Abstract
We present new methods to locate conical intersections of potential energy surfaces using the Pancharatnam connection and the Longuet-Higgins' 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 intersections', 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.
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