Electronic currents and Born-Oppenheimer molecular dynamics

Born-Oppenheimer variable separation is the mainstay of studies of chemical reactivity and dynamics. A long-standing problem of this ansatz is the absence of electronic currents in a system undergoing dynamics. I analyze the physical origin of the "missing" electronic currents in Born-Oppenheimer wavefunctions. By examining the problem within the multi-state Born-Huang ansatz, I demonstrate that electronic currents arise from the first-order non-adiabatic coupling to electronically excited states. I derive two expressions for the electronic currents induced by nuclear motion. The sum-over-the-states formula, identical to the result of "complete adiabatic" treatment of Nafie [J. Chem. Phys. 79, 4950 (1983)] leads to a transparent and intuitive physical picture of the induced currents, but is unsuitable for practical implementation in all but the simplest systems. The equivalent expression in terms of the electronic energy derivatives is straightforward to implement numerically. I present first applications of this approach to small systems of potential chemical interest.