Correlated electron-nuclear dynamics: Exact factorization of the molecular wavefunction

Abstract

It was recently shown [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.

16 pages, accepted in J. Chem. Phys. Special Issue on Non-adiabatic Dynamics

References in corpus (3)

• Exact factorization of the time-dependent electron-nuclear wavefunction
• The transfer of energy between electrons and ions in solids
• Path integral formulation for quantum nonadiabatic dynamics and the mixed quantum-classical limit

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