title: Correlated electron-nuclear dynamics: exact factorization of the molecular wavefunction.
abstract: It was recently shown [A. Abedi, N. T. Maitra, and E. K. U. Gross, Phys. Rev. Lett. 105, 123002 (2010)] that the complete wavefunction for a system of electrons and nuclei evolving in a time-dependent external potential can be exactly factorized into an electronic wavefunction and a nuclear wavefunction. The concepts of an exact time-dependent potential energy surface (TDPES) and exact time-dependent vector potential emerge naturally from the formalism. Here, we present a detailed description of the formalism, including a full derivation of the equations that the electronic and nuclear wavefunctions satisfy. We demonstrate the relationship of this exact factorization to the traditional Born-Oppenheimer expansion. A one-dimensional model of the H(2)(+) molecule in a laser field shows the usefulness of the exact TDPES in interpreting coupled electron-nuclear dynamics: we show how features of its structure indicate the mechanism of dissociation. We compare the exact TDPES with potential energy surfaces from the time-dependent Hartree-approach, and also compare traditional Ehrenfest dynamics with Ehrenfest dynamics on the exact TDPES.
authors.affiliation: Max-Planck Institut für Mikrostrukturphysik, Weinberg 2, D-06120 Halle, Germany.
authors.forename: Ali
authors.initials: A
authors.lastname: Abedi
authors.forename: Neepa T
authors.initials: NT
authors.lastname: Maitra
authors.forename: E K U
authors.initials: EK
authors.lastname: Gross