  We analytically calculate the electronic friction tensor for a molecule near
a metal surface in the case that the electronic Hamiltonian is complex-valued,
e.g. the case that there is spin-orbit coupling and/or an external magnetic
field. In such a case, even at equilibrium, we show that the friction tensor is
not symmetric. Instead, the tensor is the real-valued sum of one positive
definite tensor (corresponding to dissipation) plus one antisymmetric tensor
(corresponding to a Berry pseudomagnetic force). Moreover, we find that this
Berry force can be much larger than the dissipational force, suggesting the
possibility of strongly spin-polarized chemicurrents or strongly spin-dependent
rate constants for systems with spin-orbit coupling.
