Algebraic models vibron model

To reiterate, we prefer to describe the one-dimensional model first because of its mathematical simplicity in comparison to the three-dimensional model. From a strictly historical point of view, the situation is slightly more involved. The vibron model was officially introduced in 1981 by lachello [26]. In his work one can find the fundamental idea of the dynamical symmetry, based on U(4), for realizing an algebraic version of the three-dimensional Hamiltonian operator of a single diatomic molecule. After this work, many other realizations followed (see specific... 

Let US consider a practical example. We want to use the algebraic model for describing the vibrational spectrum of HCN, a linear nonsymmetric molecule (Fig. 35). As per custom, we first determine the vibron numbers Aj and N2 of the CN and HC bonds, respectively, by using Eq. (4.114). We obtain Aj = 156 and Aj = 43. As in Section IV.B.l [Eq. (4.41)] we then recover from the purely local model, the initial guesses of the algebraic parameters... 

The algebraic forms of the inorganic vibronic coupling constants etc., computed on the basis of a point charge model, have not been previously published. For the sake of completeness, we list these below ... 

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