On the effects of spin-orbit coupling on conical intersection seams in molecules with an odd number of electrons. I. Locating the seam

In molecules with an odd number of electrons when the spin-orbit interaction is added to the nonrelativistic Coulomb Hamiltonian the dimension of the seam of conical intersection is reduced from $Nint−2$ to $Nint−3$ or $Nint−5.$ A generally applicable algorithm for locating points of conical intersection in such molecules is derived. The algorithm is based on a perturbative description of the vicinity of a point of conical intersection analogous to that used previously in the nonrelativistic case. It is tested using model Hamiltonians with quite promising results. An implementation of the algorithm based on ab initio wave functions is presented which treats the spin-orbit interaction within the Breit–Pauli approximation and incorporates it into the electronic Hamiltonian using the adiabatic states of the nonrelativistic Hamiltonian as a basis. An initial test of this implementation also yielded quite promising results.