Sequence-adapted molecular tensors: Algebraic methods and application to crystal field theory

Tensorial sets adapted to sequences of finite subgroups are applied to the crystal field problem, and a general method for generating sequence-adapted molecular tensors using finite group algebra is formulated. All subgroup sequences of the abstract finite group G(24), isomorphic to the octahedral, O, tetrahedral, T_d, and symmetric, S(4), groups are tabulated with explicit isomorphisms provided. The sequences fall into eight equivalence classes. A catalog of irreducible representations of G(24) adapted to a member of each of the eight sequence classes is given together with the transformations which generate representations adapted to all other sequences. With this data it is possible to systematically generate tensorial sets adapted to any sequence of a realization of G(24). Unitary transformations which adapt conventional forms of first- and second-rank irreducible tensorial sets of the rotation group to the eight sequences of the octahedral group are provided. Forms suitable for use with magnetic fields are included. The problem of a d¹ ion in a trigonal crystal field is treated with sequence-adapted molecular tensors, and the utility of different sequences for descent in symmetry is discussed.