Abstract

In the last few years, algebraic models have been introduced as a computational tool for the analysis and interpretation of experimental rovibrational spectra of small and medium size molecules. These models are based on the idea of dynamic symmetry, which, in turn, is expressed through the language of unitary Lie algebras. By applying algebraic techniques, one obtains an effective Hamiltonian operator which conveniently describes the rovibrational degrees of freedom of the physical system. Within this framework, any specific mechanism relevant for the correct characterization of the molecular dynamics and spectroscopy can be accounted. Algebraic models are formulated in such a way that they contain the same physical information of both ab-initio theories (based on the solution of the Schroedinger equation) and of semi-empirical approaches (making use of phenomenological expansions in powers of appropriate quantum numbers). However, by employing the powerful method of group theory, the results can be obtained in a more rapid and straightforward way. A comprehensive and up-to-date review of mathematical concepts, physical aspects, practical applications and numerical implementation of algebraic models in molecular spectroscopy will be presented in this paper.

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