Vibron models of dynamical symmetry

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... 

In this section, we consider how the optical spectra of an impurity ion mixed-crystal system can be understood in terms of a lattice-dynamical model [6]. In particular, we consider the d manganese (IV) MnF ion doped in a CsjSiFg lattice. The sharp lines and detailed vibronic structure of the absorption and emission spectra of the A2g - Eg transition makes the Mn ion in cubic symmetry an ideal system for study [7]. 

---