A caveat of the charge-extrapolation scheme for modeling electrochemical reactions on semiconductor surfaces: an issue induced by a discontinuous Fermi level change

(Photo)electrochemical surface reactions in realistic experimental systems occur under a constant-potential condition, while the ab initio simulations of electrochemical reactions are mostly performed under a constant-charge condition. A charge-extrapolation scheme proposed by earlier theoretical studies converts constant-charge reaction energies to constant-potential reaction energies for electrochemical reactions on metal surfaces, which is based on a capacitor-model assumption to approximate the surface electrical double layer. However, the charge-extrapolation approach may be problematic when applied to models of photoelectrochemical reactions on semiconductor surfaces with a cross-bandgap Fermi level change along the reaction path. We perform density-functional-theory calculations to show that the error is induced by an abrupt change of the modeling system's potential making the capacitor model assumption invalid. We further propose an approach to avoid the cross-bandgap Fermi level change in the simulations of semiconductor surface reactions, with which the charge-extrapolation scheme still can be employed to compute the constant-potential reaction energies for the semiconductor photoelectrode cases.