On the effects of spin-orbit coupling on conical intersection seams in molecules with an odd number of electrons. II. Characterizing the local topography of the seam

摘要

Characteristic of conical intersections of Born-Oppenheimer potential energy surfaces is #eta#, the dimension of the branching space, the space in which the degeneracy is lifted linearly. In molecules with an odd number of electrons, #ea#=2 for the nonrelativistic Coulomb Hamiltonian, while #eta# = 3(5) when the spin-orbit interaction is included and the molecule has (does not have) C_s symmetry. In the #eta#=2 case, the branching space is defined by two vectors: the energy difference gradient vector, g, and the interstate coupling vector, h. G and h can, without loss of generality, be chosen orthogonal. GXh is invariant under the unitary wave function transformation that orthogonalizes g and h. The orthogonal g and h can be used to define an optimal set of coordinates for describing the vicinity of the conical intersection. Here these ideas are generalized to #eta#=3 intersections. In particular, it is shown that g, the energy difference gradient vector, and h~r and h~I, the real and imaginary parts of the interstate coupling vector, which define the #eta#=3 space, can without loss of generality be chosen orthogonal. It is also shown that gXh~r(centre dot)h~I is invariant under the unitary wave function transformation that orthogonalizes these vectors. These ideas are illustrated using a portion of the OH(A ~2#SIGMA#_(1/2)~+, X ~2II_(3/2,1/2) + H_2 seam of conical intersection.