  An accurate description of nonadiabatic dynamics of molecular species on
metallic surfaces poses a serious computational challenge associated with a
multitude of closely-spaced electronic states. We propose a mixed
quantum-classical scheme that addresses this challenge by introducing
collective electronic variables. These variables are defined through analytic
block-diagonalization applied to the time-dependent Hamiltonian matrix
governing the electronic dynamics. We compare our scheme with the Ehrenfest
approach and with a full-memory electronic friction model on a one-dimensional
"adatom + atomic chain" model. Our simulations demonstrate that collective-mode
dynamics with only few (2-3) electronic variables is robust and can describe a
variety of situations: from a chemisorbed atom on an insulator to an atom on a
metallic surface. Our molecular model also reveals that the friction approach
is prone to unpredictable and catastrophic failures.
