La. Nafie, ELECTRON TRANSITION CURRENT-DENSITY IN MOLECULES .1. NON-BORN-OPPENHEIMER THEORY OF VIBRONIC AND VIBRATIONAL TRANSITIONS, The journal of physical chemistry. A, Molecules, spectroscopy, kinetics, environment, & general theory, 101(42), 1997, pp. 7826-7833
The one-particle electron transition current density (TCD) for vibroni
c transitions between pairs of stationary states in molecules is defin
ed. 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-depend
ent contribution. For vibrational transitions within a single electron
ic state, the BO contribution vanishes, leaving only non-BO, nuclear-m
omentum-driven TCD. In the limit of pure electronic transitions, or vi
brational transitions within a single electronic state, it is shown th
at electron TCD satisfies the continuity equation for the conservation
of electron transition probability density (TPD) for any pair of stat
ionary 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 ele
ctrons in molecules under the influence of a transition-inducing pertu
rbation and that it provides direct visual information concerning the
participation of all spatial regions of the molecule in quantum transi
tions. The use of TCD provides an opportunity to view uniquely electro
nic motion associated with quantum mechanical transitions in molecules
.