Calculation of vibronic coupling constants for tetrahedral and octahedral d electron systems via dynamic ligand field theory and application to optical spectra

Abstract

A perturbative model for the calculation of electron-phonon coupling constants of tetrahedral transition metal complexes based on the electrostatic ligand field theory is presented. Orbital vibronic coupling constants are expressed in terms of common ligand field parameters, and linear many-electron coupling constants for all d2-d9 strong field states in tetrahedral and octahedral symmetry are reduced to orbital coupling constants, enabling comparisons of coupling strength and directions of nuclear distortions over a wide range of transition metal complexes in a general way. The usefulness of the model is demonstrated for well resolved optical spectra of tetrahedral [MnO4]2-, [CrO4]3-, [CoCl4]2- and octahedral [CrF6]3-, [Cr(NH3)6]3+, [VO6]8- complexes, revealing good correspondence. The method is especially valuable for the interpretation of such spectra because it is easy to apply and the prediction of band shapes does not require additional parameters to be fitted to experiment. Nuclear distortions from the cubic reference geometry and Jahn-Teller stabilization energies are calculated.