**Theoretical Verification of Photoelectrochemical Water Oxidation Using Nanocrystalline TiO2 Electrodes**

#### **Shozo Yanagida, Susumu Yanagisawa, Koichi Yamashita, Ryota Jono and Hiroshi Segawa**

**Abstract:** Mesoscopic anatase nanocrystalline TiO2 (nc-TiO2) electrodes play effective and efficient catalytic roles in photoelectrochemical (PEC) H2O oxidation under short circuit energy gap excitation conditions. Interfacial molecular orbital structures of (H2O)3 &OH(TiO2)9H as a stationary model under neutral conditions and the radical-cation model of [(H2O)3&OH(TiO2)9H]+ as a working nc-TiO2 model are simulated employing a cluster model OH(TiO2)9H (Yamashita/Jono's model) and a H2O cluster model of (H2O)3 to examine excellent H2O oxidation on nc-TiO2 electrodes in PEC cells. The stationary model, (H2O)3&OH(TiO2)9H reveals that the model surface provides catalytic H2O binding sites through hydrogen bonding, van der Waals and Coulombic interactions. The working model, [(H2O)3&OH(TiO2)9H]+ discloses to have a very narrow energy gap (0.3 eV) between HOMO and LUMO potentials, proving that PEC nc-TiO2 electrodes become conductive at photo-irradiated working conditions. DFT-simulation of stepwise oxidation of a hydroxide ion cluster model of OH<sup>í</sup> (H2O)3, proves that successive two-electron oxidation leads to hydroxyl radical clusters, which should give hydrogen peroxide as a precursor of oxygen molecules. Under working bias conditions of PEC cells, nc-TiO2 electrodes are now verified to become conductive by energy gap photo-excitation and the electrode surface provides powerful oxidizing sites for successive H2O oxidation to oxygen via hydrogen peroxide.

Reprinted from *Molecules.* Cite as: Yanagida, S.; Yanagisawa, S.; Yamashita, K.; Jono, R.; Segawa, H. Theoretical Verification of Photoelectrochemical Water Oxidation Using Nanocrystalline TiO2 Electrodes. *Molecules* **2015**, *20*, 9732-9744.

#### **1. Introduction**

Photoelectrochemical (PEC) water (H2O) oxidation on TiO2 electrodes was qualitatively explained as due to downward band bending induced by depletion layer of TiO2 rutile crystal electrodes by assuming the energy structure of TiO2, e.g., conduction band potential (Ecb) of í0.65 V(SCE) and valence band potential (Evb) of 2.35 V (SCE), energy gap 3.0 eV, and 1.23 eV of the equilibrium cell potential for H2O electrolysis at 25 °C and 1 atmospheric pressure [1,2]. We noticed recently that efficient photoelectrochemical H2O oxidation using anatase nc-TiO2 electrodes was at first reported in 1987 by Sakka *et al*. [3]. Interestingly, they reported vigorous oxygen (O2) and hydrogen (H2) evolution using acidic aqueous solution (0.1 N H2SO4) at the PEC nc-TiO2 cell. It is worth noting that the notable electron flow due to H2O oxidation to O2 becomes detectable when bias potential reaches at about 2.0 V (*vs*. SCE), and that under energy gap UV irradiation, photocurrent starts to flow at bias potential around í0.5~í0.3 V (*vs*. SCE), showing vigorous O2 and H2 evolution at bias potential around 0.5–1.0 V (*vs*. SCE). Such effective acidic H2O oxidation on mesoporous nc-TiO2 electrodes prompts us to understand the H2O photooxidation on the basis of molecular orbital (MO) theory, because the band-bending concept is based on crystal-level physics, and nc-TiO2 in PEC electrodes is too small to form depletion layer in nc-TiO2 with average size of 25 nm.

Computational chemistry using density functional theory (DFT) well explains and predicts molecular energy structures and properties functioned by self-association of molecules where hydrogen bonding or van der Waals and Coulombic interactions as non-covalent bonding play an essential role [4–9]. DFT calculations using the nc-TiO2 model of Ti9O18H-OH (Yamashita/Jono model) successfully verified that the surface complex between nc-TiO2 and 7,7,8,8 tetracyanoquinodimenthane shows charge transfer transition [10]. We now report verification of PEC oxidation of H2O on nc-TiO2 electrodes on the basis of DFT simulation using Yamashita/Jono nc-TiO2 model. Here, DFT-simulations verify that H2O forms H2O clusters via hydrogen bonding and that the H2O clusters-associated nc-TiO2 electrodes provide excellent H2O oxidation sites. In addition, the working models of H2O clusters-associated PEC-nc-TiO2 electrodes are simulated as radical cations, and effective PEC H2O oxidation is verified as well theoretically.

#### **2. Results and Discussion**

#### *2.1. Yamashita/Jono Model for Simulation of PEC-nc-TiO2 Electrodes*

Yamashita and Jono's anatase nc-TiO2 model (Ti9O18H-OH) consists of nine TiO2 units (TiO2)9 derived from the packing unit of the crystalline anatase TiO2, hydroxide on surface side of the TiO2 and hydrogen on one side of the TiO2. To optimize the non-covalent distance between hydroxyl group and nc-TiO2 unit, all heavy atoms of the nc-TiO2 unit are frozen and the model was simulated to the energetically optimized geometry (see Supplementary Figure S1). The distance (1.862 Å) become shorter, and the refined Yamashita/Jono model is abbreviated as OH(TiO2)9H hereafter and size of about 1 nm length, Mulliken charge, the energy structures and configurations of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are shown in Figure 1.

**Figure 1.** Yamashita/Jono model of OH(TiO2)9H as a model of PEC-nc-TiO2 electrodes, (**a**) Size, distance and Mulliken charge; (**b**) the energy structure and configuration of HOMO and LUMO.

Mulliken charge in OH(TiO2)9H indicates that hydroxyl group is charged negative and the protonated nc-TiO2 unit positive, and then we regard that Yamashita/Jono model is a kind of ion-dipole complex or weak charge transfer complex. The HOMO distributes exclusively on hydroxide ion and the LUMO inside of the nc-TiO2 unit, giving energy gap 2.55 eV. To know selfassociation of Yamashita/Jono model, the OH and H-detached (TiO2)9 and (TiO2)9H units are both DFT-simulated as charge is neutral and cation, respectively (Supplementary Tables S1 and S2 and Figures S1 and S2).

The DFT simulation data reveals that Mulliken charge on the hydrogen-bearing side is positive and another side negative as well as the OH(TiO2)9H model. Further, the HOMO and LUMO are almost degenerate. The association through van der Waals and Coulombic interaction and the comparable dipole to that of the Yamashita/Jono model support that Yamashita/Jono model may self-associate with (TiO2)9 and (TiO2)9H to yield surface thin-film anatase TiO2 electrodes as depicted in Figure 2.

**Figure 2.** Association of Yamashita/Jono model via van der Waals and Coulomb interactions, explaining growth of the model to larger size PEC-nc-TiO2 electrodes.

#### *2.2. Water Cluster Models for Modeling of Interface Structures of PEC-nc-TiO2 Electrodes*

Water (H2O) molecules aggregate each other via hydrogen bonding. The structures of H2O clusters (H2O)n (*n =* 1~3, 6) are simulated to understand their molecular orbital energy structures (Supplementary Table S3). One of the (H2O)3 trimer is simulated to have dipole and the highest HOMO potential í6.67 eV. The HOMO distributes on the H2O, of which hydrogen atoms have hydrogen bond with oxygen atoms of other two H2O, rationalizing the most positive HOMO potential among the examined H2O clusters. In other words, the trimer (H2O)3 is the most oxidizable H2O model.

Similarly, H2O hydroxide ion clusters and H2O hydronium ion clusters are simulated (Supplementary Tables S4 and S5). In general, H2O hydroxide ion clusters have positive HOMO potential. With increase of H2O molecules, the HOMO shifts to negative potential, which means that HOMO potential is controllable by number of associating H2O as pH is controllable by dilution. In addition, all of H2O hydronium ion clusters have very negative HOMO potential í20.2~í12.36 eV with large size of LUMO configurations (Supplementary Table S5). With increase of H2O molecules, HOMO potential shifts to positive potential, verifying that the HOMO level is changeable as is the case of H2O hydroxide ion clusters, and the hydrated hydronium ion clusters become oxidizable energetically.

With these simulations and considerations, the polar (H2O)3 and OH<sup>í</sup> (H2O)3 are employed for DFT-modeling of neutral interface of PEC-nc-TiO2 electrodes. As for hydronium ion cluster, H3O+(H2O)2, which is derived from (H2O)3, are introduced for the modeling of acidic interface of PEC-nc-TiO2 electrodes (Figure 3). The HOMO configurations indicate that the model clusters have electron rich parts with a wide variety of potentials ranging from í1.07 to í13.5 eV.

#### *2.3. Photoelectrochemical Oxidation of H2O on PEC-nc-TiO2*

As an interface model of nc-TiO2 electrodes, the Yamashita/Jono model, OH(TiO2)9H, is structurally frozen and three H2O molecules are made manually to interact via hydrogen bonding with the frozen hydroxyl group in Yamashita/Jono model. The (H2O)3-hydrogen bonded model structure is optimized by molecular mechanics (MMFF operation in Spartan), and the molecular orbital is verified by DFT-single-point simulation of an interface structure of (H2O)3&OH(TiO2)9H as a stationary model (Figure 4). Mulliken charge and electrostatic potential map indicates that negative charge locates on surface oxygen atoms of TiO2 and of the (H2O)3 cluster, and the more negative charge (stronger red color) on the H2O molecule in the cluster is worth noting in the stationary state model structure.

**Figure 3.** Water cluster models for DFT simulation of PEC oxidation of water molecules on PEC-nc-TiO2 electrodes.

In the stationary model, configurations of HOMO distributes on one H2O of the cluster (H2O)3 unit, and LUMO inside the nc-TiO2 unit. Interestingly, the energy gap (0.73 eV) between HOMO and LUMO is smaller than the energy gap (2.55 eV) in the stationary state of Yamashita/Jono model. This fact suggests that nc-TiO2 surface binds H2O molecules via hydrogen bond, forming kinds of charge transfer complexes. In addition, HOMO(í1) (í7.4 eV) distributes on the whole (H2O)3 unit, implying more effective H2O oxidation under negative potential of í7.4 eV (Figure 4).

For comparison, only one H2O-associated Yamashita/Jono model, H2O&OH(TiO2)9H, is simulated as the simplest structure of PEC-nc-TiO2 electrodes (Supplementary Figure S3). The energy gap (1.75 eV) is given and the hydrogen-bonded H2O molecule locates HOMO(í1) at í7.8 eV. The simplest orbital energy structure verifies that nc-TiO2 electrodes intrinsically work as catalytic sites of H2O oxidation through hydrogen bonding with H2O molecules.

(a)

**Figure 4.** DFT-simulation of (H2O)3&OH(TiO2)9H as a stationary state of PEC-nc-TiO2 electrodes, (**a**) Mulliken charge and electrostatic density map; (**b**) energy structures of HOMO and LUMO; (**c**) the configuration of HOMO(í1) on (H2O)3.

When nc-TiO2 electrodes are energy-filled by UV-irradiation at short circuit PEC conditions, photoelectron on nc-TiO2 is ejected to conducting grids instantly, and photocurrent become observable. The (H2O)3-associated PEC-nc-TiO2 model is simulated as radical cation model of [(H2O)3 &OH(TiO2)9H].+ as the energy-filled structure under working conditions (Figure 5). Interestingly, the radical cation model as the working model is endothermically simulated (ǻE = 192.85 kcal/mol). The orbital energy analysis of the energy-filled model of [(H2O)3&OH(TiO2)9H].+ reveals that the energy gap between HOMO and LUMO potential becomes narrow as small as 0.3 eV with largely negative HOMO (í10.2 eV) and LUMO (í9.9 eV) potential. The HOMO and LUMO distribute in the model with almost the same configurations, and that the spin (unpaired electron) density distributes with the same configuration as the HOMO and LUMO.

The orbital energy analysis of the energy-filled Yamashita/Jono model of [OH(TiO2)9H].+ reveals that the energy gap is pretty narrow (0.7 eV) (Supplementary Table S2). These facts suggest that self-organization of Yamashita/Jono model will give photoconductive nc-TiO2 electrodes when the PEC cell is kept at negative oxidation potential at short circuit conditions and energized by band gap excitation. In fact, the sharp rise in photoconductivity of nc-TiO2 electrodes was reported and discussed as an insulator-metal (Mott) transition in a donor band of anatase TiO2 [11]. It is also worth noting that in studies on dye-sensitized nc-TiO2 solar cells (DSC), adsorption of cationic species like tetrabutylammonium cation and sensitizing dye molecules enhanced electron transport in nc-TiO2 electrodes [12,13]. Accordingly, the photo-enhanced electron transport is now verified as a key function of nc-TiO2 electrodes not only in DSC but also in PEC H2O oxidation.

**Figure 5.** Energy structures of (H2O)3&[OH(TiO2)9H]+ as a radical cation model of (H2O)3-interacted PEC-nc-TiO2 electrode under UV-irradiated bias conditions of PEC-nc-TiO2 electrodes, *i.e*., a photo-energy-driven operational state model.

The HOMO configuration on the H2O unit at the stationary state of the model, and the spin density distribution on the (H2O)3 unit at the energy-filled working state strongly suggest that PEC-nc-TiO2 electrodes provides catalytic binding sites of H2O. The same functions of PEC nc-TiO2 electrodes are confirmed by the molecular orbital simulation of the energy-filled [H2O&OH(TiO2)9H]+ model (Tables S1 and S2, Figure S4). The narrowed energy gap (0.3 eV), the comparable configurations of HOMO, LUMO and spin density are quite comparable with those of [(H2O)3&OH(TiO2)9H]+ .

#### *2.4. DFT Simulation of H2O Oxidation to Hydrogen Peroxide*

In PEC H2O oxidation on nc-TiO2 electrodes, bias potential is essential to start H2O oxidation. The HOMO potential of Yamashita/Jono model, í7.18 eV and the average HOMO potential of H2O clusters, í7.48 eV (Supplementary Table S3) verify that the bias potential >0.3V is at lease required for PEC H2O oxidation under neutral working conditions. On the other hand, the HOMO potential (í10.2 eV) of the working model of [(H2O)3&OH(TiO2)9H]+ predicts that successive oxidation should occur under more negative bias potential (>2.72 eV) for H2O oxidation to oxygen through formation of hydrogen peroxide.

In order to verify whether hydroxyl radical may form successively on PEC-nc-TiO2 electrodes, the two-electron oxidation structure of [H2O&OH(TiO2)9H]..++ is simulated as dication-diradical model as another working interface model of PEC-nc-TiO2 electrodes. The more energy-filled model is endothermically (ǻE = 458.43 kcal/mol) simulated as powerful working model (Figure 6). The energy gap (0.3 eV) and the configuration of HOMO and LUMO are confirmed to verify that such largely energized PEC-nc-TiO2 electrodes keep photoconductivity with keeping high oxidation potential. The spin density distributes on the (H2O)3 unit, suggesting that two-electron H2O oxidation occurs successively on the catalytic site on nc-TiO2 electrodes.

**Figure 6.** Energy structures of [(H2O)3]&OH(TiO2)9H]..++ as the model of two electron oxidation state of PEC-nc-TiO2 electrodes, *i.e*., the diradical-dication state of the electrodes.

With these simulation analyses, step-wise PEC-H2O oxidation is shown in Scheme 1. One-electron oxidation of H2O molecule yields radical cation of H2O (H2O+ ) and the removable of proton from the radical cation (deprotonation) leads to hydroxyl radical (HO) (Equations (1) and (2) in Scheme 1). When H2O hydroxide ion cluster of OH<sup>í</sup> (H2O)3 undergoes further oxidation, another hydroxyl radical favorably forms in neighbor on PEC-nc-TiO2 electrodes, and efficient and effective formation of hydrogen peroxide occurs (Equation (3) in Scheme 1).

$$\begin{aligned} \text{H}\_{\text{2}}\text{O} & \xrightarrow{\cdot\text{e}} & [\text{H}\_{2}\text{O}]^{+} & \xrightarrow{\cdot\text{H}^{+}} & \text{HO} & \xrightarrow{\cdot\text{e}} & \text{---} & \text{---} & (\text{l}) \\\\ \text{OH}^{\cdot}(\text{H}\_{2}\text{O})\_{3} & \xrightarrow{\cdot\text{e}} & [[\text{OH}^{\cdot}(\text{H}\_{2}\text{O})\_{3}]^{+} & \xrightarrow{\cdot\text{e}} & [[\text{OH}^{\cdot}(\text{H}\_{2}\text{O})\_{3}]^{+} & \xrightarrow{\cdot\text{e}} & \text{---} & (\text{2}) \\\\ \text{OH}^{\cdot}(\text{H}\_{2}\text{O})\_{3} & \xrightarrow{\cdot\text{e}} & [[\text{OH}^{\cdot}(\text{H}\_{2}\text{O})\_{3}]^{+} & \xrightarrow{\cdot\text{e}} & [[\text{OH}^{\cdot}]\_{2}(\text{H}\_{2}\text{O})\_{2}]^{+} & \xrightarrow{\cdot\text{H}^{+}} & \text{HO} & \xrightarrow{\cdot\text{e}} & \text{---} \end{aligned}$$

**Scheme 1.** PEC-H2O oxidation to hydrogen peroxide as a precursor of oxygen molecule.

Figure 7 shows DFT-simulation results of oxidation of OH<sup>í</sup> (H2O)3 to [OH<sup>í</sup> (H2O)3] .+ or [OH. (H2O)3] as one-electron oxidation products (Equation (2)), and to [OH<sup>í</sup> (H2O)3] ..++ or [(OH. )2(H2O)2H]+ as two-electron oxidation products. They are simulated endothermically, suggesting that they are in energy filled states (Supplementary Table S6). In the equilibrium geometry of [OH. (H2O)3] .+, the spin density distributes only on the hydroxyl group, and the Mulliken charge on hydroxyl group decreases largely from í0.900 to í0.404. Thus the one-electron oxidation product has the structure of [OH. (H2O)3] rather than [OH<sup>í</sup>(H2O)3] .+.

**Figure 7.** DFT-simulation of step-wise oxidation of the hydroxide ion cluster model of [OH<sup>í</sup>(H2O)3].

On the other hand, the two-electron oxidation product shows that the spin density distributes on hydroxyl group and the (H2O)3 units. The Mulliken charge on them decreases from í0.806 to í0.668. The distance between hydroxyl group and H2O is shortened from 3.148 Å to 2.239 Å and the hydrogen bonds observed in [OH<sup>í</sup>(H2O)3] .+ disappear. In addition, the hydrogen-oxygen bond distance of H2O (0.976 Å) in [OH<sup>í</sup> (H2O)3] ..++ is quite comparable with that (0.988 Å) in [OH<sup>í</sup> (H2O)3] .+. The H2O components in the most energy-filled cluster [OH<sup>í</sup>(H2O)3] ++ should be tightly aggregated one another. Detachment of (H2O)3H.+ from [(OH. )2(H2O)2H+ ] leaves two hydroxyl radical in neighbor, yielding hydrogen peroxide as a precursor of O2 molecule (Equation (3) in Scheme 1). The oxidation of neutral H2O is verified to occur initially in photocatalytic processes to give effectively hydrogen peroxide on PEC nc-TiO2 electrodes.

#### *2.5. Verification of the Sakka's PEC H2O Oxidation under Acidic Conditions*

The stationary model of H3O+ (H2O)-associated structure of H3O+ (H2O)&OH(TiO2)9H and two kinds of energy filled models, [H3O+(H2O)&OH(TiO2)9H].+ and [H3O+(H2O)&OH(TiO2)9H].++ are simulated as an interface model of PEC-nc-TiO2 electrodes under Sakka's acidic conditions (Supplementary Figures S5 and S6). However, the energy gap are rather wider and the spin density does not localize on H3O+ (H2O) in the most energized state of [H3O+ (H2O)&OH(TiO2)9H].++.

The hydronium ion cluster, H3O+ (H2O)2 represent less acidic than H3O+ (H2O) (Supplementary Table S5). The stationary states of H3O+(H2O)2-associated structure of H3O+ (H2O)2&OH(TiO2)9H is simulated as an interface model under Sakka's less acidic conditions, and analyzed as well in view of molecular orbital energy structure (Figure 8).

**Figure 8.** DFT-simulation of H3O+(H2O)2&OH(TiO2)9H as a model of hydronium ion clusters on PEC-nc-TiO2 electrodes, (**a**) electrostatic potential map; (**b**) structures of HOMO and LUMO; (**c**) Configuration of HOMO(í8).

Differently from the modeling for the neutral PEC H2O oxidation, electrostatic potential map indicates that negative charge locates much more on the nc-TiO2 unit rather than the H2O unit, and HOMO distributes only on oxygen atoms in the nc-TiO2 unit. The energy gap 2.33 eV implies weak association of acidic H2O on nc-TiO2 electrodes. The orbital energy indicates that HOMO(í8) distributes slightly on the H3O+ (H2O)2 unit with very negative potential of í11.3 eV.

The acidic interface model of [H3O+ (H2O)2&OH(TiO2)9H] is simulated to [H3O<sup>+</sup> (H2O)2& OH(TiO2)9H].+ as the radical cation of the one-electron oxidation state, and to [H3O+ (H2O)2& OH(TiO2)9H]..++ as the diradical-dication model of the two electron oxidation sate (Figure 9). The former radical cation model reveals that configurations of HOMO, LUMO and spin density distribute on the nc-TiO2 unit and not on the H3O+(H2O)2, and the energy gap 0.7eV is not favorable in view of photoconductivity compared to that under neutral conditions. However, HOMO(í1) distributes on the (H2O)2 unit with orbital potential of í13.9 eV.

As for the latter dication-diradical model, the energy gap 0.5 eV and HOMO potential, í16.6 eV are given, and the spin density distributes on H3O+ (H2O)2 unit. Accordingly, the DFT-based orbital energy structure verifies that PEC H2O oxidation occurs even under acidic conditions, when nc-TiO2 electrodes are energized by bias potential under energy-gap UV irradiation.

**Figure 9.** DFT-simulation of oxidation states of H3O+(H2O)2&OH(TiO2)9H, (**a**) energy structures of the one-electron oxidation state, [H3O+(H2O)2&OH(TiO2)9H].+; (**b**) energy structures of the two-electron oxidation state, [H3O+(H2O)2&OH(TiO2)9H]..++.

#### **3. Experimental Section**

DFT calculations were performed using the B3LYP exchange-correlation functional and the 6-31G(d) basis set with *Spartan'14* (Wavefunction, Inc. Irvine, CA, USA) installed on VAIO Model SVP132A1CN, Intel(R) core(TM)i7-4500U CPU and on VAIO PC-Z (Intel core 2 Duo processor T9900, system memory (RAM) 8G and hard disk drive, SSD 128, 2GB).

Molecular mechanic optimization (e.g., Merck Molecular Force Factor (MMFF) operation in Spartan program) and DFT (B3LYP 6-31G\*) modeling determine molecular orbital structure of equilibrium geometry as an inter-atomic potential model [7,8]. In the case of Spartan program, molecular orbital energy structures (HOMO(0~9), LUMO(0~1), their configurations, electrostatic potential map, spin (unpaired electron of radical) density are visualized by graphic conveniently.

As for interface energy-filled model structures with unpaired electron, *i.e.*, radical cations, orbital energy diagrams are shown in two ways, affixed 'a-' and 'b-' because the radical cations have two available wave functions. The 'b'-HOMO and 'b'-LUMO are employed, since 'ȕ'-HOMO configurations are almost the same as spin density configurations. Electron energy gap of the radical cation components is obtained from energy difference between 'b'-HOMO and 'b'-LUMO. Mulliken charge, spin densities and their maps are informative for theoretical understandings of energy structures of energy-filled molecular orbitals of nc-TiO2 interfaces.

The anatase nc-TiO2 model structure has a pretty large size of OH(Ti9O18)H and is named as Yamashita/Jono model. The nc-TiO2 model structure is refined as described in Figure S7. As for orbital configurations, HOMO is shown by solid or solid transparent, LUMO by mesh, and spin density by white solid or white solid transparent. As for color in electrostatic potential map, red is negative, green neutral and blue positive qualitatively. Formation energy (ǻE) of key model molecules is determined from total energy (E) of their related components in Supplementary Tables S1–S3.

#### **4. Conclusions**

DFT-based modeling enables to verify molecular orbital level interfacial structures of photo-electrochemically energized nc-TiO2 electrodes. Although nc-TiO2 electrodes are composed of nc-TiO2 particles with average size 25 nm, Yamashita/Jono nc-TiO2 model (length size = ~1 nm) is large enough to model nc-TiO2 electrodes because the model may self-aggregate to larger sizes through hydrogen bond and van der Waals and Coulombic interactions. Water (H2O) cluster models (H2O)3 and H3O+ (H2O)2 are appropriate to bind Yamashita/Jono model cluster, providing interfacial PEC-nc-TiO2 electrode structures at neutral and acidic H2O conditions.

Molecular orbital analyses of the stationary and the working PEC-nc-TiO2 cluster models reveal that H2O clusters are adsorbed effectively (catalytically) via hydrogen bonding to PEC-nc-TiO2 electrodes at stationary state, and that the conductivity of PEC-nc-TiO2 electrodes is enhanced without loosing oxidation potential, leading to successive water oxidation to oxygen molecules through hydrogen peroxide in PEC cells. The molecular modeling of nc-TiO2 electrodes in PEC cells verifies that the photo-induced conductivity is the most important driving force of PEC H2O oxidation on nc-TiO2 electrodes. The DFT-verified photoconductivity is true for understanding of photocatalysis of Pt-deposited nc-TiO2 particles and dye-sensitized nc-TiO2 solar cells, rationalizing their remarkable efficiencies and effectiveness.

#### **Supplementary Materials**

Supplementary materials can be accessed at: http://www.mdpi.com/1420-3049/20/06/9732/s1.

#### **Acknowledgments**

The authors thank W. J. Hehre (Wavefunction, Inc. Irvine, CA, USA) and N. Uchida and M. Takahashi (Wavefunction, Inc., Japan Branch Office, Kouji-machi, Chiyoda-ku, Tokyo, Japan) for discussion on DFT simulation using '*Spartan 14*'.

#### **Author Contributions**

Shozo Yanagida, Susumu Yanagisawa, KY, RJ and HS designed research; Shozo Yanagida, Susumu Yanagisawa, KY, RJ and HS performed research, analyzed the data and discussed; Shozo Yanagida, Susumu Yanagisawa wrote the paper. All authors read and approved the final manuscript.

#### **Conflicts of Interest**

The authors declare no conflict of interest.

#### **References**


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