Paramagnetic NMR Shifts for Triplet Systems and Beyond with Modern Relativistic Density Functional Methods

An efficient framework for the calculation of paramagnetic NMR (pNMR) shifts within exact two-component (X2C) theory and (current-dependent) density functional theory (DFT) up to the class of local hybrid functionals is presented. Generally, pNMR shifts for systems with more than one unpaired electron depend on the orbital shielding contribution and a temperature-dependent term. The latter includes the zero-field splitting, the hyperfine coupling, and the g- tensor. For consistency, we calculate these three tensors at the same level of theory, i.e. using scalar-relativistic X2C augmented with spin–orbit perturbation theory. Results for pNMR chemical shifts of transition-metal complexes reveal that this X2C-DFT framework can yield good results for both the shifts and the individual tensor contributions of metallocenes and related systems, especially if the hyperfine coupling (HFC) constant is large. For small HFC constants, the relative error is often large and sometimes the sign may be off. 4d and 5d complexes with more complicated structures demonstrate the limitations of a fully DFT-based approach. Additionally, a Co-based complex with very large zero-field splitting and pronounced multireference character is not well described. Here, a hybrid DFT-multireference framework is necessary for accurate results. Our results show that X2C is sufficient to describe relativistic effects and computationally cheaper than a fully relativistic approach. Thus, it allows to use large basis sets for converged hyperfine couplings. Overall, current-dependent meta-generalized gradient approximations (meta-GGAs) and local hybrid functionals show some potential, however, the currently available functionals leave a lot to be desired.