# First-Principles View on Photoelectrochemistry: Water-Splitting as Case Study

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Processes Involved in Photoelectrochemistry

#### 2.1. Creation of Electron-Hole Pairs

#### 2.2. Charge Carrier Transport

#### 2.3. Electrochemical Surface Reactions

#### Pourbaix Surface Diagrams

#### 2.4. Reaction Mechanism

#### 2.5. Overpotential

## 3. Conclusions

## Acknowledgments

## Conflicts of Interest

## Appendix A. Theoretical Methodologies of Density Functional Theory [211,212]

#### Appendix A.1. The Hohenberg-Kohn Theorems

**Theorem**

**A1.**

**Theorem**

**A2.**

#### Appendix A.2. The Kohn-Sham Equations

#### Appendix A.3. The Exchange and Correlation Functionals

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**Figure 1.**A schematic energy diagram for a photoanode (n-type semiconductor). Several important steps are illustrated, namely: (i) light absorption ${\mathsf{\eta}}_{{e}^{-}/{h}^{+}}$; (ii) charge transport ${\mathsf{\eta}}_{tr}$; and (iii) surface chemical reactions ${\mathsf{\eta}}_{ct}$. Photons with energy equal to or larger than the band-gap E${}_{g}$ are absorbed with efficiency ${\mathsf{\eta}}_{{e}^{-}/{h}^{+}}$. The built-in electric field drives holes towards the photoanode/electrolyte interface and electrons to the cathode (usually via a charge collector and an external circuit). ${\mathsf{\eta}}_{tr}$ is the fraction of photogenerated charges reaching the respective solid/liquid interface. Holes are transferred to the electrolyte with efficiency ${\mathsf{\eta}}_{ct}$ and take part in the oxygen evolution reaction (OER). An external bias/PV device supplies electrons with sufficient energy so that they take part in the hydrogen evolution reaction (HER). Reproduced with permission from ref. [40], published by The Royal Society of Chemistry.

**Figure 2.**PEC performance gap between a state-of-the-art photoanode and the ideal photoanode. The arrows indicate the main performance limiting factors for increasingly anodic potential: first charge transfer at the photoanode/electrolyte interface and the small photovoltage, then charge transport within photoanode and finally light absorption in the semiconductor. Reproduced with permission from ref. [40], published by The Royal Society of Chemistry.

**Figure 3.**The relaxation process of hot electron-hole pairs. There exist several pathways for dissipation of the energy of the electron-hole pairs. More details of these are given in the text. Reprinted by permission from Nature Nanotechnology, copyright 2015 [54].

**Figure 4.**Schematic picture showing the electronic energy levels at the interface between an n-type semiconductor and an electrolyte containing a redox couple. The four cases indicated are: (

**a**) flat band potential, where no space-charge layer exists in the semiconductor; (

**b**) accumulation layer, where excess electrons have been injected into the solid producing a downward bending of the conduction and valence band towards the interface; (

**c**) depletion layer, where electrons have moved from the semiconductor to the electrolyte, producing an upward bending of the bands; and (

**d**) inversion layer, where the electrons have been depleted below their intrinsic level, enhancing the upward band bending and rendering the semiconductor p-type at the surface [96]. Reprinted by permission from Macmillan Publishers Ltd.: Nature 414 338, copyright 2001.

**Figure 5.**The color map shows the local density of states (LDOS) along the direction normal to the interface. The Nb-dopant is marked as Nb${}_{\mathrm{Ti}}$ in the inserted structure plot. The dopant state below the bottom of the conduction band traps most of the excess electron donated by Nb${}_{\mathrm{Ti}}$. The band edges of the pristine TiO${}_{2}$ are also shown (gray dashed lines). The band bending is caused by the dopant-induced charge polarization. Reprinted with permission from ref. [104].

**Figure 6.**Schematic density profile of interfacial water near the solid–aqueous interface. Reprinted with permission from ref. [168]. Copyright 2004 Elsevier.

**Figure 7.**The relative stability of all considered surface terminations as a function of applied potential and at two different pH, namely pH = 0 (

**left**) and pH = 14 (

**right**). Reprinted with permission from [181]. Copyright 2011 American Chemical Society.

**Figure 8.**The water splitting reaction at different potentials. At potentials between 0 and 0.78 V all steps in the oxygen reduction are exothermic. For potentials beyond 2.55 V all water splitting reaction steps become exothermic. This variation is obtained by varying the term eU in the free energy per electron transferred to the electrode. Reprinted from Chemical Physics 319 (2005) 178, Copyright 2005, with permission from Elsevier [158].

**Figure 9.**(

**a**) Adsorption energies of HOO* as a function of adsorption energies of HO* on rutile, perovskites, anatase, Mn${}_{x}$O${}_{y}$, Co${}_{3}$O${}_{4}$ and NiO oxides. Open and solid symbols represent the adsorption energies on clean surfaces and on high-coverage surfaces, respectively. The star represents the binding energies required for an ideal electrocatalyst. The dotted line represents the relationship between $\Delta $E${}_{{\mathrm{HOO}}^{*}}$ and $\Delta $E${}_{{\mathrm{HO}}^{*}}$ for an ideal catalyst, which is given by $\Delta $E${}_{{\mathrm{HOO}}^{*}}$ = $\Delta $E${}_{{\mathrm{HO}}^{*}}$ + 2.44 eV; (

**b**) Activity trends toward oxygen evolution for rutile oxides, Co${}_{3}$O${}_{4}$, and Mn${}_{x}$O${}_{y}$. The negative value of the theoretical overpotential is plotted as a function of the standard free energy of $\Delta $G${}_{{\mathrm{O}}^{*}}$and $\Delta $G${}_{{\mathrm{OH}}^{*}}$; (

**c**) Standard free-energy diagram for the OER on O*-covered RuO${}_{2}$ at three different potentials: U = 0, 1.23, and 1.60 V. Reprinted with permission from [200].

**Figure 10.**Scaling relation between the Gibbs free energies of adsorption of *OH, *O, and *OOH. Squares represent metal porphyrine, triangles hangman metalloporphyrins and rectangles metaltetrafluorophenyloporphyrines molecules, respectively. The dashed lines at 0 and 4.92 eV represent energy of H${}_{2}$O and O${}_{2}$, respectively. The grey area separates the metals from the Group 9 and before from the 10 and after of the periodic table. Reprinted with permission from [208]. Copyright 2014 American Chemical Society.

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Hellman, A.; Wang, B.
First-Principles View on Photoelectrochemistry: Water-Splitting as Case Study. *Inorganics* **2017**, *5*, 37.
https://doi.org/10.3390/inorganics5020037

**AMA Style**

Hellman A, Wang B.
First-Principles View on Photoelectrochemistry: Water-Splitting as Case Study. *Inorganics*. 2017; 5(2):37.
https://doi.org/10.3390/inorganics5020037

**Chicago/Turabian Style**

Hellman, Anders, and Baochang Wang.
2017. "First-Principles View on Photoelectrochemistry: Water-Splitting as Case Study" *Inorganics* 5, no. 2: 37.
https://doi.org/10.3390/inorganics5020037