Electron transition current density in molecules .1. Non-Born-Oppenheimer theory of vibronic and vibrational transitions

The one-particle electron transition current density (TCD) for vibronic transitions between pairs of stationary states in molecules is defined. Expressions for TCD are developed using the complete adiabatic (CA) formalism in which the electronic wave function carries an explicit dependence on the nuclear momenta, as well as the usual dependence on nuclear positions. In the case of vibronic transitions, the principal non-Born-Oppenheimer (non-BO), nuclear-momentum-dependent contribution to TCD is accompanied by a less important BO, nuclear-position-dependent contribution. For vibrational transitions within a single electronic state, the BO contribution vanishes, leaving only non-BO, nuclear-momentum-driven TCD. In the limit of pure electronic transitions, or vibrational transitions within a single electronic state, it is shown that electron TCD satisfies the continuity equation for the conservation of electron transition probability density (TPD) for any pair of stationary states. TCD is a vector field having a unique representation at each point in the Cartesian space of a molecule. It is shown that TCD is a dynamic representation of the changes in TPD associated with electrons in molecules under the influence of a transition-inducing perturbation and that it provides direct visual information concerning the participation of all spatial regions of the molecule in quantum transitions. The use of TCD provides an opportunity to view uniquely electronic motion associated with quantum mechanical transitions in molecules.