Optical Activity of Transition Metal Compounds. I. Sector Rules for Metal Complexes of the Pseudotetragonal Class

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Abstract
The sector (or symmetry) rules which govern the signs and relative magnitudes of the rotatory strengths associated with ligand‐field transitions are examined for metal complexes of the pseudotetragonal class. An independent systems model is adopted in which the complex is partitioned into three separate parts: (a) σ‐bond structure of the ML4Z2 cluster, (b) the π‐bonding orbitals of the ligating groups, and (c) the nonligating parts of the ligands. Interactions between these three parts of the complex are treated by perturbation theory. Using first‐order perturbed wavefunctions, the rotatory strength can be obtained to fourth order. To first order in both the wavefunctions and rotatory strength, the sign and magnitude of the “net” circular dichroism (ellipticity) associated with all ligand‐field transitions in a particular complex are determined by a hexadecant rule with respect to the positions of the individual perturber groups. The “relative” signs and magnitudes of the first‐order rotatory strengths of the ligand‐field transitions cannot be predicted from a single symmetry rule applicable to an entire class of metal complexes. It is shown that the signs and magnitudes of the second‐ and higher‐order contributions to the rotatory strength are determined by “mixed” sector rules in which the positions and charges of two or more perturber groups must be considered simultaneously. These contributions arise from products of pairwise interactions between the chromophoric electron and different perturber groups. In those cases in which the second‐, third‐, or fourth‐order terms are expected to dominate, it is usually possible to pick correctly the appropriate “mixed” sector rule.