  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).
