We analytically calculate the electronic friction tensor for a molecule near a metal surface in the case where the electronic Hamiltonian is complex valued, e.g., the case where 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.

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• Adsorbed biomolecules
• Spin-orbit coupling
• Surface & interfacial phenomena
• Transport phenomena