Challenges in Multireference Perturbation Theory for the Calculations of the g-Tensor of First-Row Transition-Metal Complexes

In this article, we have studied 34 S = ¹/₂ complexes of first-row transition-metal complexes in d¹, d⁵, d⁷, and d⁹ configurations in an attempt to determine the intrinsic accuracy of the scalar-relativistic complete active space self-consistent field (CASSCF) and N-electron valence perturbation theory (NEVPT2) methods, with respect to predicting molecular g-values. CASSCF calculations based on active spaces that contain only metal-based orbitals largely overestimate the g-values, compared to experiment and often fail to provide chemically meaningful results. Incorporation of dynamic correlation by means of the NEVPT2 method significantly improves the transition energies, with a typical error, relative to the experiment, of 2000-3000 cm^-1. As a result, a lowering in the g-shift by almost an order of magnitude is obtained, relative to the CASSCF results. However, the g-shifts are still overestimated, compared to the experiment, since CASSCF leads to an overly ionic description of the metal-ligand bond and, hence, to spin-orbit coupling matrix elements that are too large. Inclusion of the double d-shell, along with appropriate bonding counterparts to the antibonding d-orbitals in the active space, led to the correct trends in the g-values for all studied complexes, with the linear regression coefficient (R) equal to 0.93 over the entire dataset. Various technical aspects of the calculations such as the influence of relativity, importance of picture change effects, solvation effects, and comparison between second-order perturbation and effective Hamiltonian-based theories have also been systematically studied. In addition, g-tensor calculations were performed with five popular density functional theory (DFT) methods (B3LYP, M06L, M06, TPSSh, and PBE0) to compare with wave function (WF) methods. Our results suggest that WF-based methods are remarkably better than DFT methods. However, despite the fact that WF theory has come a long way in computing the properties of large, open-shell transition-metal complexes, methodological work is still necessary for truly high accuracies to be reached.