Summary
The Morse inequalities linking the critical points of a potential function on the whole configuration space and its restrictions to either planar or linear configurations are derived from the Morse theory in its equivariant form. Brute potential functions arising from standard models of quantum chemistry need eventually morsification which can be achieved without altering the main chemical significances of the potential. Illustrative applications follow in the case of magnesium clusters.
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Liotard, D., Rérat, M. Equivariant Morse theory of theN-body problem: Application to potential surfaces in chemistry. Theoret. Chim. Acta 86, 297–313 (1993). https://doi.org/10.1007/BF01128519
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DOI: https://doi.org/10.1007/BF01128519