  We derive an explicit form for the electronic friction as felt by a molecule
near a metal surface for the general case that molecule-metal couplings depend
on nuclear coordinates. Our work generalizes a previous study by von Oppen et
al [Beilstein Journal of Nanotechnology, 3, 144, 2012], where we now go beyond
the Condon approximation (i.e. molecule-metal couplings are not held constant).
Using a non-equilibrium Green's function formalism in the adiabatic limit, we
show that fluctuating metal-molecule couplings lead to new frictional damping
terms and random forces, plus a correction to the potential of mean force.
Numerical tests are performed and compared with a modified classical master
equation; our results indicate that violating the Condon approximation can have
a large effect on dynamics.
