Understanding Normal Modes of Molecules and Clusters

Traditional methods for characterizing molecular vibrations were developed for small molecules and are not well suited for understanding nuclear motions of large molecules and of clusters. We present a procedure based on representing normal modes, including translations and rotations, as vectors in 3N dimensional space, where N is the number of nuclei. Double-contracting dyads formed from them allows for a quantitative definition of the overlap and the similarity of nuclear motions of whole molecules, of clusters of molecules, and of arbitrary fragments.