan
    Journal of Physical Chemistry C (2014), 118 (14), 7615-7621CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
    We investigate the performance of the dispersion correction D3 with and without an explicit three-body dispersion term for the energetic and structural properties of rare gas and mol. crystals. Therefore, the two- and three-body gradient of the dispersion energy is implemented in the periodic plane-wave program VASP. It is combined with different d. functionals at the level of the general gradient approxn. (GGA) and hybrid functionals. Cohesive energies and lattice parameters for the rare gas crystals Ar, Kr, and Xe and a set of 23 mol. crystals are calcd. and compared to exptl. ref. values. In general, all tested methods yield very good results. For the mol. crystals the mean abs. deviation of lattice energies from ref. data (about 1-2 kcal/mol) is close to or below their uncertainties. The influence of the three-body Axilrod-Teller-Muto dispersion term on energy and structure is found to be rather small. While on a GGA level cohesive energies become slightly worse, for hybrid functionals the three-body term improves the results.
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    Reilly, A. M.; Tkatchenko, A. Understanding the role of vibrations, exact exchange, and many-body van der Waals interactions in the cohesive properties of molecular crystals. J. Chem. Phys. 2013, 139, 024705,  DOI: 10.1063/1.4812819
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    Understanding the role of vibrations, exact exchange, and many-body van der Waals interactions in the cohesive properties of molecular crystals
    Reilly, Anthony M.; Tkatchenko, Alexandre
    Journal of Chemical Physics (2013), 139 (2), 024705/1-024705/12CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    The development and application of computational methods for studying mol. crystals, particularly d.-functional theory (DFT), is a large and ever-growing field, driven by their numerous applications. Here we expand on our recent study of the importance of many-body van der Waals interactions in mol. crystals , with a larger database of 23 mol. crystals. Particular attention has been paid to the role of the vibrational contributions that are required to compare expt. sublimation enthalpies with calcd. lattice energies, employing both phonon calcns. and exptl. heat-capacity data to provide harmonic and anharmonic ests. of the vibrational contributions. Exact exchange, which is rarely considered in DFT studies of mol. crystals, is shown to have a significant contribution to lattice energies, systematically improving agreement between theory and expt. When the vibrational and exact-exchange contributions are coupled with a many-body approach to dispersion, DFT yields a mean abs. error (3.92 kJ/mol) within the coveted "chem. accuracy" target (4.2 kJ/mol). The role of many-body dispersion for structures has also been investigated for a subset of the database, showing good performance compared to X-ray and neutron diffraction crystal structures. The results show that the approach employed here can reach the demanding accuracy of crystal-structure prediction and org. material design with minimal empiricism. (c) 2013 American Institute of Physics.
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    O’Connor, D.; Bier, I.; Hsieh, Y.-T.; Marom, N. Performance of Dispersion-Inclusive Density Functional Theory Methods for Energetic Materials. J. Chem. Theory Comput. 2022, 18, 4456– 4471,  DOI: 10.1021/acs.jctc.2c00350
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    Performance of Dispersion-Inclusive Density Functional Theory Methods for Energetic Materials
    O'Connor, Dana; Bier, Imanuel; Hsieh, Yun-Ting; Marom, Noa
    Journal of Chemical Theory and Computation (2022), 18 (7), 4456-4471CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    Mol. crystals of energetic materials (EMs) are denser than typical mol. crystals and are characterized by distinct intermol. interactions between nitrogen-contg. moieties. To assess the performance of dispersion-inclusive d. functional theory (DFT) methods, we have compiled a data set of exptl. sublimation enthalpies of 31 energetic materials. We evaluate the performance of three methods: the semilocal Perdew-Burke-Ernzerhof (PBE) functional coupled with the pairwise Tkatchenko-Scheffler (TS) dispersion correction, PBE with the many-body dispersion (MBD) method, and the PBE-based hybrid functional (PBE0) with MBD. Zero-point energy contributions and thermal effects are described using the quasi-harmonic approxn. (QHA), including explicit treatment of thermal expansion, which we find to be non-negligible for EMs. The lattice energies obtained with PBE0 + MBD are the closest to exptl. sublimation enthalpies with a mean abs. error of 9.89 kJ/mol. However, the state-of-the-art treatment of vibrational and thermal contributions makes the agreement with expt. worse. Pressure-vol. curves are also examd. for six representative materials. For pressure-vol. curves, all three methods provide reasonable agreement with exptl. data with mean abs. relative errors of 3% or less. Most of the intermol. interactions typical of EMs, namely nitro-amine, nitro-nitro, and nitro-hydrogen interactions, are more sensitive to the choice of the dispersion method than to the choice of the exchange-correlation functional. The exception is π-π stacking interactions, which are also very sensitive to the choice of the functional. Overall, we find that PBE + TS, PBE + MBD, and PBE0 + MBD do not perform as well for energetic materials as previously reported for other classes of mol. crystals. This highlights the importance of testing dispersion-inclusive DFT methods for diverse classes of materials and the need for further method development.
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    Price, S. L.; Braun, D. E.; Reutzel-Edens, S. M. Can computed crystal energy landscapes help understand pharmaceutical solids?. Chem. Commun. 2016, 52, 7065– 7077,  DOI: 10.1039/C6CC00721J
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    Can computed crystal energy landscapes help understand pharmaceutical solids?
    Price, Sarah L.; Braun, Doris E.; Reutzel-Edens, Susan M.
    Chemical Communications (Cambridge, United Kingdom) (2016), 52 (44), 7065-7077CODEN: CHCOFS; ISSN:1359-7345. (Royal Society of Chemistry)
    A review. Computational crystal structure prediction (CSP) methods can now be applied to the smaller pharmaceutical mols. currently in drug development. Recent uses of computed crystal energy landscapes for pharmaceuticals are discussed, concg. on examples where they were used in collaboration with industrial-style exptl. solid form screening. There is a strong complementarity in aiding expt. to find and characterize practically important solid forms and understanding the nature of the solid form landscape.
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    Shtukenberg, A. G.; Zhu, Q.; Carter, D. J.; Vogt, L.; Hoja, J.; Schneider, E.; Song, H.; Pokroy, B.; Polishchuk, I.; Tkatchenko, A. Powder diffraction and crystal structure prediction identify four new coumarin polymorphs. Chem. Sci. 2017, 8, 4926– 4940,  DOI: 10.1039/C7SC00168A
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    Powder diffraction and crystal structure prediction identify four new coumarin polymorphs
    Shtukenberg, Alexander G.; Zhu, Qiang; Carter, Damien J.; Vogt, Leslie; Hoja, Johannes; Schneider, Elia; Song, Hongxing; Pokroy, Boaz; Polishchuk, Iryna; Tkatchenko, Alexandre; Oganov, Artem R.; Rohl, Andrew L.; Tuckerman, Mark E.; Kahr, Bart
    Chemical Science (2017), 8 (7), 4926-4940CODEN: CSHCCN; ISSN:2041-6520. (Royal Society of Chemistry)
    Coumarin, a simple, commodity chem. isolated from beans in 1820, has, to date, only yielded one solid state structure. Here, we report a rich polymorphism of coumarin grown from the melt. Four new metastable forms were identified and their crystal structures were solved using a combination of computational crystal structure prediction algorithms and X-ray powder diffraction. With five crystal structures, coumarin has become one of the few rigid mols. showing extensive polymorphism at ambient conditions. We demonstrate the crucial role of advanced electronic structure calcns. including many-body dispersion effects for accurate ranking of the stability of coumarin polymorphs and the need to account for anharmonic vibrational contributions to their free energy. As such, coumarin is a model system for studying weak intermol. interactions, crystn. mechanisms, and kinetic effects.
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    Inverse design in search of materials with target functionalities
    Zunger, Alex
    Nature Reviews Chemistry (2018), 2 (4), 0121CODEN: NRCAF7; ISSN:2397-3358. (Nature Research)
    Solid-state chemists have been consistently successful in envisioning and making new compds., often enlisting the tools of theor. solid-state physics to explain some of the obsd. properties of the new materials. Here, a new style of collaboration between theory and expt. is discussed, whereby the desired functionality of the new material is declared first and theor. calcns. are then used to predict which stable and synthesizable compds. exhibit the required functionality. Subsequent iterative feedback cycles of prediction-synthesis-characterization result in improved predictions and promise not only to accelerate the discovery of new materials but also to enable the targeted design of materials with desired functionalities via such inverse design.
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    Franceschetti, A.; Zunger, A. The inverse band-structure problem of finding an atomic configuration with given electronic properties. Nature 1999, 402, 60– 63,  DOI: 10.1038/46995
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    The inverse band-structure problem of finding an atomic configuration with given electronic properties
    Franceschetti, Alberto; Zunger, Alex
    Nature (London) (1999), 402 (6757), 60-63CODEN: NATUAS; ISSN:0028-0836. (Macmillan Magazines)
    Modern crystal-growth techniques, such as mol. beam epitaxy or metal-org. chem.-vapor deposition, are capable of producing prescribed crystal structures, sometimes even in defiance of equil., bulk thermodn. These techniques open up the possibility of exploring different at. arrangements in search of a configuration that possesses given electronic and optical properties. Unfortunately, the no. of possible combinations is so vast, and the electronic properties are so sensitive to the details of the crystal structure, that simple trial-and-error methods (such as those used in combinatorial synthesis) are unlikely to be successful. Here we describe a theor. method that addresses the problem of finding the at. configuration of a complex, multicomponent system having a target electronic-structure property. As an example, we predict that the configuration of an Al0.25Ga0.75As alloy having the largest optical bandgap is a (GaAs)2(AlAs)1(GaAs)4(AlAs)1 superlattice oriented in the [201] direction.
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    Hiener, D.; Hutchison, G. Pareto Optimization of Oligomer Polarizability and Dipole Moment using a Genetic Algorithm. J. Phys. Chem. A 2022, 126, 2750– 2760,  DOI: 10.1021/acs.jpca.2c01266
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    Pareto Optimization of Oligomer Polarizability and Dipole Moment Using a Genetic Algorithm
    Hiener, Danielle C.; Hutchison, Geoffrey R.
    Journal of Physical Chemistry A (2022), 126 (17), 2750-2760CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
    High-performance electronic components are highly sought after in order to produce increasingly smaller and cheaper electronic devices. Drawing inspiration from inorg. dielec. materials, in which both polarizability and polarization contribute, org. materials can also maximize both. For a large set of small mols. drawn from PubChem, a Pareto-like front appears between the polarizability and dipole moment, indicating the presence of an apparent trade-off between these two properties. We tested this balance in π-conjugated materials by searching for novel conjugated hexamers with simultaneously large polarizabilities and dipole moments with potential use for dielec. materials. Using a genetic algorithm (GA) screening technique in conjunction with an approx. d. functional tight-binding method for property calcns., we were able to efficiently search chem. space for optimal hexamers. Given the scope of chem. space, using the GA technique saves considerable time and resources by speeding up mol. searches compared to a systematic search. We also explored the underlying structure-function relationships, including sequence and monomer properties, that characterize large polarizability and dipole moment regimes.
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    d’Avezac, M.; Luo, J.-W.; Chanier, T.; Zunger, A. Genetic-algorithm discovery of a direct-gap and optically allowed superstructure from indirect-gap Si and Ge semiconductors. Phys. Rev. Lett. 2012, 108, 027401,  DOI: 10.1103/PhysRevLett.108.027401
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    86
    Genetic-algorithm discovery of a direct-gap and optically allowed superstructure from indirect-gap Si and Ge semiconductors
    d'Avezac, Mayeul; Luo, Jun-Wei; Chanier, Thomas; Zunger, Alex
    Physical Review Letters (2012), 108 (2), 027401/1-027401/5CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    Combining two indirect-gap materials-with different electronic and optical gaps-to create a direct gap material represents an ongoing theor. challenge with potentially rewarding practical implications, such as optoelectronics integration on a single wafer. We provide an unexpected soln. to this classic problem, by spatially melding two indirect-gap materials (Si and Ge) into one strongly dipole-allowed direct-gap material. We leverage a combination of genetic algorithms with a pseudopotential Hamiltonian to search through the astronomic no. of variants of Sin/Gem/.../Sip/Geq superstructures grown on (001) Si1-xGex. The search reveals a robust configurational motif-SiGe2Si2Ge2SiGen on (001) SixGe1-x substrate (x ≤ 0.4) presenting a direct and dipole-allowed gap resulting from an enhanced Γ-X coupling at the band edges.
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    Bhattacharya, S.; Sonin, B. H.; Jumonville, C. J.; Ghiringhelli, L. M.; Marom, N. Computational design of nanoclusters by property-based genetic algorithms: tuning the electronic properties of (TiO2)n clusters. Phys. Rev. B 2015, 91, 241115,  DOI: 10.1103/PhysRevB.91.241115
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    Computational design of nanoclusters by property-based genetic algorithms: tuning the electronic properties of (TiO2)n clusters
    Bhattacharya, Saswata; Sonin, Benjamin H.; Jumonville, Christopher J.; Ghiringhelli, Luca M.; Marom, Noa
    Physical Review B: Condensed Matter and Materials Physics (2015), 91 (24), 241115/1-241115/5CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
    In order to design clusters with desired properties, we have implemented a suite of genetic algorithms tailored to optimize for low total energy, high vertical electron affinity (VEA), and low vertical ionization potential (VIP). Applied to (TiO2)n clusters, the property-based optimization reveals the underlying structure-property relations and the structural features that may serve as active sites for catalysis. High VEA and low VIP are correlated with the presence of several dangling-O atoms and their proximity, resp. We show that the electronic properties of (TiO2)n up to n = 20 correlate more strongly with the presence of these structural features than with size.
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    Cheng, C. Y.; Campbell, J. E.; Day, G. M. Evolutionary chemical space exploration for functional materials: computational organic semiconductor discovery. Chem. Sci. 2020, 11, 4922– 4933,  DOI: 10.1039/D0SC00554A
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    Evolutionary chemical space exploration for functional materials: computational organic semiconductor discovery
    Cheng, Chi Y.; Campbell, Josh E.; Day, Graeme M.
    Chemical Science (2020), 11 (19), 4922-4933CODEN: CSHCCN; ISSN:2041-6520. (Royal Society of Chemistry)
    Computational methods, including crystal structure and property prediction, have the potential to accelerate the materials discovery process by enabling structure prediction and screening of possible mol. building blocks prior to their synthesis. However, the discovery of new functional mol. materials is still limited by the need to identify promising mols. from a vast chem. space. We describe an evolutionary method which explores a user specified region of chem. space to identify promising mols., which are subsequently evaluated using crystal structure prediction. We demonstrate the methods for the exploration of aza-substituted pentacenes with the aim of finding small mol. org. semiconductors with high charge carrier mobilities, where the space of possible substitution patterns is too large to exhaustively search using a high throughput approach. The method efficiently explores this large space, typically requiring calcns. on only ~ 1% of mols. during a search. The results reveal two promising structural motifs: aza-substituted naphtho[1,2-a]anthracenes with reorganisation energies as low as pentacene and a series of pyridazine-based mols. having both low reorganisation energies and high electron affinities.
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    Pfund, L. Y.; Matzger, A. J. Towards exhaustive and automated high-throughput screening for crystalline polymorphs. ACS Comb. Sci. 2014, 16, 309– 313,  DOI: 10.1021/co500043q
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    Towards Exhaustive and Automated High-Throughput Screening for Crystalline Polymorphs
    Pfund, Laura Y.; Matzger, Adam J.
    ACS Combinatorial Science (2014), 16 (7), 309-313CODEN: ACSCCC; ISSN:2156-8944. (American Chemical Society)
    Methods capable of exhaustively screening for crystal polymorphism remain an elusive goal in solid-state chem. Particularly promising among the new generation of approaches is polymer-induced heteronucleation (PIHn), a tool utilizing hundreds of unique polymers for granting kinetic access to polymorphs. Here PIHn is redeployed in a high d. format in which 288 distinct polymers, each acting as a heteronucleant, are arrayed on one substrate. This format allows detg. the outcome of thousands of crystns. in an automated fashion with only a few milligrams of sample. This technol. enables the study of a broader range of targets, including preclin. candidates, facilitating detn. of polymorphism propensity much earlier in the drug development process. Here the efficacy of this approach is demonstrated using four pharmaceutically relevant compds.: acetaminophen, tolfenamic acid, ROY, and curcumin.
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    Gu, C.-H.; Young Jr, V.; Grant, D. J. Polymorph screening: Influence of solvents on the rate of solvent-mediated polymorphic transformation. J. Pharm. Sci. 2001, 90, 1878– 1890,  DOI: 10.1002/jps.1137
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    Polymorph screening: influence of solvents on the rate of solvent-mediated polymorphic transformation
    Gu, Chong-Hui; Young, Victor, Jr.; Grant, David J. W.
    Journal of Pharmaceutical Sciences (2001), 90 (11), 1878-1890CODEN: JPMSAE; ISSN:0022-3549. (Wiley-Liss, Inc.)
    Solvent-mediated polymorphic transformation is an efficient technique to obtain the most stable polymorph. The rate of solvent-mediated polymorphic transformation of sulfamerazine at 24°C in various solvents and solvent mixts. is controlled by the nucleation rate of the more stable Form II. The transformation rate is generally higher in the solvent giving a higher soly. and is low in the solvent giving a low soly. (8 mmol/L). In these solvents, because of a high interfacial energy, the metastable zone may be wider than the soly. difference between two polymorphs, such that the crit. free energy barrier for nucleation cannot be overcome. In addn. to the soly., the strength of the solvent-solute interactions is also important in detg. the transformation rate. For sulfamerazine, the transformation rate is lower in the solvent with a stronger hydrogen bond acceptor propensity. Because soly. is higher in the solvent with stronger hydrogen bond acceptor propensity, the balance of soly. and strength of hydrogen bonding interactions between the solute and solvent mols. dets. the polymorphic transformation rate. Degree of agitation and temp. also change the polymorphic transformation rate by influencing the crystn. kinetics of the more stable polymorph.
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    Lee, E. H. A practical guide to pharmaceutical polymorph screening & selection. Asian J. Pharm. Sci. 2014, 9, 163– 175,  DOI: 10.1016/j.ajps.2014.05.002
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    Neumann, M.; Van De Streek, J.; Fabbiani, F.; Hidber, P.; Grassmann, O. Combined crystal structure prediction and high-pressure crystallization in rational pharmaceutical polymorph screening. Nat. Commun. 2015, 6, 7793,  DOI: 10.1038/ncomms8793
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    Combined crystal structure prediction and high-pressure crystallization in rational pharmaceutical polymorph screening
    Neumann, M. A.; van de Streek, J.; Fabbiani, F. P. A.; Hidber, P.; Grassmann, O.
    Nature Communications (2015), 6 (), 7793CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)
    Org. mols., such as pharmaceuticals, agro-chems. and pigments, frequently form several crystal polymorphs with different physicochem. properties. Finding polymorphs has long been a purely exptl. game of trial-and-error. Here we utilize in silico polymorph screening in combination with rationally planned crystn. expts. to study the polymorphism of the pharmaceutical compd. Dalcetrapib, with 10 torsional degrees of freedom one of the most flexible mols. ever studied computationally. The exptl. crystal polymorphs are found at the bottom of the calcd. lattice energy landscape, and two predicted structures are identified as candidates for a missing, thermodynamically more stable polymorph. Pressure-dependent stability calcns. suggested high pressure as a means to bring these polymorphs into existence. Subsequently, one of them could indeed be crystd. in the 0.02 to 0.50 GPa pressure range and was found to be metastable at ambient pressure, effectively derisking the appearance of a more stable polymorph during late-stage development of Dalcetrapib.
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    Weissbuch, I.; Lahav, M.; Leiserowitz, L. Toward stereochemical control, monitoring, and understanding of crystal nucleation. Cryst. Growth Des. 2003, 3, 125– 150,  DOI: 10.1021/cg0200560
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    Toward Stereochemical Control, Monitoring, and Understanding of Crystal Nucleation
    Weissbuch, Isabelle; Lahav, Meir; Leiserowitz, Leslie
    Crystal Growth & Design (2003), 3 (2), 125-150CODEN: CGDEFU; ISSN:1528-7483. (American Chemical Society)
    In this review, the delicate interplay between stereochem. control, monitoring at the subnanometer level, and an understanding of crystal nucleation is probed. Control of crystal nucleation may be achieved employing tailor-made auxiliaries, which are either nucleation inhibitors or promoters. The process may be monitored at an interface via grazing incidence x-ray diffraction (GIXD). By these means, the authors can glean exptl. knowledge of crystal nucleation in various mol. systems. A hypothesis was invoked that supersatd. solns. contg. mol. clusters adopt various arrangements and shapes, some of which resemble the crystals into which they develop. This hypothesis was taken advantage of for the design of tailored inhibitors in achieving kinetic resoln. of enantiomers and induced pptn. of particular crystal polymorphs. The control and behavior of polymorphic crystn. may be understood at the mol. level through the interplay between inhibitor, solvent, solute, and the surface layer crystal structures. With respect to promotion of crystal nucleation, it may be achieved by Langmuir monolayers at the air-aq. soln. interface, acting as a templating agent. Detn. of the monolayer crystal structure by GIXD yields the extent and nature of the complementary fit between nucleator and nucleant. Finally, GIXD was applied to monitor by a snapshot technique the layer-by-layer cryst. assembly of cholesterol mols. at the air-H2O interface, which involved changes in mol. packing as the film grew in thickness.
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    Torbeev, V. Y.; Shavit, E.; Weissbuch, I.; Leiserowitz, L.; Lahav, M. Control of crystal polymorphism by tuning the structure of auxiliary molecules as nucleation inhibitors. The β-polymorph of glycine grown in aqueous solutions. Cryst. Growth Des. 2005, 5, 2190– 2196,  DOI: 10.1021/cg050200s
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    Control of Crystal Polymorphism by Tuning the Structure of Auxiliary Molecules as Nucleation Inhibitors. The β-Polymorph of Glycine Grown in Aqueous Solutions
    Torbeev, Vladimir Yu.; Shavit, Edna; Weissbuch, Isabelle; Leiserowitz, Leslie; Lahav, Meir
    Crystal Growth & Design (2005), 5 (6), 2190-2196CODEN: CGDEFU; ISSN:1528-7483. (American Chemical Society)
    The control of crystal polymorphism of the trimorphic crystals of glycine (Gly) grown in aq. solns. in the presence of amino acids operating as stereospecific nucleation inhibitors is reported. The presence of enantiopure amino acids phenylalanine (Phe), methionine (Met), and tryptophan (Trp) in crystg. aq. solns. induces changes in the morphol. of α-Gly leading to the formation of pyramidal instead of bipyramidal crystals. Increased concns. of racemic Phe and Met inhibit both the α- and β-polymorphs of glycine and induce pptn. of the thermodynamically most stable γ-polymorph. Amino acids that bear bulky side groups such as racemic tryptophan (Trp), N-MeTrp, and α-naphthylalanine induce pptn. of the least stable β-Gly polymorph. Quasi-racemic mixts. of R-Trp and S-Phe (or S-Met), for example, lead to the pptn. of one of the enantiomorphs of β-Gly. The roles played by the different amino acids in affecting morphol. and polymorphism are discussed in terms of their interactions with and stereoselective occlusion in the various sectors of the {010} faces of the β-Gly crystals.
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    Ma, W.; Reinspach, J.; Zhou, Y.; Diao, Y.; McAfee, T.; Mannsfeld, S. C.; Bao, Z.; Ade, H. Tuning local molecular orientation-composition correlations in binary organic thin films by solution shearing. Adv. Funct. Mater. 2015, 25, 3131– 3137,  DOI: 10.1002/adfm.201500468
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    Tuning Local Molecular Orientation-Composition Correlations in Binary Organic Thin Films by Solution Shearing
    Ma, Wei; Reinspach, Julia; Zhou, Yan; Diao, Ying; McAfee, Terry; Mannsfeld, Stefan C. B.; Bao, Zhenan; Ade, Harald
    Advanced Functional Materials (2015), 25 (21), 3131-3137CODEN: AFMDC6; ISSN:1616-301X. (Wiley-VCH Verlag GmbH & Co. KGaA)
    A general impact of soln. shearing on mol. orientation correlation is obsd. in polymer:fullerene org. solar cells in which one of the components forms fibrils or aggregates. Further investigation with polarized soft X-ray scattering reveals that soln. shearing induces more face-to-face orientation relative to the interface of two components compared to spin-coating. This impact is shearing speed dependent, i.e., slow shearing speed can induce more face-to-face orientation than a fast shearing speed. These results demonstrate that soln. shearing is an effective method to control the relative mol. orientation. Soln. shearing can also modify the domain size and av. compn. variations.
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    Riera-Galindo, S.; Tamayo, A.; Mas-Torrent, M. Role of polymorphism and thin-film morphology in organic semiconductors processed by solution shearing. ACS omega 2018, 3, 2329– 2339,  DOI: 10.1021/acsomega.8b00043
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    Role of Polymorphism and Thin-Film Morphology in Organic Semiconductors Processed by Solution Shearing
    Riera-Galindo, Sergi; Tamayo, Adrian; Mas-Torrent, Marta
    ACS Omega (2018), 3 (2), 2329-2339CODEN: ACSODF; ISSN:2470-1343. (American Chemical Society)
    A review. Org. semiconductors (OSCs) are promising materials for cost-effective prodn. of electronic devices because they can be processed from soln. employing high-throughput techniques. However, small-mol. OSCs are prone to structural modifications because of the presence of weak van der Waals intermol. interactions. Hence, controlling the crystn. in these materials is pivotal to achieve high device reproducibility. In this perspective article, we focus on controlling polymorphism and morphol. in small-mol. org. semiconducting thin films deposited by soln.-shearing techniques compatible with roll-to-roll systems. Special attention is paid to the influence that the different exptl. deposition parameters can have on thin films. Further, the main characterization techniques for thin-film structures are reviewed, highlighting the in situ characterization tools that can provide crucial insights into the crystn. mechanisms.
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    Kim, K.; Santos, E. J.; Lee, T. H.; Nishi, Y.; Bao, Z. Epitaxially grown strained pentacene thin film on graphene membrane. Small 2015, 11, 2037– 2043,  DOI: 10.1002/smll.201403006
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    Epitaxially Grown Strained Pentacene Thin Film on Graphene Membrane
    Kim, Kwanpyo; Santos, Elton J. G.; Lee, Tae Hoon; Nishi, Yoshio; Bao, Zhenan
    Small (2015), 11 (17), 2037-2043CODEN: SMALBC; ISSN:1613-6810. (Wiley-VCH Verlag GmbH & Co. KGaA)
    Org.-graphene system has emerged as a new platform for various applications such as flexible org. photovoltaics and org. light emitting diodes. Due to its important implication in charge transport, the study and reliable control of mol. packing structures at the graphene-mol. interface are of great importance for successful incorporation of graphene in related org. devices. An ideal membrane of suspended graphene as a mol. assembly template was used to study thin-film epitaxial behaviors. Using TEM, two distinct mol. packing structures of pentacene on graphene are found. One obsd. packing structure is similar to the known bulk-phase, which adapts a face-on mol. orientation on graphene substrate. However, a rare polymorph of pentacene crystal, which shows significant strain along the c-axis, is identified. In particular, the strained film exhibits a specific mol. orientation and a strong azimuthal correlation with underlying graphene. Through ab initio electronic structure calcns., including van der Waals interactions, the unusual polymorph is attributed to the strong graphene-pentacene interaction. The obsd. strained org. film growth on graphene demonstrates the possibility to tune mol. packing via graphene-mol. interactions.
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    Jiang, Q.; Hu, C.; Ward, M. D. Stereochemical control of polymorph transitions in nanoscale reactors. J. Am. Chem. Soc. 2013, 135, 2144– 2147,  DOI: 10.1021/ja312511v
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    Stereochemical Control of Polymorph Transitions in Nanoscale Reactors
    Jiang, Qi; Hu, Chunhua; Ward, Michael D.
    Journal of the American Chemical Society (2013), 135 (6), 2144-2147CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    Crystn. of glycine in the cylindrical nanopores of anodic Al oxide (AAO) revealed the formation of metastable β-glycine in pores having diams. <200 nm. Two-dimensional x-ray microdiffraction indicated that the [010] axis of the embedded β-glycine nanocrystals coincided with the pore direction, identical to behavior obsd. previously in the cylindrical nanopores of polymer monoliths. Whereas the β-glycine nanocrystals were stable indefinitely in ambient air and persisted upon heating, they transformed to the α polymorph upon standing at room temp. and 90% relative humidity (RH). The α-glycine nanocrystals were oriented with the [010] axis nearly perpendicular to the pore direction, reflecting a nearly 90° rotation of the glycine mols. during the transition. When the β-glycine nanocrystals were formed in the AAO cylinders in the presence of small amts. of racemic hydrophobic amino acid auxiliaries, which are known to bind selectively to the (010) and (0‾10) faces on the fast-growing end of β-glycine enantiomorphs, the β → α phase transition at 90% RH was suppressed. In contrast, β-glycine nanocrystals grown in the presence of an enantiopure amino acid auxiliary, which binds to the fast-growing end of only one of the enantiomorphs, thus suppressing its formation and leaving the other enantiomorph unperturbed, transformed into the α polymorph under the same conditions. This observation confirms that binding of an amino acid to the {010} faces is stereoselective and that access of H2O to these faces is essential for the transition to the α polymorph.
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    Jiang, Q.; Ward, M. D. Crystallization under nanoscale confinement. Chem. Soc. Rev. 2014, 43, 2066– 2079,  DOI: 10.1039/C3CS60234F
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    Crystallization under nanoscale confinement
    Jiang, Qi; Ward, Michael D.
    Chemical Society Reviews (2014), 43 (7), 2066-2079CODEN: CSRVBR; ISSN:0306-0012. (Royal Society of Chemistry)
    A review. Classical crystal growth models posit that crystn. outcomes are detd. by nuclei that resemble mature crystal phases, but at a crit. size where the vol. free energy of nuclei begins to offset the unfavorable surface free energy arising from the interface with the growth medium. Crystn. under nanoscale confinement offers an opportunity to examine nucleation and phase transformations at length scales corresponding to the crit. size, at which kinetics and thermodn. of nucleation and growth intersect and dramatic departures in stability compared to bulk crystals can appear. This tutorial review focuses on recent investigations of the crystn. of org. compds. in nanoporous matrixes that effectively provide millions of nanoscale reactors in a single sample, ranging from controlled porous glass (CPG) beads to nanoporous block-copolymer monoliths to anodic Al2O3 membranes. Confinement of crystal growth in this manner provides a snapshot of the earliest stages of crystal growth, with insights into nucleation, size-dependent polymorphism, and thermotropic behavior of nanoscale crystals. Moreover, these matrixes can be used to screen for crystal polymorphs and assess their stability as nanocrystals. The well-aligned cylindrical nanoscale pores of polymer monoliths or AAO also allow detn. of preferred orientation of embedded nanocrystals, affording insight into the competitive nature of nucleation, crit. sizes, and phase transition mechanisms. Collectively, these investigations have increased our understanding of crystn. at length scales that are deterministic while suggesting strategies for controlling crystn. outcomes.
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    Diao, Y.; Lenn, K. M.; Lee, W.-Y.; Blood-Forsythe, M. A.; Xu, J.; Mao, Y.; Kim, Y.; Reinspach, J. A.; Park, S.; Aspuru-Guzik, A. Understanding polymorphism in organic semiconductor thin films through nanoconfinement. J. Am. Chem. Soc. 2014, 136, 17046– 17057,  DOI: 10.1021/ja507179d
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    Understanding Polymorphism in Organic Semiconductor Thin Films through Nanoconfinement
    Diao, Ying; Lenn, Kristina M.; Lee, Wen-Ya; Blood-Forsythe, Martin A.; Xu, Jie; Mao, Yisha; Kim, Yeongin; Reinspach, Julia A.; Park, Steve; Aspuru-Guzik, Alan; Xue, Gi; Clancy, Paulette; Bao, Zhenan; Mannsfeld, Stefan C. B.
    Journal of the American Chemical Society (2014), 136 (49), 17046-17057CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    Understanding crystal polymorphism is a long-standing challenge relevant to many fields, such as pharmaceuticals, org. semiconductors, pigments, food, and explosives. Controlling polymorphism of org. semiconductors (OSCs) in thin films is particularly important given that such films form the active layer in most org. electronics devices and that dramatic changes in the electronic properties can be induced even by small changes in the mol. packing. However, there are very few polymorphic OSCs for which the structure-property relations were elucidated so far. The major challenges lie in the transient nature of metastable forms and the prepn. of phase-pure, highly cryst. thin films for resolving the crystal structures and evaluating the charge transport properties. The nanoconfinement effect combined with the flow-enhanced crystal engineering technique is a powerful and likely material-agnostic method to identify existing polymorphs in OSC materials and to prep. the individual pure forms in thin films at ambient conditions. With this method the authors prepd. high quality crystal polymorphs and resolved crystal structures of 6,13-bis(triisopropylsilylethynyl)pentacene (TIPS-pentacene), including a new polymorph discovered via in situ grazing incidence x-ray diffraction and confirmed by mol. mechanic simulations. The authors further correlated mol. packing with charge transport properties using quantum chem. calcns. and charge carrier mobility measurements. The authors applied the authors' methodol. to a [1]benzothieno[3,2-b][1]1benzothiophene (BTBT) deriv. and successfully stabilized its metastable form.
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    Zhang, Y.; Chen, A.; Kim, M.-W.; Alaei, A.; Lee, S. S. Nanoconfining solution-processed organic semiconductors for emerging optoelectronics. Chem. Soc. Rev. 2021, 50, 9375– 9390,  DOI: 10.1039/D1CS00430A
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    Nanoconfining solution-processed organic semiconductors for emerging optoelectronics
    Zhang, Yuze; Chen, Alina; Kim, Min-Woo; Alaei, Aida; Lee, Stephanie S.
    Chemical Society Reviews (2021), 50 (17), 9375-9390CODEN: CSRVBR; ISSN:0306-0012. (Royal Society of Chemistry)
    A review. Soln.-processable org. materials for emerging electronics can generally be divided into two classes of semiconductors, org. small mols. and polymers. The theor. thermodn. limits of device performance are largely detd. by the mol. structure of these compds., and advances in synthetic routes have led to significant progress in charge mobilities and light conversion and light emission efficiencies over the past several decades. Still, the uncontrolled formation of out-of-equil. film microstructures and unfavorable polymorphs during rapid soln. processing remains a crit. bottleneck facing the commercialization of these materials. This tutorial review provides an overview of the use of nanoconfining scaffolds to impose order onto soln.-processed semiconducting films to overcome this limitation. For org. semiconducting small mols. and polymers, which typically exhibit strong crystal growth and charge transport anisotropy along different crystallog. directions, nanoconfining crystn. within nanopores and nanogrooves can preferentially orient the fast charge transport direction of crystals with the direction of current flow in devices. Nanoconfinement can also stabilize high-performance metastable polymorphs by shifting their relative Gibbs free energies via increasing the surface area-to-vol. ratio. Promisingly, such nanoconfinement-induced improvements in film and crystal structures have been demonstrated to enhance the performance and stability of emerging optoelectronics that will enable large-scale manufg. of flexible, lightwt. displays and solar cells.
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    Curtis, F.; Li, X.; Rose, T.; Vázquez-Mayagoitia, Á.; Bhattacharya, S.; Ghiringhelli, L. M.; Marom, N. GAtor: A first-principles genetic algorithm for molecular crystal structure prediction. J. Chem. Theory Comput. 2018, 14, 2246– 2264,  DOI: 10.1021/acs.jctc.7b01152
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    GAtor: A First-Principles Genetic Algorithm for Molecular Crystal Structure Prediction
    Curtis, Farren; Li, Xiayue; Rose, Timothy; Vazquez-Mayagoitia, Alvaro; Bhattacharya, Saswata; Ghiringhelli, Luca M.; Marom, Noa
    Journal of Chemical Theory and Computation (2018), 14 (4), 2246-2264CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    The implementation of GAtor, a massively parallel, 1st-principles genetic algorithm (GA) for mol. crystal structure prediction, is presented. GAtor is written in Python and currently interfaces with the FHI-aims code to perform local optimizations and energy evaluations using dispersion-inclusive d. functional theory (DFT). GAtor offers a variety of fitness evaluation, selection, crossover, and mutation schemes. Breeding operators designed specifically for mol. crystals provide a balance between exploration and exploitation. Evolutionary niching is implemented in GAtor by using machine learning to cluster the dynamically updated population by structural similarity and then employing a cluster-based fitness function. Evolutionary niching promotes uniform sampling of the potential energy surface by evolving several subpopulations, which helps overcome initial pool biases and selection biases (genetic drift). The various settings offered by GAtor increase the likelihood of locating numerous low-energy min., including those located in disconnected, hard to reach regions of the potential energy landscape. The best structures generated are re-relaxed and re-ranked using a hierarchy of increasingly accurate DFT functionals and dispersion methods. GAtor is applied to a chem. diverse set of 4 past blind test targets, characterized by different types of intermol. interactions. The exptl. obsd. structures and other low-energy structures are found for all 4 targets. For Target II, 5-cyano-3-hydroxythiophene, the top ranked putative crystal structure is a Z' = 2 structure with P‾1 symmetry and a scaffold packing motif, which was not reported previously.
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    Curtis, F.; Rose, T.; Marom, N. Evolutionary niching in the GAtor genetic algorithm for molecular crystal structure prediction. Faraday Discuss. 2018, 211, 61– 77,  DOI: 10.1039/C8FD00067K
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    Evolutionary niching in the GAtor genetic algorithm for molecular crystal structure prediction
    Curtis, Farren; Rose, Timothy; Marom, Noa
    Faraday Discussions (2018), 211 (Methods and Applications of Crystal Structure Prediction), 61-77CODEN: FDISE6; ISSN:1359-6640. (Royal Society of Chemistry)
    The goal of mol. crystal structure prediction (CSP) is to find all the plausible polymorphs for a given mol. This requires performing global optimization over a high-dimensional search space. Genetic algorithms (GAs) perform global optimization by starting from an initial population of structures and generating new candidate structures by breeding the fittest structures in the population. Typically, the fitness function is based on relative lattice energies, such that structures with lower energies have a higher probability of being selected for mating. GAs may be adapted to perform multi-modal optimization by using evolutionary niching methods that support the formation of several stable subpopulations and suppress the over-sampling of densely populated regions. Evolutionary niching is implemented in the GAtor mol. crystal structure prediction code by using techniques from machine learning to dynamically cluster the population into niches of structural similarity. A cluster-based fitness function is constructed such that structures in less populated clusters have a higher probability of being selected for breeding. Here, the effects of evolutionary niching are investigated for the crystal structure prediction of 1,3-dibromo-2-chloro-5-fluorobenzene. Using the cluster-based fitness function increases the success rate of generating the exptl. structure and addnl. low-energy structures with similar packing motifs.
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    Bier, I.; O’Connor, D.; Hsieh, Y.-T.; Wen, W.; Hiszpanski, A. M.; Han, T. Y.-J.; Marom, N. Crystal structure prediction of energetic materials and a twisted arene with Genarris and GAtor. CrystEngComm 2021, 23, 6023– 6038,  DOI: 10.1039/D1CE00745A
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    Crystal structure prediction of energetic materials and a twisted arene with Genarris and GAtor
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    CrystEngComm (2021), 23 (35), 6023-6038CODEN: CRECF4; ISSN:1466-8033. (Royal Society of Chemistry)
    A mol. crystal structure prediction (CSP) workflow, based on the random structure generator, Genarris, and the genetic algorithm (GA), GAtor, is applied to the energetic materials 2,4,6-trinitrobenzene-1,3,5-triamine (TATB) and 2,4,6-trinitrobenzene-1,3-diamine (DATB), and the chiral arene, 4,5-dimethylphenanthrene. The exptl. structures of all three materials are successfully generated multiple times by both Genarris and GAtor, and ranked as the most stable structures by dispersion-inclusive d. functional theory (DFT) methods. For 4,5-dimethylphenanthrene the evolutionary niching feature of GAtor helps find the exptl. structure by penalizing the fitness of over-sampled regions and steering the GA to an under-explored basin. For DATB, a putative structure with a sheet packing motif, which is assocd. with reduced sensitivity, is found to be very close in energy to the exptl. structure and could be a viable polymorph. Principal component anal. of atom-centered symmetry functions is used to compare the crystal structure landscapes of TATB and DATB. Genarris and GAtor exhibit robust performance for diverse targets with varied intermol. interactions. This work demonstrates the potential of including CSP as a part of the energetic materials development process.
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    Bier, I.; Marom, N. Machine learned model for solid form volume estimation based on packing-accessible surface and molecular topological fragments. J. Phys. Chem. A 2020, 124, 10330– 10345,  DOI: 10.1021/acs.jpca.0c06791
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    Machine Learned Model for Solid Form Volume Estimation Based on Packing-Accessible Surface and Molecular Topological Fragments
    Bier, Imanuel; Marom, Noa
    Journal of Physical Chemistry A (2020), 124 (49), 10330-10345CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
    A machine learned model is presented for predicting the vol. of a homomol. crystal based on the single-mol. structure, implemented in the open-source Python package for Mol. Vol. Estn. (PyMoVE). The model is based on 2 descriptors: the vol. enclosed by the packing-accessible surface and mol. topol. fragments. To calc. the vol. enclosed by the mol. surface, the authors have developed a new projected marching cubes algorithm. The new algorithm achieves a higher accuracy with a smaller no. of elements than the traditional marching cubes algorithm, the marching tetrahedron variant, and Monte Carlo methods. The packing-accessible surface is then calcd. using an optimized probe radius. The mol. topol. fragments are used to construct a representation that captures the bonding environments of the atoms in the mol. Feature selection is used to det. which fragments to include in the model. The accuracy and robustness of the model may be attributed to including both geometric and chem. features. The vol. enclosed by the packing-accessible surface accounts for the presence of voids and sterically hindered regions as well as for the effect of conformational changes. The mol. topol. fragments account for the effect of intermol. interactions on the packing d. The model is trained on a dataset of structures extd. from the Cambridge Structural Database. Excellent performance is demonstrated for 3 validation sets of unseen data.
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    Journal of Chemical Physics (2011), 134 (7), 074106/1-074106/13CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    Neural networks offer an unbiased and numerically very accurate approach to represent high-dimensional ab initio potential-energy surfaces. Once constructed, neural network potentials can provide the energies and forces many orders of magnitude faster than electronic structure calcns., and thus enable mol. dynamics simulations of large systems. However, Cartesian coordinates are not a good choice to represent the at. positions, and a transformation to symmetry functions is required. Using simple benchmark systems, the properties of several types of symmetry functions suitable for the construction of high-dimensional neural network potential-energy surfaces are discussed in detail. The symmetry functions are general and can be applied to all types of systems such as mols., cryst. and amorphous solids, and liqs. (c) 2011 American Institute of Physics.
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    Clustering data by identifying a subset of representative examples is important for processing sensory signals and detecting patterns in data. Such "exemplars" can be found by randomly choosing an initial subset of data points and then iteratively refining it, but this works well only if that initial choice is close to a good soln. We devised a method called "affinity propagation," which takes as input measures of similarity between pairs of data points. Real-valued messages are exchanged between data points until a high-quality set of exemplars and corresponding clusters gradually emerges. We used affinity propagation to cluster images of faces, detect genes in microarray data, identify representative sentences in this manuscript, and identify cities that are efficiently accessed by airline travel. Affinity propagation found clusters with much lower error than other methods, and it did so in less than one-hundredth the amt. of time.
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    Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996, 77, 3865,  DOI: 10.1103/PhysRevLett.77.3865
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    Generalized gradient approxns. (GGA's) for the exchange-correlation energy improve upon the local spin d. (LSD) description of atoms, mols., and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental consts. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential.
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    Tkatchenko, A.; Scheffler, M. Accurate molecular van der Waals interactions from ground-state electron density and free-atom reference data. Phys. Rev. Lett. 2009, 102, 073005,  DOI: 10.1103/PhysRevLett.102.073005
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    Accurate Molecular Van Der Waals Interactions from Ground-State Electron Density and Free-Atom Reference Data
    Tkatchenko, Alexandre; Scheffler, Matthias
    Physical Review Letters (2009), 102 (7), 073005/1-073005/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    We present a parameter-free method for an accurate detn. of long-range van der Waals interactions from mean-field electronic structure calcns. Our method relies on the summation of interat. C6 coeffs., derived from the electron d. of a mol. or solid and accurate ref. data for the free atoms. The mean abs. error in the C6 coeffs. is 5.5% when compared to accurate exptl. values for 1225 intermol. pairs, irresp. of the employed exchange-correlation functional. We show that the effective at. C6 coeffs. depend strongly on the bonding environment of an atom in a mol. Finally, we analyze the van der Waals radii and the damping function in the C6R-6 correction method for d.-functional theory calcns.
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    Tkatchenko, A.; DiStasio Jr, R. A.; Car, R.; Scheffler, M. Accurate and efficient method for many-body van der Waals interactions. Phys. Rev. Lett. 2012, 108, 236402,  DOI: 10.1103/PhysRevLett.108.236402
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    Accurate and efficient method for many-body van der Waals interactions
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    Physical Review Letters (2012), 108 (23), 236402/1-236402/5CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    An efficient method is developed for the microscopic description of the frequency-dependent polarizability of finite-gap mols. and solids. This is achieved by combining the Tkatchenko-Scheffler van der Waals (vdW) method with the self-consistent screening equation of classical electrodynamics. This leads to a seamless description of polarization and depolarization for the polarizability tensor of mols. and solids. The screened long-range many-body vdW energy is obtained from the soln. of the Schroedinger equation for a system of coupled oscillators. We show that the screening and the many-body vdW energy play a significant role even for rather small mols., becoming crucial for an accurate treatment of conformational energies for biomols. and binding of mol. crystals. The computational cost of the developed theory is negligible compared to the underlying electronic structure calcn.
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    Ambrosetti, A.; Reilly, A.; DiStasio, R.; Tkatchenko, A. Long-range correlation energy calculated from coupled atomic response functions. J. Chem. Phys. 2014, 140, 18A508,  DOI: 10.1063/1.4865104
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    Adamo, C.; Barone, V. Toward reliable density functional methods without adjustable parameters: The PBE0 model. J. Chem. Phys. 1999, 110, 6158– 6170,  DOI: 10.1063/1.478522
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    Adamo, Carlo; Barone, Vincenzo
    Journal of Chemical Physics (1999), 110 (13), 6158-6170CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    We present an anal. of the performances of a parameter free d. functional model (PBE0) obtained combining the so called PBE generalized gradient functional with a predefined amt. of exact exchange. The results obtained for structural, thermodn., kinetic and spectroscopic (magnetic, IR and electronic) properties are satisfactory and not far from those delivered by the most reliable functionals including heavy parameterization. The way in which the functional is derived and the lack of empirical parameters fitted to specific properties make the PBE0 model a widely applicable method for both quantum chem. and condensed matter physics.
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    Reilly, A.; Tkatchenko, A. Seamless and Accurate Modeling of Organic Molecular Materials. J. Phys. Chem. Lett. 2013, 4, 1028– 1033,  DOI: 10.1021/jz400226x
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    Seamless and Accurate Modeling of Organic Molecular Materials
    Reilly, Anthony M.; Tkatchenko, Alexandre
    Journal of Physical Chemistry Letters (2013), 4 (6), 1028-1033CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
    The near endless possibilities for assembling mol. materials has long posed a difficult challenge for theory. All crystal-structure prediction methods acknowledge the crucial contribution of van der Waals or dispersion interactions, but few go beyond a pairwise additive description of dispersion, ignoring its many-body nature. Here we use two databases to show how a many-body approach to dispersion can seamlessly model both solid and gas-phase interactions within the coveted "chem. accuracy" benchmark, while the underlying pairwise approach fails for solid-state interactions due to the absence of many-body polarization and energy contributions. Our results show that recently developed methods that treat the truly collective nature of dispersion interactions are able to reach the accuracy required for predicting mol. materials, when coupled with nonempirical d. functionals.
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    Hoja, J.; Tkatchenko, A. First-principles stability ranking of molecular crystal polymorphs with the DFT+MBD approach. Faraday Discuss. 2018, 211, 253– 274,  DOI: 10.1039/C8FD00066B
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    First-principles stability ranking of molecular crystal polymorphs with the DFT+MBD approach
    Hoja, Johannes; Tkatchenko, Alexandre
    Faraday Discussions (2018), 211 (Methods and Applications of Crystal Structure Prediction), 253-274CODEN: FDISE6; ISSN:1359-6640. (Royal Society of Chemistry)
    The ability to accurately calc. the relative stabilities of numerous polymorphs of a given mol. crystal is crucial for the success of any mol. crystal structure prediction (CSP) approach. We have recently presented a hierarchical CSP procedure based on van-der-Waals-inclusive d. functional theory [Hoja et al., 2018, arXiv:1803.07503], which yields excellent stability rankings for mol. crystals involving rigid mols., salts, co-crystals, and highly polymorphic drug-like mols. This approach includes many-body dispersion effects, exact exchange, as well as vibrational free energies. Here, we discuss in detail the impact of these effects on the obtained stability rankings. In addn., we assess the impact of the approxns. used in our hierarchical procedure. We show that our procedure is generally robust to 1-2 kJ mol-1 for the systems in the latest CSP blind test but vibrational free energies for crystals involving flexible mols. would benefit from directly including many-body dispersion interactions. In addn., we also discuss the effect of temp. on the structure of mol. crystals and a simple but effective method for estg. anharmonic effects.
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    Marom, N.; DiStasio, R.; Atalla, V.; Levchenko, S.; Reilly, A.; Chelikowsky, J.; Leiserowitz, L.; Tkatchenko, A. Many-Body Dispersion Interactions in Molecular Crystal Polymorphism. Angew. Chem., Int. Ed. 2013, 52, 6629– 6632,  DOI: 10.1002/anie.201301938
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    Many-Body Dispersion Interactions in Molecular Crystal Polymorphism
    Marom, Noa; DiStasio, Robert A. Jr.; Atalla, Viktor; Levchenko, Sergey; Reilly, Anthony M.; Chelikowsky, James R.; Leiserowitz, Leslie; Tkatchenko, Alexandre
    Angewandte Chemie, International Edition (2013), 52 (26), 6629-6632CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
    Accounting for the nonadditive many-body dispersion (MBD) energy beyond the std. pairwise approxn. is crucial for the correct qual. and quant. description of polymorphism in mol. crystals. The authors demonstrate this through three fundamental and stringent benchmark examples: glycine, oxalic acid, and tetrolic acid. These systems represent a broad class of mol. crystals, comprising hydrogen-bonded networks of amino acids and carboxylic acids. The improvement obtained with the MBD method as compared to the simple pairwise dispersion model is attributed to the sensitive dependence of the dispersion energy on the polymorph geometry and the dynamic internal elec. fields produced in mol. crystals. The DFT + MBD method yields an unprecedented accuracy of 1% in the description of the structures of mol. crystal polymorphs and of 0.2 kcal mol-1 in their relative energies. Such accuracy is essential for the reliable modeling of polymorphism in mol. crystals.
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    Nyman, J.; Day, G. M. Static and lattice vibrational energy differences between polymorphs. CrystEngComm 2015, 17, 5154– 5165,  DOI: 10.1039/C5CE00045A
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    Static and lattice vibrational energy differences between polymorphs
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    CrystEngComm (2015), 17 (28), 5154-5165CODEN: CRECF4; ISSN:1466-8033. (Royal Society of Chemistry)
    A computational study of 1061 exptl. detd. crystal structures of 508 polymorphic org. mols. has been performed with state-of-the-art lattice energy minimisation methods, using a hybrid method that combines d. functional theory intramol. energies with an anisotropic atom-atom intermol. model. Rigid mol. lattice dynamical calcns. have also been performed to est. the vibrational contributions to lattice free energies. Distributions of the differences in lattice energy, free energy, zero point energy, entropy and heat capacity between polymorphs are presented. Polymorphic lattice energy differences are typically very small: over half of polymorph pairs are sepd. by less than 2 kJ mol-1 and lattice energy differences exceed 7.2 kJ mol-1 in only 5% of cases. Unsurprisingly, vibrational contributions to polymorph free energy differences at ambient conditions are dominated by entropy differences. The distribution of vibrational energy differences is narrower than lattice energy differences, rarely exceeding 2 kJ mol-1. However, these relatively small vibrational free energy contributions are large enough to cause a re-ranking of polymorph stability below, or at, room temp. in 9% of the polymorph pairs.
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    New method for calculating the one-particle Green's function with application to the electron-gas problem
    Hedin, Lars
    Physical Review (1965), 139 (3A), 796-823CODEN: PHRVAO; ISSN:0031-899X.
    A set of successively more accurate self-consistent equations for the 1-electron Green's function were derived. They correspond to an expansion in a screened potential rather than the bare Coulomb potential. The 1st equation is adequate for many purposes. Each equation follows from the demand that a corresponding expression for the total energy be stationary with respect to variations in the Green's function. The main information to be obtained, besides the total energy, is 1-particle-like excitation spectra, i.e., spectra characterized by the quantum nos. of a single particle. This includes the low-excitation spectra in metals as well as configurations in atoms, mols., and solids with one electron outside or one electron missing from a closed-shell structure. In the latter cases, an approx. description is obtained by a modified Hartree-Fock equation involving a "Coulomb hole" and a static screened potential in the exchange term. As an example, spectra of some atoms are discussed. To investigate the convergence of successive approxn. for the Green's function, extensive calcns. were made for the electron gas at a range of metallic ds. The results are expressed in terms of quasiparticle energies Ε(k) and quasiparticle interactions f(k,k'). The very 1st approxn. gives a good value for the magnitude of Ε(k.). To est. the deriv. of Ε(k), both the 1st- and the 2nd-order terms are needed. The derivative, and thus the sp. heat, differs from the free-particle value by only a few percent. The correction to the sp. heat keeps the same sign down to the lowest alkalimetal ds., and is smaller than those obtained recently by Silverstein (CA 59, 144d) and by Rice (CA 62, 7218f). The results for the paramagnetic susceptibility are unreliable in the alkalimetal-d.-region owing to poor convergence of the expansion for f. Besides the proof of a modified Luttinger-Ward-Klein variational principle and a related self-consistency idea, there is not much new in principle but emphasis is on the development of a numerically manageable approxn. scheme.
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    Marom, N. Accurate description of the electronic structure of organic semiconductors by GW methods. J. Phys.: Condens. Matter 2017, 29, 103003,  DOI: 10.1088/1361-648X/29/10/103003
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    Accurate description of the electronic structure of organic semiconductors by GW methods
    Marom, Noa
    Journal of Physics: Condensed Matter (2017), 29 (10), 103003/1-103003/20CODEN: JCOMEL; ISSN:0953-8984. (IOP Publishing Ltd.)
    A review. Electronic properties assocd. with charged excitations, such as the ionization potential (IP), the electron affinity (EA), and the energy level alignment at interfaces, are crit. parameters for the performance of org. electronic devices. To computationally design org. semiconductors and functional interfaces with tailored properties for target applications it is necessary to accurately predict these properties from 1st principles. Many-body perturbation theory is often used for this purpose within the GW approxn., where G is the one particle Green's function and W is the dynamically screened Coulomb interaction. Here, the formalism of GW methods at different levels of self-consistency is briefly introduced and some recent applications to org. semiconductors and interfaces are reviewed.
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    Sharifzadeh, S. Many-body perturbation theory for understanding optical excitations in organic molecules and solids. J. Phys.: Condens. Matter 2018, 30, 153002,  DOI: 10.1088/1361-648X/aab0d1
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    Many-body perturbation theory for understanding optical excitations in organic molecules and solids
    Sharifzadeh Sahar
    Journal of physics. Condensed matter : an Institute of Physics journal (2018), 30 (15), 153002 ISSN:.
    Semiconductors composed of organic molecules are promising as components for flexible and inexpensive optoelectronic devices, with many recent studies aimed at understanding their electronic and optical properties. In particular, computational modeling of these complex materials has provided new understanding of the underlying properties which give rise to their excited-state phenomena. This article provides an overview of recent many-body perturbation theory (MBPT) studies of optical excitations within organic molecules and solids. We discuss the accuracy of MBPT within the GW/BSE approach in predicting excitation energies and absorption spectra, and assess the impact of two commonly used approximations, the DFT starting point and the Tamm-Dancoff approximation. Moreover, we summarize studies that elucidate the role of solid-state structure on the nature of excitons in organic crystals. These studies show that a rich physical understanding of organic materials can be obtained from GW/BSE.
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    Golze, D.; Dvorak, M.; Rinke, P. The GW Compendium: A Practical Guide to Theoretical Photoemission Spectroscopy. Front. Chem. 2019, 7, 377,  DOI: 10.3389/fchem.2019.00377
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    The GW compendium: a practical guide to theoretical photoemission spectroscopy
    Golze, Dorothea; Dvorak, Marc; Rinke, Patrick
    Frontiers in Chemistry (Lausanne, Switzerland) (2019), 7 (), 377CODEN: FCLSAA; ISSN:2296-2646. (Frontiers Media S.A.)
    A review. The GW approxn. in electronic structure theory has become a widespread tool for predicting electronic excitations in chem. compds. and materials. In the realm of theor. spectroscopy, the GW method provides access to charged excitations as measured in direct or inverse photoemission spectroscopy. The no. of GW calcns. in the past two decades has exploded with increased computing power and modern codes. The success of GW can be attributed to many factors: favorable scaling with respect to system size, a formal interpretation for charged excitation energies, the importance of dynamical screening in real systems, and its practical combination with other theories. In this review, we provide an overview of these formal and practical considerations. We expand, in detail, on the choices presented to the scientist performing GWcalcns. for the first time. We also give an introduction to the many-body theory behind GW a review of modern applications like mols. and surfaces, and a perspective on methods which go beyond conventional GW calcns. This review addresses chemists, physicists and material scientists with an interest in theor. spectroscopy. It is intended for newcomers to GW calcns. but can also serve as an alternative perspective for experts and an up-to-date source of computational techniques.
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    Rohlfing, M.; Louie, S. G. Electron-hole excitations and optical spectra from first principles. Phys. Rev. B 2000, 62, 4927,  DOI: 10.1103/PhysRevB.62.4927
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    Electron-hole excitations and optical spectra from first principles
    Rohlfing, Michael; Louie, Steven G.
    Physical Review B: Condensed Matter and Materials Physics (2000), 62 (8), 4927-4944CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
    The authors present a recently developed approach to calc. electron-hole excitations and the optical spectra of condensed matter from 1st principles. The key concept is to describe the excitations of the electronic system by the corresponding 1- and two-particle Green's function. The method combines three computational techniques. First, the electronic ground state is treated within d.-functional theory. Second, the single-particle spectrum of the electrons and holes was obtained within the GW approxn. to the electron self-energy operator. Finally, the electron-hole interaction is calcd. and a Bethe-Salpeter equation is solved, yielding the coupled electron-hole excitations. The resulting solns. allow the calcn. of the entire optical spectrum. This holds both for bound excitonic states below the band gap, as well as for the resonant spectrum above the band gap. The authors discuss a no. of tech. developments needed for the application of the method to real systems. To illustrate the approach, the authors discuss the excitations and optical spectra of spatially isolated systems (atoms, mols., and semiconductor clusters) and of extended, periodic crystals (semiconductors and insulators).
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    Blase, X.; Duchemin, I.; Jacquemin, D. The Bethe-Salpeter equation in chemistry: Relations with TD-DFT, applications and challenges. Chem. Soc. Rev. 2018, 47, 1022– 1043,  DOI: 10.1039/C7CS00049A
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    The Bethe-Salpeter equation in chemistry: relations with TD-DFT, applications and challenges
    Blase, Xavier; Duchemin, Ivan; Jacquemin, Denis
    Chemical Society Reviews (2018), 47 (3), 1022-1043CODEN: CSRVBR; ISSN:0306-0012. (Royal Society of Chemistry)
    We review the many-body Green's function Bethe-Salpeter equation (BSE) formalism that is rapidly gaining importance for the study of the optical properties of mol. org. systems. We emphasize in particular its similarities and differences with time-dependent d. functional theory (TD-DFT), both methods sharing the same formal O(N4) computing time scaling with system size. By comparison with higher level wavefunction based methods and exptl. results, the advantages of BSE over TD-DFT are presented, including an accurate description of charge-transfer states and an improved accuracy for the challenging cyanine dyes. We further discuss the models that have been developed for including environmental effects. Finally, we summarize the challenges to be faced so that BSE reaches the same popularity as TD-DFT.
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    Ong, S. P.; Richards, W. D.; Jain, A.; Hautier, G.; Kocher, M.; Cholia, S.; Gunter, D.; Chevrier, V. L.; Persson, K. A.; Ceder, G. Python Materials Genomics (pymatgen): A robust, open-source python library for materials analysis. Comput. Mater. Sci. 2013, 68, 314– 319,  DOI: 10.1016/j.commatsci.2012.10.028
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    Python Materials Genomics (pymatgen): A robust, open-source python library for materials analysis
    Ong, Shyue Ping; Richards, William Davidson; Jain, Anubhav; Hautier, Geoffroy; Kocher, Michael; Cholia, Shreyas; Gunter, Dan; Chevrier, Vincent L.; Persson, Kristin A.; Ceder, Gerbrand
    Computational Materials Science (2013), 68 (), 314-319CODEN: CMMSEM; ISSN:0927-0256. (Elsevier B.V.)
    We present the Python Materials Genomics (pymatgen) library, a robust, open-source Python library for materials anal. A key enabler in high-throughput computational materials science efforts is a robust set of software tools to perform initial setup for the calcns. (e.g., generation of structures and necessary input files) and post-calcn. anal. to derive useful material properties from raw calcd. data. The pymatgen library aims to meet these needs by (1) defining core Python objects for materials data representation, (2) providing a well-tested set of structure and thermodn. analyses relevant to many applications, and (3) establishing an open platform for researchers to collaboratively develop sophisticated analyses of materials data obtained both from first principles calcns. and expts. The pymatgen library also provides convenient tools to obtain useful materials data via the Materials Project's REpresentational State Transfer (REST) Application Programming Interface (API). As an example, using pymatgen's interface to the Materials Project's RESTful API and phase diagram package, we demonstrate how the phase and electrochem. stability of a recently synthesized material, Li4SnS4, can be analyzed using a min. of computing resources. We find that Li4SnS4 is a stable phase in the Li-Sn-S phase diagram (consistent with the fact that it can be synthesized), but the narrow range of lithium chem. potentials for which it is predicted to be stable would suggest that it is not intrinsically stable against typical electrodes used in lithium-ion batteries.
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    Blum, V.; Gehrke, R.; Hanke, F.; Havu, P.; Havu, V.; Ren, X.; Reuter, K.; Scheffler, M. Ab initio molecular simulations with numeric atom-centered orbitals. Comput. Phys. Commun. 2009, 180, 2175– 2196,  DOI: 10.1016/j.cpc.2009.06.022
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    Ab initio molecular simulations with numeric atom-centered orbitals
    Blum, Volker; Gehrke, Ralf; Hanke, Felix; Havu, Paula; Havu, Ville; Ren, Xinguo; Reuter, Karsten; Scheffler, Matthias
    Computer Physics Communications (2009), 180 (11), 2175-2196CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier B.V.)
    We describe a complete set of algorithms for ab initio mol. simulations based on numerically tabulated atom-centered orbitals (NAOs) to capture a wide range of mol. and materials properties from quantum-mech. first principles. The full algorithmic framework described here is embodied in the Fritz Haber Institute "ab initio mol. simulations" (FHI-aims) computer program package. Its comprehensive description should be relevant to any other first-principles implementation based on NAOs. The focus here is on d.-functional theory (DFT) in the local and semilocal (generalized gradient) approxns., but an extension to hybrid functionals, Hartree-Fock theory, and MP2/GW electron self-energies for total energies and excited states is possible within the same underlying algorithms. An all-electron/full-potential treatment that is both computationally efficient and accurate is achieved for periodic and cluster geometries on equal footing, including relaxation and ab initio mol. dynamics. We demonstrate the construction of transferable, hierarchical basis sets, allowing the calcn. to range from qual. tight-binding like accuracy to meV-level total energy convergence with the basis set. Since all basis functions are strictly localized, the otherwise computationally dominant grid-based operations scale as O(N) with system size N. Together with a scalar-relativistic treatment, the basis sets provide access to all elements from light to heavy. Both low-communication parallelization of all real-space grid based algorithms and a ScaLapack-based, customized handling of the linear algebra for all matrix operations are possible, guaranteeing efficient scaling (CPU time and memory) up to massively parallel computer systems with thousands of CPUs.
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    Deslippe, J.; Samsonidze, G.; Strubbe, D. A.; Jain, M.; Cohen, M. L.; Louie, S. G. BerkeleyGW: A massively parallel computer package for the calculation of the quasiparticle and optical properties of materials and nanostructures. Comput. Phys. Commun. 2012, 183, 1269– 1289,  DOI: 10.1016/j.cpc.2011.12.006
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    BerkeleyGW: A massively parallel computer package for the calculation of the quasiparticle and optical properties of materials and nanostructures
    Deslippe, Jack; Samsonidze, Georgy; Strubbe, David A.; Jain, Manish; Cohen, Marvin L.; Louie, Steven G.
    Computer Physics Communications (2012), 183 (6), 1269-1289CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier B.V.)
    BerkeleyGW is a massively parallel computational package for electron excited-state properties that is based on the many-body perturbation theory employing the ab initio GW and GW plus Bethe-Salpeter equation methodol. It can be used in conjunction with many d.-functional theory codes for ground-state properties, including PARATEC, PARSEC, Quantum ESPRESSO, SIESTA, and Octopus. The package can be used to compute the electronic and optical properties of a wide variety of material systems from bulk semiconductors and metals to nanostructured materials and mols. The package scales to 10,000 s of CPUs and can be used to study systems contg. up to 100 s atoms.
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    Giannozzi, P.; Baroni, S.; Bonini, N.; Calandra, M.; Car, R.; Cavazzoni, C.; Ceresoli, D.; Chiarotti, G. L.; Cococcioni, M.; Dabo, I. QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys.: Condens. Matter 2009, 21, 395502,  DOI: 10.1088/0953-8984/21/39/395502
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    QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials
    Giannozzi Paolo; Baroni Stefano; Bonini Nicola; Calandra Matteo; Car Roberto; Cavazzoni Carlo; Ceresoli Davide; Chiarotti Guido L; Cococcioni Matteo; Dabo Ismaila; Dal Corso Andrea; de Gironcoli Stefano; Fabris Stefano; Fratesi Guido; Gebauer Ralph; Gerstmann Uwe; Gougoussis Christos; Kokalj Anton; Lazzeri Michele; Martin-Samos Layla; Marzari Nicola; Mauri Francesco; Mazzarello Riccardo; Paolini Stefano; Pasquarello Alfredo; Paulatto Lorenzo; Sbraccia Carlo; Scandolo Sandro; Sclauzero Gabriele; Seitsonen Ari P; Smogunov Alexander; Umari Paolo; Wentzcovitch Renata M
    Journal of physics. Condensed matter : an Institute of Physics journal (2009), 21 (39), 395502 ISSN:.
    QUANTUM ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). The acronym ESPRESSO stands for opEn Source Package for Research in Electronic Structure, Simulation, and Optimization. It is freely available to researchers around the world under the terms of the GNU General Public License. QUANTUM ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main focus, with special attention paid to massively parallel architectures, and a great effort being devoted to user friendliness. QUANTUM ESPRESSO is evolving towards a distribution of independent and interoperable codes in the spirit of an open-source project, where researchers active in the field of electronic-structure calculations are encouraged to participate in the project by contributing their own codes or by implementing their own ideas into existing codes.
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    Troullier, N.; Martins, J. L. Efficient pseudopotentials for plane-wave calculations. Phys. Rev. B 1991, 43, 1993,  DOI: 10.1103/PhysRevB.43.1993
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    Efficient pseudopotentials for plane-wave calculations
    Troullier, N.; Martins, Jose Luis
    Physical Review B: Condensed Matter and Materials Physics (1991), 43 (3), 1993-2006CODEN: PRBMDO; ISSN:0163-1829.
    We present a simple procedure to generate first-principles norm-conserving pseudopotentials, which are designed to be smooth and therefore save computational resources when used with a plane-wave basis. We found that these pseudopotentials are extremely efficient for the cases where the plane-wave expansion has a slow convergence, in particular, for systems contg. first-row elements, transition metals, and rare earth elements. The wide applicability of the pseudopotentials are exemplified with plane-wave calcns. for copper, zinc blende, diamond, α-quartz, rutile, and cerium.
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    Alagna, N.; Han, J.; Wollscheid, N.; Perez Lustres, J. L.; Herz, J.; Hahn, S.; Koser, S.; Paulus, F.; Bunz, U. H.; Dreuw, A. Tailoring ultrafast singlet fission by the chemical modification of phenazinothiadiazoles. J. Am. Chem. Soc. 2019, 141, 8834– 8845,  DOI: 10.1021/jacs.9b01079
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    Tailoring Ultrafast Singlet Fission by the Chemical Modification of Phenazinothiadiazoles
    Alagna, Nicolo; Han, Jie; Wollscheid, Nikolaus; Lustres, J. Luis Perez; Herz, Julia; Hahn, Sebastian; Koser, Silke; Paulus, Fabian; Bunz, Uwe H. F.; Dreuw, Andreas; Buckup, Tiago; Motzkus, Marcus
    Journal of the American Chemical Society (2019), 141 (22), 8834-8845CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    Quantum chem. and time-resolved spectroscopy are applied to rationalize how singlet fission (SF) is affected by systematic chem. modifications introduced into phenazinothiadiazoles (PTD). Substitution of the terminal arom. ring of TIPS-tetracene by a thiadiazole group leads to a considerable change in the relative energies of its S1 and T1 states. Thus, in contrast to TIPS-tetracene, SF becomes exothermic for various PTD derivs., which show S1-2T1 energy differences as high as 0.15 eV. This enables SF in PTD as corroborated by femtosecond transient absorption spectroscopy and TD-DFT calcns. The latter report T-T spectra consistent with thin film UV-vis femtosecond transient absorption of PTDs at long delays. TD-DFT calcns. also show that the S1-T1 energy gap can be rationally tuned by introducing N atoms into the arom. scaffold and by the halogenation of one side ring of the PTD. In addn., the specific S1-to-1(T1T1) electronic coupling depends on the crystal morphol. and the electronic properties simultaneously. Thus, both of them govern the strength and the interplay between direct and superexchange couplings, which in the most favorable cases accelerate SF to rate consts. beyond (100 fs)-1. Remarkably, direct coupling was found to contribute considerably to the total effective coupling and even to dominate it for some PTDs investigated here. A quantum yield of 200% is obtained on the early picosecond time scale for all compds. studied here, which is reduced to 100% due to triplet-triplet annihilation after a few nanoseconds.
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    Van Schenck, J.; Mayonado, G.; Anthony, J.; Graham, M.; Ostroverkhova, O. Molecular packing-dependent exciton dynamics in functionalized anthradithiophene derivatives: From solutions to crystals. J. Chem. Phys. 2020, 153, 164715,  DOI: 10.1063/5.0026072
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    Molecular packing-dependent exciton dynamics in functionalized anthradithiophene derivatives: From solutions to crystals
    Van Schenck, J. D. B.; Mayonado, G.; Anthony, J. E.; Graham, M. W.; Ostroverkhova, O.
    Journal of Chemical Physics (2020), 153 (16), 164715CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    Understanding the impact of inter-mol. orientation on the optical properties of org. semiconductors is important for designing next-generation org. (opto)electronic and photonic devices. However, fundamental aspects of how various features of mol. packing in cryst. systems det. the nature and dynamics of excitons have been a subject of debate. Toward this end, we present a systematic study of how various mol. crystal packing motifs affect the optical properties of a class of high-performance org. semiconductors: functionalized derivs. of fluorinated anthradithiophene. In soln., in the emission band, two states were identified: a Franck-Condon state present at all concns. and an excimer that emerged at higher concns. These delocalized Frenkel states were dominant across the full temp. range (78 K-293 K), though at lower temps., the entangled triplet states and STEs were present. In the deriv. with the "brickwork" packing, all three emissive species were obsd. across the full temp. range and, most notably, the 1(TT) state was present at room temp. Finally, the deriv. with the "sandwich-herringbone" packing exhibited localized Frenkel excitons and had a strong propensity for self-trapped exciton formation even at higher temps. In this deriv., no formation of the 1(TT) state was obsd. The temp.-dependent dynamics of these emissive states are reported, as well as their origin in fundamental inter-mol. interactions. (c) 2020 American Institute of Physics.
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    Pensack, R. D.; Purdum, G. E.; Mazza, S. M.; Grieco, C.; Asbury, J. B.; Anthony, J. E.; Loo, Y.-L.; Scholes, G. D. Excited-State Dynamics of 5, 14-vs 6, 13-Bis (trialkylsilylethynyl)-Substituted Pentacenes: Implications for Singlet Fission. J. Phys. Chem. C 2022, 126, 9784– 9793,  DOI: 10.1021/acs.jpcc.2c00897
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    Excited-State Dynamics of 5,14- vs 6,13-Bis(trialkylsilylethynyl)-Substituted Pentacenes: Implications for Singlet Fission
    Pensack, Ryan D.; Purdum, Geoffrey E.; Mazza, Samuel M.; Grieco, Christopher; Asbury, John B.; Anthony, John E.; Loo, Yueh-Lin; Scholes, Gregory D.
    Journal of Physical Chemistry C (2022), 126 (23), 9784-9793CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
    Singlet fission is a process in conjugated org. materials that has the potential to considerably improve the performance of devices in many applications, including solar energy conversion. In any application involving singlet fission, efficient triplet harvesting is essential. At present, not much is known about mol. packing arrangements detrimental to singlet fission. In this work, we report a mol. packing arrangement in cryst. films of 5,14-bis(triisopropylsilylethynyl)-substituted pentacene, specifically a local (pairwise) packing arrangement, responsible for complete quenching of triplet pairs generated via singlet fission. We first demonstrate that the energetic condition necessary for singlet fission is satisfied in amorphous films of the 5,14-substituted pentacene deriv. However, while triplet pairs form highly efficiently in the amorphous films, only a modest yield of independent triplets is obsd. In cryst. films, triplet pairs also form highly efficiently, although independent triplets are not obsd. because triplet pairs decay rapidly and are quenched completely. We assign the quenching to a rapid nonadiabatic transition directly to the ground state. Detrimental quenching is obsd. in cryst. films of two addnl. 5,14-bis(trialkylsilylethynyl)-substituted pentacenes with either Et or iso-Bu substituents. Developing a better understanding of the losses identified in this work, and assocd. mol. packing, may benefit overcoming losses in solids of other singlet fission materials.
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    Burdett, J. J.; Müller, A. M.; Gosztola, D.; Bardeen, C. J. Excited state dynamics in solid and monomeric tetracene: The roles of superradiance and exciton fission. J. Chem. Phys. 2010, 133, 144506,  DOI: 10.1063/1.3495764
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    Excited state dynamics in solid and monomeric tetracene: The roles of superradiance and exciton fission
    Burdett, Jonathan J.; Mueller, Astrid M.; Gosztola, David; Bardeen, Christopher J.
    Journal of Chemical Physics (2010), 133 (14), 144506/1-144506/12CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    The excited state dynamics in polycryst. thin films of tetracene are studied using both picosecond fluorescence and femtosecond transient absorption. The solid-state results are compared with those obtained for monomeric tetracene in dil. soln. The room temp. solid-state fluorescence decays are consistent with earlier models that take into account exciton-exciton annihilation and exciton fission but with a reduced delayed fluorescence lifetime, ranging from 20-100 ns as opposed to 2 μs or longer in single crystals. Femtosecond transient absorption measurements on the monomer in soln. reveal several excited state absorption features that overlap the ground state bleach and stimulated emission signals. On longer timescales, the initially excited singlet state completely decays due to intersystem crossing, and the triplet state absorption superimposed on the bleach is obsd., consistent with earlier flash photolysis expts. In the solid-state, the transient absorption dynamics are dominated by a neg. stimulated emission signal, decaying with a 9.2 ps time const. The enhanced bleach and stimulated emission signals in the solid are attributed to a superradiant, delocalized S1 state that rapidly fissions into triplets and can also generate a 2nd superradiant state, most likely a crystal defect, that dominates the picosecond luminescence signal. The enhanced absorption strength of the S0→S1 transition, along with the partially oriented nature of polycryst. films, obscures the weaker T1→TN absorption features. To confirm that triplets are the major species produced by relaxation of the initially excited state, the delayed fluorescence and ground state bleach recovery are compared. Their identical decays are consistent with triplet diffusion and recombination at trapping or defect sites. Complications like exciton delocalization, the presence of luminescent defect sites, and crystallite orientation must be taken into account to fully describe the photophys. behavior of tetracene thin films. The exptl. results are consistent with the traditional picture that tetracene's photodynamics are dominated by exciton fission and triplet recombination, but suggest that fission occurs within 10 ps, much more rapidly than previously believed. (c) 2010 American Institute of Physics.
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    Burdett, J. J.; Bardeen, C. J. The Dynamics of Singlet Fission in Crystalline Tetracene and Covalent Analogs. Acc. Chem. Res. 2013, 46, 1312– 1320,  DOI: 10.1021/ar300191w
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    The Dynamics of Singlet Fission in Crystalline Tetracene and Covalent Analogs
    Burdett, Jonathan J.; Bardeen, Christopher J.
    Accounts of Chemical Research (2013), 46 (6), 1312-1320CODEN: ACHRE4; ISSN:0001-4842. (American Chemical Society)
    A review. Singlet fission (SF) is a spin-allowed process in which an excited singlet state spontaneously splits into a pair of triplet excitons. This relaxation pathway is of interest as a mechanism for increasing the efficiency of photovoltaic solar cells, since ionization of the triplets could produce 2 charge carriers per absorbed photon. In this Account, the authors summarize recent work on trying to understand how SF occurs using both covalent and noncovalent assemblies of tetracene. The authors 1st give a brief overview of the SF process and discuss why tetracene, where the singlet and triplet pair energies are nearly degenerate, is a particularly useful mol. for studying this process. Then the authors describe expts., beginning with the study of phenylene-linked tetracene dimers as covalent analogs for the crystal form, where SF is known to be very efficient. Only 2-3% of the initially excited singlets underwent SF in these dimers. These results motivated one to study cryst. tetracene in more detail. Transient absorption and photoluminescence expts. on polycryst. thin films provided evidence for a delocalized singlet exciton that decays with a complicated temp.-dependence, but the authors were unable to unambiguously identify the signature of the triplet pair formed by SF. Then, using ultrathin single crystals, the authors obsd. quantum beats in the delayed fluorescence arising from recombination of spin-coherent triplet pairs. Analyzing these quantum beats revealed that SF proceeds through a direct 1-step process occurring within 200 ps at room temp. The product of this reaction is a pair of unperturbed triplets that have negligible interaction with each other. Looking at the overall SF process in tetracene, remaining issues that need to be clarified include the role of exciton diffusion, the temp. dependence of the SF rate, and how to use insights gained from the solid-state studies to generate design principles for high-efficiency covalent systems. Expts. provide a good illustration of why the polyacenes, and tetracene in particular, play an important role as systems for the study of SF.
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    Singlet exciton fission is a spin-allowed process in org. semiconductors by which one absorbed photon generates two triplet excitons. Theory predicts that singlet fission is mediated by intermol. charge-transfer states in solid-state materials with appropriate singlet-triplet energy spacing, but direct evidence for the involvement of such states in the process has not been provided yet. Here, we report on the observation of subpicosecond singlet fission in mixed films of pentacene and perfluoropentacene. By combining transient spectroscopy measurements to nonadiabatic quantum-dynamics simulations, we show that direct excitation in the charge-transfer absorption band of the mixed films leads to the formation of triplet excitons, unambiguously proving that they act as intermediate states in the fission process. (c) 2019 American Institute of Physics.
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    This account aims at providing an understanding of singlet fission, i.e., the photophys. process of a singlet state (S1) splitting into two triplet states (2 × T1) in mol. chromophores. A review. Since its discovery 50 years ago, the field of singlet fission has enjoyed rapid expansion in the past 8 years. However, there have been lingering confusion and debates on the nature of the all-important triplet pair intermediate states and the definition of singlet fission rates. Here we clarify the confusion from both theor. and exptl. perspectives. We distinguish the triplet pair state that maintains electronic coherence between the two constituent triplets, 1(TT), from one which does not, 1(T···T). Only the rate of formation of 1(T···T) is defined as that of singlet fission. We present distinct exptl. evidence for 1(TT), whose formation may occur via incoherent and/or vibronic coherent mechanisms. We discuss the challenges in treating singlet fission beyond the dimer approxn., in understanding the often neglected roles of delocalization on singlet fission rates, and in realizing the much lauded goal of increasing solar energy conversion efficiencies with singlet fission chromophores.
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    Direct Observation of a Charge-Transfer State Preceding High-Yield Singlet Fission in Terrylenediimide Thin Films
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    Journal of the American Chemical Society (2017), 139 (2), 663-671CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    Singlet exciton fission (SF) in org. chromophore assemblies results in the conversion of one singlet exciton (S1) into two triplet excitons (T1), provided that the overall process is exoergic, i.e., E(S1) > 2E(T1). We report on SF in thin polycryst. films of two terrylene-3,4:11,12-bis(dicarboximide) (TDI) derivs. 1 and 2, which crystallize into two distinct π-stacked structures. Femtosecond transient absorption spectroscopy (fsTA) reveals a charge-transfer state preceding a 190% T1 yield in films of 1, where the π-stacked TDI mols. are rotated by 23° along an axis perpendicular to their π systems. In contrast, when the TDI mols. are slip-stacked along their N-N axes in films of 2, fsTA shows excimer formation, followed by a 50% T1 yield.
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    The Quantum Coherent Mechanism for Singlet Fission: Experiment and Theory
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    Accounts of Chemical Research (2013), 46 (6), 1321-1329CODEN: ACHRE4; ISSN:0001-4842. (American Chemical Society)
    A review. The absorption of 1 photon by a semiconductor material usually creates 1 electron-hole pair. This general rule breaks down in a few org. semiconductors, such as pentacene and tetracene, where 1 photon absorption may result in 2 electron-hole pairs. This process, where a singlet exciton transforms to 2 triplet excitons, can have quantum yields ≤200%. Singlet fission may be useful to solar cell technols. to increase the power conversion efficiency beyond the so-called Shockley-Queisser limit. Through time-resolved 2-photon photoemission (TR-2PPE) spectroscopy in cryst. pentacene and tetracene, the lab. has recently provided the 1st spectroscopic signatures in singlet fission of a crit. intermediate known as the multiexciton state (also called a correlated triplet pair). Population of the multiexciton state rises at the same time as the singlet state on the ultrafast time scale upon photoexcitation. This observation does not fit with the traditional view of singlet fission involving the incoherent conversion of a singlet to a triplet pair. It provides an exptl. foundation for a quantum coherent mechanism in which the electronic coupling creates a quantum superposition of the singlet and the multiexciton state immediately after optical excitation. Key exptl. findings from TR-2PPE expts. are discussed, and a theor. anal. of the quantum coherent mechanism based on electronic structural and d. matrix calcns. for cryst. tetracene lattices is presented. Using multistate d. functional theory, the direct electronic coupling between singlet and multiexciton states is too weak to explain the exptl. observation. Indirect coupling via charge transfer intermediate states is 2 orders of magnitude stronger, and dominates the dynamics for ultrafast multiexciton formation. D. matrix calcn. for the cryst. tetracene lattice satisfactorily accounts for the exptl. observations. The crit. roles of the charge transfer states and the high dephasing rates in ensuring the ultrafast formation of multiexciton states are revealed. The origins of microscopic relaxation and dephasing rates are addressed, and these rates are adopted in a quantum master equation description. The need to take the theor. effort 1 step further in the near future is shown by combining high-level electronic structure calcns. with accurate quantum relaxation dynamics for large systems.
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    Advanced Functional Materials (2015), 25 (13), 2038-2046CODEN: AFMDC6; ISSN:1616-301X. (Wiley-VCH Verlag GmbH & Co. KGaA)
    Theory and expt. are combined to study the nature of low-energy excitons within ordered domains of 6,13-bis(triisopropylsilylethynyl)pentacene (TIPS-PEN) polycryst. thin films. First-principles d. functional theory and many-body perturbation theory calcns., along with polarization-dependent optical absorption spectromicroscopy on ordered domains, show multiple low-energy absorption peaks that are composed of excitonic states delocalized over several mols. While the 1st absorption peak is composed of a single excitonic transition and retains the polarization-dependent behavior of the mol., higher energy peaks are composed of multiple transitions with optical properties that can not be described by those of the mol. The predicted structure-dependence of polarization-dependent absorption reveals the exact inter-grain orientation within the TIPS-PEN film. The degree of exciton delocalization can be significantly tuned by modest changes in the solid-state structure and the spatial extent of the excitations along a given direction is correlated with the degree of electronic dispersion along the same direction. These findings pave the way for tailoring the singlet fission efficiency of org. crystals by solid-state structure.
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    Singlet fission is a spin-allowed process in which an excited singlet state evolves into two triplet states. We use femtosecond stimulated Raman spectroscopy, an ultrafast vibrational technique, to follow the mol. structural evolution during singlet fission in order to det. the mechanism of this process. In cryst. pentacene, we observe the formation of an intermediate characterized by pairs of excited state peaks that are red- and blue-shifted relative to the ground state features. We hypothesize that these features arise from the formation of cationic and anionic species due to partial transfer of electron d. from one pentacene mol. to a neighboring mol. These observations provide exptl. evidence for the role of states with significant charge-transfer character which facilitate the singlet fission process in pentacene. Our work both provides new insight into the singlet fission mechanism in pentacene and demonstrates the utility of structurally-sensitive time-resolved spectroscopic techniques in monitoring ultrafast processes.
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    Advanced Materials (Weinheim, Germany) (2008), 20 (3), 435-438CODEN: ADVMEW; ISSN:0935-9648. (Wiley-VCH Verlag GmbH & Co. KGaA)
    Two-terminal electronic devices, such as diodes and solar cells, based on a heterojunction structure incorporating a tetracene single crystal and a C60 thin film are fabricated. The photovoltaic devices demonstrate an external power conversion efficiency of ca. 0.34 % and a high open-circuit voltage of 0.57 V.
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    A review. The investigation of the microscopic processes underlying structural phase transformations in solids is extremely challenging for both simulation and expt. Atomistic simulations of solid-solid phase transitions require extensive sampling of the corresponding high-dimensional and often rugged energy landscape. Here, we propose a rigorous construction of a 1D path collective variable that is used in combination with enhanced sampling techniques for efficient exploration of the transformation mechanisms. The path collective variable is defined in a space spanned by global classifiers that are derived from local structural units. A reliable identification of the local structural environments is achieved by employing a neural-network-based classification scheme. The proposed path collective variable is generally applicable and enables the investigation of both transformation mechanisms and kinetics.
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  1. Marina Gerhard, Julian Hausch, Nico Hofeditz, Jona Bredehöft, Katharina Broch, Frank Schreiber. Singlet Fission in a Binary System: Effect of Structural Changes and Temperature. The Journal of Physical Chemistry C 2024, 128 (33) , 13926-13936. https://doi.org/10.1021/acs.jpcc.4c03155
  2. Xiaopeng Wang, Siyu Gao, Yiqun Luo, Xingyu Liu, Rithwik Tom, Kaiji Zhao, Vincent Chang, Noa Marom. Computational Discovery of Intermolecular Singlet Fission Materials Using Many-Body Perturbation Theory. The Journal of Physical Chemistry C 2024, 128 (19) , 7841-7864. https://doi.org/10.1021/acs.jpcc.4c01340
  3. Amit Kadan, Kevin Ryczko, Andrew Wildman, Rodrigo Wang, Adrian Roitberg, Takeshi Yamazaki. Accelerated Organic Crystal Structure Prediction with Genetic Algorithms and Machine Learning. Journal of Chemical Theory and Computation 2023, 19 (24) , 9388-9402. https://doi.org/10.1021/acs.jctc.3c00853
  4. Sourav Maiti, Laurens D. A. Siebbeles. Developments and Challenges Involving Triplet Transfer across Organic/Inorganic Heterojunctions for Singlet Fission and Photon Upconversion. The Journal of Physical Chemistry Letters 2023, 14 (49) , 11168-11176. https://doi.org/10.1021/acs.jpclett.3c03013
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  • Abstract

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    Figure 1

    Figure 1. Two experimentally observed forms of tetracene: (a) the common T1 polymorph (54) and (b) the second form, T2, (55) viewed along the c-axis with the molecules colored green and the T1 molecules colored black, overlaid using the Cambridge Crystallographic Data Centre (CCDC) packing similarity tool. (59) (c) Overlay of the molecules of the T1 form in gray and the T2 form in green.

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    Figure 2

    Figure 2. Overview of the inverse design workflow for finding putative molecular crystal polymorphs with improved SF performance. (a) Initial pool generation with Genarris. (b) GAtor runs are conducted using the traditional energy-based fitness function, the niching fitness function, and the SF+energy based fitness function. (c) Workflow of GAtor with the SF+energy based fitness function. (d) Postprocessing.

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    Figure 3

    Figure 3. (a) The minimum energy and (b) the maximum SF rate in the pool after each GAtor iteration for different fitness functions and crossover to mutation probabilities. The energy-based fitness does not improve the SF rate of the pool with GA iterations. The cross marks the (distorted) T1 structure.

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    Figure 4

    Figure 4. Evolutionary routes that produced the T1 experimental structure of tetracene in GA runs using different fitness functions and crossover probabilities. All routes start from initial pool structures. The packing motifs and space groups of all structures are also shown. The a-, b-, and c-axes are colored red, green, and blue, respectively.

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    Figure 5

    Figure 5. Evolutionary routes that produced the T2 experimental structure of tetracene in GA runs using different fitness functions and crossover probabilities. All routes start from initial pool structures. The packing motifs and space groups of all structures are also shown. The a-, b-, and c-axes are colored red, green, and blue, respectively.

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    Figure 6

    Figure 6. SF rates as a function of relative energy for the structures generated by GAtor runs with a crossover probability of 25% using (a) the energy-based fitness function, (b) evolutionary niching, and (c) the SF+energy-based fitness function. The red line denotes the polymorph range of 4 kJ/mol. The T1 and T2 polymorphs of tetracene are indicated by red and blue crosses, respectively. The relative energies presented here are as computed during the GAtor runs using PBE+TS with lower-level settings. Slight differences in the relaxed geometries at this level of theory produce somewhat different SF rates for the T1 and T2 structures generated in different GA runs.

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    Figure 7

    Figure 7. Lattice parameter distributions of the structures generated by GAtor runs with different fitness functions and 25% crossover to mutation probability. Panels a and b present the SF rate and relative energy, respectively, as a function of lattice parameters for the GA run using the energy-based fitness function. Panels c and d present the SF rate and relative energy, respectively, as a function of lattice parameters for the GA run using evolutionary niching. Panels e and f present the SF rate and relative energy, respectively, as a function of lattice parameters for the GA run using the SF+energy-based fitness function. The T1 and T2 polymorphs of tetracene are marked by red and blue crosses, respectively.

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    Figure 8

    Figure 8. Comparison of the highest SF dimers of different crystal structures viewed along directions of: (a) the in-plane long axis and (b) the in-plane short axis of the tetracene molecule. T1 is colored red. T2 is colored blue. The structure with the overall highest-rate SF dimer in the GA pool is colored lime green.

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    Figure 9

    Figure 9. Re-ranking of tetracene structures generated by GAtor using increasingly accurate DFT functionals and dispersion methods. Relative energies are referenced to the lowest-energy structure with each method. The experimental structures and some low-energy putative structures are also shown.

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    Figure 10

    Figure 10. (a) Putative polymorphs of tetracene compared to the T1 and T2 structures based on a two-dimensional descriptor calculated with GW+BSE. The thermodynamic driving force for SF, ES – 2ET, is displayed on the x-axis, and the singlet exciton charge transfer character, %CT, is displayed on the y-axis. The error bars represent the range of %CT values obtained using double-Bader analysis with the hole located at different sites. Exciton wave functions for (b) T1, (c) T2, and (d) P3 are also shown. The electron distribution is colored yellow with respect to the hole position colored in red.

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    Figure 11

    Figure 11. Absorption spectra of the T1, T2, and P3 structures computed using GW+BSE. The spectrum of T1 is compared with experimental data, adapted with permission from ref (140), Copyright 2008 John Wiley and Sons. The vertical lines denote the optical gap, which is equal to the lowest singlet excitation energy. The solar spectral energy distribution is also shown.

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    2. 2
      Schaller, R. D.; Klimov, V. I. High efficiency carrier multiplication in PbSe nanocrystals: implications for solar energy conversion. Phys. Rev. Lett. 2004, 92, 186601,  DOI: 10.1103/PhysRevLett.92.186601
      2
      High Efficiency Carrier Multiplication in PbSe Nanocrystals: Implications for Solar Energy Conversion
      Schaller, R. D.; Klimov, V. I.
      Physical Review Letters (2004), 92 (18), 186601/1-186601/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      Impact ionization (II) (the inverse of Auger recombination) occurs with very high efficiency in semiconductor nanocrystals (NCs). Interband optical excitation of PbSe NCs at low pump intensities, for which on av. less than one exciton is initially generated per NC, gave ≥2 excitons (carrier multiplication) when pump photon energies are >3 times the NC band gap energy. The generation of multi-excitons from a single photon absorption event occurs on a picosecond time scale with up to 100% efficiency, depending on the excess energy of the absorbed photon. Efficient II in NCs can be used to increase the power conversion efficiency of NC-based solar cells.
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    3. 3
      Hanna, M.; Nozik, A. Solar conversion efficiency of photovoltaic and photoelectrolysis cells with carrier multiplication absorbers. J. Appl. Phys. 2006, 100, 074510,  DOI: 10.1063/1.2356795
      3
      Solar conversion efficiency of photovoltaic and photoelectrolysis cells with carrier multiplication absorbers
      Hanna, M. C.; Nozik, A. J.
      Journal of Applied Physics (2006), 100 (7), 074510/1-074510/8CODEN: JAPIAU; ISSN:0021-8979. (American Institute of Physics)
      The max. power conversion efficiency for conversion of solar radiation to elec. power or to a flux of chem. free energy for H prodn. from H2O photoelectrolysis, was calcd. Several types of ideal absorbers were considered where absorption of one photon can produce more than one electron-hole pair that are based on semiconductor quantum dots with efficient multiple exciton generation (MEG) or mols. that undergo efficient singlet fission (SF). Using a detailed balance model with 1 sun AM1.5G illumination, for single gap photovoltaic (PV) devices the max. efficiency increases from 33.7% for cells with no carrier multiplication to 44.4% for cells with carrier multiplication. Also the max. efficiency of an ideal 2 gap tandem PV device increases from 45.7% to 47.7% when carrier multiplication absorbers are used in the top and bottom cells. For an ideal H2O electrolysis 2 gap tandem device, the max. conversion efficiency is 46.0% using a SF top cell and a MEG bottom cell vs. 40.0% for top and bottom cell absorbers with no carrier multiplication. Absorbers with less than ideal MEG quantum yields were obsd. exptl.
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    4. 4
      Smith, M. B.; Michl, J. Singlet fission. Chem. Rev. 2010, 110, 6891– 6936,  DOI: 10.1021/cr1002613
      4
      Singlet Fission
      Smith, Millicent B.; Michl, Josef
      Chemical Reviews (Washington, DC, United States) (2010), 110 (11), 6891-6936CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
      A review. A theory of singlet fission is discussed along with its relation to photovoltaics. The literature is reviewed dealing with singlet fission in org. chromophores from the time of initial discovery of singlet fission to the present day.
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    5. 5
      Smith, M. B.; Michl, J. Recent advances in singlet fission. Annu. Rev. Phys. Chem. 2013, 64, 361– 386,  DOI: 10.1146/annurev-physchem-040412-110130
      5
      Recent advances in singlet fission
      Smith, Millicent B.; Michl, Josef
      Annual Review of Physical Chemistry (2013), 64 (), 361-386CODEN: ARPLAP; ISSN:0066-426X. (Annual Reviews Inc.)
      A review. A survey is provided of recent progress in the understanding of singlet fission, a spin-allowed process in which a singlet excited mol. shares its energy with a ground-state neighbor to produce two triplet excited mols. It has been obsd. to occur in single-crystal, polycryst., and amorphous solids, on timescales from 80 fs to 25 ps, producing triplet yields as high as 200%. Photovoltaic devices using the effect have shown external quantum efficiencies in excess of 100%. Almost all the efficient materials are alternant hydrocarbons of the acene series or their simple derivs., and it is argued that a wider structural variety would be desirable. The current state of the development of mol. structure design rules, based on first-principles theor. considerations, is described along with initial examples of implementation.
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    6. 6
      Casanova, D. Theoretical Modeling of Singlet Fission. Chem. Rev. 2018, 118, 7164– 7207,  DOI: 10.1021/acs.chemrev.7b00601
      6
      Theoretical Modeling of Singlet Fission
      Casanova, David
      Chemical Reviews (Washington, DC, United States) (2018), 118 (15), 7164-7207CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
      A review. Singlet fission is a photophys. reaction in which a singlet excited electronic state splits into two spin-triplet states. Singlet fission was discovered more than 50 years ago, but the interest in this process has gained a lot of momentum in the past decade due to its potential as a way to boost solar cell efficiencies. This review presents and discusses the most recent advances with respect to the theor. and computational studies on the singlet fission phenomenon. The work revisits important aspects regarding electronic states involved in the process, the evaluation of fission rates and interstate couplings, the study of the excited state dynamics in singlet fission, and the advances in the design and characterization of singlet fission compds. and materials such as mol. dimers, polymers, or extended structures. Finally, the review tries to pinpoint some aspects that need further improvement and proposes future lines of research for theor. and computational chemists and physicists in order to further push the understanding and applicability of singlet fission.
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    7. 7
      Singh, S.; Jones, W.; Siebrand, W.; Stoicheff, B.; Schneider, W. Laser generation of excitons and fluorescence in anthracene crystals. J. Chem. Phys. 1965, 42, 330– 342,  DOI: 10.1063/1.1695695
      7
      Laser generation of excitons and fluorescence in anthracene crystals
      Singh, S.; Jones, W. J.; Siebrand, W.; Stoicheff, B. P.; Schneider, W. G.
      Journal of Chemical Physics (1965), 42 (1), 330-42CODEN: JCPSA6; ISSN:0021-9606.
      Exptl. and theoretical studies are reported of the short-lived and delayed fluorescence of anthracene single crystals, excited by single- and double-proton absorption. A giant-pulse ruby laser provides the primary source of radiation of 14,400 cm.-1 (up to 1027 photons/cm.2 sec.) and is also used to generate 2nd-harmonic radiation from adenosine 5'-diphosphate, as well as stimulated Raman radiation of 12,800 and 17,500 cm.-1 from liquid O. The time dependence of the fluorescence intensity is studied as a function of laser intensity, crystal temp., and excitation wavelength. The very intense fast fluorescence with a half-life of 30 nsec. at 300°K., characteristic of singlet exciton decay, and the relatively weak delayed fluorescence which involves intermediate triplet states, are sepd. by using sectored disks. The triplet state at 14,750 cm.-1 can be populated (1) by direct absorption of laser photons, involving an activation energy of 350 cm.-1; (2) via 2-photon absorption, presumably leading to a vibrationally excited state of the 1B2u exciton, followed by intersystem crossing; (3) via 1-photon (2nd-harmonic) excitation from levels ≥700 cm.-1 into the singlet absorption band, followed by conversion of the singlet exciton into a triplet pair. The latter process is suggested by the observed activation energy of 700 cm.-1 In agreement with these interpretations, the delayed fluorescence intensity varies with the 2nd to 4th power of the laser intensity, depending on the exptl. conditions. Also, light of 17,500 cm.-1 leads exclusively to process (1), light of 12,800 cm.-1 exclusively to (2). Triplet lifetimes from 2-17 msec. are obtained, depending on crystal purity, which indicates that unimol. triplet decay is an extrinsic, radiationless process. A singlet-triplet intersystem crossing rate const. of ∼3 × 10-5 sec.-1 is estd. The triplet-triplet annihilation rate const. is ∼5 × 10-11 cm.3 sec.-1 This value, considered together with the triplet-pair creation process, suggests a triplet exchange rate ⪆1013 sec.-1 and a triplet diffusion const. ⪆5 × 10-4 cm.2/sec.
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    8. 8
      Wilson, M. W.; Rao, A.; Johnson, K.; Gélinas, S.; Di Pietro, R.; Clark, J.; Friend, R. H. Temperature-independent singlet exciton fission in tetracene. J. Am. Chem. Soc. 2013, 135, 16680– 16688,  DOI: 10.1021/ja408854u
      8
      Temperature-Independent Singlet Exciton Fission in Tetracene
      Wilson, Mark W. B.; Rao, Akshay; Johnson, Kerr; Gelinas, Simon; di Pietro, Riccardo; Clark, Jenny; Friend, Richard H.
      Journal of the American Chemical Society (2013), 135 (44), 16680-16688CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      The authors use transient absorption spectroscopy to demonstrate that the dynamics of singlet exciton fission in tetracene are independent of temp. (10-270 K). Low-intensity, broad-band measurements allow the identification of spectral features while minimizing bimol. recombination. Hence, by directly observing both species, the time const. for the conversion of singlets to triplet pairs is ∼90 ps. However, in contrast to pentacene, where fission is effectively unidirectional, the emissive singlet in tetracene is readily regenerated from spin-correlated geminate triplets following fission, leading to equil. dynamics. Although free triplets are efficiently generated at room temp., the interplay of superradiance and frustrated triplet diffusion contributes to a nearly 20-fold increase in the steady-state fluorescence as the sample is cooled. Together, these results require that singlets and triplet pairs in tetracene are effectively degenerate in energy, and begin to reconcile the temp. dependence of many macroscopic observables with a fission process which does not require thermal activation.
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    9. 9
      Broch, K.; Dieterle, J.; Branchi, F.; Hestand, N.; Olivier, Y.; Tamura, H.; Cruz, C.; Nichols, V.; Hinderhofer, A.; Beljonne, D. Robust singlet fission in pentacene thin films with tuned charge transfer interactions. Nat. Commun. 2018, 9, 954,  DOI: 10.1038/s41467-018-03300-1
      9
      Robust singlet fission in pentacene thin films with tuned charge transfer interactions
      Broch K; Dieterle J; Hinderhofer A; Schreiber F; Broch K; Branchi F; Cerullo G; Hestand N J; Spano F C; Olivier Y; Beljonne D; Tamura H; Cruz C; Nichols V M; Bardeen C J; Beljonne D
      Nature communications (2018), 9 (1), 954 ISSN:.
      Singlet fission, the spin-allowed photophysical process converting an excited singlet state into two triplet states, has attracted significant attention for device applications. Research so far has focused mainly on the understanding of singlet fission in pure materials, yet blends offer the promise of a controlled tuning of intermolecular interactions, impacting singlet fission efficiencies. Here we report a study of singlet fission in mixtures of pentacene with weakly interacting spacer molecules. Comparison of experimentally determined stationary optical properties and theoretical calculations indicates a reduction of charge-transfer interactions between pentacene molecules with increasing spacer molecule fraction. Theory predicts that the reduced interactions slow down singlet fission in these blends, but surprisingly we find that singlet fission occurs on a timescale comparable to that in pure crystalline pentacene. We explain the observed robustness of singlet fission in such mixed films by a mechanism of exciton diffusion to hot spots with closer intermolecular spacings.
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    10. 10
      Sanders, S. N.; Kumarasamy, E.; Fallon, K. J.; Sfeir, M. Y.; Campos, L. M. Singlet fission in a hexacene dimer: energetics dictate dynamics. Chem. Sci. 2020, 11, 1079– 1084,  DOI: 10.1039/C9SC05066C
      10
      Singlet fission in a hexacene dimer: energetics dictate dynamics
      Sanders, Samuel N.; Kumarasamy, Elango; Fallon, Kealan J.; Sfeir, Matthew Y.; Campos, Luis M.
      Chemical Science (2020), 11 (4), 1079-1084CODEN: CSHCCN; ISSN:2041-6520. (Royal Society of Chemistry)
      Singlet fission (SF) is an exciton multiplication process with the potential to raise the efficiency limit of single junction solar cells from 33% to up to 45%. Most chromophores generally undergo SF as solid-state crystals. However, when such mols. are covalently coupled, the dimers can be used as model systems to study fundamental photophys. dynamics where a singlet exciton splits into two triplet excitons within individual mols. Here we report the synthesis and photophys. characterization of singlet fission of a hexacene dimer. Comparing the hexacene dimer to analogous tetracene and pentacene dimers reveals that excess exoergicity slows down singlet fission, similar to what is obsd. in mol. crystals. Conversely, the lower triplet energy of hexacene results in an increase in the rate of triplet pair recombination, following the energy gap law for radiationless transitions. These results point to design rules for singlet fission chromophores: the energy gap between singlet and triplet pair should be minimal, and the gap between triplet pair and ground state should be large.
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    11. 11
      Sun, D.; Deng, G.-H.; Xu, B.; Xu, E.; Li, X.; Wu, Y.; Qian, Y.; Zhong, Y.; Nuckolls, C.; Harutyunyan, A. R. Anisotropic singlet fission in single crystalline hexacene. Iscience 2019, 19, 1079– 1089,  DOI: 10.1016/j.isci.2019.08.053
      11
      Anisotropic Singlet Fission in Single Crystalline Hexacene
      Sun, Dezheng; Deng, Gang-Hua; Xu, Bolei; Xu, Enshi; Li, Xia; Wu, Yajing; Qian, Yuqin; Zhong, Yu; Nuckolls, Colin; Harutyunyan, Avetik R.; Dai, Hai-Lung; Chen, Gugang; Chen, Hanning; Rao, Yi
      iScience (2019), 19 (), 1079-1089CODEN: ISCICE; ISSN:2589-0042. (Elsevier B.V.)
      Singlet fission is known to improve solar energy utilization by circumventing the Shockley-Queisser limit. The two essential steps of singlet fission are the formation of a correlated triplet pair and its subsequent quantum decoherence. However, the mechanisms of the triplet pair formation and decoherence still remain elusive. Here we examd. both essential steps in single cryst. hexacene and discovered remarkable anisotropy of the overall singlet fission rate along different crystal axes. Since the triplet pair formation emerges on the same timescale along both crystal axes, the quantum decoherence is likely responsible for the directional anisotropy. The distinct quantum decoherence rates are ascribed to the notable difference on their assocd. energy loss according to the Redfield quantum dissipation theory. Our hybrid exptl./theor. framework will not only further our understanding of singlet fission, but also shed light on the systematic design of new materials for the third-generation solar cells.
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    12. 12
      Albrecht, W.; Michel-Beyerle, M.; Yakhot, V. Exciton fission in excimer forming crystal. Dynamics of an excimer build-up in α-perylene. Chem. Phys. 1978, 35, 193– 200,  DOI: 10.1016/0301-0104(78)85205-7
      12
      Exciton fission in excimer forming crystal. Dynamics of an excimer build-up in α-perylene
      Albrecht, W. G.; Michel-Beyerle, M. E.; Yakhot, V.
      Chemical Physics (1978), 35 (1-2), 193-200CODEN: CMPHC2; ISSN:0301-0104.
      The optically induced fission of singlet states in both α- and β-perylene crystals is investigated at room temp. In the monomeric β-perylene the fission threshold coincides with the energy of two triplet excitons whereas it is blue-shifted by ≈3500 cm-1 in the excimer forming α-crystal. This indicates that the excimer is formed prior to fission, emerging from the initially excited monomer state, and it implies that the rate of excimer formation kexc > 1012 s-1. Theor. ests. led to kexc ≈1013 s-1. Two adjacent perylene mols. in the α-crystal, each of them in the T1 electronic state, are bound with a binding energy B2T1 ≈350 cm-1.
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    13. 13
      Eaton, S. W.; Shoer, L. E.; Karlen, S. D.; Dyar, S. M.; Margulies, E. A.; Veldkamp, B. S.; Ramanan, C.; Hartzler, D. A.; Savikhin, S.; Marks, T. J. Singlet exciton fission in polycrystalline thin films of a slip-stacked perylenediimide. J. Am. Chem. Soc. 2013, 135, 14701– 14712,  DOI: 10.1021/ja4053174
      13
      Singlet exciton fission in polycrystalline thin films of a slip-stacked perylenediimide
      Eaton, Samuel W.; Shoer, Leah E.; Karlen, Steven D.; Dyar, Scott M.; Margulies, Eric A.; Veldkamp, Brad S.; Ramanan, Charusheela; Hartzler, Daniel A.; Savikhin, Sergei; Marks, Tobin J.; Wasielewski, Michael R.
      Journal of the American Chemical Society (2013), 135 (39), 14701-14712CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      The crystal structure of N,N-bis-(n-octyl)-2,5,8,11-tetraphenylperylene-3,4:9,10-bis-(dicarboximide), 1, obtained by X-ray diffraction reveals that 1 has a nearly planar perylene core and π-π stacks at a 3.5 Å interplanar distance in well-sepd. slip-stacked columns. Theory predicts that slip-stacked, π-π-stacked structures should enhance interchromophore electronic coupling and thus favor singlet exciton fission. Photoexcitation of vapor-deposited polycryst. 188 nm thick films of 1 results in a 140 ± 20% yield of triplet excitons (3*1) in τSF = 180 ± 10 ps. These results illustrate a design strategy for producing perylenediimide and related perylene derivs. that have the optimized interchromophore electronic interactions which promote high-yield singlet exciton fission for potentially enhancing org. solar cell performance and charge sepn. in systems for artificial photosynthesis.
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    14. 14
      Aulin, Y. V.; Felter, K. M.; Günbas, D. D.; Dubey, R. K.; Jager, W. F.; Grozema, F. C. Morphology-Independent Efficient Singlet Exciton Fission in Perylene Diimide Thin Films. ChemPlusChem. 2018, 83, 230– 238,  DOI: 10.1002/cplu.201700449
      14
      Morphology-Independent Efficient Singlet Exciton Fission in Perylene Diimide Thin Films
      Aulin, Yaroslav V.; Felter, Kevin M.; Guenbas, D. Deniz; Dubey, Rajeev K.; Jager, Wolter F.; Grozema, Ferdinand C.
      ChemPlusChem (2018), 83 (4), 230-238CODEN: CHEMM5; ISSN:2192-6506. (Wiley-VCH Verlag GmbH & Co. KGaA)
      Perylene diimides are conjugated chromophores that are of considerable interest owing to their ability to transform a singlet excited state into two triplets by singlet fission. Although singlet fission has previously been reported for certain perylene diimide derivs., there is some uncertainty about the rates and yield of the process in these materials. In this report, ultrafast transient absorption spectroscopy is used to demonstrate that singlet fission in perylene diimides can occur on a sub-picosecond timescale with quantum yields approaching the theor. limit of 200 %.
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    15. 15
      Hall, C. L.; Andrusenko, I.; Potticary, J.; Gao, S.; Liu, X.; Schmidt, W.; Marom, N.; Mugnaioli, E.; Gemmi, M.; Hall, S. R. 3D electron diffraction structure determination of terrylene, a promising candidate for intermolecular singlet fission. ChemPhysChem 2021, 22, 1631– 1637,  DOI: 10.1002/cphc.202100320
      15
      3D Electron Diffraction Structure Determination of Terrylene, a Promising Candidate for Intermolecular Singlet Fission
      Hall, Charlie L.; Andrusenko, Iryna; Potticary, Jason; Gao, Siyu; Liu, Xingyu; Schmidt, Werner; Marom, Noa; Mugnaioli, Enrico; Gemmi, Mauro; Hall, Simon R.
      ChemPhysChem (2021), 22 (15), 1631-1637CODEN: CPCHFT; ISSN:1439-4235. (Wiley-VCH Verlag GmbH & Co. KGaA)
      Herein we demonstrate the prowess of the 3D electron diffraction approach by unveiling the structure of terrylene, the third member in the series of peri-condensed naphthalene analogs, which has eluded structure detn. for 65 years. The structure was detd. by direct methods using electron diffraction data and corroborated by dispersion-inclusive d. functional theory optimizations. Terrylene crystalizes in the monoclinic space group P21/a, arranging in a sandwich-herringbone packing motif, similar to analogous compds. Having solved the crystal structure, we use many-body perturbation theory to evaluate the excited-state properties of terrylene in the solid-state. We find that terrylene is a promising candidate for intermol. singlet fission, comparable to tetracene and rubrene.
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    16. 16
      Johnson, J. C.; Nozik, A. J.; Michl, J. High triplet yield from singlet fission in a thin film of 1, 3-diphenylisobenzofuran. J. Am. Chem. Soc. 2010, 132, 16302– 16303,  DOI: 10.1021/ja104123r
      16
      High Triplet Yield from Singlet Fission in a Thin Film of 1,3-Diphenylisobenzofuran
      Johnson, Justin C.; Nozik, Arthur J.; Michl, Josef
      Journal of the American Chemical Society (2010), 132 (46), 16302-16303CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      Direct observation of triplet absorption and ground-state depletion upon pulsed excitation of a polycryst. thin solid film of 1,3-diphenylisobenzofuran at 77 K revealed a 200 ± 30% triplet yield, which was attributed to singlet fission.
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    17. 17
      Ryerson, J. L.; Schrauben, J. N.; Ferguson, A. J.; Sahoo, S. C.; Naumov, P.; Havlas, Z.; Michl, J.; Nozik, A. J.; Johnson, J. C. Two thin film polymorphs of the singlet fission compound 1, 3-diphenylisobenzofuran. J. Phys. Chem. C 2014, 118, 12121– 12132,  DOI: 10.1021/jp502122d
      17
      Two Thin Film Polymorphs of the Singlet Fission Compound 1,3-Diphenylisobenzofuran
      Ryerson, Joseph L.; Schrauben, Joel N.; Ferguson, Andrew J.; Sahoo, Subash Chandra; Naumov, Pance; Havlas, Zdenek; Michl, Josef; Nozik, Arthur J.; Johnson, Justin C.
      Journal of Physical Chemistry C (2014), 118 (23), 12121-12132CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
      Polycryst. thin films of 1,3-diphenylisobenzofuran (1) with a morphol. referred to here as α exhibit highly efficient singlet fission, producing two triplet states for every absorbed photon at 77 K, and about 1.4 triplet states per absorbed photon at room temp. However, the triplet yield depends strongly on the specific cryst. form of 1, and for the morphol. referred to as β the triplet yields are roughly an order of magnitude smaller. In this study, α, β, and mixed α/β films of 1 are prepd. by thermal evapn. and soln. drop-casting, and the structural and photophys. differences that may account for the very different triplet quantum yields are explored. The crystallites of 1 in thin films have been identified with two bulk crystal polymorphs grown from soln. and structurally characterized. Anal. of absorption spectra of the films reveals a 600 cm-1 blue shift in the onset and a unique spectral profile for the form α crystallites as compared to form β. Intermol. interactions between columns of slip-stacked mols. are different in the two polymorphs, and this likely gives rise to the much smaller triplet quantum yield for β-1.
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    18. 18
      Gradinaru, C. C.; Kennis, J. T.; Papagiannakis, E.; Van Stokkum, I. H.; Cogdell, R. J.; Fleming, G. R.; Niederman, R. A.; Van Grondelle, R. An unusual pathway of excitation energy deactivation in carotenoids: singlet-to-triplet conversion on an ultrafast timescale in a photosynthetic antenna. Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 2364– 2369,  DOI: 10.1073/pnas.051501298
      18
      An unusual pathway of excitation energy deactivation in carotenoids: singlet-to-triplet conversion on an ultrafast timescale in a photosynthetic antenna
      Gradinaru, Claudiu C.; Kennis, John T. M.; Papagiannakis, Emmanouil; Van Stokkum, Ivo H. M.; Cogdell, Richard J.; Fleming, Graham R.; Niederman, Robert A.; Van Grondelle, Rienk
      Proceedings of the National Academy of Sciences of the United States of America (2001), 98 (5), 2364-2369CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
      Carotenoids are important biomols. that are ubiquitous in nature and find widespread application in medicine. In photosynthesis, they have a large role in light harvesting (LH) and photoprotection. They exert their LH function by donating their excited singlet state to nearby (bacterio)chlorophyll mols. In photosynthetic bacteria, the efficiency of this energy transfer process can be as low as 30%. Here, evidence is presented that an unusual pathway of excited state relaxation in carotenoids underlies this poor LH function, by which carotenoid triplet states are generated directly from carotenoid singlet states. This pathway, operative on a femtosecond and picosecond timescale, involves an intermediate state, which was identified as a new, hitherto uncharacterized carotenoid singlet excited state. In LH complex-bound carotenoids, this state is the precursor on the reaction pathway to the triplet state, whereas in extd. carotenoids in soln., this state returns to the singlet ground state without forming any triplets. The authors discuss the possible identity of this excited state and argue that fission of the singlet state into a pair of triplet states on individual carotenoid mols. constitutes the mechanism by which the triplets are generated. This is, to our knowledge, the first ever direct observation of a singlet-to-triplet conversion process on an ultrafast timescale in a photosynthetic antenna.
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    19. 19
      Manawadu, D.; Valentine, D. J.; Marcus, M.; Barford, W. Singlet triplet-pair production and possible singlet-fission in carotenoids. J. Phys. Chem. Lett. 2022, 13, 1344– 1349,  DOI: 10.1021/acs.jpclett.1c03812
      19
      Singlet Triplet-Pair Production and Possible Singlet-Fission in Carotenoids
      Manawadu, Dilhan; Valentine, Darren J.; Marcus, Max; Barford, William
      Journal of Physical Chemistry Letters (2022), 13 (5), 1344-1349CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
      Internal conversion from the photoexcited state to a correlated singlet triplet-pair state is believed to be the precursor of singlet fission in carotenoids. We present numerical simulations of this process using a π-electron model that fully accounts for electron-electron interactions and electron-nuclear coupling. The time-evolution of the electrons is detd. rigorously using the time-dependent d. matrix renormalization group method, while the nuclei are evolved via the Ehrenfest equations of motion. We apply this to zeaxanthin, a carotenoid chain with 18 fully conjugated carbon atoms. We show that the internal conversion of the primary photoexcited state, S2, to the singlet triplet-pair state occurs adiabatically via an avoided crossing within ~ 50 fs with a yield of ~ 60%. We further discuss whether this singlet triplet-pair state will undergo exothermic vs. endothermic intra- or interchain singlet fission.
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    20. 20
      Musser, A. J.; Maiuri, M.; Brida, D.; Cerullo, G.; Friend, R. H.; Clark, J. The nature of singlet exciton fission in carotenoid aggregates. J. Am. Chem. Soc. 2015, 137, 5130– 5139,  DOI: 10.1021/jacs.5b01130
      20
      The Nature of Singlet Exciton Fission in Carotenoid Aggregates
      Musser, Andrew J.; Maiuri, Margherita; Brida, Daniele; Cerullo, Giulio; Friend, Richard H.; Clark, Jenny
      Journal of the American Chemical Society (2015), 137 (15), 5130-5139CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      Singlet exciton fission allows the fast and efficient generation of two spin triplet states from one photoexcited singlet. It has the potential to improve org. photovoltaics, enabling efficient coupling to the blue to UV region of the solar spectrum to capture the energy generally lost as waste heat. However, many questions remain about the underlying fission mechanism. The relation between intermol. geometry and singlet fission rate and yield is poorly understood and remains one of the most significant barriers to the design of new singlet fission sensitizers. Here the authors explore the structure-property relation and examine the mechanism of singlet fission in aggregates of astaxanthin, a small polyene. The authors isolate five distinct supramol. structures of astaxanthin generated through self-assembly in soln. Each is capable of undergoing intermol. singlet fission, with rates of triplet generation and annihilation that can be correlated with intermol. coupling strength. In contrast with the conventional model of singlet fission in linear mols., no intermediate states are involved in the triplet formation: instead, singlet fission occurs directly from the initial 1Bu photoexcited state on ultrafast time scales. This result demands a reevaluation of current theories of polyene photophysics and highlights the robustness of carotenoid singlet fission.
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    21. 21
      Beljonne, D.; Cornil, J.; Friend, R.; Janssen, R.; Brédas, J.-L. Influence of chain length and derivatization on the lowest singlet and triplet states and intersystem crossing in oligothiophenes. J. Am. Chem. Soc. 1996, 118, 6453– 6461,  DOI: 10.1021/ja9531135
      21
      Influence of Chain Length and Derivatization on the Lowest Singlet and Triplet States and Intersystem Crossing in Oligothiophenes
      Beljonne, D.; Cornil, J.; Friend, R. H.; Janssen, R. A. J.; Bredas, J. L.
      Journal of the American Chemical Society (1996), 118 (27), 6453-6461CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      On the basis of CI calcns., we first describe the nature of the lowest singlet and triplet excited states in oligothiophenes ranging in size from two to six rings. We calc. the vertical excitation energies from the singlet ground state S0 to the first one-photon allowed singlet excited state S1 as well as the energy difference between the ground state and the lowest triplet state T1. The computed transition energies are in very good agreement with the measured values and indicate a strong confinement of the lowest triplet. We also uncover the nature of the higher-lying triplet excited state Tn that is coupled via a large oscillator strength to T1. The evolution with chain length of the T1-Tn excitation energies compares well with the exptl. evolution based on photoinduced absorption data. Next, we investigate the geometry relaxation phenomena occurring in the S1 and T1 states; more pronounced and localized bond-length deformations are calcd. in the triplet state than in the singlet, confirming the more localized character of T1. We also analyze the influence on the lowest excited states of grafting electroactive end-groups on the conjugated path of terthiophene. Finally, the various mechanisms involved in the nonradiative decay of the singlet excitations are discussed, and results are presented as a guide toward the optimization of light emission efficiency in conjugated systems.
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    22. 22
      Busby, E.; Xia, J.; Low, J. Z.; Wu, Q.; Hoy, J.; Campos, L. M.; Sfeir, M. Y. Fast singlet exciton decay in push-pull molecules containing oxidized thiophenes. J. Phys. Chem. B 2015, 119, 7644– 7650,  DOI: 10.1021/jp511704r
      22
      Fast Singlet Exciton Decay in Push-Pull Molecules Containing Oxidized Thiophenes
      Busby, Erik; Xia, Jianlong; Low, Jonathan Z.; Wu, Qin; Hoy, Jessica; Campos, Luis M.; Sfeir, Matthew Y.
      Journal of Physical Chemistry B (2015), 119 (24), 7644-7650CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
      A common synthetic strategy used to design low-bandgap org. semiconductors employs the use of push-pull building blocks, where electron -rich and electron-deficient monomers are alternated along the π-conjugated backbone of a mol. or polymer. Incorporating strong pull units with high electron affinity is a means to further decrease the optical gap for IR optoelectronics or to develop n-type semiconducting materials. The use of thiophene-1,1-dioxide as a strong acceptor in push-pull oligomers affects the electronic structure and carrier dynamics in unexpected ways. Critically, the overall excited-state lifetime is reduced by several orders of magnitude relative to unoxidized analogs due to the introduction of low-energy optically dark states and low-energy triplet states that allow for fast internal conversion and intramol. singlet fission. The electronic structure and excited-state lifetime are strongly dependent on the no. of sequential thiophene-1,1-dioxide units. Probably both the static and dynamical optical properties are highly tunable via small changes in chem. structure that have drastic effects on the optoelectronic properties, which can impact the types of applications that involve these materials.
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    23. 23
      Dean, J. C.; Zhang, R.; Hallani, R. K.; Pensack, R. D.; Sanders, S. N.; Oblinsky, D. G.; Parkin, S. R.; Campos, L. M.; Anthony, J. E.; Scholes, G. D. Photophysical characterization and time-resolved spectroscopy of a anthradithiophene dimer: exploring the role of conformation in singlet fission. Phys. Chem. Chem. Phys. 2017, 19, 23162– 23175,  DOI: 10.1039/C7CP03774K
      23
      Photophysical characterization and time-resolved spectroscopy of a anthradithiophene dimer: exploring the role of conformation in singlet fission
      Dean, Jacob C.; Zhang, Ruomeng; Hallani, Rawad K.; Pensack, Ryan D.; Sanders, Samuel N.; Oblinsky, Daniel G.; Parkin, Sean R.; Campos, Luis M.; Anthony, John E.; Scholes, Gregory D.
      Physical Chemistry Chemical Physics (2017), 19 (34), 23162-23175CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
      Quant. singlet fission has been obsd. for a variety of acene derivs. such as tetracene and pentacene, and efforts to extend the library of singlet fission compds. is of current interest. Preliminary calcns. suggest anthradithiophenes exhibit significant exothermicity between the first optically-allowed singlet state, S1, and 2 × T1 with an energy difference of >5000 cm-1. Given the fulfillment of this ingredient for singlet fission, here we investigate the singlet fission capability of a difluorinated anthradithiophene dimer (2ADT) covalently linked by a (dimethylsilyl)ethane bridge and derivatized by triisobutylsilylethynyl (TIBS) groups. Photophys. characterization of 2ADT and the single functionalized ADT monomer were carried out in toluene and acetone soln. via absorption and fluorescence spectroscopy, and their photo-initiated dynamics were investigated with time-resolved fluorescence (TRF) and transient absorption (TA) spectroscopy. In accordance with computational predictions, two conformers of 2ADT were obsd. via fluorescence spectroscopy and were assigned to structures with the ADT cores trans or cis to one another about the covalent bridge. The two conformers exhibited markedly different excited state deactivation mechanisms, with the minor trans population being representative of the ADT monomer showing primarily radiative decay, while the dominant cis population underwent relaxation into an excimer geometry before internally converting to the ground state. The excimer formation kinetics were found to be solvent dependent, yielding time consts. of ∼1.75 ns in toluene, and ∼600 ps in acetone. While the difference in rates elicits a role for the solvent in stabilizing the excimer structure, the rate is still decidedly long compared to most singlet fission rates of analogous dimers, suggesting that the excimer is neither a kinetic nor a thermodn. trap, yet singlet fission was still not obsd. The result highlights the sensitivity of the electronic coupling element between the singlet and correlated triplet pair states, to the dimer conformation in dictating singlet fission efficiency even when the energetic requirements are met.
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    24. 24
      Zhao, T.; Kloc, C.; Ni, W.; Sun, L.; Gurzadyan, G. G. Revealing ultrafast relaxation dynamics in six-thiophene thin film and single crystal. J. Photochem. Photobiol. A: Chem. 2021, 404, 112920,  DOI: 10.1016/j.jphotochem.2020.112920
      24
      Revealing ultrafast relaxation dynamics in six-thiophene thin film and single crystal
      Zhao, Tongyu; Kloc, Christian; Ni, Wenjun; Sun, Licheng; Gurzadyan, Gagik G.
      Journal of Photochemistry and Photobiology, A: Chemistry (2021), 404 (), 112920CODEN: JPPCEJ; ISSN:1010-6030. (Elsevier B.V.)
      The excited state dynamics of six-thiophene (6T) thin film and single crystal was studied by time-resolved fluorescence and femtosecond transient absorption techniques under different excitation conditions. The dominant process in 6T system is the generation of ion pairs, dissocd. to polarons staying for up to 130-3700 ns in film and 1 ms in crystal. Singlet fission (SF) was directly obsd. from the upper vibrational levels of the first excited singlet state S1 in 6T thin film/single crystal within 30 fs, which competes with intramol. vibrational relaxation. Triplet state lifetime is dramatically shortened from 6T single crystal (1 ms) to thin film (4 ns) due to triplet-triplet annihilation, which is influenced by structural defects in amorphous regions of 6T film. Compared with 6T crystal, the partially ordered semicryst. morphol. of 6T film suggests the impact of well-structured crystallinity and mol. packing on the photocarriers transport dynamics and lifetime of triplet state. Moreover, excitation to upper excited singlet state (4.96 eV) leads to a higher yield of polarons (factor of 4), while SF in film/crystal is fully suppressed. Existence of long-lived photogenerated polarons may count π-conjugated oligomers as promising materials for developing org.-mol.-based optoelectronic devices.
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    25. 25
      Sharifzadeh, S.; Darancet, P.; Kronik, L.; Neaton, J. B. Low-energy charge-transfer excitons in organic solids from first-principles: The case of pentacene. J. Phys. Chem. Lett. 2013, 4, 2197– 2201,  DOI: 10.1021/jz401069f
      25
      Low-Energy Charge-Transfer Excitons in Organic Solids from First-Principles: The Case of Pentacene
      Sharifzadeh, Sahar; Darancet, Pierre; Kronik, Leeor; Neaton, Jeffrey B.
      Journal of Physical Chemistry Letters (2013), 4 (13), 2197-2201CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
      The nature of low energy optical excitations, or excitons, in org. solids is of central relevance to many optoelectronic applications, including solar energy conversion. Excitons in solid pentacene, a prototypical org. semiconductor, have been the subject of many exptl. and theor. studies, with differing conclusions as to the degree of their charge-transfer character. Using first-principles calcns. based on d. functional theory and many-body perturbation theory, the authors compute the av. electron-hole distance and quantify the degree of charge-transfer character within optical excitations in solid-state pentacene. The authors show that several low-energy singlet excitations are characterized by a weak overlap between electron and hole and an av. electron-hole distance greater than 6 Å. Addnl., the authors show that the character of the lowest-lying singlet and triplet excitons is well-described with a simple analytic envelope function of the electron-hole distance.
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    26. 26
      Beljonne, D.; Yamagata, H.; Brédas, J.-L.; Spano, F.; Olivier, Y. Charge-transfer excitations steer the Davydov splitting and mediate singlet exciton fission in pentacene. Phys. Rev. Lett. 2013, 110, 226402,  DOI: 10.1103/PhysRevLett.110.226402
      26
      Charge-transfer excitations steer the Davydov splitting and mediate singlet exciton fission in pentacene
      Beljonne, D.; Yamagata, H.; Bredas, J. L.; Spano, F. C.; Olivier, Y.
      Physical Review Letters (2013), 110 (22), 226402/1-226402/5CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      Quantum-chem. calcns. are combined to a model Frenkel-Holstein Hamiltonian to assess the nature of the lowest electronic excitations in the pentacene crystal. We show that an admixt. of charge-transfer excitations into the lowest singlet excited states form the origin of the Davydov splitting and mediate instantaneous singlet exciton fission by direct optical excitation of coherently coupled single and double exciton states, in agreement with recent expts.
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    27. 27
      Wang, X.; Liu, X.; Tom, R.; Cook, C.; Schatschneider, B.; Marom, N. Phenylated acene derivatives as candidates for intermolecular singlet fission. J. Phys. Chem. C 2019, 123, 5890– 5899,  DOI: 10.1021/acs.jpcc.8b12549
      27
      Phenylated Acene Derivatives as Candidates for Intermolecular Singlet Fission
      Wang, Xiaopeng; Liu, Xingyu; Tom, Rithwik; Cook, Cameron; Schatschneider, Bohdan; Marom, Noa
      Journal of Physical Chemistry C (2019), 123 (10), 5890-5899CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
      Singlet fission (SF), a spin-conserving process where one singlet exciton is converted into two triplet excitons, may improve the efficiency of org. photovoltaics. Only a few materials have been exptl. obsd. to undergo intermol. SF, most of which are acenes and their derivs. Using many-body perturbation theory in the GW approxn. and the Bethe-Salpeter equation, we systematically investigate the electronic and excitonic properties of tetracene, pentacene, and their phenylated derivs. in the gas phase and solid state. Their potential for SF is evaluated with respect to the thermodn. driving force and the singlet exciton charge-transfer character. In both the gas phase and solid state, pentacene and its derivs. are more promising than tetracene analogs. Within a family of mols. contg. the same acene backbone, increasing the no. of Ph side groups is detrimental for the SF driving force in the gas phase. However, in the solid state, the SF driving force and the exciton character are modulated by intermol. interactions present within different packing arrangements. Mols. with a higher no. of Ph side groups often form crystals with less cofacial interactions between the acene backbones. These crystals are found to exhibit a higher SF driving force and a higher degree of singlet exciton charge-transfer character. In particular, 5,7,12,14-tetraphenylpentacene, 1,4,6,8,11,13-hexaphenylpentacene, and 1,2,3,4,6,8,9,10,11,13-decaphenylpentacene emerge as promising candidates for intermol. SF in the solid state.
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    28. 28
      Wang, X.; Liu, X.; Cook, C.; Schatschneider, B.; Marom, N. On the possibility of singlet fission in crystalline quaterrylene. J. Chem. Phys. 2018, 148, 184101,  DOI: 10.1063/1.5027553
      28
      On the possibility of singlet fission in crystalline quaterrylene
      Wang, Xiaopeng; Liu, Xingyu; Cook, Cameron; Schatschneider, Bohdan; Marom, Noa
      Journal of Chemical Physics (2018), 148 (18), 184101/1-184101/10CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      Singlet fission (SF), the spontaneous down-conversion of a singlet exciton into two triplet excitons residing on neighboring mols., is a promising route to improve org. photovoltaic (OPV) device efficiencies by harvesting two charge carriers from one photon. However, only a few materials have been discovered that exhibit intermol. SF in the solid state, most of which are acene derivs. Recently, there has been a growing interest in rylenes as potential SF materials. We use many-body perturbation theory in the GW approxn. and the Bethe-Salpeter equation to investigate the possibility of intermol. SF in cryst. perylene and quaterrylene. A new method is presented for detg. the percent charge transfer (%CT) character of an exciton wave-function from double-Bader anal. This enables relating exciton probability distributions to crystal packing. Based on comparison to known and predicted SF materials with respect to the energy conservation criterion (ES-2ET) and %CT, cryst. quaterrylene is a promising candidate for intermol. SF. Furthermore, quaterrylene is attractive for OPV applications, thanks to its high stability and narrow optical gap. Perylene is not expected to exhibit SF; however, it is a promising candidate for harvesting sub-gap photons by triplet-triplet annihilation. (c) 2018 American Institute of Physics.
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    29. 29
      Monahan, N.; Zhu, X.-Y. Charge transfer–mediated singlet fission. Annu. Rev. Phys. Chem. 2015, 66, 601– 618,  DOI: 10.1146/annurev-physchem-040214-121235
      29
      Charge transfer-mediated singlet fission
      Monahan, N.; Zhu, X.-Y.
      Annual Review of Physical Chemistry (2015), 66 (), 601-618CODEN: ARPLAP; ISSN:0066-426X. (Annual Reviews)
      Singlet fission, the splitting of a singlet exciton into two triplet excitons in mol. materials, is interesting not only as a model many-electron problem, but also as a process with potential applications in solar energy conversion. Here we discuss limitations of the conventional four-electron and mol. dimer model in describing singlet fission in cryst. org. semiconductors, such as pentacene and tetracene. We emphasize the need to consider electronic delocalization, which is responsible for the decisive role played by the Mott-Wannier exciton, also called the charge transfer (CT) exciton, in mediating singlet fission. At the strong electronic coupling limit, the initial excitation creates a quantum superposition of singlet, CT, and triplet-pair states, and we present exptl. evidence for this interpretation. We also discuss the most recent attempts at translating this mechanistic understanding into design principles for CT state-mediated intramol. singlet fission in oligomers and polymers.
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    30. 30
      Rao, A.; Friend, R. H. Harnessing singlet exciton fission to break the Shockley–Queisser limit. Nat. Rev. Mater. 2017, 2, 17063,  DOI: 10.1038/natrevmats.2017.63
      30
      Harnessing singlet exciton fission to break the Shockley-Queisser limit
      Rao, Akshay; Friend, Richard H.
      Nature Reviews Materials (2017), 2 (11), 17063CODEN: NRMADL; ISSN:2058-8437. (Nature Research)
      A review. Singlet exciton fission is a carrier multiplication process in org. semiconductors that generates two electron-hole pairs for each photon absorbed. Singlet fission occurs on sub-100 fs timescales with yields of up to 200%, and photovoltaic devices based on singlet fission have achieved external quantum efficiencies above 100%. The major challenge for the field is to use singlet fission to improve the efficiency of conventional inorg. solar cells, such as silicon, and to break the Shockley-Queisser limit on the efficiency of single-junction photovoltaics. Achieving this goal requires a broader and more collaborative effort than the one used at present. Synthetic chemists, spectroscopists, theorists, materials scientists, device physicists and engineers will need to work together. In this Review, we critically assess the current status of the field, highlight the key results and identify the challenges ahead. In doing so, we seek to open the field to new expertise and ideas, which will in turn promote both fundamental science and device applications.
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    31. 31
      Lu, H.; Chen, X.; Anthony, J. E.; Johnson, J. C.; Beard, M. C. Sensitizing singlet fission with perovskite nanocrystals. J. Am. Chem. Soc. 2019, 141, 4919– 4927,  DOI: 10.1021/jacs.8b13562
      31
      Sensitizing singlet fission with perovskite nanocrystals
      Lu, Haipeng; Chen, Xihan; Anthony, John E.; Johnson, Justin C.; Beard, Matthew C.
      Journal of the American Chemical Society (2019), 141 (12), 4919-4927CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      The marriage of colloidal semiconductor nanocrystals and functional org. mols. has brought unique opportunities in emerging photonic and optoelectronic applications. Traditional semiconductor nanocrystals have been widely demonstrated to initiate efficient triplet energy transfer at the nanocrystal-acene interface. Herein, we report that unlike conventional semiconductor nanocrystals, lead halide perovskite nanocrystals promote an efficient Dexter-like singlet energy transfer to surface-anchored pentacene mols. rather than triplet energy transfer. Subsequently, mol. pentacene triplets are efficiently generated via singlet fission on the nanocrystal surface. Our demonstrated strategy not only unveils the obscure energy dynamics between perovskite nanocrystal and acenes, but also brings important perspectives of utilizing singlet fission throughout the solar spectrum.
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    32. 32
      Budden, P. J.; Weiss, L. R.; Müller, M.; Panjwani, N. A.; Dowland, S.; Allardice, J. R.; Ganschow, M.; Freudenberg, J.; Behrends, J.; Bunz, U. H. Singlet exciton fission in a modified acene with improved stability and high photoluminescence yield. Nat. Commun. 2021, 12, 1527,  DOI: 10.1038/s41467-021-21719-x
      32
      Singlet exciton fission in a modified acene with improved stability and high photoluminescence yield
      Budden, Peter J.; Weiss, Leah R.; Muller, Matthias; Panjwani, Naitik A.; Dowland, Simon; Allardice, Jesse R.; Ganschow, Michael; Freudenberg, Jan; Behrends, Jan; Bunz, Uwe H. F.; Friend, Richard H.
      Nature Communications (2021), 12 (1), 1527CODEN: NCAOBW; ISSN:2041-1723. (Nature Research)
      We report a fully efficient singlet exciton fission material with high ambient chem. stability. 10,21-Bis(triisopropylsilylethynyl)tetrabenzo[a,c,l,n]pentacene (TTBP) combines an acene core with triphenylene wings that protect the formal pentacene from chem. degrdn. The electronic energy levels position singlet exciton fission to be endothermic, similar to tetracene despite the triphenylenes. TTBP exhibits rapid early time singlet fission with quant. yield of triplet pairs within 100 ps followed by thermally activated sepn. to free triplet excitons over 65 ns. TTBP exhibits high photoluminescence quantum efficiency, close to 100% when dil. and 20% for solid films, arising from triplet-triplet annihilation. In using such a system for exciton multiplication in a solar cell, max. thermodn. performance requires radiative decay of the triplet population, obsd. here as emission from the singlet formed by recombination of triplet pairs. Combining chem. stabilization with efficient endothermic fission provides a promising avenue towards singlet fission materials for use in photovoltaics.
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    33. 33
      Liu, X.; Tom, R.; Gao, S.; Marom, N. Assessing zethrene derivatives as singlet fission candidates based on multiple descriptors. J. Phys. Chem. C 2020, 124, 26134– 26143,  DOI: 10.1021/acs.jpcc.0c08160
      33
      Assessing Zethrene Derivatives as Singlet Fission Candidates Based on Multiple Descriptors
      Liu, Xingyu; Tom, Rithwik; Gao, Siyu; Marom, Noa
      Journal of Physical Chemistry C (2020), 124 (48), 26134-26143CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
      Singlet fission (SF) is a process where one singlet exciton splits into two triplet excitons. Utilizing SF may potentially increase the efficiency of solar cells beyond the Shockley-Queisser limit. To discover new SF materials, predictive descriptors for SF performance are needed. We consider multiple descriptors to assess several zethrene derivs. as candidate materials for intermol. SF in the solid state. The descriptors include single mol. multiradical characters, many-body perturbation theory calcns. of the thermodn. driving force for SF and the singlet exciton charge transfer character in crystals, and a kinetic model based on mol. dimers extd. from the crystal structures. The zethrenes are compared to acenes known to exhibit SF with respect to these descriptors. The results indicate that all zethrene and heptazethrene derivs. studied here may exhibit SF. In particular, 7,14-bis(2,4,6-trimethylphenyl)dibenzo[de,mn]naphthacene (Z-T) emerges as a promising candidate. Its SF driving force is higher than tetracene, whose fission process is slightly endoergic, but lower than pentacene. Its singlet exciton charge transfer character is close to pentacene, and its crystal packing leads to a higher SF rate than other zethrene derivs. Therefore, it may undergo fast SF with high energy efficiency. The approach of considering multiple descriptors may be useful for evaluating addnl. candidate materials for SF.
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    34. 34
      Liu, X.; Tom, R.; Wang, X.; Cook, C.; Schatschneider, B.; Marom, N. Pyrene-stabilized acenes as intermolecular singlet fission candidates: importance of exciton wave-function convergence. J. Phys.: Condens. Matter 2020, 32, 184001,  DOI: 10.1088/1361-648X/ab699e
      34
      Pyrene-stabilized acenes as intermolecular singlet fission candidates: importance of exciton wave-function convergence
      Liu, Xingyu; Tom, Rithwik; Wang, Xiaopeng; Cook, Cameron; Schatschneider, Bohdan; Marom, Noa
      Journal of Physics: Condensed Matter (2020), 32 (18), 184001CODEN: JCOMEL; ISSN:0953-8984. (IOP Publishing Ltd.)
      Singlet fission (SF) is a photophys. process considered as a possible scheme to bypass the Shockley-Queisser limit by generating two triplet-state excitons from one high-energy photon. Polyacene crystals, such as tetracene and pentacene, have shown outstanding SF performance both theor. and exptl. However, their instability prevents them from being utilized in SF-based photovoltaic devices. In search of practical SF chromophores, we use many-body perturbation theory within the GW approxn. and Bethe-Salpeter equation to study the excitonic properties of a family of pyrene-stabilized acenes. We propose a criterion to define the convergence of exciton wave-functions with respect to the fine k-point grid used in the BerkeleyGW code. An open-source Python code is presented to perform exciton wave-function convergence checks and streamline the double Bader anal. of exciton character. We find that the singlet excitons in pyrene-stabilized acenes have a higher degree of charge transfer character than in the corresponding acenes. The pyrene-fused tetracene and pentacene derivs. exhibit comparable excitation energies to their corresponding acenes, making them potential SF candidates. The pyrene-stabilized anthracene deriv. is considered as a possible candidate for triplet-triplet annihilation because it yields a lower SF driving force than anthracene.
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    35. 35
      Wang, X.; Garcia, T.; Monaco, S.; Schatschneider, B.; Marom, N. Effect of crystal packing on the excitonic properties of rubrene polymorphs. CrystEngComm 2016, 18, 7353– 7362,  DOI: 10.1039/C6CE00873A
      35
      Effect of crystal packing on the excitonic properties of rubrene polymorphs
      Wang, Xiaopeng; Garcia, Taylor; Monaco, Stephen; Schatschneider, Bohdan; Marom, Noa
      CrystEngComm (2016), 18 (38), 7353-7362CODEN: CRECF4; ISSN:1466-8033. (Royal Society of Chemistry)
      Singlet fission (SF), the conversion of one singlet exciton into two triplet excitons, may lead to the realization of high efficiency org. photovoltaics by generating two carriers from one photon. Recently, SF has been obsd. in mol. crystals of rubrene. While the orthorhombic form of rubrene is most often obsd. under ambient conditions, metastable monoclinic and triclinic polymorphs are known. Here, dispersion-inclusive d. functional theory (DFT) is used to investigate the relative stability of all three phases. Many-body perturbation theory is then employed to study the effect of crystal structure on the electronic and excitonic properties. Band structures are calcd. within the GW approxn. and optical properties are calcd. by solving the Bethe-Salpeter equation (BSE). We find that crystal packing significantly affects the electronic and excitonic properties of rubrene. Based on our calcns., the triclinic and esp. the monoclinic forms of rubrene are expected to exhibit higher SF efficiencies than the orthorhombic form.
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    36. 36
      Liu, X.; Wang, X.; Gao, S.; Chang, V.; Tom, R.; Yu, M.; Ghiringhelli, L. M.; Marom, N. Finding predictive models for singlet fission by machine learning. npj Comput. Mater. 2022, 8, 70,  DOI: 10.1038/s41524-022-00758-y
      There is no corresponding record for this reference.
    37. 37
      Minami, T.; Nakano, M. Diradical character view of singlet fission. J. Phys. Chem. Lett. 2012, 3, 145– 150,  DOI: 10.1021/jz2015346
      37
      Diradical Character View of Singlet Fission
      Minami, Takuya; Nakano, Masayoshi
      Journal of Physical Chemistry Letters (2012), 3 (2), 145-150CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
      The feasibility conditions of singlet fission on the excitation energy differences are revealed as functions of the multiple diradical characters yi [defined by the occupation nos. of the LUNO (= Lowest Unoccupied Natural Orbital) + i (i = 0, 1, ...), where 0 ≤ yi ≤ 1 and yi ≥ yj (i > j)] using the linear H4 full CI model. The diradical characters suited for singlet fission are found to lie in the region with y0 > 0.10 except for y0 ∼ y1, though its energy efficiency is better in case of smaller y0, to which diradical and multiradical compds. with low/intermediate diradical characters such as open-shell singlet polycyclic arom. hydrocarbons belong. These findings indicate that the multiple diradical character is an effective indicator for exploring mol. systems for efficient singlet fission.
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    38. 38
      Padula, D.; Omar, Ö. H.; Nematiaram, T.; Troisi, A. Singlet fission molecules among known compounds: finding a few needles in a haystack. Energy Environ. Sci. 2019, 12, 2412– 2416,  DOI: 10.1039/C9EE01508F
      There is no corresponding record for this reference.
    39. 39
      Nogueira, B. A.; Castiglioni, C.; Fausto, R. Color polymorphism in organic crystals. Commun. Chem. 2020, 3, 34,  DOI: 10.1038/s42004-020-0279-0
      39
      Color polymorphism in organic crystals
      Nogueira Bernardo A; Fausto Rui; Nogueira Bernardo A; Castiglioni Chiara; Fausto Rui
      Communications chemistry (2020), 3 (1), 34 ISSN:.
      Color polymorphism is an interesting property of chemical systems which present crystal polymorphs of different colors. It is a rare phenomenon, with only a few examples reported in the literature hitherto. Nevertheless, systems exhibiting color polymorphism have many potential applications in different domains, such as pigment, sensor, and technology industries. Here, known representative chemical systems showing color polymorphism are reviewed, and the reasons for them to present such property discussed. Also, since some of the concepts related to color polymorphism have been frequently used imprecisely in the scientific literature, this article provides concise, systematic definitions for these concepts.
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    40. 40
      Moliterni, A.; Altamura, D.; Lassandro, R.; Olieric, V.; Ferri, G.; Cardarelli, F.; Camposeo, A.; Pisignano, D.; Anthony, J. E.; Giannini, C. Synthesis, crystal structure, polymorphism and microscopic luminescence properties of anthracene derivative compounds. Acta. Crystallogr. B Struct. Sci. Cryst. Eng. Mater. 2020, 76, 427– 435,  DOI: 10.1107/S2052520620004424
      40
      Synthesis, crystal structure, polymorphism and microscopic luminescence properties of anthracene derivative compounds
      Moliterni, Anna; Altamura, Davide; Lassandro, Rocco; Olieric, Vincent; Ferri, Gianmarco; Cardarelli, Francesco; Camposeo, Andrea; Pisignano, Dario; Anthony, John E.; Giannini, Cinzia
      Acta Crystallographica, Section B: Structural Science, Crystal Engineering and Materials (2020), 76 (3), 427-435CODEN: ACSBDA; ISSN:2052-5206. (International Union of Crystallography)
      Anthracene deriv. compds. are currently investigated because of their unique phys. properties (e.g. bright luminescence and emission tunability), which make them ideal candidates for advanced optoelectronic devices. Intermol. interactions are the basis of the tunability of the optical and electronic properties of these compds., whose prediction and exploitation benefit from knowledge of the crystal structure and the packing architecture. Polymorphism can occur due to the weak intermol. interactions, requiring detailed structural anal. to clarify the origin of obsd. material property modifications. Addnl., laser confocal microscopy and fluorescence lifetime imaging microscopy confirm the results obtained by the X-ray diffraction characterization, i.e. shifting the substituents towards the external benzene rings of the anthracene unit favors π-π interactions, impacting on both the morphol. and the microscopic optical properties of the crystals. The compds. with more isolated anthracene units feature shorter lifetime and emission spectra, more similar to those of isolated mols. The crystallog. study, supported by the optical investigation, sheds light on the influence of non-covalent interactions on the crystal packing and luminescence properties of anthracene derivs., providing a further step towards their efficient use as building blocks in active components of light sources and photonic networks.
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    41. 41
      Bhattacharyya, K.; Datta, A. Polymorphism controlled singlet fission in tips-anthracene: role of stacking orientation. J. Phys. Chem. C 2017, 121, 1412– 1420,  DOI: 10.1021/acs.jpcc.6b10075
      41
      Polymorphism Controlled Singlet Fission in TIPS-Anthracene: Role of Stacking Orientation
      Bhattacharyya, Kalishankar; Datta, Ayan
      Journal of Physical Chemistry C (2017), 121 (3), 1412-1420CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
      Generation of multiple triplet excitons from one singlet exciton (singlet fission, SF) has been reported in several org. mols. recently. The overall SF yield in such mol. materials, however, is controlled by polymorphism in org. semiconductors through noncovalent interactions like van der Waals and weak electrostatic interactions. In this article, we demonstrate how SF is strongly perturbed by even small variations in mol. packing for polymorphic crystals of triisopropylsilyethnyl-anthracene derivs., TIPS-Ant (PI and PII). Based on quantum chem. calcns., SF dynamics have been computed for both PI and PII polymorphs. PI and PII differ in their intermol. π···π stacking patterns, which eventually control their electronic properties. Using the incoherent hopping model for the crystals, we computed SF rate through the Marcus electron transfer theory. For both PI and PII, the direct two-electron pathway predominates over the charge-transfer (CT) mediated mechanism. PII has higher triplet yield (∼196%) compared to PI (∼178%). Both time-dependent DFT as well as Weller equation reveal that the charge transfer (CT) state is a high energy state, and hence, CT mediated SF barely influences triplet yield. Interplay of the local excitation (LE), multiple excitation (ME), and correlated triplet (T1T1) energy levels controlled the overall exciton dynamics/diffusion in TIPS-Ant polymorphs. Polymorphism is shown to be a key factor for the rational design of optimal SF in polyarom. hydrocarbons (PAH).
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    42. 42
      Mayonado, G.; Vogt, K. T.; Van Schenck, J. D.; Zhu, L.; Fregoso, G.; Anthony, J.; Ostroverkhova, O.; Graham, M. W. High-symmetry anthradithiophene molecular packing motifs promote thermally activated singlet fission. J. Phys. Chem. C 2022, 126, 4433– 4445,  DOI: 10.1021/acs.jpcc.1c10977
      42
      High-Symmetry Anthradithiophene Molecular Packing Motifs Promote Thermally Activated Singlet Fission
      Mayonado, Gina; Vogt, Kyle T.; Van Schenck, Jonathan D. B.; Zhu, Liangdong; Fregoso, Garrett; Anthony, John; Ostroverkhova, Oksana; Graham, Matt W.
      Journal of Physical Chemistry C (2022), 126 (9), 4433-4445CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
      When considering the optimal mol. packing to realize charge multiplication in org. photovoltaic materials, subtle changes in intermol. charge transfer (CT) coupling can strongly modulate singlet fission. To understand why certain packing arrangements are more conducive to charge multiplication by triplet pair (TT) formation, we measure the diffraction-limited transient absorption (TA) response from four single-crystal functionalized derivs. of fluorinated anthradithiophene: diF R-ADT (R = TES, TSBS, TDMS, TBDMS). diF TES-ADT and diF TDMS-ADT both exhibit 2D brickwork packing structures, diF TSBS-ADT adopts a 1D sandwich-herringbone packing structure, and diF TBDMS-ADT exhibits a 1D twisted-columnar packing structure. When brickwork or twisted-columnar single crystals are resonantly probed parallel to their charge transfer (CT)-axis projections, the TA signal is dominated by a rising component on the picosecond time scale (rate kTT), attributed to TT state population. When probed orthogonal to the CT-axis, we instead recover the falling TA kinetics of singlet state depletion at rate kA. The rising to falling rate ratio ests. the TT formation efficiency, εTT = kTT/kA relative to exciton self-trapping. εTT ranged from near 100% in diF TES-ADT to 84% in diF TDMS-ADT. Interestingly, diF TSBS-ADT crystals only manifest falling kinetics of CT-mediated self-trapping and singlet state depletion. Singlet fission is prohibitive in diF TSBS-ADT crystals owing to its lower symmetry sandwich-herringbone packing that leads to S1 to CT-state energy sepn. that is ~ 3x larger than in other packings. Collectively, these results highlight optimal packing configurations that either enhance or completely suppress CT-mediated TT formation.
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    43. 43
      Buchanan, E. A.; Michl, J. Optimal arrangements of 1, 3-diphenylisobenzofuran molecule pairs for fast singlet fission. Photochem. Photobiol. Sci. 2019, 18, 2112– 2124,  DOI: 10.1039/c9pp00283a
      43
      Optimal arrangements of 1,3-diphenylisobenzofuran molecule pairs for fast singlet fission
      Buchanan, Eric A.; Michl, Josef
      Photochemical & Photobiological Sciences (2019), 18 (9), 2112-2124CODEN: PPSHCB; ISSN:1474-905X. (Royal Society of Chemistry)
      A simplified version of the frontier orbital model has been applied to pairs of C2, C2v, Cs, and C1 symmetry 1,3-diphenylisobenzofuran rotamers to det. their best packing for fast singlet fission (SF). For each rotamer the square of the electronic matrix element for SF was calcd. at 2.2 x 109 pair geometries and a few thousand most significant phys. accessible local maxima were identified in the six-dimensional space of mutual arrangements. At these pair geometries, SF energy balance was evaluated, relative SF rate consts. were approximated using Marcus theory, and the SF rate const. kSF was maximized by further optimization of the geometry of the mol. pair. The process resulted in 142, 67, 214, and 291 unique geometries for the C2, C2v, Cs, and C1 symmetry mol. pairs, resp., predicted to be superior to the C2 symmetrized known crystal pair structure. These optimized pair geometries and their triplet biexciton binding energies are reported as targets for crystal engineering and/or covalent dimer synthesis, and as possible starting points for high-level pair geometry optimizations.
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    44. 44
      Piland, G. B.; Bardeen, C. J. How morphology affects singlet fission in crystalline tetracene. J. Phys. Chem. Lett. 2015, 6, 1841– 1846,  DOI: 10.1021/acs.jpclett.5b00569
      44
      How Morphology Affects Singlet Fission in Crystalline Tetracene
      Piland, Geoffrey B.; Bardeen, Christopher J.
      Journal of Physical Chemistry Letters (2015), 6 (10), 1841-1846CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
      The dependence of exciton dynamics on the cryst. morphol. of tetracene is studied using time-resolved photoluminescence. Single crystals exhibit relatively slow singlet decays with times that range from 130 to 300 ps depending on the sample. This decay has an activation energy of ∼450 cm-1 at 200-400 K. Single-crystal samples also exhibit more pronounced quantum beats due to the triplet pair spin coherences. Polycryst. thin films grown by thermal evapn. have singlet decay times ∼70-90 ps with a much weaker temp. dependence. Many thin-film samples also exhibit a red-shifted excimer-like emission. When a polycryst. thin film is thermally annealed to produce larger crystal domains, single-crystal behavior is recovered. The authors hypothesize that the different dynamics arise from the ability of singlet excitons in the thin films to sample regions with defects or packing motifs that accelerate singlet fission.
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    45. 45
      Buchanan, E. A.; Kaleta, J.; Wen, J.; Lapidus, S. H.; Císařová, I.; Havlas, Z.; Johnson, J. C.; Michl, J. Molecular packing and singlet fission: the parent and three fluorinated 1, 3-diphenylisobenzofurans. J. Phys. Chem. Lett. 2019, 10, 1947– 1953,  DOI: 10.1021/acs.jpclett.8b03875
      45
      Molecular Packing and Singlet Fission: The Parent and Three Fluorinated 1,3-Diphenylisobenzofurans
      Buchanan, Eric A.; Kaleta, Jiri; Wen, Jin; Lapidus, Saul H.; Cisarova, Ivana; Havlas, Zdenek; Johnson, Justin C.; Michl, Josef
      Journal of Physical Chemistry Letters (2019), 10 (8), 1947-1953CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
      Crystal structures, singlet fission (SF) rate consts., and other photophys. properties are reported for three fluorinated derivs. of 1,3-diphenylisobenzofuran and compared with those of the two crystal forms of the parent. The results place constraints on the notion that the effects of mol. packing on SF rates could be studied sep. from effects of chromophore structural changes by examg. groups of chromophores related by weakly perturbing substitution if their crystal structures are different. The results further provide exptl. evidence that dimer-based models of SF are not sufficiently general and that trimer- and possibly even higher oligomer-based or many-body models need to be formulated.
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    46. 46
      Sondermann, U.; Kutoglu, A.; Bassler, H. X-ray diffraction study of the phase transition in crystalline tetracene. J. Phys. Chem. 1985, 89, 1735– 1741,  DOI: 10.1021/j100255a039
      46
      X-ray diffraction study of the phase transition in crystalline tetracene
      Sondermann, U.; Kutoglu, A.; Bassler, H.
      Journal of Physical Chemistry (1985), 89 (9), 1735-41CODEN: JPCHAX; ISSN:0022-3654.
      Cryst. tetracene undergoes a structural transition to a 2nd triclinic phase at <200 K. The transition temp. depends on external parameters, such as the strength of mech. coupling of the crystal to a supporting surface, and is subject to a hysteresis effect. The parameters of the new phase were detd. and a structure proposed on the basis of lattice energy calcns. The transition involves a rotation of the mol. at 1/2,1/2,0 around the axis normal to the mol. plane. Translational displacement of the face-centered mol., equiv. to a redn. of crystal symmetry from P‾1 to P1, stabilizes the new phase.
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    47. 47
      Venuti, E.; Della Valle, R. G.; Farina, L.; Brillante, A.; Masino, M.; Girlando, A. Phonons and structures of tetracene polymorphs at low temperature and high pressure. Phys. Rev. B 2004, 70, 104106,  DOI: 10.1103/PhysRevB.70.104106
      47
      Phonons and structures of tetracene polymorphs at low temperature and high pressure
      Venuti, Elisabetta; Della Valle, Raffaele Guido; Farina, Luca; Brillante, Aldo; Masino, Matteo; Girlando, Alberto
      Physical Review B: Condensed Matter and Materials Physics (2004), 70 (10), 104106/1-104106/8CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
      Crystals of tetracene were studied by lattice phonon Raman spectroscopy as a function of temp. and pressure. Two different phases (polymorphs I and II) were obtained, depending on sample prepn. and history. Polymorph I is the most frequently grown phase, stable at ambient conditions. Application of pressure >1 GPa yields polymorph II, which is also obtained by cooling the sample <140 K. However, the conditions for inducing the phase transitions depend on sample prepn. and history, and polymorph II can also be maintained at ambient conditions. The authors have calcd. the crystallog. structures and phonon frequencies as a function of temp., starting from the configurations of the energy min. found by exploring the potential energy surface of cryst. tetracene. The spectra calcd. for the 1st and 2nd deepest min. match satisfactorily those measured for polymorphs I and II, resp. The temp. dependence of the spectra is described correctly. All published x-ray structures, once assigned to the appropriate polymorph, are also reproduced.
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    48. 48
      Della Valle, R. G.; Venuti, E.; Brillante, A.; Girlando, A. Inherent structures of crystalline tetracene. J. Phys. Chem. A 2006, 110, 10858– 10862,  DOI: 10.1021/jp0611020
      48
      Inherent Structures of Crystalline Tetracene
      Della Valle, Raffaele Guido; Venuti, Elisabetta; Brillante, Aldo; Girlando, Alberto
      Journal of Physical Chemistry A (2006), 110 (37), 10858-10862CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
      The authors have systematically sampled the potential energy surface of cryst. tetracene to identify its local min. These min. represent all possible stable configurations and constitute the inherent structures of the system. The crystal is described in terms of rigid mols. with Coulombic and atom-atom interactions. Hundreds of distinct min. are identified, mostly belonging to the space groups P‾1 (triclinic) and P21/c (monoclinic), with a variety of structural arrangements. The deepest min. corresponds to the high temp.-low pressure polymorph. This is the only polymorph with a completely described x-ray structure, which is satisfactorily described by the calcns. The next deep min. is likely to correspond to the low temp.-high pressure polymorph, which was exptl. identified but not yet fully described.
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    49. 49
      Groff, R.; Avakian, P.; Merrifield, R. Coexistence of exciton fission and fusion in tetracene crystals. Phys. Rev. B 1970, 1, 815,  DOI: 10.1103/PhysRevB.1.815
      There is no corresponding record for this reference.
    50. 50
      Groom, C. R.; Bruno, I. J.; Lightfoot, M. P.; Ward, S. C. The Cambridge structural database. Acta Crystallographica Section B: Structural Science, Crystal Engineering and Materials 2016, 72, 171– 179,  DOI: 10.1107/S2052520616003954
      50
      The Cambridge Structural Database
      Groom, Colin R.; Bruno, Ian J.; Lightfoot, Matthew P.; Ward, Suzanna C.
      Acta Crystallographica, Section B: Structural Science, Crystal Engineering and Materials (2016), 72 (2), 171-179CODEN: ACSBDA; ISSN:2052-5206. (International Union of Crystallography)
      The Cambridge Structural Database (CSD) contains a complete record of all published org. and metal-org. small-mol. crystal structures. The database has been in operation for over 50 years and continues to be the primary means of sharing structural chem. data and knowledge across disciplines. As well as structures that are made public to support scientific articles, it includes many structures published directly as CSD Communications. All structures are processed both computationally and by expert structural chem. editors prior to entering the database. A key component of this processing is the reliable assocn. of the chem. identity of the structure studied with the exptl. data. This important step helps ensure that data is widely discoverable and readily reusable. Content is further enriched through selective inclusion of addnl. exptl. data. Entries are available to anyone through free CSD community web services. Linking services developed and maintained by the CCDC, combined with the use of std. identifiers, facilitate discovery from other resources. Data can also be accessed through CCDC and third party software applications and through an application programming interface.
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    51. 51
      Campbell, R.; Robertson, J. M.; Trotter, J. The crystal structure of hexacene, and a revision of the crystallographic data for tetracene. Acta crystallogr. 1962, 15, 289– 290,  DOI: 10.1107/S0365110X62000699
      51
      The crystal structure of hexacene, and a revision of the crystallographic data for tetracene and pentacene
      Campbell, R. B.; Robertson, J. Monteath; Trotter, J.
      Acta Crystallographica (1962), 15 (), 289-90CODEN: ACCRA9; ISSN:0365-110X.
      cf. Robertson, et al., CA 55, 21745d. A redetn. of the crystal structures of tetracene and pentacene yielded slightly different triclinic unit cell consts. which now are: for tetracene, a 7.90, b 6.03, c 13.53 A., α 100.3°, β 113.2°, γ 86.3°, Z = 2, and space group P‾1; for pentacene, a 7.90, b 6.06, c 16.01 A., α 101.9°, β 112.6°, γ 85.8°, Z = 2, and space group P‾1. New data for the orientation of the mols. in the unit cell are given, but they lead to insignificant changes in bond lengths and angles. Hexacene has a structure very similar to the lower benzologues, with a 7.9, b 6.1, c 18.4, α 102.7°, β 112.3°, γ 83.6°, Z = 2, and space group P‾1. Although insufficient data were observed for a detn. of at. parameters, the similarity of diffraction-intensity distribution indicates a mol. arrangement in the unit cell similar to the other members of the series.
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      Rang, Z.; Haraldsson, A.; Kim, D. M.; Ruden, P. P.; Nathan, M. I.; Chesterfield, R. J.; Frisbie, C. D. Hydrostatic-pressure dependence of the photoconductivity of single-crystal pentacene and tetracene. Appl. Phys. Lett. 2001, 79, 2731– 2733,  DOI: 10.1063/1.1410878
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      Hydrostatic-pressure dependence of the photoconductivity of single-crystal pentacene and tetracene
      Rang, Zhenlin; Haraldsson, Anders; Kim, Dong M.; Ruden, P. Paul; Nathan, Marshall I.; Chesterfield, Reid J.; Frisbie, C. Daniel
      Applied Physics Letters (2001), 79 (17), 2731-2733CODEN: APPLAB; ISSN: