Suitable for advanced undergraduates and graduate students, this text covers V coefficients for the octahedral group and other symmetry groups, W coefficients, irreducible products and their matrix elements, two-electron formulae for the octahedral group, fractional parentage, X coefficients, spin, and matrices of one-electron operators. 1962 edition.

Irreducible Tensor Methods: An Introduction for Chemists explains the theory and application of irreducible tensor operators. The book discusses a compact formalism to describe the effect that results on an arbitrary function of a given set of coordinates when that set is subjected to a rotation about its origin. The text also explains the concept of irreducible tensor operators, particularly, as regards the transformation properties of operators under coordinate transformations, and, in a special way, the group of rotations. The book examines the systematic construction of compound tensor operators from simple operators to classify the behavior of any operator under coordinate rotations. This classification is a significant component of the irreducible tensor method. The text explains the use of the 6-j and 9-j symbols to complete theoretical concepts that are applied in irreducible tensor methods dealing with problems of atomic and molecular physics. The book describes the matrix elements in multielectron systems, as well as the reduced matrix elements found in these systems. The book is suitable for nuclear physicists, molecular physicists, scientists, and academicians in the field of quantum mechanics or advanced chemistry.

Prof. McClain has, quite simply, produced a new kind of tutorial book. It is written using the logic engine Mathematica, which permits concrete exploration and development of every concept involved in Symmetry Theory. It is aimed at students of chemistry and molecular physics who need to know mathematical group theory and its applications, either for their own research or for understanding the language and concepts of their field. The book begins with the most elementary symmetry concepts, then presents mathematical group theory, and finally the projection operators that flow from the Great Orthogonality are automated and applied to chemical and spectroscopic problems.

Advances in Quantum Chemistry

Twenty years ago Tanabe and Sugano published the first ligand field energy diagrarns which are applicable to dN electronic configurations. These diagrams are limited in scope in that they can be used only for octahedral symmetry and for a limited number of terms. The present volume is an attempt to fill the gap by providing a reasonable nurober of complete and accurate ligand field energy diagrarns for dN configurations in the most commonly encountered symmetries. Despite their limited nature, the diagrarns of Tanabe and Sugano were exten sively used in the past in order to rationalize optical and luminescence spectra and to discuss various electronic properties of transition metal ions, their coordination compounds and solids. Moreover, Tanabe-Sugano diagrams have an established place in the theory of transition metal compounds and are included in most textbooks of inorganic and coordination chemistry. It is expected that the present diagrarns will be found useful for a similar purpose.