On the determination of Born–Oppenheimer nuclear motion wave functions including complications due to conical intersections and identical nuclei

We show how the presence of a conical intersection in the adiabatic potential energy hypersurface can be handled by including a new vector potential in the nuclear-motion Schrödinger equation. We show how permutational symmetry of the total wave function with respect to interchange of nuclei can be enforced in the Born–Oppenheimer approximation both in the absence and the presence of conical intersections. The treatment of nuclear-motion wave functions in the presence of conical intersections and the treatment of nuclear-interchange symmetry in general both require careful consideration of the phases of the electronic and nuclear-motion wave functions, and this is discussed in detail.