Four-Component Relativistic Density Functional Theory Calculations of EPR g- and Hyperfine-Coupling Tensors Using Hybrid Functionals: Validation on Transition-Metal Complexes with Large Tensor Anisotropies and Higher-Order Spin-Orbit Effects.

The four-component matrix Dirac-Kohn-Sham (mDKS) implementation of EPR g- and hyperfine A-tensor calculations within a restricted kinetic balance framework in the ReSpect code has been extended to hybrid functionals. The methodology is validated for an extended set of small 4d(1) and 5d(1) MEXn systems, and for a series of larger Ir(II) and Pt(III) d(7) complexes (S = 1/2) with particularly large g-tensor anisotropies. Different density functionals (PBE, BP86, B3LYP-xHF, PBE0-xHF) with variable exact-exchange admixture x (ranging from 0% to 50%) have been evaluated, and the influence of structure and basis set has been examined. Notably, hybrid functionals with an exact-exchange admixture of about 40% provide the best agreement with experiment and clearly outperform the generalized-gradient approximation (GGA) functionals, in particular for the hyperfine couplings. Comparison with computations at the one-component second-order perturbational level within the Douglas-Kroll-Hess framework (1c-DKH), and a scaling of the speed of light at the four-component mDKS level, provide insight into the importance of higher-order relativistic effects for both properties. In the more extreme cases of some iridium(II) and platinum(III) complexes, the widely used leading-order perturbational treatment of SO effects in EPR calculations fails to reproduce not only the magnitude but also the sign of certain g-shift components (with the contribution of higher-order SO effects amounting to several hundreds of ppt in 5d complexes). The four-component hybrid mDKS calculations perform very well, giving overall good agreement with the experimental data.