A theory of phonon-induced friction on molecular adsorbates

Abstract

In this manuscript, we provide a general theory for how surface phonons couple to molecular adsorbates. Our theory maps the extended dynamics of a surface's atomic vibrational motions to a generalized Langevin equation, and by doing so captures these dynamics in a single quantity: the non-Markovian friction. The different frequency components of this friction are the phonon modes of the surface slab weighted by their coupling to the adsorbate degrees of freedom. Using this formalism, we demonstrate that physisorbed species couple primarily to acoustic phonons while chemisorbed species couple to dispersionless local vibrations. We subsequently derive equations for phonon-adjusted reaction rates using transition state theory and demonstrate that these corrections improve agreement with experimental results for CO desorption rates from Pt(111).

Keywords: generalized Langevin equation; molecular adsorption/desorption; surface phonons.

Fig. 1.

2D schematic illustrating the dominant phonon modes in terms of their coupling to the adsorbate or contribution to the friction kernel. ${\omega }_{\mathrm{as}}$ is the frequency of the adsorbate–surface bond and the ${\omega }_{\mathrm{D}}$ is the solid’s Debye frequency.

Fig. 2.

(A) Friction kernel, (B) spectral density, and (C) density of states for Pt(111) and three values of ${\omega }_{\mathrm{as}}$. The density of states in (C) was calculated using the 4 $\times$ 4 $\times$ 8 surface slab.

Fig. 3.

Phonon dispersion curves. (A) Bulk Pt dispersion curves calculated using an EMT forcefield and a 10 $\times$ 10 $\times$ 10 atom supercell. (B) Dispersion curves for a 4 $\times$ 4 $\times$ 8 atom surface slab replicated in a 6 $\times$ 6 surface cell (C) Same as middle but with an adsorbed CO molecule corresponding to ${\omega }_{\mathrm{AS}}=480{\mathrm{cm}}^{-1}$.

Fig. 4.

Friction kernel for a model adsorbate on Pt(111) in a finite system (black) and in the infinite system size limit (blue). The finite system is equivalent to the 4 $\times$ 4 $\times$ 8 results presented in Fig. 2.

Fig. 5.

Rate constants for desorption from a Pt(111) surface. (A) CO desorption. Gray squares are experimental data which mixed contributions from both steps and terraces. Black circles refer experimental data where the kinetics of terrace desorption was isolated. (B) Xe desorption.