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Advances in Physical Chemistry
Volume 2011 (2011), Article ID 593872, 38 pages
Review Article

Potential Energy Surfaces Using Algebraic Methods Based on Unitary Groups

Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, 04510 México, DF, Mexico

Received 14 July 2011; Revised 13 October 2011; Accepted 21 October 2011

Academic Editor: Sylvio Canuto

Copyright © 2011 Renato Lemus. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This contribution reviews the recent advances to estimate the potential energy surfaces through algebraic methods based on the unitary groups used to describe the molecular vibrational degrees of freedom. The basic idea is to introduce the unitary group approach in the context of the traditional approach, where the Hamiltonian is expanded in terms of coordinates and momenta. In the presentation of this paper, several representative molecular systems that permit to illustrate both the different algebraic approaches as well as the usual problems encountered in the vibrational description in terms of internal coordinates are presented. Methods based on coherent states are also discussed.