A new approach and some criteria to deal with the theory of the normal modes of vibrations in the elpasolite stoichiometric type systems short range intramolecular interactions

We have been working on systems such as Cs2NaLnCl6 for Ln = Pr, Eu, Tb, Dy, Ho, Er, and Tm, aiming to advance our understanding in those electronic and vibrational factors, upon which the one photon electronic transitions depend upon. We have chosen in this article, to report a novel strategy to rationalize the normal coordinate analysis so as to get a closer and more realistic approach to deal with those contributions which determine, what we regard as a natural potential energy distribution (NPED). It is essential to agree on the conditions upon which, we develop our convergence tests based on a physical view, so as to discern between selections of experimental assignments from a more comprehensive viewpoint. As a starting point, we review the magnificent contribution put forward by Lentz, who may claim priority in this area of the vibrational spectroscopy for the cryolite and elpasolite compounds and subsequently by other authors, whom have introduced some correction terms in the description of the vibrational force field. It is indeed a major task to produce a better description for this interacting potential, based on a maximum of 10 vibrational frequencies. In this work, our description is based upon a total of 72 internal coordinates and an initial number of 98 internal force constants. We show that the potential energy matrix F may be symmetrized by reducing the number of these latter to 81 internal force constants. For each of the elpasolite type systems, we have considered a total of three more representatives F-matrices, and calculated both the diagonal and non diagonal contributions to the observed vibrational wave numbers, λi=(νi/1303.16) for each of the experimental data. Following this procedure, we have been able to understand the sensitivity of the mixing between the symmetry coordinates for the same symmetry species with reference to a given vibrational frequency. It is shown that our current approach is both flexible and general so as to work out the most important contributions to the vibrational factor. The current formalism may be employed for other more complicated systems.