Behaviour of DFT-based approaches to the spin-orbit term of zero-field splitting tensors: a case study of metallocomplexes, M(acac) (M = V, Cr, Mn, Fe and Mo).

Spin-orbit contributions to the zero-field splitting (ZFS) tensor (D tensor) of M(acac) complexes (M = V, Cr, Mn, Fe and Mo; acac = acetylacetonate anion) are evaluated by means of ab initio (a hybrid CASSCF/MRMP2) and DFT (Pederson-Khanna (PK) and natural orbital-based Pederson-Khanna (NOB-PK)) methods, focusing on the behaviour of DFT-based approaches to the D tensors against the valence d-electron configurations of the transition metal ions in octahedral coordination. Both the DFT-based approaches reproduce trends in the D tensors. Significantly, the differences between the theoretical and experimental D (D = D - (D + D)/2) values are smaller in NOB-PK than in PK, emphasising the usefulness of the natural orbital-based approach to the D tensor calculations of transition metal ion complexes. In the case of d and d electronic configurations, the D(NOB-PK) values are considerably underestimated in the absolute magnitude, compared with the experimental ones. The D tensor analysis based on the orbital region partitioning technique (ORPT) revealed that the D contributions attributed to excitations from the singly occupied region (SOR) to the unoccupied region (UOR) are significantly underestimated in the DFT-based approaches to all the complexes under study. In the case of d and d configurations, the (SOR → UOR) excitations contribute in a nearly isotropic manner, which causes fortuitous error cancellations in the DFT-based D values. These results indicate that more efforts to develop DFT frameworks should be directed towards the reproduction of quantitative D tensors of transition metal complexes with various electronic configurations and local symmetries around metal ions.