Regioselectivity of H₂ Adsorption on Ga₂O₃ Surface Based on Vibronic Coupling Density Analysis

Abstract

Regioselectivity of H₂ adsorption on the Ga₂O₃ surface is investigated using the vibronic coupling density (VCD) as a reactivity index. The cluster model of Ga₂O₃ surface obtained by Step-by-Step Hydrogen-Terminated (SSHT) approach is employed. The VCD analysis shows that H₂ is dissociatively adsorbed as H⁺ on the Lewis basic O atoms and as H⁻ on the adjacent Ga atoms. The heterolytic dissociation implies that the H⁻ atom bonded to the Ga atom is a reductant responsible for photocatalytic reduction of CO₂ to CO.

1 Introduction

$\beta$-Ga₂O₃ is a photocatalyst that reduces CO₂ to CO using H₂ as a reductant [1,2]. Fourier transform infrared (FT-IR) spectroscopy confirms the existence of OH groups on the $\beta$-Ga₂O₃ surface [2,3,4]. In addition, H₂ dissociatively adsorbs over the $\beta$-Ga₂O₃ surface to form Ga-H and Ga-OH species. It has been proposed that the dissociatively adsorbed H₂ reduces the monodentate bicarbonate species to bidentate formate species on photoirradiation, which is further decomposed into CO. Since the use of H₂ as a reductant improves the photocatalytic activity, it is important to know the adsorption sites of H₂ on the $\beta$-Ga₂O₃ surface. This knowledge is required to study the mechanism of photocatalytic reduction.

$\beta$-Ga₂O₃ is composed of Ga atoms surrounded by O atoms in tetrahedral and octahedral configurations [5,6]. Figure 1 (a) shows a unit cell of the $\beta$-Ga₂O₃ crystal. The unit cell has four Ga atoms at octahedral and tetrahedral sites. The two adjacent Ga atoms at octahedral sites are separated by Ga atoms at tetrahedral sites. Previously, we proposed a step-by-step hydrogen-terminated (SSHT) cluster model for the $\beta$-Ga₂O₃ surface, as shown in Figure 1 (b) [7]. The SSHT model consists of eight adjacent Ga atoms at octahedral sites aligned in the b-axis direction. The dangling bonds generated at O atoms on cleaving the cluster from the crystal structure are terminated by H atoms. This addition of H atoms can be regarded as electron doping. The H atoms are step-by-step bonded to the O atoms with large orbital coefficients for unoccupied molecular orbitals until the model has an energy gap in agreement with experiments. The SSHT model consists of 28 O atoms, of which 20, 6, and 2 O atoms are bonded to 1, 2, and 0 H atoms, respectively. The O atoms without hydrogen termination are found to be Lewis basic, and can react with H₂.

Figure 1.

 (a) Unit cell of the $\beta$-Ga₂O₃ crystal with lattice parameters a=12.21Å, b=3.04Å, c= 5.80Å, and $\beta$=103.7° [6]. (b) SSHT cluster model of the $\beta$-Ga₂O₃ surface [7]. The Lewis basic O atoms are encircled. The H₂O moieties enclosed by rectangle are to be removed.

The adsorption sites for a molecule on a solid surface can be predicted by the vibronic coupling density (VCD). The VCD identifies a region on a surface where stabilization by structural relaxation, which occurs following charge transfer between a molecule and solid surface, is large. In other words, the VCD can be utilized as a reactivity index for investigating the regioselectivity of molecular adsorption on a solid surface. In this study, we determined the sites for adsorption of H₂ on the SSHT cluster model of the $\beta$-Ga₂O₃ surface based on VCD analysis.

2 Theory

Structural relaxation after charge transfer between the reactants is induced by vibronic coupling. The strength of vibronic coupling is quantified in terms of the vibronic coupling constant (VCC). The VCC $V_s$ with respect to reaction coordinate $s$ is defined by [8,9]   

$\begin{array}{c}{V}_s={\text{Ψ}}_{\text{CT}}\text{|}{\left(\frac{\partial U}{\partial s}\right)}_{{\text{R}}_0}{\text{|Ψ}}_{\text{CT}},\#\left(1\right)\end{array}$1

()where $|{\text{Ψ}}_{\text{CT}}$ is the charge-transfer state, and ${\text{R}}_0$ is the equilibrium molecular geometry before charge transfer. $U$ is the sum of electron-electron, electron-nucleus, and nucleus-nucleus potentials. Thus, $V_s$ can be decomposed into contributions from the electron-nucleus and nucleus-nucleus potentials. Using the Hellmann-Feynman theorem, equation (1) is transformed into   

$\begin{array}{c}{V}_s={\left(\frac{\partial E_{\text{CT}}}{\partial s}\right)}_{R_0}, \#\#\left(2\right)\end{array}$2

()where $E_{\text{CT}}$ is the energy of the charge-transfer state. The reaction coordinate is taken at the steepest descent direction of the potential surface in the charge-transfer state,   

$\begin{array}{c}s=\sum _{\alpha }\frac{V_{\alpha }}{\sqrt{{\sum }_{\alpha }{\left|V_{\alpha }\right|}^2}}{Q}_{\alpha }.\#\left(3\right)\end{array}$3

()

$Q_{\alpha }$ are the normal coordinate of vibrational mode $\alpha$, and $V_{\alpha }$ is the VCC with respect to $Q_{\alpha }$. The VCD ${\eta }_s$ is given by the integrand of the VCC as [8,9]   

$\begin{array}{c}{V}_s=\int {\eta }_s\left(r\right) d^{3}r.\#\left(4\right)\end{array}$4

()

The VCD can be represented as the product of electronic and vibrational contributions:   

$\begin{array}{c}{\eta }_s\left(r\right)=�\rho \left(r\right)\times v_s\left(r\right).\#\left(5\right)\end{array}$5

()

$�\rho \left(r\right)$ is the electron density difference between the neutral and charge-transfer states, and $v_s\left(r\right)$ is the derivative of the attractive electron-nucleus potential acting on an electron with respect to $s$.

R. G. Parr and W. Yang derived the frontier orbital theory for chemical reactivity in terms of the conceptual density functional theory [10,11,12]. The chemical potential $\mu =\mu \left[N,u\right]$ is a functional of the number of electrons $N$ and the potential acting on a single electron from all the nuclei $u$. The differential of the chemical potential is written as   

$\begin{array}{c}\begin{array}{c}d\mu =2{\eta }_{N}dN+\int f\left(r\right) du{d}^{3}r,\#\left(6\right)\end{array}\end{array}$6

()where ${\eta }_N$ is the absolute hardness, and $f\left(r\right)$ is the Fukui function. R. G. Parr and W. Yang assumed that the preferred direction for the incoming reagent is the one that gives the maximum $\left|d\mu \right|$. Furthermore, they assumed that chemical reactions occur at a region where $f\left(r\right)$ is the largest because the first term on the right-hand side of equation (5) is less direction sensitive than the second term. We have shown that equation (4) can be rewritten by using the VCD as [8,9]   

$\begin{array}{c}d\mu =2{\eta }_{N}dN+\int {\eta }_s\left(r\right) ds{d}^{3}r.\#\left(7\right)\end{array}$7

()

Therefore, the region with the largest ${\eta }_s\left(r\right)$ is regarded as a reactive site for chemical reactions.

3 Computational Method

We performed geometry optimization and vibrational analysis of the neutral Ga₂O₃ cluster. Then, we calculated the forces acting on the nuclei of the cationic Ga₂O₃ cluster at the neutral optimized structure. The cationic state was chosen as the charge-transfer state. The calculations were performed using density functional theory at the B3LYP/6-31G (d,p) level by GAUSSIAN 09 [13,14]. The VCD was calculated using our program.

4 Results

Ga₂O₃ was synthesized by calcination of gallium oxide hydroxide, a precursor of gallium oxide [1,2]. It is expected to dehydrate during this thermal treatment. Therefore, H₂O located at the front and back surfaces of the SSHT cluster model are removed. There are three types of H₂O moieties in the SSHT model. It is found that the removal of H₂O moiety near the Lewis basic O atoms is energetically most stable (Figure 1 (b)). All the H₂O moieties are not removed because, after the introduction of H₂, there are the broad bands in the FT-IR spectrum that can be assigned to the vibrations arising from the hydrogen bonds [2].

Figure 2 shows $�\rho \left(r\right)$, $v_s\left(r\right)$, and ${\eta }_s\left(r\right)$ of the SSHT cluster model from which two H₂O molecules are removed. $�\rho \left(r\right)$ is localized on the Lewis basic O atoms, whereas $v_s\left(r\right)$ is localized on the bonds between the Lewis basic O atoms and the adjacent Ga atoms. As a result, ${\eta }_s\left(r\right)$, the product of $�\rho \left(r\right)$ and $v_s\left(r\right)$, is localized on the Lewis basic O atoms and on the bonds with the adjacent Ga atoms. $V_s$ is calculated to be −4.54×10⁻⁴ a.u., which is decomposed into contributions from the electron-nucleus potential with 1.37830×10⁻¹ a.u. and the nucleus-nucleus potential with −1.38284×10⁻¹ a.u.

Figure 2.

 (a) $�\rho \left(r\right)$, (b) $v_s\left(r\right)$, and (c) ${\eta }_s\left(r\right)$ of the SSHT cluster model with two H₂O moieties removed. Isosurface values of $�\rho \left(r\right)$, $v_s\left(r\right)$, and ${\eta }_s\left(r\right)$ are $5.0\times {10}^{-3}$, $2.0\times {10}^{-5}$, and $1.5\times {10}^{-5}$ a.u., respectively.

Stabilization by structural relaxation following charge transfer from the Ga₂O₃ cluster to the reactant molecule is large at a region where the VCD is localized. Therefore, geometry optimization is performed after placing H₂ on the Lewis basic O atoms. Figure 3 shows the optimized structure of Ga₂O₃ cluster after the addition of H₂. H₂ are dissociatively adsorbed on the Lewis basic O atoms as well as the adjacent Ga atoms. The calculated natural charges on the H atoms bonded to the Lewis basic O atoms and to the Ga atoms are +0.52 and −0.35, respectively. This indicates that the H₂ undergoes heterolytic cleavage to adsorb on the Lewis basic O atoms as H⁺ and the adjacent Ga atoms as H⁻, as confirmed experimentally [2,3].

Figure 3.

 Structure of the Ga₂O₃ cluster with H₂ dissociatively adsorbed. Natural charges on the H atoms are mentioned.

Figure 4 shows the HOMOs of the Ga₂O₃ cluster on which H₂ are dissociatively adsorbed. The HOMO is doubly pseudo-degenerate because the cluster has the front and back surface. It is large at the dissociatively adsorbed H on Ga atoms. Thus, it is predicted that the H atoms bonded to Ga atoms act as a reductant donating electrons, which is suggested based on the experimental observations [2].

Figure 4.

 Doubly pseudo-degenerate HOMOs of the Ga₂O₃ cluster. The HOMOs are localized on H atoms dissociatively adsorbed on Ga atoms.

5 Conclusion

We investigated the regioselectivity of H₂ adsorption on the Ga₂O₃ surface using the VCD as a reactivity index. H₂ is found to heterolytically dissociate as H⁺ on the Lewis basic O atoms and as H⁻ on the adjacent Ga atoms. Of these, H⁻ acts as a reductant by donating electrons. The resultant Ga₂O₃ cluster with dissociatively adsorbed H₂ can be used as a model for further theoretical investigation of the photocatalytic mechanism of CO₂ reduction.

Acknowledgment

This work was supported by the Elements Strategy Initiative for Catalysts and Batteries (ESICB). The computations were partially performed at the Supercomputer Laboratory of Kyoto University and Research Center for Computational Science, Okazaki, Japan.

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