Electron Transfer and Spin-Orbit Coupling: How Strong are Berry Force Effects In and Out of Equilibrium in the Presence of Nuclear Friction?

We investigate a spin-boson inspired model of electron transfer, where the diabatic coupling is given by a position-dependent phase, exp(iWx). We consider both equilibrium and nonequilibrium initial conditions. We show that, for this model, all equilibrium results are completely invariant to the sign of W(to infinite order). However, the nonequilibrium results do depend on the sign of W, suggesting that photo-induced electron transfer dynamics are meaningfully affected by Berry forces even in the presence of nuclear friction; furthermore, whenever there is spin-orbit coupling, electronic spin polarization can emerge (at least for some time).