Four-Component Relativistic Density Functional Theory Calculations of EPR <b>g</b>- 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 <b>g</b>- and hyperfine <b>A</b>-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 4d¹ and 5d¹ [MEX_<i>n</i>]^<i>q</i> systems, and for a series of larger Ir­(II) and Pt­(III) d⁷ complexes (<i>S</i> = 1/2) with particularly large <b>g</b>-tensor anisotropies. Different density functionals (PBE, BP86, B3LYP-<i>x</i>HF, PBE0-<i>x</i>HF) with variable exact-exchange admixture <i>x</i> (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 <i>g</i>-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