Covalency and chemical bonding in transition metal complexes: An ab initio based ligand field perspective

In this work, a general, user-friendly method – ab initio ligand field theory (AILFT), is described and illustrated. AILFT allows one to unambiguously extract all ligand field parameters (the ligand field one-electron matrix V_LFT, the Racah parameters B and C, and the spin-orbit coupling parameter ζ) from relatively straightforward multi-reference ab initio calculations. The method applies to mononuclear complexes in dⁿ or fⁿ configurations. The method is illustrated using complete active space self-consistent field (CASSCF) and N-electron valence perturbation theory (NEVPT2) calculations on a series of well documented octahedral complexes of Cr^III with simple ligands such as F⁻, Cl⁻, Br⁻, I⁻, NH₃ and CN⁻. It is shown that all well-known trends for the value of 10Dq (the spectrochemical series) are faithfully reproduced by AILFT. By comparison of B and ζ for Cr^III in these complexes with the parameters calculated for the free ion Cr³⁺, the covalency of the Cr-ligand bond can be assessed quantitatively (the non-relativistic and relativistic nephelauxetic effects). The variation of ligand field parameters for complexes of 3d, 4d and 5d elements is studied using MCl₆ ³⁻ (M = Cr^III, Mo^III, W^III) as model examples. As reflected in variations of 10Dq, B and ζ across this series, metal-ligand covalency increases from CrCl₆ ³⁻ to MoCl₆ ³⁻ to WCl₆ ³⁻. Using the angular overlap model, the one-electron parameters of the ligand field matrix are decomposed into increments for σ- and π- metal-ligand interactions. This allows for the quantification of variations in σ- and π-ligand donor properties of these ligands. Using these results, the well documented two-dimensional spectroscopic series for complexes of Cr^III is quantitatively reproduced. Comparison of the results obtained using CASSCF and NEVPT2 reveals the importance of dynamic electron correlation. Finally, the limitations of the AILFT method for complexes with increasing metal-ligand covalency are analyzed and discussed.