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.