The performance of various density functional approaches for the calculation of electron paramagnetic resonance (EPR) hyperfine coupling constants in transition metal complexes has been evaluated critically by comparison with experimental data and high-level coupled-cluster results for 21 systems, representing a large variety of different electronic situations. While both gradient-corrected and hybrid functionals allow the calculation of isotropic metal hyperfine coupling constants to within ca. 10-15% for the less critical cases (e.g., ScO, TiN, TiO, VO, MnO, MnF), none of the functionals investigated performs well for all complexes. Gradient-corrected functionals tend to underestimate the important core-shell spin polarization. While this may be improved by exact-exchange mixing in some cases, the accompanying spin contamination may even lead to a deterioration of the results for other complexes. We also identify cases, where essentially none of the functionals performs satisfactorily. In the absence of a "universal functional", the functionals to be applied to the calculation of hyperfine couplings in certain areas of transition metal chemistry have to be carefully selected. Desirable, improved functionals should provide sufficiently large spin polarization for core and valence shells without exaggerating it for the latter (and thus introducing spin contamination). Coupling anisotropies and coupling constants for ligand nuclei are also discussed. The computationally much more demanding coupled cluster (CCSD and CCSD(T)) methods, which have been applied to a subset of complexes, show good performance, even when a UHF reference wave function is moderately spin-contaminated.

Modern density-functional methods for the calculation of electronic g-tensors have been implemented within the framework of the deMon code. All relevant perturbation operators are included. Particular emphasis has been placed on accurate yet efficient treatment of the two-electron spin−orbit terms. At an all-electron level, the computationally inexpensive atomic mean-field approximation is shown to provide spin−orbit contributions in excellent agreement with the results obtained using explicit one- and two-electron spin−orbit integrals. Spin−other−orbit contributions account for up to 25−30% of the two-electron terms and may thus be non-negligible. For systems containing heavy atoms we use a pseudopotential treatment, where quasirelativistic pseudopotentials are included in the Kohn−Sham calculation whereas appropriate spin−orbit pseudopotentials are used in the perturbational treatment of the g-tensors. This approach is shown to provide results in good agreement with the all-electron treatment, at moderate computational cost. Due to the atomic nature of both mean-field all-electron and pseudopotential spin−orbit operators used, the two approaches may even be combined in one calculation. The atomic character of the spin−orbit operators may also be used to analyze the contributions of certain atoms to the paramagnetic terms of the g-tensors. The new methods have been applied to a wide variety of species, including small main group systems, aromatic radicals, as well as transition metal complexes.