A Modern First-Principles View on Ligand Field Theory Through the Eyes of Correlated Multireference Wavefunctions

Recent developments in AI methods for strongly correlated electronic systems and their implementations in highly efficient quantum chemistry programs allow one to calculate - from first principles - the spectroscopic and magnetic properties of transition metal complexes with open d- and f-shells. For a long time, this field was the domain of ligand field theory (LFT), subject to various assumptions and approximations which are solely justified by the success of using this theory for the interpretation of experimental data. Yet the chemical significance of the ligand field parameters, while being under intense debate, remains unclear as far as the roots of LFT in its relation to rigorous quantum chemistry are concerned. In the present review, we attempt to answer the question how well ligand field theory performs from the point of view of state-of-art first principle calculations and how to connect the two areas. To achieve this goal, energies of electronic states originating from d(n) configurations of spectroscopically and structurally well-documented complexes of 3d metals from complete active space self-consistent field (CASSCF) wavefunctions and their improved energy eigenvalues from N-electron valence perturbation theory (NEVPT2) have been analyzed employing various ligand field parameterization schemes. Case studies include classical coordination compounds such as octahedral CrX63- and tetrahedral CrX4 complexes (X = F, Cl, Br, I), distorted tetrahedral to square planar CuCl42- complexes and the distorted pseudotetrahedral NiCl42-. In addition, bis and tris-chelate complexes of Ni-II, and M-III = Cr, Mn, respectively [Ni(L-L)(2), L-L = ethyldithiocarbamate (Et(2)dtc(-)), 2,2,6,6-tetramethylheptane-3,5-dionato (DPM-), pentane-2,4 dionato (acac(-)), and M(acac)(3) (M-III = Cr, Mn), all complex ligands possessing pi-conjugate electronic systems] have been included in the analysis. Values of 10Dq, the energy difference between the e- and t(2)-type orbitals in octahedral or tetrahedral complexes, identified as the energy of the first spin-allowed transition, in for example, octahedral Cr-III and Ni-II complexes, and the angular overlap parameters for sigma and pi metal 3d-ligand interactions (e(sigma) and e(pi)) for CrX63- and CrX4 (X- = F, Cl, Br, I) compare nicely with their counterparts deduced from a fit to experimental d-d spectra. The expected variations of these parameters embodied in the well-known orderings of ligands, according to the spectrochemical series and two-dimensional maps accounting for the ligand sigma- and pi-functions toward the metal 3d orbitals (quantified by the parameters e(sigma) and e(pi)) are reasonably well reproduced and hence also justified by AI theory. In addition, the parameters of the covalently reduced d-d interelectronic repulsion B and C (the nephelauxetic series) are also well reproduced from a fit of these parameters to AI data, more specifically to NEVPT2 results. Being able to reproduce the AI data for all multiplets of a given d(n)-complex using only three to four parameters, we conclude from these studies that the CASSCF and NEVPT2 AI methods and classical LFT are remarkably well compatible. A procedure of obtaining ligand field parameters from AI data described in this work opens the unique possibility to analyze numerical data from AI calculations. In turn, comparison between ligand field parameters, deduced from AI data and, independently, from available high-resolution electronic d-d absorption spectra can stimulate the validation and further development of multireference AI theory. Using this approach, the effects of pi-bonding (in Ni(L-L)(2), L = Et(2)dtc, acac, DPM and Cr(acac)(3)) and the interplay between pi-bonding and Jahn-Teller coupling in the case of Mn(acac)(3) on their optical spectra and the magnetic anisotropy (the zero-field splitting tensor) as studied by EPR spectroscopy are discussed. Finally optically detected transitions between the Zeeman levels of Cr(acac)(3) and Mn(acac)(3) have been analyzed in detail.