Methods For The Simulation Of Coupled Electronic And Nuclear Motion In Molecules Beyond The Born-Oppenheimer Approximation

We review theoretical methods which can be used for the simulation of time-dependent electronic and nuclear dynamics of gas-phase molecules beyond the Born-Oppenheimer approximation. We concentrate on methods which allow for a description of extensive electronic excitation and ionization. Particular emphasis is placed on the extended multiconfiguration time-dependent Hartree-Fock (Ex-MCTDHF) method. We provide a derivation of the equations of motion of the Ex-MCTDHF method, and discuss its advantages and disadvantages over the methods based on the Born-Huang expansion.