  Due to a continuum of electronic states present in periodic systems, the
description of molecular dynamics on surfaces poses a serious computational
challenge. One of the most used families of approaches in these settings are
friction theories, which are based on the Ehrenfest (EH) approach. Yet, a
mean-field treatment of electronic degrees of freedom in the EH method makes
this approach inaccurate in some cases. Our aim is to clarify when EH breaks
down for molecular dynamics on surfaces. Answering this question provides
limits of applicability for more approximate friction theories derived from EH.
We assess the EH method on one-dimensional, numerically exactly solvable models
with a large but finite number of electronic states. Using the Landau-Zener
formula and the Massey parameter, an expression that determines when EH breaks
down is deduced.
