A new formulation of the phase change approach in the theory of conical intersections

We have reformulated the phase change approach to the theory of conical intersections suggested by Zilberg and Haas [S. Zilberg, Y. Haas, Adv. Chem. Phys. 124 (2002) 433]. We use the fact that the phase change loop variable ϕ in polar co-ordinates in the space of nuclear co-ordinates is related to the transformation θ=ϕ2 of the diabatic VB states defined at the apex of the cone in a conical intersection. Thus one can use the basis transformation generated by θ to yield a sequence of orthogonal pairs of VB structures (anchors) at any value of ϕ in the loop in nuclear configuration space. In this way the branching plane concept becomes related to VB wavefunctions based on the correspondence between the two angles. The theory is developed in detail using a simple three orbital three electron example. Examples are presented for four and six orbitals. In the later case, our results differ from those of Zilberg and Haas.