Conical intersections in a system of four identical nuclei

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Abstract
The general properties of conical intersections between Born–Oppenheimer potential energy surfaces for the X4 system are considered. This system is one of intermediate complexity, sharing some, but not all, of the simplifying features of the X 3 system studied previously. As in X 3, one can define an internal coordinate system in terms of the internuclear distances which treats all nuclei equivalently. For X 4, however, the degeneracy manifolds are of higher dimension than the symmetry manifolds, which has as a consequence that the degeneracy manifolds are only partially determined by symmetry. We obtain general properties of the locations of the conical intersections, and of the phase factors which compensate the sign change in the electronic wave function resulting from traversing a closed path around the intersection. The phase factor is also chosen in such a way that the resulting electronic wave functions have simple behavior under permutations of the nuclei. This choice of phase factor leads to consistency defined electronic functions which are smooth functions of the nuclear coordinates everywhere. The application of permutation operators to the nuclear functions in the presence of the altered phase factor is also considered. We also consider some simple consequences for scattering in this system. A result of practical interest is that the superposition of direct and exchange scattering for H2+H2 should be superposed with opposite sign from what one would obtain with a conventional calculation.

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