A pragmatic protocol for determining charge transfer states of molecules at metal surfaces by constrained density...

Electron transfer from a metal surface to a molecule is very important at the gas-surface interface, which can lead to electron-mediated energy transfer during molecular scattering from the surface, as evidenced by numerous state-to-state molecular beam experiments of NO and CO scattering from noble metal surfaces. However, it remains challenging to determine relevant charge-transfer states and their nonadiabatic couplings from first principles in such systems involving a continuum of metallic electronic states. In this work, we propose a pragmatic protocol for this purpose based on the constrained density functional theory (CDFT) approach. In particular, we discuss the influence of the charge partitioning algorithm used in CDFT to define the constraint property in molecule-metal systems. It is found that the widely used Bader charge analysis is adequate to define the physically sound CDFT diabatic states corresponding to a molecule with or without extra electron transferred from the metal. Numerical tests validate that the proposed CDFT scheme properly describes the electron transfer behaviors in several benchmark systems, namely, NO or CO interacting with Au(111) or Ag(111). The effects of the surface work function and the molecular electron affinity on electron transfer are discussed in detail by comparing the CDFT states of the four systems. This pragmatic CDFT protocol lays the foundation for constructing accurate global diabatic potential energy surfaces for these important systems and can be generalized to study other interfacial electron transfer related problems.