Extended approximated Born-Oppenheimer equation. I. Theory

In this study we consider Born-Oppenheimer coupled equations with the aim of deriving a single approximated Born-Oppenheimer-type equation which contains the effect of the nonadiabatic coupling terms. The derivation is done for a situation where N (>=2) adiabatic surfaces, including the ground-state surface, have a degeneracy along a single line (e.g., conical intersection). The new equation can be considered as an extended version of the Born-Oppenheimer approximation. Although derived for a nongeneral case, the extension to a general case is also discussed. As special cases we treat, in the present paper, the two-state system and, in the following paper, the three-state system.