Journal of Physical Chemistry A, Vol.116, No.11, 2728-2735, 2012
Coupled-Channels Quantum Theory of Electronic Flux Density in Electronically Adiabatic Processes: Fundamentals
The Born-Oppenheimer (BO) description of electronically. =1/2 integral dR[Delta b (x;R)-Delta a(x;R)]< jb,a(R,t)> adiabatic molecular processes predicts a vanishing electronic flux density (j(e)), even though the electrons certainly move in response to the movement of the nuclei. This article, the first of a pair, proposes a quantum-mechanical "coupled-channels" (CC) theory that allows the approximate extraction of j(e) from the electronically adiabatic BO wave function. The CC theory is detailed for H-2(+), in which case j(e) can be resolved into components associated with two channels alpha (=a,b), each of which corresponds to the "collision" of an "internal" atom alpha (proton a orb plus electron) with the other nucleus beta (proton b or a). The dynamical role of the electron, which accommodates itself instantaneously to the motion of the nuclei, is submerged in effective electronic probability (population) densities, Delta(omega) associated with each channel (alpha). The Delta(alpha) densities are determined by the (time-independent) BO electronic energy eigenfunction, which depends parametrically on the configuration of the nuclei, the motion of which is governed by the usual BO nuclear Schrodinger equation. Intuitively appealing formal expressions for the electronic flux density are derived for H-2(+).