Modeling surface vibrations and their role in molecular adsorption: a generalized Langevin approach

The atomic vibrations of a solid surface can play a significant role in the reactions of surface-bound molecules, as well as their adsorption and desorption. Relevant phonon modes can involve the collective motion of atoms over a wide array of length scales. In this manuscript, we demonstrate how the generalized Langevin equation can be utilized to describe these collective motions weighted by their coupling to individual sites. Our approach builds upon the generalized Langevin oscillator (GLO) model originally developed by Tully \textit{et al.} We extend the GLO by deriving parameters from atomistic simulation data. We apply this approach to study the memory kernel of a model platinum surface and demonstrate that the memory kernel has a bimodal form due to coupling to both low-energy acoustic modes and high-energy modes near the Debye frequency. The same bimodal form was observed across a wide variety of solids of different elemental compositions, surface structures, and solvation states. By studying how these dominant modes depend on simulation size, we argue that the acoustic modes are frozen in the limit of macroscopic lattices. By simulating periodically replicated slabs of various sizes we quantify the influence of phonon confinement effects in the memory kernel and their concomitant effect on simulated sticking coefficients.