Metal and ligand hyperfine couplings in transition metal complexes: The effect of spin–orbit coupling as studied by coupled perturbed Kohn–Sham theory

The derivation, implementation, and validation of a method to calculate spin–orbit coupling (SOC) contributions to the hyperfine coupling (HFC) is reported. Due to this development it is now possible to calculate the complete ligand and metal nuclei HFCs at a consistent level of theory, i.e., spin unrestricted Hartree–Fock (HF) or density functional theory (DFT). The SOC contributions to the HFC are calculated as a second-order property and are treated by a coupled-perturbed HF or Kohn–Sham treatment. The method is applied to a representative collection of first row transition metal complexes. The calculated metal HFCs are in reasonable to good agreement with the experimental data, with the main error being probably due to the Fermi contact term that is not well represented by present day DFT functionals. Similarities and differences to the closely related field of electronic g-tensor calculations are discussed.