Non-adiabatic quantum molecular dynamics: Basic formalism and case study

A general formalism is presented that treats self-consistently and simultaneously classical atomic motion and quantum electronic excitations in dynamical processes of atomic many-body systems (non-adiabatic quantum molecular dynamics). On the basis of time-dependent density functional theory, coupled highly non-linear equations of motion are derived for arbitrary basis sets for the time-dependent Kohn-Sham orbitals. Possible approximations to make the approach practical for large atomic cluster systems are discussed. As a first application of the still exact equations of motion, non-adiabatic effects in the scattering of H++H, as a case study, are investigated.