Dis-adiabatic dispersion in molecular dynamics

In molecular dynamics, "adiabatic approximation" assumes that, when nuclei are moving, electrons always stay in the same instantaneous eigen-state, it loses the dispersion of electronic state caused by nuclear motion. By dispelling adiabatic approximation, this paper proposes an analytic approach to get "dis-adiabatic dispersion", which is a non-adiabatic effect, and it can improve quantitative calculation in molecular dynamics. In mathematics, this approach demonstrates an application of fibre bundle in chemical physics.