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Implications of rotation–inversion–permutation invariance for analytic molecular potential energy surfaces

Collins, M.A. and Parsons, D.F. (1993) Implications of rotation–inversion–permutation invariance for analytic molecular potential energy surfaces. The Journal of Chemical Physics, 99 (9). p. 6756.

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Abstract

A molecular potential energy surface has the symmetry properties of invariance to rotation of the whole molecule, inversion of all atomic coordinates, and permutation of indistinguishable nuclei. While some of this invariance character can be easily incorporated in a local description of the surface, a formal application of these symmetry restrictions is useful in considering the form of the globalsurface which must account for large amplitude changes of the atomic coordinates. The form of a global molecular potential energy surface as a properly symmetrized analytic function of Cartesian coordinates is derived by extending Molien’s theorem of invariants for finite groups to cover the continuous rotation–inversion group. O(3), and the product of O(3) with the complete nuclear permutation group. The role of so‐called redundant internal coordinates in molecular potential energy surfaces is clarified.

Publication Type: Journal Article
Publisher: American Institute of Physics
Copyright: © 1993 American Institute of Physics
URI: http://researchrepository.murdoch.edu.au/id/eprint/27279
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