Strategies for Design of Potential Singlet Fission Chromophores Utilizing a Combination of Ground-State and Excited-State Aromaticity Rules

Singlet exciton fission photovoltaic technology requires chromophores with their lowest excited states arranged so that 2E(T1) < E(S1) and E(S1) < E(T2). Herein, qualitative theory and quantum chemical calculations are used to develop explicit strategies on how to use Baird’s 4n rule on excited-state aromaticity, combined with Hückel’s 4n + 2 rule for ground-state aromaticity, to tailor new potential chromophores for singlet fission. We first analyze the E(T1), E(S1), and E(T2) of benzene and cyclobutadiene (CBD) as excited-state antiaromatic and aromatic archetypes, respectively, and reveal that CBD fulfills the criteria on the state ordering for a singlet fission chromophore. We then look at fulvenes, a class of compounds that can be tuned by choice of substituents from Baird-antiaromatic to Baird-aromatic in T1 and S1 and from Hückel-aromatic to Hückel-antiaromatic in S0. The T1 and S1 states of most substituted fulvenes (159 of 225) are described by singly excited HOMO → LUMO configurations, providing a rational for the simultaneous tuning of E(T1) and E(S1) along an approximate (anti)aromaticity coordinate. Key to the tunability is the exchange integral (KH,L), which ideally is constant throughout the compound class, providing a constant ΔE(S1 – T1). This leads us to a geometric model for the identification of singlet fission chromophores, and we explore what factors limit the model. Candidates with calculated E(T1) values of ∼1 eV or higher are identified among benzannelated 4nπ-electron compound classes and siloles. In brief, it is clarified how the joint utilization of Baird’s 4n and Hückel’s 4n + 2 rules, together with substituent effects (electronic and steric) and benzannelation, can be used to tailor new chromophores with potential use in singlet fission photovoltaics.


CHOICE OF COMPUTATIONAL METHOD
Choosing the method for computing excitation energies is important. Kaupp and co-workers used a TD-DFT-based protocol for the screening of singlet fission chromophores, and they proposed vertical excitation energies computed with local hybrid functionals. S1 Yet, M06-2X was found to perform similarly, and we used this functional as we showed earlier that it gives good T1 state geometries for substituted fulvenes when compared to the T1 state geometries calculated with CASPT2. We first used the computational scheme derived by Zeng, Hoffmann, and Ananth which gives the correct ordering of the T1, S1, and T2 states of pentacene. S2 This approach uses adiabatic excitations to the T1 state and vertical excitations to the S1 (T2) states from the S0 (T1) optimized structures. Additionally, the vertical excitations to the T1 state were computed for most of the compounds. To assess the performance of M06-2X in the present study we compare experimental excitation energies of two compounds known to undergo singlet fission; pentacene and 1,3-diphenylisobenzofuran (DPB). The same energy ordering is obtained with the M06-2X based protocol as in the experiments. Moreover, both singlet fission criteria are satisfied for pentacene and nearly satisfied in case of DPB, which reveals that M06-2X should be a suitable method. For benzene and CBD, the arrangement of the electronic excited states is the same in both methods.
NICS-XY scans have also been carried out using B3LYP and CAM-B3LYP, apart from M06-2X, in order for us to see how the different amounts of exact exchange as well as rangecorrections impacted on the NICS-XY scans of extensively π-conjugated compounds. Table S1. Electronic excitation energies (eV) of cyclobutadiene (CBD), benzene, pentacene and 1,3-diphenylisobenzofuran (DPB) computed at TD-M06-2X/def2-TZVPD//M06-2X/6-311+G(d,p) and, in parenthesis, CASPT2/ANO-RCC-VDZP//M06-2X/6-311+G(d,p) levels.  S3 and, for DPB see ref. S4, S5 ). Table S2. The E(T1)v, E(T1)a, E(S1) and E(T2) of the differently substituted fulvenes sorted by substituents X and Y. The label "REARRANGED" means that the optimal structure is not the one expected due to the rearrangement of the substituents or the formation of chemical bonds between substituents. Such cases are therefore not corresponding to original fulvenic structures. Not a clear HOMO-to-LUMO excitation Y = NO2 Both T1 and S1 excitations are different to that of the parent fulvene Y = OH Not a clear HOMO-to-LUMO excitation Y = OMe Not a clear HOMO-to-LUMO excitation Y = SH Both T1 and S1 excitations are different to that of the parent fulvene Y = SiH3

Spin-orbit coupling calculations
As the T1 excitons formed in an efficient singlet fission chromophore should be long-lived, we investigated the probability for spin-forbidden T1/S0 state processes such as intersystem crossing and phosphorescence in fulvenes. If a triplet exciton is close to a T1/S0 crossing point with high spin-orbit coupling (SOC), leading to rapid decay to the S0 state, the efficiency will be hampered. However, the SOC elements for T1/S0 in our eight fulvenes computed at TD-M06-2X level range from 0.4 to 2.8 cm -1 (Table S9) which is typical of weak couplings and indicating that intersystem crossing will not impede the singlet fission process.

Assessment of the multiconfigurational character in fulvenes
Excitation energies calculated with TDDFT are reliable only if there is no evidence of multiconfigurational character, at least at the geometry in the S0 state. To probe for multiconfigurational character, we used the %TAEe[(T)], i.e., the percentage of the perturbative triples correction (T) to the total CCSD(T) atomization energy, proposed by Karton et al.. S6 The computed %TAEe[(T)] values for the S0 states of the fulvenes in Figure 5 are found in the range 2.0 -4.1 % (Table S9), indicating lack of multiconfigurational character as the values are below the recommended threshold of 10%. 4 Figure S1: Plots of HOMO and LUMO of (A) the fulvene with X = CN and Y = NH2, and (B) the fulvene with X = NH2 and Y = CN. Calculated for the S0 state at M06-2X/6-311+G(d,p) level.

Calculation of the diradical character
The diradical character was computed using the spin-projected spin-unrestricted Hartree-Fock (PUHF) proposed by Yamaguchi S7 given by, where Tn is the orbital overlap between the corresponding orbital pairs than can be also expressed in the terms of natural occupation numbers, η, of UHF natural orbitals as, Diradical (n=0) and tetraradical (n=1) characters have been calculated (Table S10).  Figure S2. Table S11. The ΔE(S1-T1) of the parent fulvene and substituted fulvenes in Figure 2 and Figure  S2. ΔE(S1-T1) C2-C3 bond C1-C2/C3-C4 X = H 1.00 -1.13 1.04 -1.16 X = CN 0.83 -0.86 0.84 -0.96 X = NH2 1.04 -1.48* 1.04 -1.17 X = F, Y = BF2 1.40 -1.49 1.41 -1.51 X = F, Y = NH2 0.92 -0.98 0.94 -1.08 * The S1 and T1 excitations of this fulvene is not described by the same configurations, i.e. the singly excited configuration involving the proper HOMO and LUMO.  The poorer correlation of plot B when compared to plot A comes from the fact that HOMA is not ideal to describe the T1 aromaticity of molecules with small four-and five-membered rings. A clear example is cyclopentadienyl cation (Cp + ), a Baird-aromatic reference, which has an HOMA value (0.73), significantly for below the ideal aromatic HOMA value of 1.0. S35 Figure S5. A comparison of the dependence of E(S1)v and E(T1)v on (A) NICS(1)zz,S0 and (B) HOMAS0 of fulvenes. R 2 is the squared correlation coefficient. Calculations at M06-2X/6-311+G(d,p).

SUBSTITUTED CBDs
Weights of the singly excited HOMO to LUMO configurations of substituted CBDs In all cases the major configuration in the S1 state is the HOMO to LUMO transition. Figure S6. Percentage of the singly excited HOMO to LUMO configuration in the S1 state of CBD and substituted CBDs (SCBD)s.  Figure S7. Dependence of E(T1) and E(S1) on ΔNICS(1)zz,T1-S0 of the SCBD derivatives. R 2 is the squared correlation coefficient. The correlation does not include the red points which correspond to SCBD1. Calculations at M06-2X/6-311+G(d,p).

SUBSTITUTED PENTALENES
Weights of the singly excited HOMO to LUMO configurations of substituted pentalenes In all cases the major configuration in the S1 state is the HOMO to LUMO transition. Figure S8. Percentage of the singly excited HOMO to LUMO configuration in the S1 state of pentalene (PENT) and substituted pentalenes (SPENT).  Figure S9. HOMO-1, HOMO and LUMO of the parent pentalene calculated at M06-2X/6-311+G(d,p) level.

SUBSTITUTED INDACENES
Weights of the singly excited HOMO to LUMO configurations of substituted as-and sindacenes. In all the cases the major configuration in the S1 state is the HOMO to LUMO transition. Figure S10. Percentage of the singly excited HOMO to LUMO configuration in the S1 state of s-and as-indacenes and substituted derivatives.    Figure S12. HOMO and LUMO of the parent s-indacene (A) and as-indacene (B) obtained at M06-2X/6-311+G(d,p). Symmetries are given in parenthesis.

BENZANNELATED CBDs
Weights of the major configurations of substituted BENZCBDs. In all cases except BENZCBD7 the major configuration in the S1 state is the HOMO to LUMO transition. Figure S13. Percentage of the singly excited HOMO to LUMO configuration in the S1 state of benzannelated CBDs (BENZCBD). character. Yet, in contrast to the observation made for fulvenes, bond length distortions did not extensively impact on E(T1), E(S1) and E(T2) of naphthoCBD ( Figure S15). The maximal change in E(T1) and E(S1) are 0.18 and 0.14 eV, respectively. Thus, bond length distortions as a design tool is inefficient for PAAHs (also small PAAHs) as the frontier orbitals extend over too many bonds leading to only small relative impact from each bond on the orbital energy.

BENZANNELATED PENTALENES
Weights of the singly excited HOMO to LUMO configurations of substituted BENZPENTs. In all cases except one the major configuration in the S1 state is the HOMO to LUMO transition. The exception is BENZPENT10 for which the S1 transition is a two-configurational transition described by the HOMO-2 to LUMO configuration (63%) and HOMO to LUMO (37%). Figure S21. Percentage the singly excited HOMO to LUMO configuration in the S1 state of benzannelated pentalenes (BENZPENT). S53   Table S22. Coefficients of the major configurations from Gaussian output of benzannelated pentalenes (BENZPENT).  Figure S22. Electronic excitation energies (eV) and spin density of BENZPENT5, bis(styryl)BENZPENT5 and BENZPENT20. Computations at TD-M06-2X/def2-TZVPD//(U)M06-2X/6-311+G(d,p) level.

Bis(styryl)BENZPENT5
has shown to provide an entry point to singlet fission as the excitation occurs in the S2 state, and such molecule compared to BENZPENT5 satisfies the criteria. The spin density is accumulated on the pentalene unit in the case of BENZPENT5 while in bis(styryl)BENZPENT5, it is concentrated on C1/C4 and C3/C6. For BENZPENT5, the S1 excitation is from HOMO to LUMO, yet for bis(styryl)BENZPENT5, the excitation if from HOMO-1 to LUMO. Yet, as the S1 state of bis(styryl)BENZPENT5 has double excitation character, TD-DFT is not suitable to describe the excitation energies. As a comparison, for 1,8diphenyloctatetraene, E(S1) = 3.37 eV and E(T1) = 1.88 eV; for bis(styryl)BENZPENT5, E(S1) = 2.46 eV and E(T1) = 1.59 eV; for BENZPENT5, E(S1) = 2.69 eV and E(T1) = 2.07 eV.