Nonadiabatic conical nodes are near but not at an elliptical conical intersection

Abstract

Numerical nonadiabatic eigenfunctions are calculated for 2D Jahn-Teller conical intersections with the elliptical shape found in square-symmetric molecules. Hunter’s exact factorization is used to visualize the complete real-valued vibronic eigenfunctions. Point nodes are observed in the vibrational factor and the nodal structures are compared with those for circularly symmetric conical intersections. Without pseudo-rotation symmetry, essential nth order nodes at circular conical intersections split into n accidental conical nodes that are near but not at the elliptical conical intersection. For each eigenfunction, the integer electronic index that measures electronic state vector rotation around a closed vibrational path is locally stable to perturbations. Pairs of oppositely signed conical nodes can be generated or annihilated as Hamiltonian parameters are continuously varied. At annihilation, a tangential node with an electronic index of zero is created. For elliptical conical intersections, all eigenfunctions examined generate nonzero total vibrational probability density at the conical intersection.