Knowledge Bank

Conical intersections do not exist as isolated points but as continuous seams of dimension $Nint-2$ for the nonrelativistic Coulomb hamiltonian, where $Nint$ is the number of internal coordinates. Including the spin-orbit interaction can change the situation qualitatively. For odd-electron systems the hamiltonian is complex causing the dimension to reduce to $Nint-3$ or even $Nint-5$ when there is no spatial symmetry present. In order to be able to study the effect of the spin-orbit interaction quantitatively we have implemented an algorithm that can locate conical intersections in the presence of the spin-orbit interaction. The system $H2+OH$ has been found to have conical intersections between $\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}\Sigma -2\Pi$ states in linear symmetry or $12A\prime -22A\prime$ states in $Cs$ symmetry, in the nonrelativistic case. Points of the seam including the spin-orbit coupling have been located and compared with the nonrelativistic results.