Theory of the normal modes of vibrations in the lanthanide type crystals

For the lanthanide type crystals, a vast and rich, though incomplete amount of experimental data has been accumulated, from linear and non linear optics, during the last decades. The main goal of the current research work is to report a new methodology and strategy to put forward a more representative approach to account for the normal modes of vibrations for a complex N-body system. For illustrative purposes, the chloride lanthanide type crystals Cs2NaLnCl6 have been chosen and we develop new convergence tests as well as a criterion to deal with the details of the F-matrix (potential energy matrix). A novel and useful concept of natural potential energy distributions (NPED) is introduced and examined throughout the course of this work. The diagonal and non diagonal contributions to these NPED-values, are evaluated for a series of these crystals explicitly. Our model is based upon a total of seventy two internal coordinates and ninety eight internal Hooke type force constants. An optimization mathematical procedure is applied with reference to the series of chloride lanthanide crystals and it is shown that the strategy and model adopted is sound from both a chemical and a physical viewpoints. We can argue that the current model is able to accommodate a number of interactions and to provide us with a very useful physical insight. The limitations and advantages of the current model and the most likely sources for improvements are discussed in detail.