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Mechanism of photocatalytic water oxidation on small TiO2 nanoparticles

Nonadiabatic molecular dynamics simulations suggest an excited state electron proton transfer mechanism and explain the observation of mobile hydroxyl radicals.


Introduction
TiO 2 is the prototypical redox photocatalyst because it is inexpensive, abundant, versatile, and non-toxic. 1,2 Ever since the ability of TiO 2 to split water was discovered in 1972, 3 the use of TiO 2 for solar fuel generation has been intensely studied. However, the efficiency of TiO 2 -based photocatalysts has remained moderate, which was attributed to a lack of mechanistic understanding and models to inform synthetic improvements. 4 Apart from sample preparation, heterogeneity, and system size, a key challenge of mechanistic studies of TiO 2 photocatalysis are ultra-fast processes involving nonadiabatic transitions between electronic states, which are exceedingly difficult to characterize experimentally and theoretically.
Here we propose a detailed mechanistic model for photocatalytic water oxidation on TiO 2 nanoparticles. Our model explicitly accounts for exciton dynamics, nonadiabatic transitions, and bond breaking for the rst time, and is based on recent methodological developments of on-the-y non-adiabatic molecular dynamics (NAMD) simulations. [5][6][7][8] The high kinetic barrier for photolytic water splitting on TiO 2 surfaces is caused by the oxygen evolution reaction (OER), [9][10][11][12] The rst of the four one-electron oxidation steps is likely rate-limiting; 10,12-14 however, the mechanism of this step is controversial and several conicting models have been proposed. The earliest models based on spectroscopic experiments suggested that the photohole (h + ) oxidizes a surface bound hydroxyl group pTi IV -OH, 15,16 pTi IV -OH + h + / pTi IV -($OH) + . ( This mechanism was challenged by the results of density functional theory (DFT) calculations suggesting that pTi IV -OH groups trap electrons, not holes. 17 An alternative mechanism, involves oxidation of a surface bound water pTi IV -OH 2 instead of pTi IV -OH by the photohole. 10 The high barrier of this step can be lowered by deprotonation of pTi IV -OH 2 with base, resulting a barrierless hole transfer. 12,18,19 The resulting proton-coupled electron transfer (PCET) mechanism, where a strongly localized photohole h + is transferred from a bridging oxygen O br to the pTi IV -(OH) À species, is consistent with the observed pH dependence of the OER. 9,20 However, the recent experimental detection of mobile rather than surface bound OH radicals in three different experiments casts doubts on the hypothesis that the oxidized water is bound to the TiO 2 surface. 21 Recent Ehrenfest NAMD simulations of periodic TiO 2 surfaces also considered this mechanism, 25 but the simulation times were too short (up to 20 fs) to be conclusive. Nakato and coworkers suggested that nucleophilic attack of water on a O br , activated by h + , might initiate the OER, 26,27 pO br (h + ) + H 2 O(l) / p$O br OH + H + , generating a surface-bound hydroperoxyl radical. Later, Imanishi and coworkers suggested that this mechanism will dominate at low and intermediate pH, while at high pH the photohole could readily oxidize the Ti-O À species present in high pH. 20 Based on a transition state (TS) study for Ti(OH) 4 , Kazaryan and coworkers questioned mechanism (5) and proposed that Ti(OH) 4 thus producing an intermediate similar to the one proposed in mechanism (4).

Methods
The PBE0 (ref. 29) hybrid functional and polarized double-z valence def2-SVP 30 basis sets were used for NAMD simulations.
To account for van der Waals interactions, D3 dispersion corrections were employed. 31 The forces on the S 1 and S 0 potential energy surfaces (PESs) and the non-adiabatic couplings between them were computed analytically at each time step. 32,33 The nuclear dynamics used Tully's surface hopping algorithm and a leapfrog-Verlet integrator with timestep of 40 a.u. (1 fs). 34,35 115 trajectories were initiated with random nuclear velocities consistent with a 350 K thermal ensemble, and the trajectories were propagated for up to 1 ps. To describe homolytic bond cleavage, the spin symmetry was allowed to break if triplet instability was found for the reference state. We recently showed that this methodology can treat both closed and open shell pathways semiquantitatively in photodissociation of acetaldehyde. 8 To avoid convergence and stability problems close to the conical intersections (CIs), a surface hop was forced if the S 1 -S 0 gap is below 0.5 eV. 6

Results and discussion
To compare the reactivity of surface-bound vs. physisorbed water, we simulated small hydrated (TiO 2 ) 4 (OH) 4 nanoparticles with two, four, eight or ten additional water molecules, see Fig. 1 and S3. † These models can accommodate all proposed mechanisms (2)-(6) with the exception of mechanisms requiring deprotonation of water by added base, and enabled total simulation times up to 60 ps. Even though the initial oneelectron oxidation is much faster, these long simulation times were necessary to capture reactive trajectories without imposing articial bias on the system. According to our simulations, the reaction starts by electronproton transfer (EPT) from physisorbed water to the photohole strongly localized on O br as depicted in The electron transfer reaction is displayed in Fig. 3 for (TiO 2 ) 4 (OH) 4 (H 2 O) 8 . At 200 fs, the photohole (green) is localized  strongly on bridging oxygen O 1 , forming the intermediate 1. The hole is transferred to physisorbed water at 213 fs and intermediate 2 forms at 219 fs via concerted proton transfer without substantial nuclear reorientation. Intermediate 2 subsequently decays rapidly to S 0 through a CI and forms a stable ground state intermediate followed by dissociation of the hydroxyl radical (see ESI †).
The structure of the intermediate observed in the NAMD simulations is in close agreement with STM measurements. 22 Moreover, our mechanism yields mobile OH radicals, in accordance with several recent experiments. 21,23,24 The chargetransfer (CT) reactivity seen in our simulations is indirectly supported by a TS study of Ti(OH) 4 28 and NAMD simulations of the oxidation of chemisorbed methanol on a TiO 2 surface. 38 To further analyze the exciton dynamics and the resulting EPT, we consider the difference in atomic natural bonding orbital 39 (NBO) charges between the S 1 and the S 0 states, see Fig. 4a. Positive values of the population difference indicate hole charge, i.e., loss of electron density on atoms relative to the ground state, and negative values indicate electron charge, i.e., gain of electron density relative to the ground state. In the Franck-Condon geometry, the hole is shared between all bridging oxygens, O 1 -O 4 , and the electron is distributed equally to Ti 1 and Ti 2 . During the rst 100 fs, the hole localizes strongly on the bridging oxygen O 1 until EPT from the physisorbed water H 2 O 6 occurs at 213 fs. The other bridging oxygens, O 2 -O 4 , gain electron density and thus act as electron traps. This allows them to hydrogen bond with liquid water more efficiently, but does not lead to any reactivity. A consequence of the hole localization is the subsequent localization of the electron on Ti 1 adjacent to the reactive O 1 , The localization of the two opposite charges provides coulombic stabilization of the exciton and drives the reaction to form pTi III -(O br H) + -Ti IV  species, which are stable on a picosecond timescale in ab initio molecular dynamics simulations. 40 While less connement may increase the exciton size, the energy gain from localization also increases in larger particles. Larger rutile hydrated and hydroxylated (TiO 2 ) 23 nanoparticles exhibit exciton localization aer self-trapping (i.e. at the S 1 PES minimum) on a similar scale as the ones studied here, 41 suggesting that the self-trapped exciton size may not depend strongly on the particle size. Photohole localization is not the only driving force of the reaction, however, since EPT only occurs 100 fs aer the photohole localizes: starting at $150 fs, the reactive physisorbed water hydrogen bonds more strongly with the Ti 1 bound water (O 6 -H 1 distance decreases from 220 pm to 170 pm), see Fig. 4b; concurrently, the electron starts to localize on Ti 1 , see Fig. 4a. The EPT follows these changes as seen in the O 1 -H 2 and O 6 -H 2 distances. This suggests that the localized electron on Ti 1 also favors EPT by some electron transfer to the water bound to Ti 1 . The electron rich water then stabilizes the nascent H 2 O + by solvating the hole, thus facilitating the reaction. This interpretation is also supported by the observation that the reaction is faster in the smaller (TiO 2 ) 4 (OH) 4  Why did previous simulations not show the present mechanism? These simulations were based on free charge carriers, i.e., cationic and anionic species in the electronic ground state, which do not include electron-hole interaction. For (TiO 2 ) 4 -(OH) 4 (H 2 O) 8 , the reaction is exothermic by approximately 10 kcal mol À1 compared to the Franck-Condon geometry on the S 1 PES (Fig. 2b). On the other hand, for a free hole the reaction is endothermic by approximately 7 kcal mol À1 (ESI †). This 17 kcal mol À1 difference is mainly due to coulombic stabilization of the exciton ("exciton binding energy"), of the H 2 O + species, and of the protonated bridging oxygen O 1 by the electron component of the exciton. This was conrmed by BOMD simulations for free holes which did not show any reactivity up to 135 ps of total simulation time. Explicit simulation of both, the electron and the hole and their interaction, i.e., electronic excitation beyond the single-particle picture, is necessary to explain the reactivity. Furthermore,the oxidation occurs only aer relaxation of the S 1 state, and thus the reactivity cannot be rationalized from the Franck-Condon geometry.

Conclusions
The rst unconstrained NAMD simulations of water oxidation by small TiO 2 nanoparticles show EPT from physisorbed liquid water to a strongly localized hole on O br . This mechanism is consistent with STM experiments, 22 and generates mobile hydroxyl radicals in accordance with recent experiments based on three different uorescence probe methods and total internal reection uorescence microscopy. 21,23,24 The calculations reveal two key driving forces of the oxidation reaction: (i) localization of the exciton with close proximity of the electron and hole charges leads to a gain of coulombic stabilization. (ii) Simultaneously, hydrogen bonding stabilizes the emerging H 2 O + species, which is deprotonated to free OH in the excited state.
These results provide a rationale for the low catalytic activity of TiO 2 in water splitting: while exciton localization is necessary to drive the reaction, it can also promote recombination of the electron and hole charges, i.e., non-radiative decay to the ground state. This is seen in the vast majority of our trajectories. Similarly, the effective stabilization of the photohole by hydrogen bonding requires a specic orientation of surface bound water, which has a large entropic penalty. While additional validation of the proposed mechanism is desirable, e.g., by exploring the effects of the particle size and bulk solvation, the present results could inform future efforts to increase the water splitting activity of TiO 2 -based photocatalysts by targeted synthetic modication.