Localized Mode Analysis Of Zeolite Complex Vibrational Motion

Abstract

Usually we strive to understand vibrational modes as built from elementary ``zero-order'' motions such as bending and stretches. However, it is difficult to elucidate these localized motions for large molecules and solids with large unit cells. We have determined methods to obtain local vibrational motions from normal modes for large systems. These procedures have their roots the local orbital concept of Edmiston and Ruedenberg, the theory of localized electronic states in the context of Anderson localization, and in the group theoretic equivalent orbital approach of Lennard-Jones. One example of where our approach is useful is the analysis of zeolite normal modes. Experimentalists have long speculated on the relationship between the structure and spectral properties of zeolites. We find that spectral features can be associated with localized motion on the rings that comprise these silicates.