Electron transfer, diabatic couplings, and vibronic energy gaps in a phase space electronic structure framework

We investigate the well-known Shin-Metiu model for an electronic crossing, using both a standard Born-Huang (BH) framework and a novel phase space (PS) electronic Hamiltonian framework. We show that as long as we are not in the strongly nonadiabatic region, a PS framework can obtain a relative error in vibrational energy gap and other vibronic matrix elements that are consistently one order of magnitude smaller than what is found within a BH framework. In line with recent results showing that dynamics on one PS surface can outperform dynamics on one Born-Oppenheimer surface, our results indicate that the same advantages should largely hold for curve crossings and dynamics on two or a handful of electronic surfaces, from which several implications can be surmised as far as the possibility of spin-dependent electron transfer dynamics.