Potential Energy Surfaces Using Algebraic Methods Based on Unitary Groups

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.