Application of the Born-Oppenheimer principle to classification of time scales in molecules interacting with time-dependent external fields

An analysis of the Hamiltonian of a molecule interacting with time-dependent external fields leads to the identification of various time scales governing the motion of the electrons and the nuclei. The most important role is played by the Born-Oppenheimer approximation, which considers the nuclear kinetic energy to be bounded and small compared to the gradient of the electronic-potential surfaces. The relative electronic-excitation operator is defined and is shown to be slowly dependent on time. This is a consequence of the Born-Oppenheimer approximation in the context of the time-dependent Schrödinger equation and the interaction with an external electric field. We show how to capitalize on this identified slow motion in the presence of rapid Rabi oscillations driven by the external field. The stroboscopic- integration technique is used in an illustrative calculation for the case of two electronic states coupled by the external field.