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DOE OSTI · 21511470

Algebraic methods in vibrational spectroscopy

Lemus, Renato
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Abstract

These lectures review some advances in the algebraic description of molecules from two point of views: structure and dynamics. We start by presenting the basic ideas involved in the traditional description of molecular structure in configuration space, where the Born-Oppenheimer and rotor-rigid approximations are assumed to be valid. We then focus on the vibrational degrees of freedom in order to introduce the traditional algebraic realization in terms of bosonic operators of harmonic oscillators. This analysis allows the algebraic methods based on dynamical unitary groups to be introduced as a anharmonization procedure where the local bosonic operators are translated into operators satisfying the su(2) commutation relations. Some examples of the vibrational spec-troscopic description are presented. Concerned with the dynamical point of view an algebraic model to describe collinear collisions in the semiclassical approximation is presented.

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74 ATOMIC AND MOLECULAR PHYSICS97 MATHEMATICS AND COMPUTINGALGEBRAAPPROXIMATIONSBORN-OPPENHEIMER APPROXIMATIONBOSONSCALCULATION METHODSCOLLISIONSCONFIGURATIONDEGREES OF FREEDOMDIFFERENTIAL EQUATIONSENERGY LEVELSEQUATIONSEXCITED STATESHARMONIC OSCILLATORSLIE GROUPSMATHEMATICAL OPERATORSMATHEMATICSMOLECULAR STRUCTUREMOLECULESPARTIAL DIFFERENTIAL EQUATIONSQUANTUM OPERATORSSCHROEDINGER EQUATIONSEMICLASSICAL APPROXIMATIONSPACESPECTROSCOPYSU GROUPSSU-2 GROUPSSYMMETRY GROUPSVIBRATIONAL STATESWAVE EQUATIONS

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Lemus, Renato. 2011-03-21. Algebraic methods in vibrational spectroscopy. https://doi.org/10.1063/1.3575533

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