The concept of regularized diabatic states for a general conical intersection

The concept of regularized diabatic states was introduced as a simple, but efficient, technique for removing the singular derivative coupling terms at a symmetry-allowed conical intersection [ H. Koppel, J. Gronki, and S. Mahapatra, J. Chem. Phys. 115, 2377 ( 2001)]. Here, this scheme is extended to deal with general, i.e. not symmetry-allowed, conical intersections. Focussing on the case of two relevant nuclear degrees of freedom, where the intersection occurs at an isolated point in nuclear coordinate space, it is argued that the singular derivative couplings are also removed rigorously by the extended scheme. Moreover, the necessary information for constructing the diabatic electronic states can be extracted from the adiabatic potential energy surfaces alone. This seemingly counterintuitive statement follows from an analysis of the adiabatic potential energy difference and the vibronic coupling matrix in the vicinity of the conical point. A numerical example demonstrates the high accuracy of this novel construction scheme.