Strong Crystalline Field Perturbation Calculations for d3, d7 Penta-Coordinate Complexes. II. The Square Pyramid

Abstract

Crystal field calculations for d3, d7 square pyramidal complexes are carried out via the strong field formalism and in the limit of zero spin-orbit coupling. The field produced by the lone axial ligand is treated as an integral part of the crystal field potential. In the ionic model approximation the three crystal field parameters: Dq, Ds, and Dt; depend markedly on the angle of distortion, β, defined as that portion of the La—M—Lb bond angle in excess of 90°. The square pyramidal d3 symmetry eigenfunctions are constructed from the one-electron crystal field eigenfunctions. Spin is only implicitly included, but both types of doublet wavefunctions are identified. The crystal field matrix in parametric form is strictly diagonal, but Coulombic interactions connect states arising from different strong field configurations. Coulombic calculations are performed in terms of the Slater–Condon–Shortley parameters: F0, F2, and F4; then converted to the Racah parameters: A, B, and C, The complete (crystal field and Coulombic) perturbation matrices are used to interpret the spectroscopic properties of a strong field Co(II) square pyramidal complex. Both the symmetry and multiplicity of the ground state are dependent on β. An energy level diagram showing all doublets and quartets is calculated for β = 0°. Partial energy level diagrams are also given depicting behavior of the doublet and quartet states, individually, as functions of β. As β increases the crystal field bands shift to lower energy and become more clustered. Current experimental applications are also briefly cited.