Adiabatic molecular properties beyond the Born–Oppenheimer approximation. Complete adiabatic wave functions and vibrationally induced electronic current density

The conceptual and mathematical basis for describing adiabatic molecular behavior beyond the Born–Oppenheimer (BO) approximation is presented. The traditional nonadiabatic corrections to the BO approximation are shown to contain a kinetic energy induced adiabatic part and a complete nonadiabatic, or diabatic, part. The lowest order contributions to the new adiabatic terms can be described as momentum adiabatic and are complementary to the traditional BO position adiabatic terms. A complete adiabatic wave function comprised of contributions involving position and momentum is obtained that provides a complete description of the response of the electron probability density to the dynamics of the nuclear motion. This response is comprised of nuclear momentum induced electronic current density and nuclear displacement induced electronic charge flux density for all points in the Cartesian coordinate space of the molecule. These nuclear induced charge fluxes and currents are shown to obey an equation of continuity for the conservation of electronic charge. Relations between the position and velocity formulations of infrared absorption intensity and the charge fluxes and currents are provided.