Hyperspherical coordinates and energy partitions for reactive processes and clusters

The hyperspherical coordinate systems have been developed for the study of few-body scattering problems of nuclear and molecular physics, for example in the practical implementation of demanding quantum calculations typical of chemical reactions. The hyperangular momenta and their eigenfunctions, the hyperspherical harmonics, are the mathematical apparatus characterizing the hyperspherical representation of molecular dynamics. To circumvent the restriction to the application of the hyperspherical methods, due to exceedingly high computational costs, a classical mechanics hyperspherical formulation has been developed suitable for applications to clusters and large molecular system dynamics. The asymptotic theory of generalized harmonics connected with that of spin networks establishes semiclassical connections for treating discretization procedures, specifically, the hyperquantization algorithm treated by us elsewhere.