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Modeling the Water Splitting Activity of a TiO2 Rutile Nanoparticle

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Department of Chemistry, University College London, 20 Gordon Street, London, WC1H 0AJ, U.K.
*E-mail: [email protected]. Phone: +44-(0)20-7679 4665.
Cite this: J. Phys. Chem. C 2015, 119, 24, 13384–13393
Publication Date (Web):May 21, 2015
https://doi.org/10.1021/acs.jpcc.5b01512

Copyright © 2022 American Chemical Society. This publication is licensed under CC-BY.

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Abstract

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We explore, from a theoretical perspective, the effect of particle size on the photocatalytic water splitting activity of TiO2 rutile (nano)particles by a combination of explicit quantum chemistry calculations on a hydroxylated rutile nanoparticle in a realistic solvation environment and a comparison with the calculated properties of bulk rutile (surfaces) from the literature. Specifically, we use density functional theory (DFT) and time-dependent DFT to calculate the nanoparticle thermodynamic driving force for the water splitting half-reactions and identify in the process the crucial role of self-trapping of the free charge carriers responsible for proton reduction and water oxidation.

Introduction

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TiO2 nanoparticles are the quintessential photocatalyst, a material that allows a reaction to happen in the presence of light that otherwise would not take place. Loaded with a noble metal cocatalyst (Pd, Pt, Rh), both rutile (1-4) and anatase (5-7) nanoparticles catalyze the overall splitting of water into molecular hydrogen and oxygen when illuminated with ultraviolet light, while without noble metals they act as photocatalysts for the degradation of organic molecules (8-11) and drive the individual water splitting half-reactions in the presence of a suitable electron or hole donor. (12-14) Some of these reactions are endothermic, and part of the photon energy becomes incorporated in the reaction products (e.g., overall water splitting), a situation commonly referred to as artificial photosynthesis or solar fuel synthesis. (15) In other cases, the photocatalyzed reactions are exothermic in the dark, e.g., organic pollutant degradation, and the illuminated photocatalyst acts as a catalyst in the classical chemical sense and improves the reaction rate.
Even if only active in the ultraviolet part of the solar spectrum, at least in the absence of heavy doping, TiO2 nanoparticles and related nanostructures, e.g., thin films, are probably the world’s most studied photocatalyst. TiO2 is hence the natural starting point for computational studies into the fundamental physical and chemical processes that underlie photocatalysis in inorganic solids, work that is needed because, even in the case of TiO2, many fundamental issues are still unresolved. For example, there is an ongoing discussion about the relative position of the (reduction potentials associated with the) conduction band in anatase and rutile, (16-20) as well as the defect chemistry of TiO2 and how this can be used to reduce the optical gap from the ultraviolet to the visible part of the spectrum. (19) Finally, there is the issue of the dependence of the photocalytic activity on particle size and morphology, about which there are very contrasting reports in the literature. For example, work on the reduction of protons, as part of overall water splitting or in the presence of a sacrificial electron donor, suggests a decrease in photocatalytic activity with decreasing particle size, (7, 21, 22) while other studies that focus on the degradation of organic molecules report an increase in activity instead. (3, 13, 23, 24)
During use as a photocatalyst, the particle can exist in a number of different electronic states: the electronic ground state (P), an electronically excited excitonic state (P*), or indeed an anionic (P–) or cationic (P+) state. Starting from the ground state, absorption of light with energy higher than the optical gap results in the excitation of the particle and the formation of an exciton, an excited electron–hole pair bound through their mutual electrostatic interaction. This exciton subsequently can dissociate into a free electron and free hole, where free signifies that the excited electron and hole are sufficiently spatially separated so that their effective interaction is negligible, for example, by being localized on different particles. This free electron and hole can take part in interesting chemistry but also recombine to re-form an exciton in a process referred to as electron–hole recombination. Excitons can decay at any stage back to the ground state under the emission of light, (photo)luminescence, or via a nonradiative route, internal conversion, where the excess energy is dissipated in the form of phonons (vibrations).
Both the exciton and the free charge carriers can in principle localize on a fragment of the particle (self-trap, e.g., a self-trapped exciton) or become trapped on a structural defect (e.g., a free electron trapped by an oxygen vacancy). (25-29) Especially, self-trapped exciton formation appears to be very structure sensitive; bulk rutile only has free nontrapped excitons, while in bulk anatase, excitons appear to self-trap. (30-33) Experimentally, self-trapping is observable by the different spectroscopic signatures of free and trapped states. For example, in the case of excitons, a red shift between the optical gap and the photoluminescence maxima is a signature of a self-trapped exciton.
Modeling such complex processes is not straightforward, especially deciding what to include and what not. However, we believe a number of essential features should be incorporated in the model. Both the free charge carriers (Figure 1A) and the exciton (Figure 1B) can in principle drive the water splitting half-reactions by providing electrons and holes with the necessary chemical potential. Any attempt at modeling a photocatalyst should therefore, in our opinion, consider both free charge carriers and excitons. This is especially true when considering nanoparticles. For many bulk solids the difference between the energy required for creating a pair of free charge carriers and that needed to make an exciton is very small (for example, 4 meV for bulk rutile (34)) and the potentials associated with excitons and free charge carriers thus approximately degenerate. The same is not necessarily true in the case of nanoparticles, and excitons in such systems might be hard(er) to dissociate. Furthermore, because of the known potential for (self)trapping in TiO2 (see above), one ideally should also consider the effect of structural relaxation when studying photocatalysts. Finally, taking into account the need to understand the explicit effect of particle size and the fact that at least in the case of overall water splitting, the photocatalyst will operate immersed in water, it appears sensible to explicitly study hydroxylated nanoparticles, the surface of which is further covered by a monolayer of adsorbed water molecules. The latter explicit description of surface water is possibly used in conjunction with a dielectric continuum solvation model to reproduce the effect of bulk water. Relevant previous work on TiO2 generally did not consider excitons and focused instead on studies of free charge carriers either in periodic 2D slabs (26, 28, 35) or in nanoparticles, (19, 36-39) while the selected papers (40-55) that do consider excitons, mostly in the case of nanoparticles, as a rule do not take into account exciton self-trapping and often focus on unhydroxylated naked particles in vacuum.

Figure 1

Figure 1. Scheme showing how the (standard) reduction potentials (IP, EA, EA*, and IP*) of the ideal photocatalyst (nanoparticle) straddle the proton reduction and water oxidation potentials (green and red broken lines for HER and OER, respectively). hν defines the energy of the photon absorbed by the nanoparticle. e– and h+ stand for electron and hole, respectively, while VB and CB are the valence and conduction bands of the particle. Box A represents the free charge carriers scenario, where the excited electron and hole are spatially separated within the particle and have negligible Coulombic interaction. Box B represents the exciton scenario, where the excited electron and hole are strongly interacting and can be described as an excited electron–hole pair, or exciton.

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Following the logic set out above, we report here our first results of DFT/TD-DFT calculations on a ∼1 nm hydroxylated rutile nanoparticle (taken from previous work by Freisner and co-workers; (36, 38, 39) see Figure 2), where we explicitly include the effect of solvation and trapping. This nanoparticle structure, even if small compared to rutile nanoparticles synthesized experimentally, is perhaps the smallest rutile particle that still preserves essential features of the bulk structure.

Figure 2

Figure 2. TiO2 rutile nanoparticle containing 23 TiO2 units and 34 water molecules, 18 split as hydroxyl groups on the particle’s surface and 16 in their molecular state (pictured as blue lines), which amounts to a total of 171 atoms. The crystal planes that define the particle are also shown: four 110 (light green, top middle figure) and two 001 planes (light orange, top right figure). Red spheres denote oxygen atoms, whereas gray and white spheres represent titanium and hydrogen atoms, respectively.

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We report a range of optical and excited state properties for this particle including the optical gap, the predicted photoluminescence signal, the sites within the particle on which the exciton self-traps, and the structural distortion associated with the localization. We also calculate the standard reduction potentials of the free charge carriers and exciton in this particle and compare them with those of the water splitting half-reactions to examine the thermodynamic ability of this rutile particle, and small TiO2 nanoparticles in general, to drive the photocatalytic splitting of water. Finally, we use all these data to discuss how the photocatalytic ability of nanoparticles might differ from their larger counterparts and the role of surface flexibility therein.

Theoretical Picture

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In the following section we will discuss a possible theoretical picture of photocatalysis, from the perspective of the reaction that is photocatalyzed and that of the photocatalyst. In the latter we will build on our recent work on photocatalytic polymers. (56-58)

Water Splitting Reaction Perspective

The overall water splitting reaction is a combination of two half-reactions (both expressed as reductions, in line with convention):(A)(B)During water splitting half-reaction A, the hydrogen evolution reaction (HER) will run in the forward direction, the reduction of protons to molecular hydrogen, and in reaction B, the oxygen evolution reaction (OER) will run in the direction opposite to that written, oxidation of water to molecular oxygen and protons.
In order for both of these half-reactions to take place and overall water splitting to occur, a photocatalyst will have to provide electrons for the HER and accept electrons, or in other words donate holes, to drive the OER. The (standard) reduction potential of the electrons and holes provided by a photocatalyst should thus straddle those of HER and OER half-reactions (see Figure 1A and Figure 1B). Moreover, as the HER experimentally has a standard reduction potential of 0 V relative to the standard hydrogen electrode (SHE) at pH 0 and the OER a standard reduction potential of 1.23 V, a successful photocatalyst needs therefore to provide at least this amount of potential to split water. In practice, a larger overall potential than 1.23 V (e.g., 1.8 V) is required to overcome energetic losses and kinetic barriers, the difference between the effective and equilibrium potentials being the overpotential. For endergonic overall redox reactions other than water splitting, e.g., reduction of protons in the presence of a sacrificial electron donor, a very similar analysis can be performed.
In the case of overall redox reactions that are exergonic in the dark, the situation is slightly different. As there is no need for the photocatalyst to drive such reactions to make them thermodynamically feasible, the photocatalytic activity arises purely because the photocatalysts allow for larger overpotentials to be overcome than possible in its absence. We plan to discus the case of endergonic reactions in future work and focus here exclusively on the case of photosynthesis.

Photocatalyst Perspective

As discussed in the Introduction, a photocatalyst can provide electrons and holes to drive redox reactions in the form of free charge carriers (Figure 1A) and (as part of) excitons (Figure 1B). When analyzing the ability of a particle (P) to act as a photocatalyst for the redox reactions discussed above, we thus, following our previous work, (56, 57) need to consider the potentials associated with four different half-reactions (written, again in line with convention, as reductions):(C)(D)(E)(F)where in half-reactions C and E, the exciton and the free electron, respectively, serve as reductants for species in solution; the particle donates electrons, and the half-reactions will run in the opposite direction to that written above. In the other two half-reactions (D and F), the particle accepts electrons (donates holes) and the exciton and the free holes act as oxidants for species in solution. The reduction potential of half-reaction F is equal to the ionization potential, the free energy required to remove an electron from the top of the photocatalyst’s valence band, and is hence further labeled as IP. Similarly, the reduction potential of half-reaction E equals the electron affinity, the free energy released upon adding one electron to the bottom of the photocatalyst conduction band, and labeled as EA. Finally, the potentials of half-reactions C and D can be thought of as the excited state ionization potential IP*, the free energy required to remove the excited electron from the exciton, and the excited state electron affinity EA*, the free energy released upon adding an electron to the exciton and annihilating the exciton’s hole component, respectively.
The thermodynamic preference for excitons versus free charge carriers can be analyzed in terms of the following nonredox reaction:(G)The (free) energy change associated with reaction G is commonly referred to as the exciton binding energy, the difference between the free energy required for forming a pair of free charge carriers and that needed to form an exciton. Positive values of the exciton binding energy signify that an exciton is more stable than the free charge carriers and that additional energy needs to be invested to dissociate the exciton. This thermodynamic analysis, in the case of the exciton, can be complemented with kinetic arguments about the expected exciton lifetime based on the oscillator strength of the exciton. An alternative source of free charge carriers, beyond simple exciton dissociation described by reaction G, is as byproduct of half-reactions C and D, which can then also be thought of as describing dissociation of the exciton at the particle–water interface.
The potentials, as well as the exciton binding energy and the exciton lifetime, depend on the exact atomic geometry of the nanoparticle. As a result, the nanoparticle’s properties involving free (vertical) and self-trapped (adiabatic) species are generally different. Which of these extremes is most relevant depends on the inherent time scale of the phenomena we are interested in relative to that of nuclear relaxation: much shorter, vertical, and much longer, adiabatic.

Methods

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Here we employ a combination of DFT and TD-DFT to calculate the properties of the photocatalyst nanoparticles in their different states and the potentials associated with them. We use DFT to describe the properties of the P, P+, and P– states and TD-DFT for those of P*. As we are modeling whole nanoparticles, we use a molecular approach, which gives us direct access to the vacuum reference state. This approach furthermore allows for convenient treatment of charged states (P– and P+, particle with a free electron or hole) without the need to introduce further approximations, such as a homogeneous background charge. The potentials are calculated from the DFT/TD-DFT total energies via(1)(2)where n is the is the number of electrons involved in the half-reaction, F is the Faraday constant, U is the DFT/TD-DFT electronic total energy, Gvib is the sum of the vibrational, rotational, and translational contributions to the free energy, and Gsol is the solvation free energy.
Finally, since both of the water splitting half-reactions involve protons, for which the calculation of the free energy is a challenging task, (59, 60) we use the experimentally determined absolute value of the standard hydrogen electrode (4.44 V) (61, 62) for the potential of HER half-reaction. We then determine the proton free energy (G(H+)), required for the calculation of the potential of the OER half-reaction, via(3)Within our computational scheme, we first optimize the geometry of the nanoparticle in the P, P+, and P– states using DFT. Second, we calculate the vertical excitation spectrum at the ground state geometry and subsequently relax the geometry of the nanoparticle in its excited P* state (modeled as the lowest singlet, S1, excitation) using TD-DFT. Third, we calculate the vertical triplet excitation energies on the P and P* geometries, as well as at an approximate T1 minimum-energy geometry obtained by optimizing the particle in its triplet state using DFT (Δ-SCF). For the solution reaction potentials, finally we optimize all relevant species using DFT and subsequently perform frequency calculations on the obtained minimum-energy structures to calculate the vibrational contribution to the free energy Gvib(x) (see eq 2 above). For numerical tractability reasons, calculating the (excited state) frequencies of particles with more than 150 atoms is computationally very expensive, and because our experience in other systems has told us that the effect of neglecting it on the photocatalyst’s potentials is generally very small, (56, 57) we ignore Gvib(x) in the case of the nanoparticle. Finally, in all calculations except when explicitly stated, the effect of bulk water is incorporated through use of a dielectric continuum solvent model, where the properties of the environment are characterized by its relative dielectric permittivity (ε). This approach allowed us to determine the contribution to the free energy of each species (Gsol(x), see eq 2 above).
The primary nanoparticle structural model considered in this work corresponds to a solvated and hydroxylated cut of the bulk rutile structure, a 3 × 3 × 3 rutile nanoparticle previously discussed by Friesner and co-workers, (36, 38, 39) defined by four (110) and two (001) planes, respectively, and with a ∼1 nm core. This is perhaps the smallest rutile particle that still preserves essential features of the bulk structure. The central titanium atom in the particle has a bulklike 6-fold coordination environment, while all the other titanium atoms have at least four oxygen atoms in their first coordination sphere, of which at most two are part of a surface hydroxyl. The coordination environments of the titanium atoms at the surface of this particle are further saturated by a monolayer of molecular water. To probe methodological issues, calculations on the rutile nanoparticle were complemented with calculations on a smaller hydrated particle, (TiO2)4(OH)4(H2O)6, for which some of the excited state properties were already investigated in our previous works. (53, 54)
We focus in this paper on DFT and TD-DFT calculations using the CAM-B3LYP XC potential. (63) Previously, we found that use of range-separated XC potentials, such as CAM-B3LYP, was critical for a correct description of excited state properties in TiO2 nanoparticles. (53, 54) Commonly used XC potentials with no or a low percentage of Hartree–Fock like exchange (HFLE), such as PBE (0%) and B3LYP (20%), in contrast, were observed to yield generally problematic results for these particles, especially in the case of excited state relaxation, due to their inability to correctly describe so-called charge transfer (CT) states. (53, 54) The latter corresponds to excitations where there is only (very) limited spatial overlap between the hole and excited electron contributions to the excited state. We complement the CAM-B3LYP calculations with selected B3LYP (64) calculations, results of which can be found in the Supporting Information.
All the DFT/TD-DFT calculations employ the all-electron double-ς DZDP basis set (DZP for oxygen and hydrogen atoms). (65) In the CAM-B3LYP calculations, the solvent effects were approximated with the conductor-like polarizable continuum method (C-PCM) (66) dielectric solvent model, whereas for the B3LYP calculations we employed the COSMO (67) dielectric screening model. The two different approaches lead to similar results (comparisons for the B3LYP results of the test system can be found in the Supporting Information, section ESI-1), as in both cases the ε was chosen equal to 78, resembling solvation in water, and the solvation cavity for the solute was generated using van der Waals radii of 2.293, 1.72, and 1.3 Å for Ti, O, and H atoms, respectively. In all the calculations, we have considered full geometry optimizations in the presence of solvent effects except in the case of TD-DFT excitations involving the COSMO model, as no COSMO excited state gradients are currently available in the code that we use. For those B3LYP calculations, we optimized the TD-DFT excited state in vacuum and then considered the effect of COSMO as single point calculations on the gas phase excited state minimum geometries. Finally, for all the ground and excited state optimizations, the convergence criteria for the maximum Cartesian component of the gradient is chosen to be equal to 1 × 10–3 hartree bohr–1.
All the CAM-B3LYP results were obtained using the GAMESS-US code, (68) while Turbomole (69-71) was employed for the calculations using the B3LYP XC potential. Finally, for plotting the relevant orbitals of the nanoparticles the WXMacMolPlt visualization software (72) was used.

Results and Discussion

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We will now discuss the predicted optical, electronic, and photocatalytic properties of the hydrated rutile nanoparticle and contrast these with those of smaller nanoparticles, as well as bulk TiO2.

Free Exciton

The TD-CAM-B3LYP predicted optical gap of the hydrated rutile nanoparticle, the energy required to make the free S1 exciton, is 4 eV. The rutile nanoparticle is thus clearly predicted to absorb only ultraviolet or higher-energy/shorter-wavelength light, even if TD-CAM-B3LYP probably slightly overestimates the absorption onset. (53, 54) The optical gap of the rutile nanoparticle is red-shifted relative to that of smaller hydroxylated nanoparticles (53, 54) and blue-shifted relative to that of bulk rutile (3.0 eV). (30, 34, 73) While the relative size of the optical gap of the rutile nanoparticle is thus suggestive of quantum confinement, one has to be careful that one is comparing like with like (see section ESI-2 of the Supporting Information).
The excitation responsible for the S1 exciton is predicted to have essentially HOMO/VBM → LUMO/CBM character. The HOMO/VBM (hole component of the exciton) is found to essentially be delocalized over all the oxygen atoms in the core of the particle and the LUMO/CBM (excited electron component of the exciton) delocalized over the titanium atoms in the middle plane of the particle (see Figure 3). This assignment is supported by the difference between the Löwdin charges of the atoms in the ground and S1 excited state, shown in section ESI-4 of the Supporting Information. These Löwdin S1–S0 charge differences display clear evidence of excess negative charge on the titanium atoms in the middle plane (excited electron component) and excess positive charge (hole component) on the oxygen atoms in the core of the particle.

Figure 3

Figure 3. Leading orbital contributions to the lowest TD-CAM-B3LYP S1 excitation for the TiO2 rutile nanoparticle (only orbitals with a contribution larger than 5% are shown). The isodensity plots for the orbitals are calculated at a value of 0.1 au, where the green and purple lobes represent the sign of the wave function (see Figure S1 in section ESI-3 of the Supporting Information for the equivalent figure for the self-trapped exciton).

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The predicted oscillator strength of the free S1 exciton is rather low (7 × 10–6). While not dark, the absorption onset is likely to be low in intensity compared to excitonic excitations at higher energy/shorter wavelength. On the basis of this oscillator strength, the lifetime of the free S1 exciton, or at least the lifetime neglecting radiationless de-excitation through internal conversion, can be estimated using the Einstein equation to be approximately 0.2 ms, rather long in line with the low oscillator strength.

Exciton Self-Trapping

After excited state relaxation on the S1 potential energy surface, we found an excited state minimum (S1min) at which the self-trapped S1 exciton (S1/S1min) is 0.7 eV more stable than at the ground state geometry (S1/S0min). The vertical singlet photoluminescence (fluorescence) signature of this self-trapped exciton is predicted to be 2.95 eV, red-shifted by ∼1.0 eV compared with the optical gap.
The considerable excited state relaxation and Stokes’ shift, though smaller than that of the smaller hydrated nanoparticles previously studied, (54) are clearly linked to the significant localization induced by self-trapping. Analysis of S1–S0 Löwdin charge differences for the self-trapped exciton geometry shows that both components of the exciton have become localized on atoms on the top (110) face of the particle (see also section ESI-4 of the Supporting Information, Table S4), and we will henceforth refer to this S1 minimum as that of a self-trapped surface exciton. The majority of the hole component is localized on a two-coordinated oxygen atom and the majority of the excited electron component on two 4 + 1b + 1t coordinated titanium atoms adjacent to this oxygen atom (see Figure 4, where 4 + 1b + 1t signifies that these titanium atoms are coordinated by four oxygen atoms, one bridging hydroxyl, and one terminal hydroxyl). The largest structural distortion associated with the exciton localization is the elongation of the bond distances between the two-coordinated oxygen atom and the two adjacent titanium atoms by ∼10%.

Figure 4

Figure 4. Geometry of the TD-CAM-B3LYP relaxed S1 excited state minimum (S1/S1min) for the TiO2 rutile nanoparticle corresponding to the self-trapped surface exciton. Red spheres denote oxygen atoms, whereas gray and white represent titanium and hydrogen atoms, respectively. The green (Ti atoms) and blue (O atoms) spheres represent the atoms that are mostly involved with the exciton (hole and electron) self-trapping.

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The oscillator strength of this S1 self-trapped surface exciton (1 × 10–6) is slightly reduced compared to that of its free counterpart at the ground state geometry. This, together with the resulting predicted relatively long lifetime of the self-trapped exciton (3 ms), again calculated using the Einstein equation, might make the fluorescence hard to observe experimentally. Radiationless de-excitation through internal conversion, possibly coupled with phosphorescence from the lowest triplet state (T1 exciton) populated through intersystem crossing modulated by spin–orbit coupling, is likely to be the more prominent route for the system to relax back to the ground state.
The predicted bright S1 exciton lifetimes, for both the free and the self-trapped surface versions, are roughly 3 orders of magnitudes longer than the overall exciton lifetime determined experimentally for rutile single crystals through transient adsorption spectroscopy (<1 ns). (74) We cannot practically calculate the dark internal conversion contribution to the exciton de-excitation rate for such large particles. Such a calculation would require surface-hopping excited-state molecular dynamic calculations, which are currently tractable for systems containing ∼20 heavy atoms only. However, as the direct gap of bulk rutile goes together with a short exciton lifetime in rutile single crystals and vice versa the nondirect gap in bulk anatase with a long(er) exciton lifetime in anatase single crystals (>10 ns  (74)), it is likely that the bulk exciton lifetime is dominated by bright de-excitation. In which case, it appears that going from the bulk to nanoparticles at least significantly reduces the bright exciton de-excitiation rate.
Excited state relaxation is also a good illustration for the need to employ the range-separated CAM-B3LYP functional when studying TiO2 particles. As can be seen in section ESI-5 of the Supporting Information, TD-B3LYP predicts a much red-shifted fluorescence signal (1.1 eV) and a much larger energy difference between the free and self-trapped exciton (S1/S0min and S1/S1min), i.e., a greater degree of excited state relaxation. Calculation of the Λ diagnostic developed by Peach et al. (75) suggests that, in line with our previous work on smaller nanoparticles, (53, 54) these large differences relative to what TD-CAM-B3LYP predicts arise from the fact that the lowest singlet exciton obtains a strong charge-transfer (CT) character while relaxing. Nonhybrid XC potentials or hybrid XC potentials with a low percentage of HFLE are known to severely underestimate excitation energies of such excitations with strong CT character. (53, 54) In contrast, range-separated XC-potentials, such as CAM-B3LYP, have explicitly been designed to describe both CT and local excitation in a balanced manner.
Finally, as previously observed for ZnS nanoparticles, (76, 77) further self-trapped exciton minima might exist beyond the minimum corresponding to the self-trapped surface exciton discussed above, where the latter additional minima are separated on the S1 potential energy surface from the ground state geometry by an energetic barrier. Indeed S1 relaxation starting from the approximate T1 minimum energy geometry obtained through Δ-SCF (see below) rather than the ground state geometry finds a second alternative S1 self-trapped exciton minimum energy geometry. This self-trapped exciton, which is a further 0.23 eV more stable than the surface self-trapped exciton, is localized on the center of the particle rather than the surface (for more details see section ESI-6 of the Supporting Information) and will henceforth be referred to as the bulklike exciton, where the latter name makes reference to the coordination of the atoms involved rather than the properties of the exciton.

Free Electron and Hole

The rutile nanoparticle is predicted using CAM-B3LYP to have a vertical ionization potential of 7.92 eV and a vertical electron affinity of 3.44 eV. The energy required to make a pair of free charge carriers, the quasiparticle or band gap, therefore is calculated to be 4.48 eV. As a result, our calculations suggest that 0.48 eV is required to ionize the S1 exciton into a free electron on one particle and a free hole on another particle (the rutile nanoparticle is too small for an excited electron and hole to be separated sufficiently far for them to not interact). The predicted vertical EA and IP values for the rutile nanoparticle are similar in magnitude as those calculated for the low-energy (nonhydrated) bulk rutile surfaces using GW/DFT. (35) This is especially true in the case of the vertical IP potential (IP110 of 7.51 eV), while the vertical EA potential of the nanoparticle is more negative than its predicted bulk analogue (EA110 of 4.67 eV).
Just as the S1 exciton, both the excess electron and hole are predicted to strongly and barrierlessly self-trap as small polarons on fragments of the rutile nanoparticle with self-trapping energies of 1.1 and 2.2 eV, respectively. The adiabatic ionization potential therefore at 5.75 eV is significantly reduced relative to its vertical counterpart, while the adiabatic electron affinity is moderately larger than the vertical electron affinity at 4.52 eV. Calculations using the B3LYP XC potential, see section ESI-5 of the Supporting Information, predict similar behavior. More importantly perhaps, dissociation of the (surface self-trapped) exciton into a self-trapped electron on one particle and self-trapped hole on another particle is strongly favored energetically (by 2.10 eV).
On the basis of an analysis of the Löwdin spin population, the free electron self-trapping is associated with a complete localization of the excess electron on the central six-coordinated titanium atom, forming in essence a Ti3+ center (see Table S7 in section ESI-7 of the Supporting Information). The latter six-coordinated titanium atom is the same atom on which the excited electron component of the exciton is predicted to localize on in the case of the bulk-like self-trapped exciton. The hole in comparison is predicted to self-trap nearly completely on a two-coordinated oxygen atom on the top (110) face of particle, forming an O– center (see Table S8 in section ESI-7 of the Supporting Information). The latter two-coordinated oxygen atom is the same atom where the hole component of the self-trapped surface exciton is predicted to localize. In both cases the trapping is associated with elongation of the bonds around the atom on which the charge becomes trapped (by 3–5% in the case of the trapped electron and 13.5–14.5% for the trapped hole).
The calculated electron self-trapping energy for the rutile nanoparticle (3 × 3 × 3) is slightly larger than predicted by Friesner and co-workers for its larger 5 × 5 × 5 counterpart (0.45 eV). (38) The free charge-carrier trapping energies predicted for the rutile nanoparticle are also considerably larger than those previously reported for bulk rutile and (nonhydrated) rutile surfaces, (27-29) irrespective of the XC potential used (see also section ESI-5 of the Supporting Information), even while similar small polaron Ti3+/O– centers are formed in both the bulk and the nanoparticle. This is especially apparent in the case of the free hole, where the trapping energy found for the rutile nanoparticle is an order of magnitude larger than that calculated for bulk rutile (27) and more than 2 times as large as that predicted for different unhydrated rutile surfaces. (28)

Triplet Exciton

A triplet exciton (T1) can be formed from the S1 exciton through intersystem crossing, mediated by spin–orbit coupling. At the ground state geometry the free T1 exciton is effectively degenerate with the free S1 exciton (ΔS–T < 5 meV). We cannot perform a TD-DFT energy minimization for the T1 exciton because the code we use for the TD-CAM-B3LYP calculations lacks analytical TD-DFT gradients for triplet excited states (see section ESI-8 of the Supporting Information for a discussion of Δ-SCF results). However, as the T1 and S1 excitons are also effectively degenerate at both the S1 surface and bulklike self-trapped exciton geometries (ΔS–T < 15 meV), this singlet/triplet near degeneracy appears to be a global feature of the rutile nanoparticle S1/T1 excited-state potential energy surfaces.

Redox Potentials

Using the information discussed above, one can calculate the reduction potentials associated with the free charge carriers and the excitons. Figure 5 shows the (TD-)CAM-B3LYP predicted vertical and adiabatic potentials relative to the standard hydrogen electrode, considering the self-trapped surface exciton in the case of the adiabatic IP* and EA* potentials. Figure 5 also includes the potentials for the reduction of protons and the oxidation of water, as calculated with CAM-B3LYP. While CAM-B3LYP improves the description of excited states in TiO2 relative to B3LYP, it gives a slightly worse description of the water potentials, overestimating the potential difference associated with the overall water splitting reaction (1.55 V CAM-B3LYP and 1.05 V B3LYP vs 1.23 V experimentally). The potentials for the water half-reaction are given both for the case of pH 0 and pH 7. The latter case is probably most relevant, not only because pH 7 is the pH of fresh water but also because we study here a rutile nanoparticle that is not (de)protonated and pH 7 is closer to the point of zero charge of rutile TiO2 (∼pH 5) than pH 0. A plot of the potentials calculated with (TD-)B3LYP can be found in the Supporting Information (Figure S3 in section ESI-5).
The vertical and adiabatic potentials predicted by (TD-)CAM-B3LYP, in Figure 5, are rather different, something not observed for polymer photocatalysts. (56, 57) Focusing first on the vertical potentials, there is a clear driving force for water oxidation by both free holes (IP) and the free exciton (EA*) in this case. There is also a small driving force for proton reduction by both the free electron (EA) and free exciton (IP*). The adiabatic potentials, however, suggest that after self-trapping both proton reduction and water oxidation by self-trapped charge carriers are endergonic, while both are strongly exergonic in the case of the self-trapped exciton. This latter is of limited practical use, however, as reduction or oxidation driven by the self-trapped exciton (IP* and EA*, half-reactions C and D) inherently generates the self-trapped free charge carriers discussed above that are chemically inert with respect to water and do not take part in any further reaction. The adiabatic exciton potentials IP* and EA* predicted for the case of the bulklike self-trapped exciton, see Figure S4 in the Supporting Information, are very similar to those in Figure 5 calculated for the self-trapped surface exciton, suggesting that the above observations are relatively insensitive to the exact localization of the self-trapped exciton.

Figure 5

Figure 5. (TD-)CAM-B3LYP predicted EA, IP, EA*, and IP* vertical and adiabatic potentials of the TiO2 rutile nanoparticle in water (ε = 78.0), compared to the HER (green line) and OER (red line) potentials at pH = 0 (broken lines) and pH = 7 (dotted lines). Adiabatic EA* and IP* potentials were calculated for the case of the self-trapped surface exciton; see Figure S4 in the Supporting Information for the equivalent figure for the case of the bulk-like self-trapped exciton.

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These observations are not unique to (TD-)CAM-B3LYP; the free charge carriers potentials calculated with (TD-)B3LYP in the Supporting Information show very similar behavior (see Figure S3 in section ESI-5 of the Supporting Information; the adiabatic exciton potentials IP* and EA*, in contrast, are rather different because of the problems of TD-B3LYP to accurately describe charge-transfer excitations, discussed above). Potentials for the triplet exciton are not shown in Figures 5 and S4, but because of the observed apparent near degeneracy between the T1 and S1 exciton, discussed above, they are expected to lie very close if not on top of their S1 equivalents.

Water Splitting and the Effect of Particle Size

The rutile nanoparticle potentials discussed above present an interesting situation, where the system’s thermodynamic ability to drive the water splitting half reactions is significantly different for free and self-trapped electronic states. To a certain extent, the sets of vertical and adiabatic potentials represent two different physical limits. Vertical potentials describe the situation where the rate of the elementary half-reactions driven by the photocatalyst, or the rate of hole and/or electron transport to a cocatalyst, is significantly faster than the nuclear relaxation associated with self-trapping, while adiabatic potentials represent the exact opposite limit. In the absence of the ability to perform ab initio surface-hopping excited-state molecular dynamics calculations on such particles, it is difficult to be sure which situation is most realistic for a working rutile nanoparticulate photocatalyst. However, as the rate of any chemical surface reaction is likely to be at best comparable to the rate of nuclear relaxation in the particle, the adiabatic case is probably the most relevant in practice. This would mean that small rutile nanoparticles, like that studied here, are thermodynamically unable to drive the splitting of water.
Building forward on this analysis, one can speculate that the fact that the vertical and adiabatic potentials are significantly different might be one of the reasons behind the experimentally observed change in water splitting activity with particle size. To investigate this hypothesis, we would ideally compare the vertical and adiabatic potentials calculated for the rutile nanoparticles and the rutile bulk. While, as discussed above, calculated vertical potentials for rutile slabs with different surfaces have been reported in the literature, we are not aware of any calculated adiabatic potentials for bulk rutile (surfaces). However, as the difference between the vertical and adiabatic potentials in the case of the free charge carriers (half-reactions E and F, EA and IP) is essentially their respective self-trapping energies, we can use the self-trapping energies predicted for the nanoparticle and the bulk to estimate how the difference between the two sets of potentials might change with particle size.
As discussed above, irrespective of the XC potential used, the free charge carrier self-trapping energies predicted for the rutile nanoparticle are considerably larger than those previously reported for bulk rutile and rutile surfaces, as well as slightly larger than those calculated for a larger rutile nanoparticle. It thus stands to reason that the magnitude of the difference between the adiabatic and vertical potentials will decrease with increasing particle size and will be at its largest for small nanoparticles. Assuming that the vertical potentials are relatively independent of particle size, in line with the observed similarities between our calculated nanoparticle’s vertical potentials and those reported for bulk slabs, this would suggest that the driving forces for reduction and oxidation by self-trapped free charge carriers (IP and EA) are smallest for rutile nanoparticles and will increase with increasing particle size. Following the same logic, and while we lack information on the self-trapping of excitons for bulk rutile (surfaces), it is likely that the difference between the vertical and adiabatic potentials involving the exciton (IP* and EA*) should also decrease with increasing particle size. Assuming again roughly constant vertical potentials, the driving forces for reduction and oxidation by the self-trapped exciton would then be largest for rutile nanoparticles and decrease with increasing particle size. Overall, this approximate analysis thus suggests that on thermodynamic grounds the activity of rutile nanoparticles should decrease when reducing the particle size and that the limiting factor is the decline in the driving forces for oxidation and reduction by the free charge carriers.
The origin of these large differences between the vertical and adiabatic potentials for the nanoparticle, as well as the large underlying self-trapping energies, is most likely the fact that the structure of nanoparticles is much less constrained, more polarizable, compared to that of bulk rutile TiO2 and even bulk surfaces. The atoms in the nanoparticle are therefore freer to move when accommodating the strain associated with the localization of a free charge carrier or exciton on them, allowing for a larger degree of self-trapping.

Conclusions

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We predict that small rutile TiO2 nanoparticles are thermodynamically unable to drive photocatalytic water splitting because of the strong self-trapping of free electrons and holes in such nanoparticles. A comparison with the self-trapping energy values calculated for free charge carriers in bulk rutile (surfaces), which are much smaller, further suggests that the experimentally observed reduction in water splitting activity with particle size might be the direct result of the increased stabilization of self-trapped free charge carriers, relative to their nontrapped counterparts, in nanoparticles. The origin of the strong self-trapping of free charge carriers in small nanoparticles is probably related to the fact that the atoms on the surfaces of these nanoparticles are structurally less constrained, even relative to atoms on bulk surfaces.

Supporting Information

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(TD-)B3LYP and (TD-)CAM-B3LYP data for the rutile nanoparticle, as well as data for smaller nanoparticles, the bulk-like self-trapped exciton minimum energy geometry, and results from Δ-SCF calculations for the lowest triplet excited state. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.5b01512.

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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
    • Martijn A. Zwijnenburg - Department of Chemistry, University College London, 20 Gordon Street, London, WC1H 0AJ, U.K.;  Email: [email protected]
  • Author
    • Enrico Berardo - Department of Chemistry, University College London, 20 Gordon Street, London, WC1H 0AJ, U.K.
  • Notes
    The authors declare no competing financial interest.

Acknowledgment

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We kindly acknowledge Prof. S. Bromley, Dr. C. Butchosa, Dr. A. Cowan, Prof. F. Illas, P. Guiglion, Dr. K. Kowalski, Prof. F. Osterloh, Prof. I. Parkin, Dr. S. Shevlin, Prof. A. Shluger, Prof. F. Furche, Dr. Monica Calatayud, Dr. A. A. Sokol, and Dr. S. Woodley for stimulating discussions. M.A.Z. acknowledges the UK Engineering and Physical Sciences Research Council (EPSRC) for a Career Acceleration Fellowship (Grant EP/I004424/1). This study has further been supported by a UCL Impact studentship award to E.B. Computational time on the computers of the Unity High Performance Computing Facility at University College London, the IRIDIS regional high-performance computing service provided by the e-Infrastructure South Centre for Innovation (EPSRC Grants EP/K000144/1 and EP/K000136/1), and ARCHER the UK’s national high-performance computing service (via our membership of the UK’s HPC Materials Chemistry Consortium, which is funded by EPSRC grant EP/L000202/1) is gratefully acknowledged.

References

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    Kumar, S. Girish; Devi, L. Gomathi
    Journal of Physical Chemistry A (2011), 115 (46), 13211-13241CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
    A review. Titania is one of the most widely used benchmark std. photocatalysts in the field of environmental applications. However, the large band gap of titania and massive recombination of photogenerated charge carriers limit its overall photocatalytic efficiency. The former can be overcome by modifying the electronic band structure of titania including various strategies like coupling with a narrow band gap semiconductor, metal ion/nonmetal ion doping, codoping with two or more foreign ions, surface sensitization by org. dyes or metal complexes, and noble metal deposition. The latter can be cor. by changing the surface properties of titania by fluorination or sulfation or by the addn. of suitable electron acceptors besides mol. oxygen in the reaction medium. This review encompasses several advancements made in these aspects, and also some of the new phys. insights related to the charge transfer events like charge carrier generation, trapping, detrapping, and their transfer to surface are discussed for each strategy of the modified titania to support the conclusions derived. The synergistic effects in the mixed polymorphs of titania and also the theories proposed for their enhanced activity are reported. A recent venture on the synthesis and applications of anatase titania with a large percentage of reactive {001} facets and their band gap extension to the visible region via nonmetal ion doping which is a current hot topic is briefly outlined.
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  18. 18
    Scanlon, D. O.; Dunnill, C. W.; Buckeridge, J.; Shevlin, S. A.; Logsdail, A. J.; Woodley, S. M.; Catlow, C. R. A.; Powell, M. J.; Palgrave, R. G.; Parkin, I. P.; Watson, G. W.; Keal, T. W.; Sherwood, P.; Walsh, A.; Sokol, A. A. Band Alignment Of Rutile And Anatase TiO2 Nat. Mater. 2013, 12, 798– 801
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    Band alignment of rutile and anatase TiO2
    Scanlon, David O.; Dunnill, Charles W.; Buckeridge, John; Shevlin, Stephen A.; Logsdail, Andrew J.; Woodley, Scott M.; Catlow, C. Richard A.; Powell, Michael. J.; Palgrave, Robert G.; Parkin, Ivan P.; Watson, Graeme W.; Keal, Thomas W.; Sherwood, Paul; Walsh, Aron; Sokol, Alexey A.
    Nature Materials (2013), 12 (9), 798-801CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)
    The most widely used oxide for photocatalytic applications owing to its low cost and high activity is TiO2. The discovery of the photolysis of water on the surface of TiO2 in 1972 launched four decades of intensive research into the underlying chem. and phys. processes involved. Despite much collected evidence, a thoroughly convincing explanation of why mixed-phase samples of anatase and rutile outperform the individual polymorphs has remained elusive. One long-standing controversy is the energetic alignment of the band edges of the rutile and anatase polymorphs of TiO2. We demonstrate, through a combination of state-of-the-art materials simulation techniques and X-ray photoemission expts., that a type-II, staggered, band alignment of ∼ 0.4eV exists between anatase and rutile with anatase possessing the higher electron affinity, or work function. Our results help to explain the robust sepn. of photoexcited charge carriers between the two phases and highlight a route to improved photocatalysts.
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    Kapilashrami, M.; Zhang, Y.; Liu, Y.-S.; Hagfeldt, A.; Guo, J. Probing the Optical Property and Electronic Structure of TiO2 Nanomaterials for Renewable Energy Applications Chem. Rev. 2014, 114, 9662– 9707
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    Probing the optical property and electronic structure of TiO2 nanomaterials for renewable energy applications
    Kapilashrami, Mukes; Zhang, Yangfeng; Liu, Yi-Sheng; Hagfeldt, Anders; Guo, Jinghua
    Chemical Reviews (Washington, DC, United States) (2014), 114 (19), 9662-9707CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
    A review.
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    Quesada-Cabrera, R.; Sotelo-Vazquez, C.; Bear, J. C.; Darr, J. A.; Parkin, I. P. Photocatalytic Evidence of the Rutile-to-Anatase Electron Transfer in Titania Adv. Mater. Interfaces 2014, 1, 1– 7
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    Ohtani, B.; Ogawa, Y.; Nishimoto, S. Photocatalytic Activity Of Amorphous-Anatase Mixture Of Titanium(IV) Oxide Particles Suspended In Aqueous Solutions J. Phys. Chem. B 1997, 101, 3746– 3752
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    Photocatalytic Activity of Amorphous-Anatase Mixture of Titanium(IV) Oxide Particles Suspended in Aqueous Solutions
    Ohtani, Bunsho; Ogawa, Yoshimasa; Nishimoto, Sei-ichi
    Journal of Physical Chemistry B (1997), 101 (19), 3746-3752CODEN: JPCBFK; ISSN:1089-5647. (American Chemical Society)
    Titanium(IV) oxide powders of various amorphous-anatase compns. were prepd. by heat treatment (573-1073 K) of amorphous TiO2 in air and characterized by differential scanning calorimetry, powder x-ray diffraction, and BET surface area measurements. An exothermic peak at ∼723 K in the DSC pattern was assigned to the crystn. of the amorphous phase to anatase; its heat of crystn. was used to evaluate the wt. fraction of amorphous phase. The fraction of anatase crystallites (f(anatase)) was calcd. as the remainder after the amorphous phase and contaminated water or org. residue. The size of anatase crystallites was slightly decreased but almost const. along with the increase in f(anatase), which was consistent with the small change in the BET surface area. These results suggested that each amorphous particle transforms into an anatase crystallite of similar size without sintering or crystal growth. The particles of mixt. of amorphous and anatase were used for three kinds of photocatalytic reactions in deaerated aq. suspensions: silver metal deposition, oxidn. of 2-propanol by bare powders, and dehydrogenation of 2-propanol by ex-situ and in-situ platinized powders. For all the reactions, the photocatalytic activity of amorphous TiO2 was negligible, increased almost linearly with f(anatase), and further improved by calcination of completely crystd. powder. The negligible activity of amorphous TiO2 was attributed to recombination of photoexcited electron and pos. hole at defects located on the surface and in the bulk of particles.
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    Kočí, K.; Obalová, L.; Matějová, L.; Plachá, D.; Lacný, Z.; Jirkovský, J.; Šolcová, O. Effect Of TiO2 Particle Size On The Photocatalytic Reduction Of CO2 Appl. Catal., B 2009, 89, 494– 502
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    Effect of TiO2 particle size on the photocatalytic reduction of CO2
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    Applied Catalysis, B: Environmental (2009), 89 (3-4), 494-502CODEN: ACBEE3; ISSN:0926-3373. (Elsevier B.V.)
    Pure TiO2 anatase particles with a crystallite diams. ranging from 4.5 to 29 nm were prepd. by pptn. and sol-gel method, characterized by x-ray diffraction (XRD), BET surface area measurement, UV-vis and SEM, and tested in CO2 photocatalytic redn. Methane and methanol were the main redn. products. The optimum particle size corresponding to the highest yields of both products was 14 nm. The obsd. optimum particle size is a result of competing effects of sp. surface area, charge-carrier dynamics and light absorption efficiency.
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    Anpo, M.; Shima, T.; Kodama, S.; Kubokawa, Y. Photocatalytic Hydrogenation Of Propyne With Water On Small-Particle Titania: Size Quantization Effects And Reaction Intermediates J. Phys. Chem. 1987, 91, 4305– 4310
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    Xu, N. P.; Shi, Z. F.; Fan, Y. Q.; Dong, J. H.; Shi, J.; Hu, M. Z. C. Effects Of Particle Size Of TiO2 On Photocatalytic Degradation Of Methylene Blue In Aqueous Suspensions Ind. Eng. Chem. Res. 1999, 38, 373– 379
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    Effects of Particle Size of TiO2 on Photocatalytic Degradation of Methylene Blue in Aqueous Suspensions
    Xu, Nanping; Shi, Zaifeng; Fan, Yiqun; Dong, Junhang; Shi, Jun; Hu, Michael Z.-C.
    Industrial & Engineering Chemistry Research (1999), 38 (2), 373-379CODEN: IECRED; ISSN:0888-5885. (American Chemical Society)
    The influence of particle size of TiO2 on the photocatalytic degrdn. of methylene blue (MB) in a suspended aq. soln. was studied. The results suggested that the adsorption rate and adsorbability of MB on suspended TiO2 particles increased as the particle sizes of TiO2 decreased. Photocatalytic activity of TiO2 also increased as the particle size of TiO2 became smaller, esp. when the particle size is <30 nm. The half-life (t0.5) of the photocatalytic degrdn. of MB also decreased as the particle sizes of TiO2 decreased. The 1st-order reaction rate const. for photodegrdn. of MB increased as the particle size of TiO2 decreased. The initial degrdn. rate of MB in a suspended model was higher than that of a fixed-bed model. This will overcome the difficulty of prepn. of ultrafine TiO2 catalyst particles. Once the problem of sepn. of fine TiO2 particles is solved, a TiO2 suspended photoreactor could be provided on an industrial basis.
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    Mattioli, G.; Alippi, P.; Filippone, F.; Caminiti, R.; Amore Bonapasta, A. Deep versus Shallow Behavior of Intrinsic Defects in Rutile and Anatase TiO2 Polymorphs J. Phys. Chem. C 2010, 114, 21694– 21704
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    Deep versus Shallow Behavior of Intrinsic Defects in Rutile and Anatase TiO2 Polymorphs
    Mattioli, Giuseppe; Alippi, Paola; Filippone, Francesco; Caminiti, Ruggero; Bonapasta, Aldo Amore
    Journal of Physical Chemistry C (2010), 114 (49), 21694-21704CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
    The structural and electronic properties of oxygen vacancies (VOx) and titanium interstitials (Ti(i)) in the bulk of the rutile and anatase forms of TiO2 have been investigated with LSD-GGA + U ab initio simulations. In particular, formation energies of the charged and neutral forms of the VOx and Ti(i) defects as well as the corresponding vertical and thermodn. transition levels have been estd. The achieved results can reconcile the apparent inconsistency of exptl. obsd. deep donor levels with the n-type cond. obsd. in reduced TiO2. They show indeed that both defects give rise to vertical transition levels about 1 eV below the conduction band (CB), in agreement with exptl. measures, and to thermodn. transition levels close to the CB. That is, these defects behave as deep donors, when looking at vertical transitions, and as shallow donors, when the effects of the structural relaxations are taken into account. A major part of the explanation of this behavior is played by the polaron-like character of the defect states, which was already noted, but not deepened, in literature. Finally, it is shown that the application of the U correction to both Ti and O species gives qual. similar results, but with a better agreement to exptl. findings, with respect to the application to Ti only. The former approach gives pretty similar results, for both rutile and anatase bulk properties, to those coming from HSE hybrid functional calcns.
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    Di Valentin, C.; Selloni, A. Bulk and Surface Polarons in Photoexcited Anatase TiO2 J. Phys. Chem. Lett. 2011, 2, 2223– 2228
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    Bulk and Surface Polarons in Photoexcited Anatase TiO2
    Di Valentin, Cristiana; Selloni, Annabella
    Journal of Physical Chemistry Letters (2011), 2 (17), 2223-2228CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
    Using hybrid functional electronic structure calcns., the structure and energetics of photogenerated electrons and holes in the bulk and at the (101) surface of anatase TiO2 were studied. Excitons formed upon UV irradn. become self-trapped, consistent with the observation of temp.-dependent Urbach tails in the absorption spectrum and a large Stokes shift in the luminescence band of anatase. Electron and hole polarons are localized at Ti3+ and O- lattice sites, resp. At the surface, the trapping sites generally correspond to undercoordinated Ti3+5c and O-2c surface atoms or to isolated OH species in the case of a hydroxylated surface. The polaron trapping energy is considerably larger at the surface than in the bulk, indicating that it is energetically favorable for the polarons to travel from the bulk to the surface. Computed 1-electron energy levels in the gap and hyperfine coupling consts. compare favorably with oxidn. potential and EPR measurements.
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    Varley, J. B.; Janotti, A.; Franchini, C.; Van de Walle, C. G. Role Of Self-Trapping In Luminescence And p-Type Conductivity Of Wide-Band-Gap Oxides Phys. Rev. B 2012, 85, 0811091– 0811094
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    Zawadzki, P.; Laursen, A. B.; Jacobsen, K. W.; Dahl, S.; Rossmeisl, J. Oxidative Trends Of TiO2-Hole Trapping At Anatase And Rutile Surfaces Energy Environ. Sci. 2012, 5, 9866– 9869
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    Oxidative trends of TiO2-hole trapping at anatase and rutile surfaces
    Zawadzki, Pawel; Laursen, Anders B.; Jacobsen, Karsten Wedel; Dahl, Soren; Rossmeisl, Jan
    Energy & Environmental Science (2012), 5 (12), 9866-9869CODEN: EESNBY; ISSN:1754-5706. (Royal Society of Chemistry)
    Understanding the nature of photogenerated carriers in a photocatalyst is central to understanding its photocatalytic performance. Based on d. functional theory calcn. the authors show that for TiO2, the most popular photocatalyst, the electron hole self-trapping leads to band gap states which position is dependent on the type of surface termination. Such variations in hole state energies can lead to differences in photocatalytic activity among rutile and anatase surface facets. The authors find that the calcd. hole state energies correlate with photodeposition and photoetching rates. The authors anticipated that their results can aid the design of more reactive photocatalysts based on TiO2 and their approach can be utilized for other relevant photocatalysts as well.
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    Spreafico, C.; VandeVondele, J. The Nature Of Excess Electrons In Anatase And Rutile From Hybrid DFT And RPA Phys. Chem. Chem. Phys. 2014, 16, 26144– 26152
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    The nature of excess electrons in anatase and rutile from hybrid DFT and RPA
    Spreafico, Clelia; VandeVondele, Joost
    Physical Chemistry Chemical Physics (2014), 16 (47), 26144-26152CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
    The behavior of excess electrons in undoped and defect free bulk anatase and rutile TiO2 has been investigated by state-of-the-art electronic structure methods including hybrid d. functional theory (DFT) and the RPA. Consistent with expt., charge trapping and polaron formation is obsd. in both anatase and rutile. The difference in the anisotropic shape of the polarons is characterized, confirming for anatase the large polaron picture. For anatase, where polaron formation energies are small, charge trapping is obsd. also with std. hybrid functionals, provided the simulation cell is sufficiently large (864 atoms) to accommodate the lattice relaxation. Even though hybrid orbitals are required as a starting point for RPA in this system, the obtained polaron formation energies are relatively insensitive to the amt. of Hartree-Fock exchange employed. The difference in trapping energy between rutile and anatase can be obtained accurately with both hybrid functionals and RPA. Computed activation energies for polaron hopping and delocalization clearly show that anatase and rutile might have different charge transport mechanisms. In rutile, only hopping is likely, whereas in anatase hopping and delocalization are competing. Delocalization will result in conduction-band-like and thus enhanced transport. Anisotropic conduction, in agreement with exptl. data, is obsd., and results from the tendency to delocalize in the [001] direction in rutile and the (001) plane in anatase. For future work, our calcns. serve as a benchmark and suggest RPA on top on hybrid orbitals (PBE0 with 30% Hartree-Fock exchange), as a suitable method to study the rich chem. and physics of TiO2.
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    Sildos, I.; Suisalu, A.; Aarik, J.; Sekiya, T.; Kurita, S. Self-Trapped Exciton Emission In Crystalline Anatase J. Lumin. 2000, 87–89, 290– 292
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    Self-trapped exciton emission in crystalline anatase
    Sildos, I.; Suisalu, A.; Aarik, J.; Sekiya, T.; Kurita, S.
    Journal of Luminescence (2000), 87-89 (), 290-292CODEN: JLUMA8; ISSN:0022-2313. (Elsevier Science B.V.)
    A comparative spectroscopic study of self-trapped exciton (STE) emission in anatase single crystals and thin films was carried out at 5 K In the single crystals, a strongly polarized STE emission with an elec. vector perpendicular to the c-axis was obsd. Influence of annealing on the spectral characteristics of samples was tested.
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    Watanabe, M.; Hayashi, T. Time-Resolved Study Of Self-Trapped Exciton Luminescence In Anatase TiO2 Under Two-Photon Excitation J. Lumin. 2005, 112, 88– 91
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    Time-resolved study of self-trapped exciton luminescence in anatase TiO2 under two-photon excitation
    Watanabe, M.; Hayashi, T.
    Journal of Luminescence (2005), 112 (1-4), 88-91CODEN: JLUMA8; ISSN:0022-2313. (Elsevier B.V.)
    We have studied the dynamics of photocarriers in anatase phase of TiO2 with time-resolved spectroscopy of self-trapped exciton (STE) luminescence. The decay curve of luminescence under one-photon excitation well above the band gap energy shows power-law behavior, suggesting that spatial sepn. of an electron-hole pair occurs under interband excitation. A similar result is obtained under two-photon excitation. We conclude that the carrier sepn. is ascribed to intrinsic dynamical properties of photocarriers in anatase. It is inferred that the carrier sepn. occurs during energy relaxation towards the band bottom. Temp. dependence of the decay curve is also discussed in terms of thermal dissocn. of STEs.
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    Kernazhitsky, L.; Shymanovska, V.; Gavrilko, T.; Naumov, V.; Fedorenko, L.; Kshnyakin, V.; Baran, J. Room Temperature Photoluminescence Of Anatase And Rutile TiO2 Powders J. Lumin. 2014, 146, 199– 204
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    Room temperature photoluminescence of anatase and rutile TiO2 powders
    Kernazhitsky, L.; Shymanovska, V.; Gavrilko, T.; Naumov, V.; Fedorenko, L.; Kshnyakin, V.; Baran, J.
    Journal of Luminescence (2014), 146 (), 199-204CODEN: JLUMA8; ISSN:0022-2313. (Elsevier B.V.)
    The optical absorption and photoluminescence of anatase and rutile TiO2 were studied at room temp. TiO2 nanocryst. powders were synthesized in the form of pure anatase or rutile. The samples were characterized by X-ray diffraction, X-ray fluorescence, Raman spectroscopy, optical absorption and photoluminescence (PL) methods. The PL spectra were studied under the intensive UV (3.68 eV) laser excitation. Some interesting features in the PL spectra including the well-resolved peaks of excitonic and band-band transitions in TiO2 were obsd., to our knowledge, for the first time. It is shown that PL bands including peaks at 2.71-2.81 eV and its phonon replicas in anatase and rutile TiO2 arise from the excitonic e--h+ recombination via oxygen vacancies. The excitonic peak at 2.91 eV is attributed to the recombination of self-trapped excitons in anatase or free excitons in rutile TiO2. The PL peaks within 3.0-3.3 eV in anatase TiO2 are ascribed to indirect allowed transitions due to the band-band e--h+ recombination. The peaks at 3.03 eV and 3.26 eV are attributed to the free exciton emission near the fundamental band edge of rutile and anatase TiO2, resp. The influence of TiO2 crystal structure and calcination temp. on the PL spectra is discussed.
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    Stevanovic, V.; Lany, S.; Ginley, D. S.; Tumas, W.; Zunger, A. Assessing Capability Of Semiconductors To Split Water Using Ionization Potentials And Electron Affinities Only Phys. Chem. Chem. Phys. 2014, 16, 3706– 3714
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    Stevanovic, Vladan; Lany, Stephan; Ginley, David S.; Tumas, Willam; Zunger, Alex
    Physical Chemistry Chemical Physics (2014), 16 (8), 3706-3714CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
    We show in this article that the position of semiconductor band edges relative to the water redn. and oxidn. levels can be reliably predicted from the ionization potentials (IP) and electron affinities (AE) only. Using a set of 17 materials, including transition metal compds., we show that accurate surface dependent IPs and EAs of semiconductors can be computed by combining d. functional theory and many-body GW calcns. From the extensive comparison of calcd. IPs and EAs with available exptl. data, both from photoemission and electrochem. measurements, we show that it is possible to sort candidate materials solely from IPs and EAs thereby eliminating explicit treatment of semiconductor/water interfaces. We find that at pH values corresponding to the point of zero charge there is on av. a 0.5 eV shift of IPs and EAs closer to the vacuum due to the dipoles formed at material/water interfaces.
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    Blagojevic, V.; Chen, Y.-R.; Steigerwald, M.; Brus, L.; Friesner, R. A. Quantum Chemical Investigation of Cluster Models for TiO2 Nanoparticles with Water-Derived Ligand Passivation: Studies of Excess Electron States and Implications for Charge Transport in the Gratzel Cell J. Phys. Chem. C 2009, 113, 19806– 19811
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    Li, Y.-F.; Liu, Z.-P. Particle Size, Shape And Activity For Photocatalysis On Titania Anatase Nanoparticles In Aqueous Surroundings J. Am. Chem. Soc. 2011, 133, 15743– 15752
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    Zhang, J.; Hughes, T. F.; Steigerwald, M.; Brus, L.; Friesner, R. A. Realistic Cluster Modeling of Electron Transport and Trapping in Solvated TiO2 Nanoparticles J. Am. Chem. Soc. 2012, 134, 12028– 12042
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    Zhang, J.; Steigerwald, M.; Brus, L.; Friesner, R. A. Covalent O-H Bonds as Electron Traps in Proton-Rich Rutile TiO2 Nanoparticles Nano Lett. 2014, 14, 1785– 1789
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    Rocca, D.; Gebauer, R.; De Angelis, F.; Nazeeruddin, M. K.; Baroni, S. Time-Dependent Density Functional Theory Study Of Squaraine Dye-Sensitized Solar Cells Chem. Phys. Lett. 2009, 475, 49– 53
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    Time-dependent density functional theory study of squaraine dye-sensitized solar cells
    Rocca, Dario; Gebauer, Ralph; De Angelis, Filippo; Nazeeruddin, Mohammad K.; Baroni, Stefano
    Chemical Physics Letters (2009), 475 (1-3), 49-53CODEN: CHPLBC; ISSN:0009-2614. (Elsevier B.V.)
    We employ time-dependent d. functional theory to study the optical properties of a squaraine sensitized TiO 2 system, as a model for the corresponding dye-sensitized solar cell. The all-org. squaraine dye is particularly promising for light absorption in the red spectral region. We compute the photoabsorption spectrum of a periodic TiO2 slab exposing anatase (101) surfaces, both for the clean slab and for the surface covered by the squaraine dye. Those spectra are compared to recent exptl. data. The main absorption peaks are analyzed, concluding that both direct and indirect charge injection mechanisms are active in this system.
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    Shevlin, S. A.; Woodley, S. M. Electronic and Optical Properties of Doped and Undoped (TiO2)n Nanoparticles J. Phys. Chem. C 2010, 114, 17333– 17343
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    Taylor, D. J.; Paterson, M. J. Calculations Of The Low-Lying Excited States Of The TiO2 Molecule J. Chem. Phys. 2010, 133, 204302
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    Sanchez-de-Armas, R.; Oviedo, J.; San-Miguel, M. A.; Sanz, J. F. Real-time TD-DFT Simulations in Dye Sensitized Solar Cells: The Electronic Absorption Spectrum of Alizarin Supported on TiO2 Nanoclusters J. Chem. Theory Comput. 2010, 6, 2856– 2865
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    Real-Time TD-DFT Simulations in Dye Sensitized Solar Cells: The Electronic Absorption Spectrum of Alizarin Supported on TiO2 Nanoclusters
    Sanchez-de-Armas, Rocio; Oviedo Lopez, Jaime; San-Miguel, Miguel A.; Sanz, Javier Fdez.; Ordejon, Pablo; Pruneda, Miguel
    Journal of Chemical Theory and Computation (2010), 6 (9), 2856-2865CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    The structural and electronic properties of the alizarin dye supported on TiO2 nanoclusters have been examd. by time-dependent d.-functional (TD-DFT) calcns. performed in the time-domain framework. The calcd. electronic absorption spectrum of free alizarin shows a 1st band centered at 2.67 eV that upon adsorption features a red shift by 0.31 eV, in agreement with both exptl. and previous theor. work. This red shift arises from a relative stabilization of the dye LUMO when adsorbed. To analyze the dependence of the electronic properties of the dye-support couple on the size of metal-oxide nanoparticles, different models of (TiO2)n nanoclusters have been used (with n = 1, 2, 3, 6, 9, 15, and 38). This minimal model theor. reproduces the main feature in the spectrum, the energy shift of the main band upon binding to TiO2. However, it fails in creating intermediate states which could play a significant role under real exptl. conditions (dynamics of the electronic transfer). Indeed, as the size of the nanocluster grows, the dye LUMO moves from the edge to well inside the conduction band (Ti 3d band). However, to assess the consistency of the time-domain approach in the case of such systems, conventional (frequency-domain) TD-DFT calcns. have been carried out. As far as the functional and basis set are equiv., both approaches lead to similar results. While for small systems the std. TD-DFT is better suited, for medium to large sized systems, the real-time TD-DFT becomes competitive and more efficient.
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    De Angelis, F.; Fantacci, S.; Gebauer, R. Simulating Dye-Sensitized TiO2 Heterointerfaces in Explicit Solvent: Absorption Spectra, Energy Levels, and Dye Desorption J. Phys. Chem. Lett. 2011, 2, 813– 817
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    Simulating Dye-Sensitized TiO2 Heterointerfaces in Explicit Solvent: Absorption Spectra, Energy Levels, and Dye Desorption
    De Angelis, Filippo; Fantacci, Simona; Gebauer, Ralph
    Journal of Physical Chemistry Letters (2011), 2 (7), 813-817CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
    Dye-sensitized solar cells (DSCs) represent a valuable, efficient, and low-cost alternative to conventional semiconductor photovoltaic devices. A deeper understanding of the dye/semiconductor heterointerface and of the dye-sensitized semiconductor/electrolyte interactions are fundamental for further progress in DSC technol. Here we report an ab initio mol. dynamics simulation of a dye-sensitized TiO2 heterointerface "immersed" in an explicit water environment for an efficient org. dye, followed by TDDFT excited state calcns. of the coupled dye/semiconductor/solvent system. This new computational protocol and the extended model system allows us to gain unprecedented insight into the excited state changes occurring for the solvated dye-sensitized heterointerface at room temp., and to provide an atomistic picture of water-mediated dye desorption.
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    Chiodo, L.; Salazar, M.; Romero, A. H.; Laricchia, S.; Della Sala, F.; Rubio, A. Structure, Electronic, And Optical Properties Of TiO2 Atomic Clusters: An Ab Initio Study J. Chem. Phys. 2011, 135, 244704
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    Auvinen, S.; Alatalo, M.; Haario, H.; Jalava, J. P.; Lamminmäki, R. J. Size And Shape Dependence Of The Electronic And Spectral Properties In TiO2 Nanoparticles J. Phys. Chem. C 2011, 115, 8484– 8493
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    Size and Shape Dependence of the Electronic and Spectral Properties in TiO2 Nanoparticles
    Auvinen, Sami; Alatalo, Matti; Haario, Heikki; Jalava, Juho-Pertti; Lamminmaki, Ralf-Johan
    Journal of Physical Chemistry C (2011), 115 (17), 8484-8493CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
    Electronic and spectral properties of small TiO2 particles were studied to gain more knowledge on their dependence on the crystal- and particle-size distributions. The goal is to extend the recently developed light scattering based method for detg. sub-μm size particles to nanoparticles. For that, the authors need to know how the refractive index function depends on the cluster size. As a 1st step, time-dependent d. functional theory (TDDFT) calcns. were used having a focus on the shape changes of the calcd. spectra, which can be related to changes in the refractive index function. Starting from the structure of TiO2 mol. for the 2 smallest particles and truncated bulk anatase structure for larger particles, the structures for (TiO2)n clusters, n = {1, 2, 8, 18, 28, 38}, were modeled. After the structure optimization using std. d. functional theory (DFT) approach, the photoabsorption spectra for the optimized particle structures were calcd. by using TDDFT calcns. The results show slight evidence of the band gap broadening in the case of 3 out of the smallest particles and strong structural dependence of electronic and spectral properties, which can partly be related to the transformation of the electron structure, and breaking of the crystal symmetry as the size of the particle becomes smaller. In the case of small particles their refractive index function can differ from the bulk values, and this has to be taken into account in the interpretation of light-scattering measurements.
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    Taylor, D. J.; Paterson, M. J. Vibronic Coupling Effects On The Structure And Spectroscopy Of Neutral And Charged TiO2 Clusters Chem. Phys. 2012, 408, 1– 10
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    Berardo, E.; Hu, H.; Kowalski, K.; Zwijnenburg, A. M. Coupled Cluster Calculations On TiO2 Nanoclusters J. Chem. Phys. 2013, 139, 0643131
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    Galynska, M.; Persson, P. Emerging Polymorphism in Nanostructured TiO2: Quantum Chemical Comparison of Anatase, Rutile, and Brookite Clusters Int. J. Quantum Chem. 2013, 113, 2611– 2620
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    Kandada, A. R.; Fantacci, S.; Guarnera, S.; Polli, D.; Lanzani, G.; De Angelis, F.; Petrozza, A. Role Of Hot Singlet Excited States In Charge Generation At The Black Dye/TiO2 Interface ACS Appl. Mater. Interfaces 2013, 5, 4334– 4339
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    Mattioli, G.; Amore Bonapasta, A.; Bovi, D.; Giannozzi, P. Photocatalytic and Photovoltaic Properties of TiO2 Nanoparticles Investigated by Ab Initio Simulations J. Phys. Chem. C 2014, 118, 29928– 29942
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    Hung, L.; Baishya, K.; Öğüt, S. First-Principles Real-Space Study Of Electronic And Optical Excitations In Rutile Phys. Rev. B 2014, 90, 165424
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    Berardo, E.; Hu, H.-S.; Shevlin, S. A.; Woodley, S. M.; Kowalski, K.; Zwijnenburg, M. A. Modeling Excited States in TiO2 Nanoparticles: On the Accuracy of a TD-DFT Based Description J. Chem. Theory Comput. 2014, 10, 1189– 1199
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    Modeling Excited States in TiO2 Nanoparticles: On the Accuracy of a TD-DFT Based Description
    Berardo, Enrico; Hu, Han-Shi; Shevlin, Stephen A.; Woodley, Scott M.; Kowalski, Karol; Zwijnenburg, Martijn A.
    Journal of Chemical Theory and Computation (2014), 10 (3), 1189-1199CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    We have investigated the suitability of Time-Dependent D. Functional Theory (TD-DFT) to describe vertical low-energy excitations in naked and hydrated titanium dioxide nanoparticles. Specifically, we compared TD-DFT results obtained using different exchange-correlation (XC) potentials with those calcd. using Equation-of-Motion Coupled Cluster (EOM-CC) quantum chem. methods. We demonstrate that TD-DFT calcns. with commonly used XC potentials (e.g., B3LYP) and EOM-CC methods give qual. similar results for most TiO2 nanoparticles investigated. More importantly, however, we also show that, for a significant subset of structures, TD-DFT gives qual. different results depending upon the XC potential used and that only TD-CAM-B3LYP and TD-BHLYP calcns. yield results that are consistent with those obtained using EOM-CC theory. Moreover, we demonstrate that the discrepancies for such structures originate from a particular combination of defects that give rise to charge-transfer excitations, which are poorly described by XC potentials that do not contain sufficient Hartree-Fock like exchange. Finally, we consider that such defects are readily healed in the presence of ubiquitously present water and that, as a result, the description of vertical low-energy excitations for hydrated TiO2 nanoparticles is nonproblematic.
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    Berardo, E.; Hu, H.-S.; van Dam, H. J. J.; Shevlin, S. A.; Woodley, S. M.; Kowalski, K.; Zwijnenburg, M. A. Describing Excited State Relaxation and Localization in TiO2 Nanoparticles Using TD-DFT J. Chem. Theory Comput. 2014, 10, 5538– 5548
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    Describing Excited State Relaxation and Localization in TiO2 Nanoparticles Using TD-DFT
    Berardo, Enrico; Hu, Han-Shi; van Dam, Hubertus J. J.; Shevlin, Stephen A.; Woodley, Scott M.; Kowalski, Karol; Zwijnenburg, Martijn A.
    Journal of Chemical Theory and Computation (2014), 10 (12), 5538-5548CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    We have investigated the description of excited state relaxation in naked and hydrated TiO2 nanoparticles using Time-Dependent D. Functional Theory (TD-DFT) with three common hybrid exchange-correlation (XC) potentials: B3LYP, CAM-B3LYP and BHLYP. Use of TD-CAM-B3LYP and TD-BHLYP yields qual. similar results for all structures, which are also consistent with predictions of coupled-cluster theory for small particles. TD-B3LYP, in contrast, is found to make rather different predictions; including apparent conical intersections for certain particles that are not obsd. with TD-CAM-B3LYP nor with TD-BHLYP. In line with our previous observations for vertical excitations, the issue with TD-B3LYP appears to be the inherent tendency of TD-B3LYP, and other XC potentials with no or a low percentage of Hartree-Fock like exchange, to spuriously stabilize the energy of charge-transfer (CT) states. Even in the case of hydrated particles, for which vertical excitations are generally well described with all XC potentials, the use of TD-B3LYP appears to result in CT problems during excited state relaxation for certain particles. We hypothesize that the spurious stabilization of CT states by TD-B3LYP even may drive the excited state optimizations to different excited state geometries from those obtained using TD-CAM-B3LYP or TD-BHLYP. Finally, focusing on the TD-CAM-B3LYP and TD-BHLYP results, excited state relaxation in small naked and hydrated TiO2 nanoparticles is predicted to be assocd. with a large Stokes' shift.
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    Nunzi, F.; Agrawal, S.; Selloni, A.; De Angelis, F. Structural and Electronic Properties of Photoexcited TiO2 Nanoparticles from First Principles J. Chem. Theory Comput. 2015, 11, 635– 645
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    Structural and Electronic Properties of Photoexcited TiO2 Nanoparticles from First Principles
    Nunzi, Francesca; Agrawal, Saurabh; Selloni, Annabella; De Angelis, Filippo
    Journal of Chemical Theory and Computation (2015), 11 (2), 635-645CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    The structure and energetics of excitons and individual electron and hole polarons in a model anatase TiO2 nanoparticle (NP) are investigated by means of D. Functional Theory (DFT) and Time Dependent (TD)-DFT calcns. The effect of the Hartree-Fock exchange (HF-exc) contribution in the description of TiO2 NPs with unpaired electrons is examd. by comparing the results from semilocal and hybrid DFT functionals with different HF-exc percentages, including a long-range cor. hybrid functional. The performances of TD-DFT and ground state (SCF) DFT approaches in the description of the photoexcited polaron states in TiO2 NPs are also analyzed. Our results confirm that the HF-exc contribution is essential to properly describe the self-trapping of the charge carriers. They also suggest that long-range cor. functionals are needed to properly describe excited state relaxation in TiO2 NPs. TD-DFT geometry optimization of the lowest excited singlet and triplet states deliver photoluminescence values in close agreement with the exptl. data.
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    Butchosa, C.; Guiglion, P.; Zwijnenburg, M. A. Carbon Nitride Photocatalysts for Water Splitting: A Computational Perspective J. Phys. Chem. C 2014, 118, 24833– 24842
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    Carbon nitride photocatalysts for water splitting: A computational perspective
    Butchosa, Cristina; Guiglion, Pierre; Zwijnenburg, Martijn A.
    Journal of Physical Chemistry C (2014), 118 (43), 24833-24842CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
    We study the thermodn. ability of carbon nitride materials to act as water splitting photocatalysts using a computational approach that involves a combination of d. functional theory (DFT) and time-dependent DFT (TD-DFT) calcns. on cluster models of both triazine- and heptazine-based structures. We first use TD-DFT to calc. the absorption spectra of the different cluster models and compare these spectra to those measured exptl. and then calc. using DFT and TD-DFT the redn. potentials of the free electron, free hole, and exciton in these models. We predict that all classes of carbon nitride structures considered should thermodynamically be able to reduce protons and oxidize water. We further provide evidence for the hypothesis that the exptl. lack of overall water splitting activity for pure carbon nitride arises from the fact that water oxidn. is a four-hole reaction and hence very susceptible to competition with electron-hole recombination. Finally, we propose that the recently reported overall water splitting activity of carbon nitride loaded with polypyrrole nanoparticles arises from a junction formed at the interface of both materials, which assists in keeping electrons and holes apart.
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    Guiglion, P.; Butchosa, C.; Zwijnenburg, M. A. Polymeric Watersplitting Photocatalysts; A Computational Perspective On The Water Oxidation Conundrum J. Mater. Chem. A 2014, 2, 11996– 12004
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    Polymeric water splitting photocatalysts; computational perspective on water oxidation conundrum
    Guiglion, Pierre; Butchosa, Cristina; Zwijnenburg, Martijn A.
    Journal of Materials Chemistry A: Materials for Energy and Sustainability (2014), 2 (30), 11996-12004CODEN: JMCAET; ISSN:2050-7496. (Royal Society of Chemistry)
    A computational scheme to predict the thermodn. ability of photocatalysts to drive both of the water splitting half reactions, proton redn. and water oxidn., is discussed, and applied to a no. of polymeric systems to explain their apparent inability to oxidize water. We predict that the poly(p-phenylene) (PPP) is thermodynamically unable to oxidize water and that PPP is hence unlikely to split water in the absence of an external elec. bias. For other polymers, however, for example carbon nitride, the lack of oxygen evolution activity appears kinetic in origin and hence a suitable co-catalyst could potentially transform them into true water splitting photocatalysts.
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  58. 58
    Sprick, R. S.; Jiang, J.-X.; Bonillo, B.; Ren, S.; Ratvijitvech, T.; Guiglion, P.; Zwijnenburg, M. A.; Adams, D. J.; Cooper, A. I. Tunable Organic Photocatalysts for Visible Light-Driven Hydrogen Evolution J. Am. Chem. Soc. 2015, 137, 3265– 3270
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    Zhan, C.-G.; Dixon, D. A. Absolute Hydration Free Energy of the Proton from First-Principles Electronic Structure Calculations J. Phys. Chem. A 2001, 105, 11534– 11540
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    Absolute Hydration Free Energy of the Proton from First-Principles Electronic Structure Calculations
    Zhan, Chang-Guo; Dixon, David A.
    Journal of Physical Chemistry A (2001), 105 (51), 11534-11540CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
    The abs. hydration free energy of the proton, ΔGhyd298(H+), is one of the fundamental quantities for the thermodn. of aq. systems. Its exact value remains unknown despite extensive exptl. and computational efforts. We report a first-principles detn. of ΔGhyd298(H+) by using the latest developments in electronic structure theory including solvation effects. High level ab initio calcns. have been performed with a supermol.-continuum approach based on a recently developed self-consistent reaction field model known as surface and vol. polarization for electrostatic interaction (SVPE) or fully polarizable continuum model (FPCM). In the supermol.-continuum approach, part of the solvent surrounding the solute is treated quantum mech. and the remaining bulk solvent is approximated by a dielec. continuum medium. With this approach, the calcd. results can systematically be improved by increasing the no. of quantum mech. treated solvent mols. ΔGhyd298(H+) is accurately predicted to be -262.4 kcal/mol based on high-level, first-principles solvation-included electronic structure calcns. The abs. hydration free energies of other ions can be obtained by using appropriate available thermodn. data in combination with this value. The high accuracy of the predicted abs. hydration free energy of proton is confirmed by applying the same protocol to predict ΔGhyd298(Li+).
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    Bryantsev, V. S.; Diallo, M. S.; Goddard Iii, W. A. Calculation of Solvation Free Energies of Charged Solutes Using Mixed Cluster/Continuum Models J. Phys. Chem. B 2008, 112, 9709– 9719
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    Calculation of Solvation Free Energies of Charged Solutes Using Mixed Cluster/Continuum Models
    Bryantsev, Vyacheslav S.; Diallo, Mamadou S.; Goddard, William A., III
    Journal of Physical Chemistry B (2008), 112 (32), 9709-9719CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
    The authors derive a consistent approach for predicting the solvation free energies of charged solutes in the presence of implicit and explicit solvents. Some published methodologies make systematic errors in the computed free energies because of the incorrect accounting of the std. state corrections for water mols. or water clusters present in the thermodn. cycle. This problem can be avoided by using the same std. state for each species involved in the reaction under consideration. Two different thermodn. cycles are analyzed for calcg. the solvation free energies of ionic solutes: (1) the cluster cycle with an n water cluster as a reagent and (2) the monomer cycle with n distinct water mols. as reagents. The use of the cluster cycle gives solvation free energies that are in excellent agreement with the exptl. values obtained from studies of ion-water clusters. The mean abs. errors are 0.8 kcal/mol for H+ and 2.0 kcal/mol for Cu2+. Conversely, calcns. using the monomer cycle lead to mean abs. errors that are >10 kcal/mol for H+ and >30 kcal/mol for Cu2+. The presence of hydrogen-bonded clusters of similar size on the left- and right-hand sides of the reaction cycle results in the cancelation of the systematic errors in the calcd. free energies. Using the cluster cycle with 1 solvation shell leads to errors of 5 kcal/mol for H+ (6 waters) and 27 kcal/mol for Cu2+ (6 waters), whereas using 2 solvation shells leads to accuracies of 2 kcal/mol for Cu2+ (18 waters) and 1 kcal/mol for H+ (10 waters).
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    Trasatti, S. The Concept Of Absolute Electrode Potential An Attempt At A Calculation J. Electroanal. Chem. Interfacial Electrochem. 1974, 52, 313– 329
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    Concept of absolute electrode potential an attempt at a calculation
    Trasatti, Sergio
    Journal of Electroanalytical Chemistry and Interfacial Electrochemistry (1974), 52 (3), 313-29CODEN: JEIEBC; ISSN:0022-0728.
    The problem of the conceptual significance of abs. electrode potential is examd. starting from the recent polemic between Bockris (1970, 1972) and Gileadi and Stoner (1972). The views of these authors on the meaning of the conventional position ε0(H+/H2) = 0 in terms of ΔSM.danisho., the actual p.d. at the metal/soln. interface, are crit. reviewed and shown to be questionable. The problem is reconsidered from a thermodn. and from a phys. point of view. The abs. value of the potential of the normal H electrode is calcd. and discussed. The values of ΔSM.danisho., which is defined to be not the abs. but the operative electrode potential, are also calcd. for alkali metals. Implications with respect to concepts of the theory of metals are also examd. in detail.
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    Trasatti, S. The Absolute Electrode Potential: An Explanatory Note (Recommendations 1986) Pure Appl. Chem. 1986, 58, 955– 966
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    The absolute electrode potential: an explanatory note. Recommendations 1986
    Trasatti, Sergio
    Pure and Applied Chemistry (1986), 58 (7), 955-66CODEN: PACHAS; ISSN:0033-4545.
    An illustration is given of the most widespread misunderstandings in the literature about the phys. meaning of abs. electrode potential. The correct expression for this quantity is then derived by a thermodn. anal. of the components of the emf. of an electrochem. cell. In principle 3 ref. levels can be chosen to measure an abs. value of the electrode potential. Only 1 of these possess all the requisites for a meaningful comparison on a common energy scale between electrochem. and phys. parameters. Such a comparison is the main problem for which the adoption of a correct scale for abs. electrode potentials is a prerequisite. The document concludes with the recommendation of a crit. evaluated value for the abs. potential of the std. H electrode in H2O and in a few other protic solvents.
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    Yanai, T.; Tew, D. P.; Handy, N. C. A New Hybrid Exchange-Correlation Functional Using The Coulomb-Attenuating Method (CAM-B3LYP) Chem. Phys. Lett. 2004, 393, 51– 57
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    A new hybrid exchange-correlation functional using the Coulomb-attenuating method (CAM-B3LYP)
    Yanai, Takeshi; Tew, David P.; Handy, Nicholas C.
    Chemical Physics Letters (2004), 393 (1-3), 51-57CODEN: CHPLBC; ISSN:0009-2614. (Elsevier Science B.V.)
    A new hybrid exchange-correlation functional named CAM-B3LYP is proposed. It combines the hybrid qualities of B3LYP and the long-range correction presented by Tawada et al. [J. Chem. Phys., in press]. We demonstrate that CAM-B3LYP yields atomization energies of similar quality to those from B3LYP, while also performing well for charge transfer excitations in a dipeptide model, which B3LYP underestimates enormously. The CAM-B3LYP functional comprises of 0.19 Hartree-Fock (HF) plus 0.81 Becke 1988 (B88) exchange interaction at short-range, and 0.65 HF plus 0.35 B88 at long-range. The intermediate region is smoothly described through the std. error function with parameter 0.33.
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    Becke, A. D. Density-Functional Thermochemistry. 3. The Role Of Exact Exchange J. Chem. Phys. 1993, 98, 5648– 5652
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    Density-functional thermochemistry. III. The role of exact exchange
    Becke, Axel D.
    Journal of Chemical Physics (1993), 98 (7), 5648-52CODEN: JCPSA6; ISSN:0021-9606.
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  • Abstract

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    Figure 1

    Figure 1. Scheme showing how the (standard) reduction potentials (IP, EA, EA*, and IP*) of the ideal photocatalyst (nanoparticle) straddle the proton reduction and water oxidation potentials (green and red broken lines for HER and OER, respectively). hν defines the energy of the photon absorbed by the nanoparticle. e– and h+ stand for electron and hole, respectively, while VB and CB are the valence and conduction bands of the particle. Box A represents the free charge carriers scenario, where the excited electron and hole are spatially separated within the particle and have negligible Coulombic interaction. Box B represents the exciton scenario, where the excited electron and hole are strongly interacting and can be described as an excited electron–hole pair, or exciton.

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    Figure 2

    Figure 2. TiO2 rutile nanoparticle containing 23 TiO2 units and 34 water molecules, 18 split as hydroxyl groups on the particle’s surface and 16 in their molecular state (pictured as blue lines), which amounts to a total of 171 atoms. The crystal planes that define the particle are also shown: four 110 (light green, top middle figure) and two 001 planes (light orange, top right figure). Red spheres denote oxygen atoms, whereas gray and white spheres represent titanium and hydrogen atoms, respectively.

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    Figure 3

    Figure 3. Leading orbital contributions to the lowest TD-CAM-B3LYP S1 excitation for the TiO2 rutile nanoparticle (only orbitals with a contribution larger than 5% are shown). The isodensity plots for the orbitals are calculated at a value of 0.1 au, where the green and purple lobes represent the sign of the wave function (see Figure S1 in section ESI-3 of the Supporting Information for the equivalent figure for the self-trapped exciton).

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    Figure 4

    Figure 4. Geometry of the TD-CAM-B3LYP relaxed S1 excited state minimum (S1/S1min) for the TiO2 rutile nanoparticle corresponding to the self-trapped surface exciton. Red spheres denote oxygen atoms, whereas gray and white represent titanium and hydrogen atoms, respectively. The green (Ti atoms) and blue (O atoms) spheres represent the atoms that are mostly involved with the exciton (hole and electron) self-trapping.

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    Figure 5

    Figure 5. (TD-)CAM-B3LYP predicted EA, IP, EA*, and IP* vertical and adiabatic potentials of the TiO2 rutile nanoparticle in water (ε = 78.0), compared to the HER (green line) and OER (red line) potentials at pH = 0 (broken lines) and pH = 7 (dotted lines). Adiabatic EA* and IP* potentials were calculated for the case of the self-trapped surface exciton; see Figure S4 in the Supporting Information for the equivalent figure for the case of the bulk-like self-trapped exciton.

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  • References

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      Sato, S.; White, J. M. Photodecomposition Of Water Over Pt/TiO2 Catalysts Chem. Phys. Lett. 1980, 72, 83– 86
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      Photodecomposition of water over platinum/titanium dioxide catalysts
      Sato, S.; White, J. M.
      Chemical Physics Letters (1980), 72 (1), 83-6CODEN: CHPLBC; ISSN:0009-2614.
      The decompn. of H2O is catalytic at 23° when a platinized, powd. TiO2 catalyst, illuminated with band-gap radiation, is used.
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    6. 6
      Tang, J.; Durrant, J. R.; Klug, D. R. Mechanism Of Photocatalytic Water Splitting In TiO2. Reaction Of Water With Photoholes, Importance Of Charge Carrier Dynamics, And Evidence For Four-Hole Chemistry J. Am. Chem. Soc. 2008, 130, 13885– 13891
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      6
      Mechanism of Photocatalytic Water Splitting in TiO2. Reaction of Water with Photoholes, Importance of Charge Carrier Dynamics, and Evidence for Four-Hole Chemistry
      Tang, Junwang; Durrant, James R.; Klug, David R.
      Journal of the American Chemical Society (2008), 130 (42), 13885-13891CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      The authors show for the first time that the photogenerated hole lifetime in TiO2 is a strong determinant of the ability of TiO2 to split water. Hole lifetimes were measured using transient absorption spectroscopy over a range of excitation intensities. The lifetimes of the holes were modulated by the use of exogenous scavengers and were also found to vary systematically with the excitation intensity. In all cases the quantum yield of oxygen prodn. is found to be linked to the light intensity used, ranging from below 1 sun equiv. to nearly 1 sun equiv. The authors also provide evidence that oxygen prodn. requires four photons for each mol. of oxygen, which is reminiscent of the natural photosynthetic water-splitting mechanism. This in turn suggests a mechanism for oxygen prodn. which requires four-hole chem., presumably via three, as yet unidentified intermediates. It is also shown that at excitation densities on the order of 1 sun, nongeminate electron-hole recombination limits the quantum yield significantly.
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    7. 7
      Banno, H.; Kariya, B.; Isu, N.; Ogawa, M.; Miwa, S.; Sawada, K.; Tsuge, J.; Imaizumi, S.; Kato, H.; Tokutake, K.; Deguchi, S. Effect of TiO2 Crystallite Diameter on Photocatalytic Water Splitting Rate Green Sustainable Chem. 2014, 4, 87– 94
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      7
      Effect of TiO2 crystallite diameter on photocatalytic water splitting rate
      Banno, Haruna; Kariya, Ben; Isu, Norifumi; Ogawa, Muneaki; Miwa, Saeko; Sawada, Keisuke; Tsuge, Junki; Imaizumi, Shoichiro; Kato, Hidenori; Tokutake, Kyota; Deguchi, Seiichi
      Green and Sustainable Chemistry (2014), 4 (2), 87-94, 8 pp.CODEN: GSCRCJ; ISSN:2160-696X. (Scientific Research Publishing, Inc.)
      The effect of (Pt-loaded)TiO2 crystallite diam. (i.e. Scherrer size) on the photocatalytic water splitting rate was investigated. (Pt-loaded)TiO2 powders with a wide range of crystallite diams. from about 16 to 45 nm with a blank region between about 23 and 41 nm were prepd. by various annealing processes from an identical TiO2 powder. Water splitting expts. with these powders were carried out with methanol as an oxidizing sacrificial agent. It was found that the photocatalytic water splitting rate was sensitively affected by the crystallite diam. of the (Pt-loaded)TiO2 powder. More concretely, similar steep improvements of photocatalytic water splitting rates from around 15 and a little over 2 to about 30 μmol·m-2·hr-1 were obtained in the two (Pt-loaded)TiO2 crystallite diam. range from 16 to 23 and from 41 to 45 nm, resp.
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    8. 8
      Ohno, T.; Sarukawa, K.; Matsumura, M. Photocatalytic Activities Of Pure Rutile Particles Isolated From TiO2 Powder By Dissolving The Anatase Component In HF Solution J. Phys. Chem. B 2001, 105, 2417– 2420
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      8
      Photocatalytic Activities of Pure Rutile Particles Isolated from TiO2 Powder by Dissolving the Anatase Component in HF Solution
      Ohno, Teruhisa; Sarukawa, Koji; Matsumura, Michio
      Journal of Physical Chemistry B (2001), 105 (12), 2417-2420CODEN: JPCBFK; ISSN:1089-5647. (American Chemical Society)
      The authors found that anatase TiO2 dissolves into an HF soln. more easily than rutile TiO2. Using this property, the authors succeeded in isolating pure rutile particles from TiO2 powder consisting of rutile and anatase phases by the HF treatment. The isolation of pure rutile particles was confirmed by x-ray diffraction patterns and diffuse reflection spectra. The rutile particle showed much lower photocatalytic activity than the original powder, if compared for the oxidn. of 2-propanol in aq. soln. using dissolved oxygen as the electron acceptor. On the other hand, when Fe(III) ions were used as the electron acceptor for oxidn. of 2-propanol and water, the activity scarcely changed after the HF treatment. These results indicate that rutile TiO2 has poor activity for the redn. of oxygen, and the presence of a small amt. of an anatase component is crucial for an efficient photocatalytic reaction on TiO2 particles using oxygen as the electron acceptor.
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    9. 9
      Shkrob, I. A.; Sauer, M. C. Hole Scavenging And Photo-Stimulated Recombination Of Electron–Hole Pairs In Aqueous TiO2 Nanoparticles J. Phys. Chem. B 2004, 108, 12497– 12511
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    10. 10
      Testino, A.; Bellobono, I. R.; Buscaglia, V.; Canevali, C.; D’Arienzo, M.; Polizzi, S.; Scotti, R.; Morazzoni, F. Optimizing The Photocatalytic Properties Of Hydrothermal TiO2 By The Control Of Phase Composition And Particle Morphology. A Systematic Approach J. Am. Chem. Soc. 2007, 129, 3564– 3575
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      10
      Optimizing the Photocatalytic Properties of Hydrothermal TiO2 by the Control of Phase Composition and Particle Morphology. A Systematic Approach
      Testino, Andrea; Bellobono, Ignazio Renato; Buscaglia, Vincenzo; Canevali, Carmen; D'Arienzo, Massimiliano; Polizzi, Stefano; Scotti, Roberto; Morazzoni, Franca
      Journal of the American Chemical Society (2007), 129 (12), 3564-3575CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      The possibility of controlling the photocatalytic activity of TiO2 nanoparticles by tailoring their cryst. structure and morphol. is a current topic of great interest. In this study, a broad variety of well-faceted particles with different phase compns., sizes, and shapes have been obtained from concd. TiOCl2 solns. by systematically changing temp., pH, and duration of the hydrothermal treatment. The guide to select the suitable exptl. conditions was provided by thermodn. modeling based on available thermochem. data. By combining the results of TEM, HRTEM, XRD, d., and sp. surface area measurements, a complete structural and morphol. characterization of the particles was performed. Correlation between the photocatalytic activity in the UV photodegrdn. of phenol solns. and the particle size was established. Prismatic rutile particles with length/width ratio around 5 and breadth of 60-100 nm showed the highest activity. The surface chem. of the particles was also investigated. Treatments that decrease the surface acidity, such as washing the powders with ammonia soln. and/or calcining at 400° C, have detrimental effect on photocatalytic activity. The overall results suggest correlation between particle morphol. and photocatalytic activity and indicate that both electron-hole recombination and adsorption at the surface can be rate-controlling processes. The systematic approach presented in this study demonstrates that a substantial improvement of the photocatalytic activity of TiO2 can be achieved by a careful design of the particle morphol. and the control of the surface chem.
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    11. 11
      Kim, W.; Tachikawa, T.; Moon, G.-h.; Majima, T.; Choi, W. Molecular-Level Understanding Of The Photocatalytic Activity Difference Between Anatase And Rutile Nanoparticles Angew. Chem., Int. Ed. 2014, 53, 14036– 14041
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      11
      Molecular-Level Understanding of the Photocatalytic Activity Difference between Anatase and Rutile Nanoparticles
      Kim, Wooyul; Tachikawa, Takashi; Moon, Gun-hee; Majima, Tetsuro; Choi, Wonyong
      Angewandte Chemie, International Edition (2014), 53 (51), 14036-14041CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
      The generation of oxidants on illuminated photocatalysts and their participation in subsequent reactions are the main basis of the widely investigated photocatalytic processes for environmental remediation and selective oxidn. Here, the generation and the subsequent diffusion of .OH from the illuminated TiO2 surface to the soln. bulk were directly obsd. using a single-mol. detection method and this mol. phenomenon could explain the different macroscopic behavior of anatase and rutile in photocatalysis. The mobile .OH is generated on anatase but not on rutile. Therefore, the photocatalytic oxidn. on rutile is limited to adsorbed substrates whereas that on anatase is more facile and versatile owing to the presence of mobile .OH. The ability of anatase to generate mobile .OH is proposed as a previously unrecognized key factor that explains the common observations that anatase has higher activity than rutile for many photooxidative reactions.
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    12. 12
      Ni, M.; Leung, M. K. H.; Leung, D. Y. C.; Sumathy, K. A Review And Recent Developments In Photocatalytic Water-Splitting Using TiO2 For Hydrogen Production Renewable Sustainable Energy Rev. 2007, 11, 401– 425
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      A review and recent developments in photocatalytic water-splitting using TiO2 for hydrogen production
      Ni, Meng; Leung, Michael K. H.; Leung, Dennis Y. C.; Sumathy, K.
      Renewable & Sustainable Energy Reviews (2006), 11 (3), 401-425CODEN: RSERFH; ISSN:1364-0321. (Elsevier Ltd.)
      A review. Nano-sized TiO2 photocatalytic water-splitting technol. has great potential for low-cost, environmentally friendly solar-hydrogen prodn. to support the future hydrogen economy. Presently, the solar-to-hydrogen energy conversion efficiency is too low for the technol. to be economically sound. The main barriers are the rapid recombination of photo-generated electron/hole pairs as well as backward reaction and the poor activation of TiO2 by visible light. In response to these deficiencies, many investigators have been conducting research with an emphasis on effective remediation methods. Some investigators studied the effects of addn. of sacrificial reagents and carbonate salts to prohibit rapid recombination of electron/hole pairs and backward reactions. Other research focused on the enhancement of photocatalysis by modification of TiO2 by means of metal loading, metal ion doping, dye sensitization, composite semiconductor, anion doping and metal ion-implantation. This paper aims to review the up-to-date development of the above-mentioned technologies applied to TiO2 photocatalytic hydrogen prodn. Based on the studies reported in the literature, metal ion-implantation and dye sensitization are very effective methods to extend the activating spectrum to the visible range. Therefore, they play an important role in the development of efficient photocatalytic hydrogen prodn.
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    13. 13
      Prieto-Mahaney, O.-O.; Murakami, N.; Abe, R.; Ohtani, B. Correlation between Photocatalytic Activities and Structural and Physical Properties of Titanium(IV) Oxide Powders Chem. Lett. 2009, 38, 238– 239
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      Abe, R. Development Of A New System For Photocatalytic Water Splitting Into H2 And O2 Under Visible Light Irradiation Bull. Chem. Soc. Jpn. 2011, 84, 1000– 1030
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      Ravelli, D.; Dondi, D.; Fagnoni, M.; Albini, A. Photocatalysis. A Multi-Faceted Concept For Green Chemistry Chem. Soc. Rev. 2009, 38, 1999– 2011
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      Photocatalysis. A multi-faceted concept for green chemistry
      Ravelli, Davide; Dondi, Daniele; Fagnoni, Maurizio; Albini, Angelo
      Chemical Society Reviews (2009), 38 (7), 1999-2011CODEN: CSRVBR; ISSN:0306-0012. (Royal Society of Chemistry)
      A review. Photocatalysis (by semiconductors, mols. and ions) is used in such diverse applications as water hydrolysis for producing hydrogen as fuel, org. synthesis and the recovery of polluted effluents. This tutorial review discusses the common principles of such applications and their role in green chem.
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      Li, G.; Gray, K. A. The Solid–Solid Interface: Explaining The High And Unique Photocatalytic Reactivity Of TiO2-Based Nanocomposite Materials Chem. Phys. 2007, 339, 173– 187
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      Kumar, S. G.; Devi, L. G. Review on Modified TiO2 Photocatalysis under UV/Visible Light: Selected Results and Related Mechanisms on Interfacial Charge Carrier Transfer Dynamics J. Phys. Chem. A 2011, 115, 13211– 13241
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      17
      Review on modified TiO2 photocatalysis under UV/Visible light: selected results and related mechanisms on interfacial charge carrier transfer dynamics
      Kumar, S. Girish; Devi, L. Gomathi
      Journal of Physical Chemistry A (2011), 115 (46), 13211-13241CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
      A review. Titania is one of the most widely used benchmark std. photocatalysts in the field of environmental applications. However, the large band gap of titania and massive recombination of photogenerated charge carriers limit its overall photocatalytic efficiency. The former can be overcome by modifying the electronic band structure of titania including various strategies like coupling with a narrow band gap semiconductor, metal ion/nonmetal ion doping, codoping with two or more foreign ions, surface sensitization by org. dyes or metal complexes, and noble metal deposition. The latter can be cor. by changing the surface properties of titania by fluorination or sulfation or by the addn. of suitable electron acceptors besides mol. oxygen in the reaction medium. This review encompasses several advancements made in these aspects, and also some of the new phys. insights related to the charge transfer events like charge carrier generation, trapping, detrapping, and their transfer to surface are discussed for each strategy of the modified titania to support the conclusions derived. The synergistic effects in the mixed polymorphs of titania and also the theories proposed for their enhanced activity are reported. A recent venture on the synthesis and applications of anatase titania with a large percentage of reactive {001} facets and their band gap extension to the visible region via nonmetal ion doping which is a current hot topic is briefly outlined.
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    18. 18
      Scanlon, D. O.; Dunnill, C. W.; Buckeridge, J.; Shevlin, S. A.; Logsdail, A. J.; Woodley, S. M.; Catlow, C. R. A.; Powell, M. J.; Palgrave, R. G.; Parkin, I. P.; Watson, G. W.; Keal, T. W.; Sherwood, P.; Walsh, A.; Sokol, A. A. Band Alignment Of Rutile And Anatase TiO2 Nat. Mater. 2013, 12, 798– 801
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      18
      Band alignment of rutile and anatase TiO2
      Scanlon, David O.; Dunnill, Charles W.; Buckeridge, John; Shevlin, Stephen A.; Logsdail, Andrew J.; Woodley, Scott M.; Catlow, C. Richard A.; Powell, Michael. J.; Palgrave, Robert G.; Parkin, Ivan P.; Watson, Graeme W.; Keal, Thomas W.; Sherwood, Paul; Walsh, Aron; Sokol, Alexey A.
      Nature Materials (2013), 12 (9), 798-801CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)
      The most widely used oxide for photocatalytic applications owing to its low cost and high activity is TiO2. The discovery of the photolysis of water on the surface of TiO2 in 1972 launched four decades of intensive research into the underlying chem. and phys. processes involved. Despite much collected evidence, a thoroughly convincing explanation of why mixed-phase samples of anatase and rutile outperform the individual polymorphs has remained elusive. One long-standing controversy is the energetic alignment of the band edges of the rutile and anatase polymorphs of TiO2. We demonstrate, through a combination of state-of-the-art materials simulation techniques and X-ray photoemission expts., that a type-II, staggered, band alignment of ∼ 0.4eV exists between anatase and rutile with anatase possessing the higher electron affinity, or work function. Our results help to explain the robust sepn. of photoexcited charge carriers between the two phases and highlight a route to improved photocatalysts.
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    19. 19
      Kapilashrami, M.; Zhang, Y.; Liu, Y.-S.; Hagfeldt, A.; Guo, J. Probing the Optical Property and Electronic Structure of TiO2 Nanomaterials for Renewable Energy Applications Chem. Rev. 2014, 114, 9662– 9707
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      Probing the optical property and electronic structure of TiO2 nanomaterials for renewable energy applications
      Kapilashrami, Mukes; Zhang, Yangfeng; Liu, Yi-Sheng; Hagfeldt, Anders; Guo, Jinghua
      Chemical Reviews (Washington, DC, United States) (2014), 114 (19), 9662-9707CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
      A review.
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    20. 20
      Quesada-Cabrera, R.; Sotelo-Vazquez, C.; Bear, J. C.; Darr, J. A.; Parkin, I. P. Photocatalytic Evidence of the Rutile-to-Anatase Electron Transfer in Titania Adv. Mater. Interfaces 2014, 1, 1– 7
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      Ohtani, B.; Ogawa, Y.; Nishimoto, S. Photocatalytic Activity Of Amorphous-Anatase Mixture Of Titanium(IV) Oxide Particles Suspended In Aqueous Solutions J. Phys. Chem. B 1997, 101, 3746– 3752
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      21
      Photocatalytic Activity of Amorphous-Anatase Mixture of Titanium(IV) Oxide Particles Suspended in Aqueous Solutions
      Ohtani, Bunsho; Ogawa, Yoshimasa; Nishimoto, Sei-ichi
      Journal of Physical Chemistry B (1997), 101 (19), 3746-3752CODEN: JPCBFK; ISSN:1089-5647. (American Chemical Society)
      Titanium(IV) oxide powders of various amorphous-anatase compns. were prepd. by heat treatment (573-1073 K) of amorphous TiO2 in air and characterized by differential scanning calorimetry, powder x-ray diffraction, and BET surface area measurements. An exothermic peak at ∼723 K in the DSC pattern was assigned to the crystn. of the amorphous phase to anatase; its heat of crystn. was used to evaluate the wt. fraction of amorphous phase. The fraction of anatase crystallites (f(anatase)) was calcd. as the remainder after the amorphous phase and contaminated water or org. residue. The size of anatase crystallites was slightly decreased but almost const. along with the increase in f(anatase), which was consistent with the small change in the BET surface area. These results suggested that each amorphous particle transforms into an anatase crystallite of similar size without sintering or crystal growth. The particles of mixt. of amorphous and anatase were used for three kinds of photocatalytic reactions in deaerated aq. suspensions: silver metal deposition, oxidn. of 2-propanol by bare powders, and dehydrogenation of 2-propanol by ex-situ and in-situ platinized powders. For all the reactions, the photocatalytic activity of amorphous TiO2 was negligible, increased almost linearly with f(anatase), and further improved by calcination of completely crystd. powder. The negligible activity of amorphous TiO2 was attributed to recombination of photoexcited electron and pos. hole at defects located on the surface and in the bulk of particles.
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      Kočí, K.; Obalová, L.; Matějová, L.; Plachá, D.; Lacný, Z.; Jirkovský, J.; Šolcová, O. Effect Of TiO2 Particle Size On The Photocatalytic Reduction Of CO2 Appl. Catal., B 2009, 89, 494– 502
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      Effect of TiO2 particle size on the photocatalytic reduction of CO2
      Koci, K.; Obalova, L.; Matejova, L.; Placha, D.; Lacny, Z.; Jirkovsky, J.; Solcova, O.
      Applied Catalysis, B: Environmental (2009), 89 (3-4), 494-502CODEN: ACBEE3; ISSN:0926-3373. (Elsevier B.V.)
      Pure TiO2 anatase particles with a crystallite diams. ranging from 4.5 to 29 nm were prepd. by pptn. and sol-gel method, characterized by x-ray diffraction (XRD), BET surface area measurement, UV-vis and SEM, and tested in CO2 photocatalytic redn. Methane and methanol were the main redn. products. The optimum particle size corresponding to the highest yields of both products was 14 nm. The obsd. optimum particle size is a result of competing effects of sp. surface area, charge-carrier dynamics and light absorption efficiency.
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    23. 23
      Anpo, M.; Shima, T.; Kodama, S.; Kubokawa, Y. Photocatalytic Hydrogenation Of Propyne With Water On Small-Particle Titania: Size Quantization Effects And Reaction Intermediates J. Phys. Chem. 1987, 91, 4305– 4310
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      Xu, N. P.; Shi, Z. F.; Fan, Y. Q.; Dong, J. H.; Shi, J.; Hu, M. Z. C. Effects Of Particle Size Of TiO2 On Photocatalytic Degradation Of Methylene Blue In Aqueous Suspensions Ind. Eng. Chem. Res. 1999, 38, 373– 379
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      24
      Effects of Particle Size of TiO2 on Photocatalytic Degradation of Methylene Blue in Aqueous Suspensions
      Xu, Nanping; Shi, Zaifeng; Fan, Yiqun; Dong, Junhang; Shi, Jun; Hu, Michael Z.-C.
      Industrial & Engineering Chemistry Research (1999), 38 (2), 373-379CODEN: IECRED; ISSN:0888-5885. (American Chemical Society)
      The influence of particle size of TiO2 on the photocatalytic degrdn. of methylene blue (MB) in a suspended aq. soln. was studied. The results suggested that the adsorption rate and adsorbability of MB on suspended TiO2 particles increased as the particle sizes of TiO2 decreased. Photocatalytic activity of TiO2 also increased as the particle size of TiO2 became smaller, esp. when the particle size is <30 nm. The half-life (t0.5) of the photocatalytic degrdn. of MB also decreased as the particle sizes of TiO2 decreased. The 1st-order reaction rate const. for photodegrdn. of MB increased as the particle size of TiO2 decreased. The initial degrdn. rate of MB in a suspended model was higher than that of a fixed-bed model. This will overcome the difficulty of prepn. of ultrafine TiO2 catalyst particles. Once the problem of sepn. of fine TiO2 particles is solved, a TiO2 suspended photoreactor could be provided on an industrial basis.
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    25. 25
      Mattioli, G.; Alippi, P.; Filippone, F.; Caminiti, R.; Amore Bonapasta, A. Deep versus Shallow Behavior of Intrinsic Defects in Rutile and Anatase TiO2 Polymorphs J. Phys. Chem. C 2010, 114, 21694– 21704
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      25
      Deep versus Shallow Behavior of Intrinsic Defects in Rutile and Anatase TiO2 Polymorphs
      Mattioli, Giuseppe; Alippi, Paola; Filippone, Francesco; Caminiti, Ruggero; Bonapasta, Aldo Amore
      Journal of Physical Chemistry C (2010), 114 (49), 21694-21704CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
      The structural and electronic properties of oxygen vacancies (VOx) and titanium interstitials (Ti(i)) in the bulk of the rutile and anatase forms of TiO2 have been investigated with LSD-GGA + U ab initio simulations. In particular, formation energies of the charged and neutral forms of the VOx and Ti(i) defects as well as the corresponding vertical and thermodn. transition levels have been estd. The achieved results can reconcile the apparent inconsistency of exptl. obsd. deep donor levels with the n-type cond. obsd. in reduced TiO2. They show indeed that both defects give rise to vertical transition levels about 1 eV below the conduction band (CB), in agreement with exptl. measures, and to thermodn. transition levels close to the CB. That is, these defects behave as deep donors, when looking at vertical transitions, and as shallow donors, when the effects of the structural relaxations are taken into account. A major part of the explanation of this behavior is played by the polaron-like character of the defect states, which was already noted, but not deepened, in literature. Finally, it is shown that the application of the U correction to both Ti and O species gives qual. similar results, but with a better agreement to exptl. findings, with respect to the application to Ti only. The former approach gives pretty similar results, for both rutile and anatase bulk properties, to those coming from HSE hybrid functional calcns.
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    26. 26
      Di Valentin, C.; Selloni, A. Bulk and Surface Polarons in Photoexcited Anatase TiO2 J. Phys. Chem. Lett. 2011, 2, 2223– 2228
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      26
      Bulk and Surface Polarons in Photoexcited Anatase TiO2
      Di Valentin, Cristiana; Selloni, Annabella
      Journal of Physical Chemistry Letters (2011), 2 (17), 2223-2228CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
      Using hybrid functional electronic structure calcns., the structure and energetics of photogenerated electrons and holes in the bulk and at the (101) surface of anatase TiO2 were studied. Excitons formed upon UV irradn. become self-trapped, consistent with the observation of temp.-dependent Urbach tails in the absorption spectrum and a large Stokes shift in the luminescence band of anatase. Electron and hole polarons are localized at Ti3+ and O- lattice sites, resp. At the surface, the trapping sites generally correspond to undercoordinated Ti3+5c and O-2c surface atoms or to isolated OH species in the case of a hydroxylated surface. The polaron trapping energy is considerably larger at the surface than in the bulk, indicating that it is energetically favorable for the polarons to travel from the bulk to the surface. Computed 1-electron energy levels in the gap and hyperfine coupling consts. compare favorably with oxidn. potential and EPR measurements.
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      Varley, J. B.; Janotti, A.; Franchini, C.; Van de Walle, C. G. Role Of Self-Trapping In Luminescence And p-Type Conductivity Of Wide-Band-Gap Oxides Phys. Rev. B 2012, 85, 0811091– 0811094
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      Zawadzki, P.; Laursen, A. B.; Jacobsen, K. W.; Dahl, S.; Rossmeisl, J. Oxidative Trends Of TiO2-Hole Trapping At Anatase And Rutile Surfaces Energy Environ. Sci. 2012, 5, 9866– 9869
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      Oxidative trends of TiO2-hole trapping at anatase and rutile surfaces
      Zawadzki, Pawel; Laursen, Anders B.; Jacobsen, Karsten Wedel; Dahl, Soren; Rossmeisl, Jan
      Energy & Environmental Science (2012), 5 (12), 9866-9869CODEN: EESNBY; ISSN:1754-5706. (Royal Society of Chemistry)
      Understanding the nature of photogenerated carriers in a photocatalyst is central to understanding its photocatalytic performance. Based on d. functional theory calcn. the authors show that for TiO2, the most popular photocatalyst, the electron hole self-trapping leads to band gap states which position is dependent on the type of surface termination. Such variations in hole state energies can lead to differences in photocatalytic activity among rutile and anatase surface facets. The authors find that the calcd. hole state energies correlate with photodeposition and photoetching rates. The authors anticipated that their results can aid the design of more reactive photocatalysts based on TiO2 and their approach can be utilized for other relevant photocatalysts as well.
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      Spreafico, C.; VandeVondele, J. The Nature Of Excess Electrons In Anatase And Rutile From Hybrid DFT And RPA Phys. Chem. Chem. Phys. 2014, 16, 26144– 26152
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      The nature of excess electrons in anatase and rutile from hybrid DFT and RPA
      Spreafico, Clelia; VandeVondele, Joost
      Physical Chemistry Chemical Physics (2014), 16 (47), 26144-26152CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
      The behavior of excess electrons in undoped and defect free bulk anatase and rutile TiO2 has been investigated by state-of-the-art electronic structure methods including hybrid d. functional theory (DFT) and the RPA. Consistent with expt., charge trapping and polaron formation is obsd. in both anatase and rutile. The difference in the anisotropic shape of the polarons is characterized, confirming for anatase the large polaron picture. For anatase, where polaron formation energies are small, charge trapping is obsd. also with std. hybrid functionals, provided the simulation cell is sufficiently large (864 atoms) to accommodate the lattice relaxation. Even though hybrid orbitals are required as a starting point for RPA in this system, the obtained polaron formation energies are relatively insensitive to the amt. of Hartree-Fock exchange employed. The difference in trapping energy between rutile and anatase can be obtained accurately with both hybrid functionals and RPA. Computed activation energies for polaron hopping and delocalization clearly show that anatase and rutile might have different charge transport mechanisms. In rutile, only hopping is likely, whereas in anatase hopping and delocalization are competing. Delocalization will result in conduction-band-like and thus enhanced transport. Anisotropic conduction, in agreement with exptl. data, is obsd., and results from the tendency to delocalize in the [001] direction in rutile and the (001) plane in anatase. For future work, our calcns. serve as a benchmark and suggest RPA on top on hybrid orbitals (PBE0 with 30% Hartree-Fock exchange), as a suitable method to study the rich chem. and physics of TiO2.
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      Dehaart, L. G. J.; Blasse, G. The Observation Of Exciton Emission From Rutile Single-Crystals J. Sol. State Chem. 1986, 61, 135– 136
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      Sildos, I.; Suisalu, A.; Aarik, J.; Sekiya, T.; Kurita, S. Self-Trapped Exciton Emission In Crystalline Anatase J. Lumin. 2000, 87–89, 290– 292
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      Self-trapped exciton emission in crystalline anatase
      Sildos, I.; Suisalu, A.; Aarik, J.; Sekiya, T.; Kurita, S.
      Journal of Luminescence (2000), 87-89 (), 290-292CODEN: JLUMA8; ISSN:0022-2313. (Elsevier Science B.V.)
      A comparative spectroscopic study of self-trapped exciton (STE) emission in anatase single crystals and thin films was carried out at 5 K In the single crystals, a strongly polarized STE emission with an elec. vector perpendicular to the c-axis was obsd. Influence of annealing on the spectral characteristics of samples was tested.
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      Watanabe, M.; Hayashi, T. Time-Resolved Study Of Self-Trapped Exciton Luminescence In Anatase TiO2 Under Two-Photon Excitation J. Lumin. 2005, 112, 88– 91
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      Time-resolved study of self-trapped exciton luminescence in anatase TiO2 under two-photon excitation
      Watanabe, M.; Hayashi, T.
      Journal of Luminescence (2005), 112 (1-4), 88-91CODEN: JLUMA8; ISSN:0022-2313. (Elsevier B.V.)
      We have studied the dynamics of photocarriers in anatase phase of TiO2 with time-resolved spectroscopy of self-trapped exciton (STE) luminescence. The decay curve of luminescence under one-photon excitation well above the band gap energy shows power-law behavior, suggesting that spatial sepn. of an electron-hole pair occurs under interband excitation. A similar result is obtained under two-photon excitation. We conclude that the carrier sepn. is ascribed to intrinsic dynamical properties of photocarriers in anatase. It is inferred that the carrier sepn. occurs during energy relaxation towards the band bottom. Temp. dependence of the decay curve is also discussed in terms of thermal dissocn. of STEs.
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      Kernazhitsky, L.; Shymanovska, V.; Gavrilko, T.; Naumov, V.; Fedorenko, L.; Kshnyakin, V.; Baran, J. Room Temperature Photoluminescence Of Anatase And Rutile TiO2 Powders J. Lumin. 2014, 146, 199– 204
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      Room temperature photoluminescence of anatase and rutile TiO2 powders
      Kernazhitsky, L.; Shymanovska, V.; Gavrilko, T.; Naumov, V.; Fedorenko, L.; Kshnyakin, V.; Baran, J.
      Journal of Luminescence (2014), 146 (), 199-204CODEN: JLUMA8; ISSN:0022-2313. (Elsevier B.V.)
      The optical absorption and photoluminescence of anatase and rutile TiO2 were studied at room temp. TiO2 nanocryst. powders were synthesized in the form of pure anatase or rutile. The samples were characterized by X-ray diffraction, X-ray fluorescence, Raman spectroscopy, optical absorption and photoluminescence (PL) methods. The PL spectra were studied under the intensive UV (3.68 eV) laser excitation. Some interesting features in the PL spectra including the well-resolved peaks of excitonic and band-band transitions in TiO2 were obsd., to our knowledge, for the first time. It is shown that PL bands including peaks at 2.71-2.81 eV and its phonon replicas in anatase and rutile TiO2 arise from the excitonic e--h+ recombination via oxygen vacancies. The excitonic peak at 2.91 eV is attributed to the recombination of self-trapped excitons in anatase or free excitons in rutile TiO2. The PL peaks within 3.0-3.3 eV in anatase TiO2 are ascribed to indirect allowed transitions due to the band-band e--h+ recombination. The peaks at 3.03 eV and 3.26 eV are attributed to the free exciton emission near the fundamental band edge of rutile and anatase TiO2, resp. The influence of TiO2 crystal structure and calcination temp. on the PL spectra is discussed.
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      Pascual, J.; Camassel, J.; Mathieu, H. Fine Structure In The Intrinsic Absorption Edge Of TiO2 Phys. Rev. B 1978, 18, 5606– 5614
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      Stevanovic, V.; Lany, S.; Ginley, D. S.; Tumas, W.; Zunger, A. Assessing Capability Of Semiconductors To Split Water Using Ionization Potentials And Electron Affinities Only Phys. Chem. Chem. Phys. 2014, 16, 3706– 3714
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      Assessing capability of semiconductors to split water using ionization potentials and electron affinities only
      Stevanovic, Vladan; Lany, Stephan; Ginley, David S.; Tumas, Willam; Zunger, Alex
      Physical Chemistry Chemical Physics (2014), 16 (8), 3706-3714CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
      We show in this article that the position of semiconductor band edges relative to the water redn. and oxidn. levels can be reliably predicted from the ionization potentials (IP) and electron affinities (AE) only. Using a set of 17 materials, including transition metal compds., we show that accurate surface dependent IPs and EAs of semiconductors can be computed by combining d. functional theory and many-body GW calcns. From the extensive comparison of calcd. IPs and EAs with available exptl. data, both from photoemission and electrochem. measurements, we show that it is possible to sort candidate materials solely from IPs and EAs thereby eliminating explicit treatment of semiconductor/water interfaces. We find that at pH values corresponding to the point of zero charge there is on av. a 0.5 eV shift of IPs and EAs closer to the vacuum due to the dipoles formed at material/water interfaces.
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      Blagojevic, V.; Chen, Y.-R.; Steigerwald, M.; Brus, L.; Friesner, R. A. Quantum Chemical Investigation of Cluster Models for TiO2 Nanoparticles with Water-Derived Ligand Passivation: Studies of Excess Electron States and Implications for Charge Transport in the Gratzel Cell J. Phys. Chem. C 2009, 113, 19806– 19811
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      Li, Y.-F.; Liu, Z.-P. Particle Size, Shape And Activity For Photocatalysis On Titania Anatase Nanoparticles In Aqueous Surroundings J. Am. Chem. Soc. 2011, 133, 15743– 15752
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      Zhang, J.; Hughes, T. F.; Steigerwald, M.; Brus, L.; Friesner, R. A. Realistic Cluster Modeling of Electron Transport and Trapping in Solvated TiO2 Nanoparticles J. Am. Chem. Soc. 2012, 134, 12028– 12042
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      Zhang, J.; Steigerwald, M.; Brus, L.; Friesner, R. A. Covalent O-H Bonds as Electron Traps in Proton-Rich Rutile TiO2 Nanoparticles Nano Lett. 2014, 14, 1785– 1789
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      Rocca, D.; Gebauer, R.; De Angelis, F.; Nazeeruddin, M. K.; Baroni, S. Time-Dependent Density Functional Theory Study Of Squaraine Dye-Sensitized Solar Cells Chem. Phys. Lett. 2009, 475, 49– 53
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      Time-dependent density functional theory study of squaraine dye-sensitized solar cells
      Rocca, Dario; Gebauer, Ralph; De Angelis, Filippo; Nazeeruddin, Mohammad K.; Baroni, Stefano
      Chemical Physics Letters (2009), 475 (1-3), 49-53CODEN: CHPLBC; ISSN:0009-2614. (Elsevier B.V.)
      We employ time-dependent d. functional theory to study the optical properties of a squaraine sensitized TiO 2 system, as a model for the corresponding dye-sensitized solar cell. The all-org. squaraine dye is particularly promising for light absorption in the red spectral region. We compute the photoabsorption spectrum of a periodic TiO2 slab exposing anatase (101) surfaces, both for the clean slab and for the surface covered by the squaraine dye. Those spectra are compared to recent exptl. data. The main absorption peaks are analyzed, concluding that both direct and indirect charge injection mechanisms are active in this system.
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      Shevlin, S. A.; Woodley, S. M. Electronic and Optical Properties of Doped and Undoped (TiO2)n Nanoparticles J. Phys. Chem. C 2010, 114, 17333– 17343
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      Taylor, D. J.; Paterson, M. J. Calculations Of The Low-Lying Excited States Of The TiO2 Molecule J. Chem. Phys. 2010, 133, 204302
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      Sanchez-de-Armas, R.; Oviedo, J.; San-Miguel, M. A.; Sanz, J. F. Real-time TD-DFT Simulations in Dye Sensitized Solar Cells: The Electronic Absorption Spectrum of Alizarin Supported on TiO2 Nanoclusters J. Chem. Theory Comput. 2010, 6, 2856– 2865
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      Real-Time TD-DFT Simulations in Dye Sensitized Solar Cells: The Electronic Absorption Spectrum of Alizarin Supported on TiO2 Nanoclusters
      Sanchez-de-Armas, Rocio; Oviedo Lopez, Jaime; San-Miguel, Miguel A.; Sanz, Javier Fdez.; Ordejon, Pablo; Pruneda, Miguel
      Journal of Chemical Theory and Computation (2010), 6 (9), 2856-2865CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      The structural and electronic properties of the alizarin dye supported on TiO2 nanoclusters have been examd. by time-dependent d.-functional (TD-DFT) calcns. performed in the time-domain framework. The calcd. electronic absorption spectrum of free alizarin shows a 1st band centered at 2.67 eV that upon adsorption features a red shift by 0.31 eV, in agreement with both exptl. and previous theor. work. This red shift arises from a relative stabilization of the dye LUMO when adsorbed. To analyze the dependence of the electronic properties of the dye-support couple on the size of metal-oxide nanoparticles, different models of (TiO2)n nanoclusters have been used (with n = 1, 2, 3, 6, 9, 15, and 38). This minimal model theor. reproduces the main feature in the spectrum, the energy shift of the main band upon binding to TiO2. However, it fails in creating intermediate states which could play a significant role under real exptl. conditions (dynamics of the electronic transfer). Indeed, as the size of the nanocluster grows, the dye LUMO moves from the edge to well inside the conduction band (Ti 3d band). However, to assess the consistency of the time-domain approach in the case of such systems, conventional (frequency-domain) TD-DFT calcns. have been carried out. As far as the functional and basis set are equiv., both approaches lead to similar results. While for small systems the std. TD-DFT is better suited, for medium to large sized systems, the real-time TD-DFT becomes competitive and more efficient.
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      De Angelis, F.; Fantacci, S.; Gebauer, R. Simulating Dye-Sensitized TiO2 Heterointerfaces in Explicit Solvent: Absorption Spectra, Energy Levels, and Dye Desorption J. Phys. Chem. Lett. 2011, 2, 813– 817
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      Simulating Dye-Sensitized TiO2 Heterointerfaces in Explicit Solvent: Absorption Spectra, Energy Levels, and Dye Desorption
      De Angelis, Filippo; Fantacci, Simona; Gebauer, Ralph
      Journal of Physical Chemistry Letters (2011), 2 (7), 813-817CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
      Dye-sensitized solar cells (DSCs) represent a valuable, efficient, and low-cost alternative to conventional semiconductor photovoltaic devices. A deeper understanding of the dye/semiconductor heterointerface and of the dye-sensitized semiconductor/electrolyte interactions are fundamental for further progress in DSC technol. Here we report an ab initio mol. dynamics simulation of a dye-sensitized TiO2 heterointerface "immersed" in an explicit water environment for an efficient org. dye, followed by TDDFT excited state calcns. of the coupled dye/semiconductor/solvent system. This new computational protocol and the extended model system allows us to gain unprecedented insight into the excited state changes occurring for the solvated dye-sensitized heterointerface at room temp., and to provide an atomistic picture of water-mediated dye desorption.
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      Chiodo, L.; Salazar, M.; Romero, A. H.; Laricchia, S.; Della Sala, F.; Rubio, A. Structure, Electronic, And Optical Properties Of TiO2 Atomic Clusters: An Ab Initio Study J. Chem. Phys. 2011, 135, 244704
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      Auvinen, S.; Alatalo, M.; Haario, H.; Jalava, J. P.; Lamminmäki, R. J. Size And Shape Dependence Of The Electronic And Spectral Properties In TiO2 Nanoparticles J. Phys. Chem. C 2011, 115, 8484– 8493
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      Size and Shape Dependence of the Electronic and Spectral Properties in TiO2 Nanoparticles
      Auvinen, Sami; Alatalo, Matti; Haario, Heikki; Jalava, Juho-Pertti; Lamminmaki, Ralf-Johan
      Journal of Physical Chemistry C (2011), 115 (17), 8484-8493CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
      Electronic and spectral properties of small TiO2 particles were studied to gain more knowledge on their dependence on the crystal- and particle-size distributions. The goal is to extend the recently developed light scattering based method for detg. sub-μm size particles to nanoparticles. For that, the authors need to know how the refractive index function depends on the cluster size. As a 1st step, time-dependent d. functional theory (TDDFT) calcns. were used having a focus on the shape changes of the calcd. spectra, which can be related to changes in the refractive index function. Starting from the structure of TiO2 mol. for the 2 smallest particles and truncated bulk anatase structure for larger particles, the structures for (TiO2)n clusters, n = {1, 2, 8, 18, 28, 38}, were modeled. After the structure optimization using std. d. functional theory (DFT) approach, the photoabsorption spectra for the optimized particle structures were calcd. by using TDDFT calcns. The results show slight evidence of the band gap broadening in the case of 3 out of the smallest particles and strong structural dependence of electronic and spectral properties, which can partly be related to the transformation of the electron structure, and breaking of the crystal symmetry as the size of the particle becomes smaller. In the case of small particles their refractive index function can differ from the bulk values, and this has to be taken into account in the interpretation of light-scattering measurements.
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      Taylor, D. J.; Paterson, M. J. Vibronic Coupling Effects On The Structure And Spectroscopy Of Neutral And Charged TiO2 Clusters Chem. Phys. 2012, 408, 1– 10
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      Berardo, E.; Hu, H.; Kowalski, K.; Zwijnenburg, A. M. Coupled Cluster Calculations On TiO2 Nanoclusters J. Chem. Phys. 2013, 139, 0643131
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      Galynska, M.; Persson, P. Emerging Polymorphism in Nanostructured TiO2: Quantum Chemical Comparison of Anatase, Rutile, and Brookite Clusters Int. J. Quantum Chem. 2013, 113, 2611– 2620
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      Kandada, A. R.; Fantacci, S.; Guarnera, S.; Polli, D.; Lanzani, G.; De Angelis, F.; Petrozza, A. Role Of Hot Singlet Excited States In Charge Generation At The Black Dye/TiO2 Interface ACS Appl. Mater. Interfaces 2013, 5, 4334– 4339
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      Mattioli, G.; Amore Bonapasta, A.; Bovi, D.; Giannozzi, P. Photocatalytic and Photovoltaic Properties of TiO2 Nanoparticles Investigated by Ab Initio Simulations J. Phys. Chem. C 2014, 118, 29928– 29942
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      Hung, L.; Baishya, K.; Öğüt, S. First-Principles Real-Space Study Of Electronic And Optical Excitations In Rutile Phys. Rev. B 2014, 90, 165424
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      Berardo, E.; Hu, H.-S.; Shevlin, S. A.; Woodley, S. M.; Kowalski, K.; Zwijnenburg, M. A. Modeling Excited States in TiO2 Nanoparticles: On the Accuracy of a TD-DFT Based Description J. Chem. Theory Comput. 2014, 10, 1189– 1199
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      Modeling Excited States in TiO2 Nanoparticles: On the Accuracy of a TD-DFT Based Description
      Berardo, Enrico; Hu, Han-Shi; Shevlin, Stephen A.; Woodley, Scott M.; Kowalski, Karol; Zwijnenburg, Martijn A.
      Journal of Chemical Theory and Computation (2014), 10 (3), 1189-1199CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      We have investigated the suitability of Time-Dependent D. Functional Theory (TD-DFT) to describe vertical low-energy excitations in naked and hydrated titanium dioxide nanoparticles. Specifically, we compared TD-DFT results obtained using different exchange-correlation (XC) potentials with those calcd. using Equation-of-Motion Coupled Cluster (EOM-CC) quantum chem. methods. We demonstrate that TD-DFT calcns. with commonly used XC potentials (e.g., B3LYP) and EOM-CC methods give qual. similar results for most TiO2 nanoparticles investigated. More importantly, however, we also show that, for a significant subset of structures, TD-DFT gives qual. different results depending upon the XC potential used and that only TD-CAM-B3LYP and TD-BHLYP calcns. yield results that are consistent with those obtained using EOM-CC theory. Moreover, we demonstrate that the discrepancies for such structures originate from a particular combination of defects that give rise to charge-transfer excitations, which are poorly described by XC potentials that do not contain sufficient Hartree-Fock like exchange. Finally, we consider that such defects are readily healed in the presence of ubiquitously present water and that, as a result, the description of vertical low-energy excitations for hydrated TiO2 nanoparticles is nonproblematic.
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      Berardo, E.; Hu, H.-S.; van Dam, H. J. J.; Shevlin, S. A.; Woodley, S. M.; Kowalski, K.; Zwijnenburg, M. A. Describing Excited State Relaxation and Localization in TiO2 Nanoparticles Using TD-DFT J. Chem. Theory Comput. 2014, 10, 5538– 5548
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      Describing Excited State Relaxation and Localization in TiO2 Nanoparticles Using TD-DFT
      Berardo, Enrico; Hu, Han-Shi; van Dam, Hubertus J. J.; Shevlin, Stephen A.; Woodley, Scott M.; Kowalski, Karol; Zwijnenburg, Martijn A.
      Journal of Chemical Theory and Computation (2014), 10 (12), 5538-5548CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      We have investigated the description of excited state relaxation in naked and hydrated TiO2 nanoparticles using Time-Dependent D. Functional Theory (TD-DFT) with three common hybrid exchange-correlation (XC) potentials: B3LYP, CAM-B3LYP and BHLYP. Use of TD-CAM-B3LYP and TD-BHLYP yields qual. similar results for all structures, which are also consistent with predictions of coupled-cluster theory for small particles. TD-B3LYP, in contrast, is found to make rather different predictions; including apparent conical intersections for certain particles that are not obsd. with TD-CAM-B3LYP nor with TD-BHLYP. In line with our previous observations for vertical excitations, the issue with TD-B3LYP appears to be the inherent tendency of TD-B3LYP, and other XC potentials with no or a low percentage of Hartree-Fock like exchange, to spuriously stabilize the energy of charge-transfer (CT) states. Even in the case of hydrated particles, for which vertical excitations are generally well described with all XC potentials, the use of TD-B3LYP appears to result in CT problems during excited state relaxation for certain particles. We hypothesize that the spurious stabilization of CT states by TD-B3LYP even may drive the excited state optimizations to different excited state geometries from those obtained using TD-CAM-B3LYP or TD-BHLYP. Finally, focusing on the TD-CAM-B3LYP and TD-BHLYP results, excited state relaxation in small naked and hydrated TiO2 nanoparticles is predicted to be assocd. with a large Stokes' shift.
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      Nunzi, F.; Agrawal, S.; Selloni, A.; De Angelis, F. Structural and Electronic Properties of Photoexcited TiO2 Nanoparticles from First Principles J. Chem. Theory Comput. 2015, 11, 635– 645
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      Structural and Electronic Properties of Photoexcited TiO2 Nanoparticles from First Principles
      Nunzi, Francesca; Agrawal, Saurabh; Selloni, Annabella; De Angelis, Filippo
      Journal of Chemical Theory and Computation (2015), 11 (2), 635-645CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      The structure and energetics of excitons and individual electron and hole polarons in a model anatase TiO2 nanoparticle (NP) are investigated by means of D. Functional Theory (DFT) and Time Dependent (TD)-DFT calcns. The effect of the Hartree-Fock exchange (HF-exc) contribution in the description of TiO2 NPs with unpaired electrons is examd. by comparing the results from semilocal and hybrid DFT functionals with different HF-exc percentages, including a long-range cor. hybrid functional. The performances of TD-DFT and ground state (SCF) DFT approaches in the description of the photoexcited polaron states in TiO2 NPs are also analyzed. Our results confirm that the HF-exc contribution is essential to properly describe the self-trapping of the charge carriers. They also suggest that long-range cor. functionals are needed to properly describe excited state relaxation in TiO2 NPs. TD-DFT geometry optimization of the lowest excited singlet and triplet states deliver photoluminescence values in close agreement with the exptl. data.
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      Butchosa, C.; Guiglion, P.; Zwijnenburg, M. A. Carbon Nitride Photocatalysts for Water Splitting: A Computational Perspective J. Phys. Chem. C 2014, 118, 24833– 24842
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      Carbon nitride photocatalysts for water splitting: A computational perspective
      Butchosa, Cristina; Guiglion, Pierre; Zwijnenburg, Martijn A.
      Journal of Physical Chemistry C (2014), 118 (43), 24833-24842CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
      We study the thermodn. ability of carbon nitride materials to act as water splitting photocatalysts using a computational approach that involves a combination of d. functional theory (DFT) and time-dependent DFT (TD-DFT) calcns. on cluster models of both triazine- and heptazine-based structures. We first use TD-DFT to calc. the absorption spectra of the different cluster models and compare these spectra to those measured exptl. and then calc. using DFT and TD-DFT the redn. potentials of the free electron, free hole, and exciton in these models. We predict that all classes of carbon nitride structures considered should thermodynamically be able to reduce protons and oxidize water. We further provide evidence for the hypothesis that the exptl. lack of overall water splitting activity for pure carbon nitride arises from the fact that water oxidn. is a four-hole reaction and hence very susceptible to competition with electron-hole recombination. Finally, we propose that the recently reported overall water splitting activity of carbon nitride loaded with polypyrrole nanoparticles arises from a junction formed at the interface of both materials, which assists in keeping electrons and holes apart.
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      Guiglion, P.; Butchosa, C.; Zwijnenburg, M. A. Polymeric Watersplitting Photocatalysts; A Computational Perspective On The Water Oxidation Conundrum J. Mater. Chem. A 2014, 2, 11996– 12004
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      Polymeric water splitting photocatalysts; computational perspective on water oxidation conundrum
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      A computational scheme to predict the thermodn. ability of photocatalysts to drive both of the water splitting half reactions, proton redn. and water oxidn., is discussed, and applied to a no. of polymeric systems to explain their apparent inability to oxidize water. We predict that the poly(p-phenylene) (PPP) is thermodynamically unable to oxidize water and that PPP is hence unlikely to split water in the absence of an external elec. bias. For other polymers, however, for example carbon nitride, the lack of oxygen evolution activity appears kinetic in origin and hence a suitable co-catalyst could potentially transform them into true water splitting photocatalysts.
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      Sprick, R. S.; Jiang, J.-X.; Bonillo, B.; Ren, S.; Ratvijitvech, T.; Guiglion, P.; Zwijnenburg, M. A.; Adams, D. J.; Cooper, A. I. Tunable Organic Photocatalysts for Visible Light-Driven Hydrogen Evolution J. Am. Chem. Soc. 2015, 137, 3265– 3270
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      Zhan, C.-G.; Dixon, D. A. Absolute Hydration Free Energy of the Proton from First-Principles Electronic Structure Calculations J. Phys. Chem. A 2001, 105, 11534– 11540
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      Absolute Hydration Free Energy of the Proton from First-Principles Electronic Structure Calculations
      Zhan, Chang-Guo; Dixon, David A.
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      The abs. hydration free energy of the proton, ΔGhyd298(H+), is one of the fundamental quantities for the thermodn. of aq. systems. Its exact value remains unknown despite extensive exptl. and computational efforts. We report a first-principles detn. of ΔGhyd298(H+) by using the latest developments in electronic structure theory including solvation effects. High level ab initio calcns. have been performed with a supermol.-continuum approach based on a recently developed self-consistent reaction field model known as surface and vol. polarization for electrostatic interaction (SVPE) or fully polarizable continuum model (FPCM). In the supermol.-continuum approach, part of the solvent surrounding the solute is treated quantum mech. and the remaining bulk solvent is approximated by a dielec. continuum medium. With this approach, the calcd. results can systematically be improved by increasing the no. of quantum mech. treated solvent mols. ΔGhyd298(H+) is accurately predicted to be -262.4 kcal/mol based on high-level, first-principles solvation-included electronic structure calcns. The abs. hydration free energies of other ions can be obtained by using appropriate available thermodn. data in combination with this value. The high accuracy of the predicted abs. hydration free energy of proton is confirmed by applying the same protocol to predict ΔGhyd298(Li+).
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      Bryantsev, V. S.; Diallo, M. S.; Goddard Iii, W. A. Calculation of Solvation Free Energies of Charged Solutes Using Mixed Cluster/Continuum Models J. Phys. Chem. B 2008, 112, 9709– 9719
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      Calculation of Solvation Free Energies of Charged Solutes Using Mixed Cluster/Continuum Models
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      The authors derive a consistent approach for predicting the solvation free energies of charged solutes in the presence of implicit and explicit solvents. Some published methodologies make systematic errors in the computed free energies because of the incorrect accounting of the std. state corrections for water mols. or water clusters present in the thermodn. cycle. This problem can be avoided by using the same std. state for each species involved in the reaction under consideration. Two different thermodn. cycles are analyzed for calcg. the solvation free energies of ionic solutes: (1) the cluster cycle with an n water cluster as a reagent and (2) the monomer cycle with n distinct water mols. as reagents. The use of the cluster cycle gives solvation free energies that are in excellent agreement with the exptl. values obtained from studies of ion-water clusters. The mean abs. errors are 0.8 kcal/mol for H+ and 2.0 kcal/mol for Cu2+. Conversely, calcns. using the monomer cycle lead to mean abs. errors that are >10 kcal/mol for H+ and >30 kcal/mol for Cu2+. The presence of hydrogen-bonded clusters of similar size on the left- and right-hand sides of the reaction cycle results in the cancelation of the systematic errors in the calcd. free energies. Using the cluster cycle with 1 solvation shell leads to errors of 5 kcal/mol for H+ (6 waters) and 27 kcal/mol for Cu2+ (6 waters), whereas using 2 solvation shells leads to accuracies of 2 kcal/mol for Cu2+ (18 waters) and 1 kcal/mol for H+ (10 waters).
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      A new hybrid exchange-correlation functional named CAM-B3LYP is proposed. It combines the hybrid qualities of B3LYP and the long-range correction presented by Tawada et al. [J. Chem. Phys., in press]. We demonstrate that CAM-B3LYP yields atomization energies of similar quality to those from B3LYP, while also performing well for charge transfer excitations in a dipeptide model, which B3LYP underestimates enormously. The CAM-B3LYP functional comprises of 0.19 Hartree-Fock (HF) plus 0.81 Becke 1988 (B88) exchange interaction at short-range, and 0.65 HF plus 0.35 B88 at long-range. The intermediate region is smoothly described through the std. error function with parameter 0.33.
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      Despite the remarkable thermochem. accuracy of Kohn-Sham d.-functional theories with gradient corrections for exchange-correlation, the author believes that further improvements are unlikely unless exact-exchange information is considered. Arguments to support this view are presented, and a semiempirical exchange-correlation functional (contg. local-spin-d., gradient, and exact-exchange terms) is tested for 56 atomization energies, 42 ionization potentials, 8 proton affinities, and 10 total at. energies of first- and second-row systems. This functional performs better than previous functionals with gradient corrections only, and fits expt. atomization energies with an impressively small av. abs. deviation of 2.4 kcal/mol.
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    (TD-)B3LYP and (TD-)CAM-B3LYP data for the rutile nanoparticle, as well as data for smaller nanoparticles, the bulk-like self-trapped exciton minimum energy geometry, and results from Δ-SCF calculations for the lowest triplet excited state. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.5b01512.


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