Triplet Excited States of a d6 Ligand System in a Cubic Field

Abstract

Our concern is the spin sublevels of the first excited triplet state of a d6 electron system in a cubic field. To that end, we will construct exact analytic eigenvalues and eigenfunctions for these sublevels. The essential point is that we formulate the total wave functions, space plus spin, so that they form bases for the irreducible representations of the O‘ double group. By virtue of such a choice, the matrix with respect to the total Hamiltonian, which comprises both crystal field potential and spin−orbit coupling, is a priori diagonalized for any triplet manifold. That is, the symmetry-adapted wave functions are eigenfunctions of the total Hamiltonian. Configuration interaction among the sublevels of different triplet states may also be expressed analytically, and the resulting eigenvalues and eigenfunctions may be obtained as a function of the spin−orbit coupling parameter ςnd and the 3T1−3T2 energy gap, ΔE (i.e., 8B, where B is the Racah parameter). The sublevel energies obtained in this way are co...