A modified Born-Oppenheimer equation: application to conical intersections and other types of singularities

In this publication is presented a new treatment of conical intersection effects in molecular systems. It is shown that such effects, for a low enough energy, can be included in the ordinary Born-Oppenheimer approximation. A novel single-surface Schrِdinger equation for treating the motion of nuclei results from this treatment. A method for solving this equation is discussed and it is shown that the solution is governed by a phase factor which is only reminiscent of the Berry phase but is different.