On the incorporation of the geometric phase in general single potential energy surface dynamics: A removable approximation to ab initio data

For two electronic states coupled by conical intersections, the line integral of the derivative coupling can be used to construct a complex-valued multiplicative phase factor that makes the real-valued adiabatic electronic wave function single-valued, provided that the curl of the derivative coupling is zero. Unfortunately for ab initio determined wave functions, the curl is never rigorously zero. However, when the wave functions are determined from a coupled two diabatic state Hamiltonian H d (fit to ab initio data), the resulting derivative couplings are by construction curl free, except at points of conical intersection. In this work we focus on a recently introduced diabatization scheme that produces the H d by fitting ab initio determined energies, energy gradients, and derivative couplings to the corresponding H d determined quantities in a least squares sense, producing a removable approximation to the ab initio determined derivative coupling. This approach and related numerical issues associated with the nonremovable ab initio derivative couplings are illustrated using a full 33-dimensional representation of phenol photodissociation. The use of this approach to provide a general framework for treating the molecular Aharonov Bohm effect is demonstrated.