Exact factorization of the time-dependent electron-nuclear wavefunction: Time-dependent potential energy surface

We have recently proved an exact decomposition of the electronic and nuclear degrees of freedom (Phys, Rev. Lett. 105 123002 (2010)) and introduced a set of coupled equations of motion for the electrons and nuclei that describe the evolution of the complete electron-nuclear system. The nuclear equation is particularly apealing being a Schroedinger equation with a time-dependent potential energy surface (TDPES) and a time-dependent vector potential as rigorous concepts, mediating the coupling between the nuclear and the electronic degrees of freedom in a formally exact way. By studying physically different cases, we demonstrate that the TDPES is a powerful tool to investigate molecular processes.