Dynamical symmetries triatomic molecules

Potential fluid dynamics, molecular systems, modulus-phase formalism, quantum mechanics and, 265—266 Pragmatic models, Renner-Teller effect, triatomic molecules, 618-621 Probability densities, permutational symmetry, dynamic Jahn-Teller and geometric phase effects, 705-711 Projection operators, geometric phase theory, eigenvector evolution, 16-17 Projective Hilbert space, Berry s phase, 209-210... 

An important problem of molecular spectroscopy is the assignment of quantum numbers. Quantum numbers are related to conserved quantities, and a full set of such numbers is possible only in the case of dynamical symmetries. For the problem at hand this means that three vibrational quantum numbers can be strictly assigned only for local molecules (f = 0) and normal molecules ( , = 1). Most molecules have locality parameters that are in between. Near the two limits the use of local and normal quantum numbers is still meaningful. The most difficult molecules to describe are those in the intermediate regime. For these molecules the only conserved vibrational quantum number is the multiplet number n of Eq. (4.71). A possible notation is thus that in which the quantum number n and the order of the level within each multiplet are given. Thus levels of a linear triatomic molecules can be characterized by... 

Cooper, I. L., and Levine, R. D. (1991), Computed Overtone Spectra of Linear Triatomic Molecules by Dynamical Symmetry, /. Mol. Spectr. 148, 391. 

CARS measurements have revealed an unexpected propensity for population of the even rotational levels in v" = 0 and v" = 1 (Moore et al., 1983). No explanation based on symmetry or dynamical constraints for this interesting observation is immediately forthcoming. Further elucidation of the dynamics of (8) will probably require refinement of our understanding of the role of symmetry conservation in the dissociation of triatomic molecules. 

Since nuiny processses demonstrate substantial quantum effects of tunneling, wave packet break-up and interference, and, obviously, discrete energy spectra, symmetry induced selection rules, etc., it is clearly desirable to develop meAods by which more complex dynamical problems can be solved quantum mechanically both accurately and efficiently. There is a reciprocity between the number of particles which can be treated quantum mechanically and die number of states of impcxtance. Thus the ground states of many electron systems can be determined as can the bound state (and continuum) dynamics of diatomic molecules. Our focus in this manuscript will be on nuclear dynamics of few particle systems which are not restricted to small amplitude motion. This can encompass vibrational states and isomerizations of triatomic molecules, photodissociation and exchange reactions of triatomic systems, some atom-surface collisions, etc. 

The range of problems to which electronic structure theory is applied includes potential energy surfaces for chemical dynamics studies and calculations in a small geometrical region for spectroscopic comparisons. Potential energy surface problems involve some level of symmetry for diatomic and triatomic cases and may involve very little for larger cases. Spectroscopic problems frequently involve symmetry in an essential way, but may not, depending on the molecule of interest. 

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