Relativistic Density Functional Calculations of Hyperfine Coupling with Variational versus Perturbational Treatment of Spin–Orbit Coupling

Different approaches are compared for relativistic density functional theory (DFT) and Hartree–Fock (HF) calculations of electron–nucleus hyperfine coupling (HFC) in molecules with light atoms, in transition metal complexes, and in selected actinide halide complexes with a formal metal 5<i>f</i>¹ configuration. The comparison includes hybrid density functionals with range-separated exchange. Within the variationally stable zeroth-order regular approximation (ZORA) relativistic framework, the HFC is obtained (i) with a linear response (LR) method where spin–orbit (SO) coupling is treated as a linear perturbation, (ii) with a spin-polarized approach closely related to a DFT method for calculating magnetic anisotropy (MA) previously devised by van Wüllen et al. where SO coupling is included variationally, (iii) with a quasi-restricted variational SO method previously devised by van Lenthe, van der Avoird, and Wormer (LWA). The MA and LWA approaches for HFC calculations were implemented in the open-source NWChem quantum chemistry package as part of this study. The methodology extends recent implementations for calculations of electronic <i>g</i>-factors (<i>J. Chem. Theor. Comput.</i> <b>2013</b>, <i>9</i>, 1052). The impact of electron correlation (DFT vs HF) and DFT delocalization errors, the effects of spin-polarization, the importance of treating spin–orbit coupling beyond first-order, and the magnitude of finite-nucleus effects, are investigated. Similar to calculations of <i>g</i>-factors, the MA approach in conjunction with hybrid functionals performs reasonably well for theoretical predictions of HFC in a wide range of scenarios