  We investigate the importance of including quantized initial conditions in
Langevin dynamics for adsorbates interacting with a thermal reservoir of
electrons. For quadratic potentials the time evolution is exactly described by
a classical Langevin equation and it is shown how to rigorously obtain quantum
mechanical probabilities from the classical phase space distributions resulting
from the dynamics. At short time scales, classical and quasiclassical initial
conditions lead to wrong results and only correctly quantized initial
conditions give a close agreement with an inherently quantum mechanical master
equation approach. With CO on Cu(100) as an example, we demonstrate the effect
for a system with ab initio frictional tensor and potential energy surfaces and
show that quantizing the initial conditions can have a large impact on both the
desorption probability and the distribution of molecular vibrational states.
