ELEMENTS OF IRREDUCIBLE TENSORIAL MATRICES GENERATED BY FINITE-GROUPSWITH APPLICATIONS TO LIGAND-FIELD HAMILTONIANS

Using symmetry to determine Hamiltonian matrix elements for quantum sy stems with finite group symmetry is a special case of obtaining group- generated irreducible tensorial matrices. A group-generated irreducibl e tensorial matrix transforms irreducibly under the group and is a lin ear combination of group transformations on a reference matrix. The re ference matrix elements may be appropriate integrals or parameters. Th e methods of normalized irreducible tensorial matrices (NITM) are empl oyed to express elements of the generated matrix in terms of those of the reference matrix without performing the actual transformations. On ly NITM components of the reference matrix with the same transformatio n properties as the group-generated matrix will contribute to its elem ents. The elements of invariant symmetry-generated matrices are propor tional to simple averages of certain elements of the reference matrix. This relation is substantially more efficient than previous technique s for evaluating matrix elements of octahedral and tetragonal d-type l igand-field Hamiltonians.