Location of conical intersections by the Pancharatnam connection and the sign-change theorem of Longuet-Higgins: a model calculation with the H4 potential surface

We present new methods to locate conical intersections of potential energy surfaces using the Pancharatnam connection and the Longuet-Higginsʹ sign-change theorem. We have applied the new methods to locate conical intersections for the H4 potential surface that are constructed by the valence-bond wave functions. The potential energy surface is rich in conical intersections that are not isolated in general but seen in the form of a seam or higher dimensional geometrical object. The `pair annihilation of conical intersectionsʹ, i.e., the disappearance of two conical intersections by merging into a Renner–Teller crossing and successive lifting of the Renner–Teller crossing is observed.