Conduction band edge (CBE) and valence band edge (VBE) positions of InxGa1–xN photoelectrodes were computed using density functional theory methods. The band edges of fully solvated GaN and InN model systems were aligned with respect to the standard hydrogen electrode using a molecular dynamics hydrogen electrode scheme applied earlier to TiO2/water interfaces. Similar to the findings for TiO2, we found that the Purdew–Burke–Ernzerhof (PBE) functional gives a VBE potential which is too negative by 1 V. This cathodic bias is largely corrected by application of the Heyd–Scuseria–Ernzerhof (HSE06) hybrid functional containing a fraction of Hartree–Fock exchange. The effect of a change of composition was investigated using simplified model systems consisting of vacuum slabs covered on both sides by one monolayer of H2O. The CBE was found to vary linearly with In content. The VBE, in comparison, is much less sensitive to composition. The data show that the band edges straddle the hydrogen and oxygen evolution potentials for In fractions less than 47%. The band gap was found to exceed 2 eV for an In fraction less than 54%.

All-atom methods treat solute and solvent at the same level of electronic structure theory and statistical mechanics. All-atom computation of acidity constants (pKa) and redox potentials is still a challenge. In this Account, we review such a method combining density functional theory based molecular dynamics (DFTMD) and free energy perturbation (FEP) methods. The key computational tool is a FEP based method for reversible insertion of a proton or electron in a periodic DFTMD model system. The free energy of insertion (work function) is computed by thermodynamic integration of vertical energy gaps obtained from total energy differences. The problem of the loss of a physical reference for ionization energies under periodic boundary conditions is solved by comparing with the proton work function computed for the same supercell. The scheme acts as a computational hydrogen electrode, and the DFTMD redox energies can be directly compared with experimental redox potentials.Consistent with the closed shell nature of acid dissociation, pKa estimates computed using the proton insertion/removal scheme are found to be significantly more accurate than the redox potential calculations. This enables us to separate the DFT error from other sources of uncertainty such as finite system size and sampling errors. Drawing an analogy with charged defects in solids, we trace the error in redox potentials back to underestimation of the energy gap of the extended states of the solvent. Accordingly the improvement in the redox potential as calculated by hybrid functionals is explained as a consequence of the opening up of the bandgap by the Hartree–Fock exchange component in hybrids. Test calculations for a number of small inorganic and organic molecules show that the hybrid functional implementation of our method can reproduce acidity constants with an uncertainty of 1–2 pKa units (0.1 eV). The error for redox potentials is in the order of 0.2 V.

Due to the contraints imposed on the optimization of oxygen evolution reaction (OER) catalysts, the correlations between adsorption energies of OER intermediates have received considerable interest. Computation has made important contributions uncovering and elucidating these correlations. The calculations have predominantly been of the spin-restricted type. Using both the restricted and unrestricted formalism, we have performed a DFT–PBE study of the key OER intermediates on 10 nonmagnetic metal oxide surfaces. We show that, depending on the binding energy, unrestricted DFT calculations may yield considerably higher binding energies than restricted DFT calculations. At low binding energies, spin quenching of the adsorbates is inefficient, leading to a strong open shell character that is not well described by restricted DFT. At high binding energies, spin quenching is complete, so that the unrestricted DFT binding energy equals the restricted DFT binding energy. We conclude therefore that although strong binding systems can be properly described by restricted DFT, unrestricted DFT is a necessity for weak binding systems, to which photocatalysts typically belong. The use of unrestricted DFT has little effect on the shape of volcano plots when ΔGO – ΔGOH is chosen as a descriptor. The location of the data points on the plot does show a considerable shift for weak binding substrates.

The position of electronic energy levels in a phase depends on the surface potentials at its boundaries. Bringing two phases in contact at an interface will alter the surface potentials shifting the energy levels relative to each other. Calculating such shifts for electrochemical interfaces requires a combination of methods from computational surface science and physical chemistry. The problem is closely related to the computation of potentials of electrochemically inactive electrodes. These so-called ideally polarizable interfaces are impossible to cross for electrons. In this perspective we review two density functional theory based methods that have been developed for this purpose, the workfunction method and the hydrogen insertion method. The key expressions of the two methods are derived from the formal theory of absolute electrode potentials. As an illustration of the workfunction method we review the computation of the potential of zero charge of the Pt(111)–water interface as recently published by a number of groups. The example of the hydrogen insertion method is from our own work on the rutile TiO2(110)–water interface at the point of zero proton charge. The calculations are summarized in level diagrams aligning the electronic energy levels of the solid electrode (Fermi level of the metal, valence band maximum and conduction band minimum of the semiconductor) to the band edges of liquid water and the standard potential for the reduction of the hydroxyl radical. All potentials are calculated at the same level of density functional theory using the standard hydrogen electrode as common energy reference. Comparison to experiment identifies the treatment of the valence band of water as a potentially dangerous source of error for application to electrocatalysis and photocatalysis.

The electronic states of aqueous species can mix with the extended states of the solvent if they are close in energy to the band edges of water. Using density functional theory-based molecular dynamics simulation, we show that this is the case for OH– and Cl–. The effect is, however, badly exaggerated by the generalized gradient approximation leading to systematic underestimation of redox potentials and spurious nonlinearity in the solvent reorganization. Drawing a parallel to charged defects in wide gap solid oxides, we conclude that misalignment of the valence band of water is the main source of error turning the redox levels of OH– and Cl– in resonant impurity states. On the other hand, the accuracy of energies of levels corresponding to strongly negative redox potentials is acceptable. We therefore predict that mixing of the vertical attachment level of CO2 and the unoccupied states of water is a real effect.Keywords: density functional theory; ionization potential; solvent effect;

The thermodynamics of protonation and deprotonation of the rutile TiO2(110) water interface is studied using a combination of density functional theory based molecular dynamics (DFTMD) and free energy perturbation methods. Acidity constants are computed from the free energy for chaperone assisted insertion/removal of protons in fully atomistic periodic model systems treating the solid and solvent at the same level of theory. The pKa values we find for the two active surface hydroxyl groups on TiO2(110), the bridge OH (Ti2OH+), and terminal H2O adsorbed on a 5-fold Ti site (TiOH2) are −1 and 9, leading to a point of zero proton charge of 4, well within the computational error margin (2 pKa units) from the experimental value (4.5−5.5). The computed intrinsic surface acidities have also been used to estimate the dissociation free energy of adsorbed water giving 0.6 eV, suggesting that water dissociation is unlikely on a perfect aqueous TiO2(110) surface. For further analysis, we compare to the predictions of the MUltiSIte Complexation (MUSIC) and Solvation, Bond strength, and Electrostatic (SBE) models. The conclusion regarding the MUSIC model is that, while there is good agreement for the acidity of an adsorbed water molecule, the proton affinity of the bridging oxygen obtained in the DFTMD calculation is significantly lower (more than 5 pKa units) than the MUSIC model value. Structural analysis shows that there are significant differences in hydrogen bonding, in particular to a bridging oxygen which is assumed to be stronger in the MUSIC model compared to what we find using DFTMD. Using DFTMD coordination numbers as input for the MUSIC model, however, led to a pKa prediction which is inconsistent with the estimates obtained from the DFTMD free energy calculation.

The density functional theory based ab initio molecular dynamics method combines electronic structure calculation and statistical mechanics and should, therefore, ideally be a tool for “first principle” computation of redox free energies in the sense that the redox active solutes and solvent are treated at the same level of theory. In this paper, we give a brief outline how such an approach can be implemented in the framework of the Marcus theory of electron transfer. The method is illustrated and validated using results of previous work. We then continue with a theoretical analysis of the correlation between the energies of one-electron states and redox potentials exploiting the separation in vertical ionization and reorganization contributions inherent in Marcus theory. Testing this relation on the limited set of reactions investigated sofar we find that it is satisfied within the uncertainties of the computation.

A recently developed ab initio molecular dynamics method for the simulation of electrochemical half reactions is placed in the context of commonly accepted pictures of electrode processes and the related Marcus theory of heterogeneous electron transfer. Viewing our computational approach from this perspective we comment on a number of more technical aspects of the method.

The one-electron density of states of liquid water computed from an ab initio molecular dynamics trajectory is analyzed in terms of interactions between effective molecular orbitals localized on single molecules. These orbitals are constructed from the occupied extended (Kohn–Sham) orbitals using the maximally localized Wannier function method. Band positions are related to average orbital energies. The width of a band is resolved into contributions from thermal fluctuations in the orbital energies and the electronic broadening due to intermolecular coupling. It is found that the thermal and electronic broadening are of comparable magnitude with electronic broadening being the leading effect.

The position of electronic energy levels in a phase depends on the surface potentials at its boundaries. Bringing two phases in contact at an interface will alter the surface potentials shifting the energy levels relative to each other. Calculating such shifts for electrochemical interfaces requires a combination of methods from computational surface science and physical chemistry. The problem is closely related to the computation of potentials of electrochemically inactive electrodes. These so-called ideally polarizable interfaces are impossible to cross for electrons. In this perspective we review two density functional theory based methods that have been developed for this purpose, the workfunction method and the hydrogen insertion method. The key expressions of the two methods are derived from the formal theory of absolute electrode potentials. As an illustration of the workfunction method we review the computation of the potential of zero charge of the Pt(111)–water interface as recently published by a number of groups. The example of the hydrogen insertion method is from our own work on the rutile TiO2(110)–water interface at the point of zero proton charge. The calculations are summarized in level diagrams aligning the electronic energy levels of the solid electrode (Fermi level of the metal, valence band maximum and conduction band minimum of the semiconductor) to the band edges of liquid water and the standard potential for the reduction of the hydroxyl radical. All potentials are calculated at the same level of density functional theory using the standard hydrogen electrode as common energy reference. Comparison to experiment identifies the treatment of the valence band of water as a potentially dangerous source of error for application to electrocatalysis and photocatalysis.