Journal of Mathematical Chemistry

, Volume 44, Issue 4, pp 938–966 | Cite as

Symmetry-adapted polynomial basis for global potential energy surfaces-applications to XY4 molecules

  • Patrick Cassam-ChenaïEmail author
  • Frédéric Patras
Original Paper


The nuclear potential energy surfaces (PES) used in quantum chemistry inherit the symmetry of the whole molecular system, and are therefore invariant under the action of the nuclear permutation-translation-rotation-inversion group. One can take advantage of this property, both theoretically and numerically. The present article is the prolongation of the works of Schmelzer and Murrell and of Collins and Parsons on the subject. It presents a simplified technique to obtain symmetry-adapted polynomial basis for global PES, together with algorithmic recipes that make the problem computationally tractable. The method is illustrated in detail on XY 4 type of molecules for which a full description of the algebra of invariant polynomials under the full symmetry group of the molecule is given.


Potential Energy Surface Hilbert Series Polynomial Algebra Invariant Polynomial Basic Invariant 
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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.CNRS UMR 6621Université de Nice, Laboratoire de Mathématiques J. DieudonnéNice cedex 2France

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