Coupled electronic and nuclear fluxes in molecules

We propose a new approach for evaluating nuclear and electronic fluxes in molecules. This is based on the Born-Oppenheimer approximation which, though excellent for densities and time dependent molecular properties, is not appropriate for electronic fluxes computed from the flux density equation. However making use of the Gauss's theorem and the continuity equation, we successfully solved this problem by formulating fluxes in terms of integrals of densities. This new approach, applied to coherent vibrations of small molecules, agrees quite well with the accurate one. With H2+ and D2+, we find that the electronic flux is no longer zero and, that the electron does not always adapt quasi-instantaneously to the nuclear motion. Moreover we show that the initial state preparation matters. In particular, the nuclear flux exhibits high frequency oscillations when the process starts in the inner turning point in contrast to the outer one. Considering H2, the effect of electronic correlation has been investigated by comparison of the Hartree-Fock and the full configuration interaction methods.