Geometry - General & Miscellaneous, Mathematics - Group Theory, Crystallography

Point Group Symmetry Applications: Methods and Tables

Name: Point Group Symmetry Applications: Methods and Tables
Author: Philip H. Butler
ISBN: 9780306405235

by Philip H. Butler

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Overview

In recent years there has been a resurgence in the application of group theory to the problems poised by various characteristics of transition metal and lanthanides. Highly sophisticated experimental techniques, such as magnetic circular dichroism, electron paramagnetic resonance, and single-crystal polarized spectra, have provided a wealth of significant data.

This volume deals with some of the most critical recent advances in this field. Foremost authorities discuss a wide range of topics, including point group coupling coefficients and the NMR problem. Applications of group theory to chemistry, spectroscopy, crystal physics, magnetic circular dichroism, and atomic and molecular physics are considered as well.

Synopsis

The mathematical apparatus of group theory is a means of exploring and exploiting physical and algebraic structure in physical and chemical prob lems. The existence of structure in the physical processes leads to structure in the solutions. For group theory to be useful this structure need not be an exact symmetry, although as examples of exact symmetries we have that the identity of electrons leads to permutation symmetries in many-electron wave functions, the spatial structure of crystals leads to the Bloch theory of crystal eigenfunctions, and the rotational invariance of the hydrogenic Hamiltonian leads to its factorization into angular and radial parts. In the 1930's Wigner extended what is known to mathematicians as the theory of group representations and the theory of group algebras to study the coupling coefficients of angular momentum, relating various properties of the coefficients to the properties of the abstract group of rotations in 3-space. In 1949 Racah, in a paper on rare earth spectra, showed that similar coefficients occur in other situations. Immediately a number of studies of the coefficients were begun, notably by Jahn, with his applications in nuclear physics. In the years since then a large number of physicists and chemists have added to the development of a general theory of the coefficients, or have produced specialized tables for a specific application. Applications now range from high-energy physics to biology.