Recent Advances in Group Theory and Their Application to SpectroscopyJohn C. Donini The last few years have seen a resurgence in the applications of group theory to the problems posed by various characteristics of transition metals and lanthanides. In particular with the commercial availability of more sophisticated experimental tech niques; such as Magnetic Circular Dichroism (M.C.D.), Electron Paramagnetic Resonance (E.P.R. or E.S(pin).R.) and Single Crystal Polarised Spectra; experimental data of a much more sophisticated and selective nature than the old stand-by; absorption spectra and magnetic susceptibility; has become available. This new wealth of high quality experimental data thus pre sents challenges of interpretation and organization of the data which the new developments in group theory strive to meet. The wealth and quality of this new data makes the nuances and differences implicit in the traditional strong and weak field approach testable. Thus, these approaches can be tested more fully and new formalisms can be meaningfully tested, by comparison to experiment. Hence the characteristic implicit in the strong and weak field approaches are revealed by studies into their formal structures as exemplified by Drs. E. Konig, S. Kremer, and S. Piepho. Similarly, works proceed apace on the knotty problem of correlation and gen eralization of these properties through approaches such as those of Drs. P. H. Butler, J. C. Donini and M. Kibler. On a similar vein the deep structure of group representation and correlations of representation of various groups is explored by the afore mentioned and by Drs. Fritzer, Patera and Sharp. |
Contents
FINITE SYMMETRY ADAPTION IN SPECTROSCOPY 1 | 61 |
A CHEMISTS VIEW | 97 |
PROPERTIES AND APPLICATION OF POINT GROUP COUPLING | 123 |
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Recent Advances in Group Theory and Their Application to Spectroscopy John C. Donini Limited preview - 2012 |
Recent Advances in Group Theory and Their Application to Spectroscopy John C. Donini No preview available - 2011 |
Recent Advances in Group Theory and Their Application to Spectroscopy John C. Donini No preview available - 1979 |
Common terms and phrases
5IITI 6j symbols A₁ algebra angular momentum applications atom basis functions calculations Chem complex components configuration conjugate corresponding coupling coefficients defined degeneracy derived diagrams dipole direct product EA1A EAIA EB1A EBIA electrons energy equation equivalent example exterior product factors FAIA finite group group G group theory Hamiltonian integrals interaction invariant ireps irreducible representations irrep isomorphic IT2 EB2 kets Kronecker product labels ligand field ligand field theory magnetic molecular molecule notation nuclei obtained octahedral one-electron orbital parameters permutation perturbation phase Phys point group problem properties quantum numbers Racah reduced matrix reduced matrix elements relations rotation scalar selection rules space spatial spectra spectroscopy spectrum spherical harmonics spin spin-orbit coupling subgroup symmetry adapted symmetry group Table tensor operators theorem transformation transition metal trigonal values vector wave functions Wigner-Eckart theorem