Non-adiabatic quantum molecular dynamics:: General formalism and case study H2+ in strong laser fields

A general formalism of the so-called non-adiabatic quantum molecular dynamics is presented, which applies to atomic many-body systems in external laser fields. The theory treats the nuclear dynamics and electronic transitions simultaneously and self-consistently in a mixed classical-quantum approach. The equations of motion are derived from a general action principle by combining time-dependent density functional theory in basis-set-expansion with classical molecular dynamics. Structure and properties of the resulting equations of motion as well as the energy and momentum balance equations in this formalism are discussed in detail. For the model system H-2(+), the classical-quantum equations of motion are solved. The results agree very well with that of full quantum mechanical calculations. Moreover, from the present calculation a transparent physical interpretation of the mechanisms of energy absorption and dissociation dynamics can be obtained. Future applications and approximations of the formalism presented here are briefly outlined.