Exact Factorization of the Electron-Nuclear Wavefunction: Exact Electronic Potentials in Coupled Electron-Ion Dynamics

We develop a novel approach to the coupled motion of electrons and ions that focuses on the dynamics of the electronic subsystem. Usually the description of electron dynamics involves an electronic Schr\"{o}dinger equation where the nuclear degrees of freedom appear as parameters or as classical trajectories. Here we derive the exact Schr\"{o}dinger equation for the subsystem of electrons, staying within a full quantum treatment of the nuclei. This exact Schr\"{o}dinger equation features a time-dependent potential energy surface for electrons (e-TDPES). We demonstrate that this exact e-TDPES differs significantly from the electrostatic potential produced by classical or quantum nuclei. \\[4pt] [1] Y. Suzuki, A. Abedi, N. T. Maitra, K. Yamashita and E. K. U. Gross, e-print arXiv:1311.3218v1