Non-adiabatic current densities, transitions, and power absorbed by a molecule in a time-dependent electromagnetic field.

The energy of a molecule subject to a time-dependent perturbation separates completely into adiabatic and non-adiabatic terms, where the adiabatic term reflects the adjustment of the ground state to the perturbation, while the non-adiabatic term accounts for the transition energy [A. Mandal and K. L. C. Hunt, J. Chem. Phys. 137, 164109 (2012)]. For a molecule perturbed by a time-dependent electromagnetic field, in this work, we show that the expectation value of the power absorbed by the molecule is equal to the time rate of change of the non-adiabatic term in the energy. The non-adiabatic term is given by the transition probability to an excited state k, multiplied by the transition energy from the ground state to k, and then summed over the excited states. The expectation value of the power absorbed by the molecule is derived from the integral over space of the scalar product of the applied electric field and the non-adiabatic current density induced in the molecule by the field. No net power is absorbed due to the action of the applied electric field on the adiabatic current density. The work done on the molecule by the applied field is the time integral of the power absorbed. The result established here shows that work done on the molecule by the applied field changes the populations of the molecular states.