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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