Behaviour of DFT-based approaches to the spin–orbit term of zero-field splitting tensors: a case study of metallocomplexes, MIII(acac)3 (M = V, Cr, Mn, Fe and Mo)

Abstract

Spin–orbit contributions to the zero-field splitting (ZFS) tensor (D^SO tensor) of M^III(acac)₃ 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^SO 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_ZZ − (D_XX + D_YY)/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 d² and d⁴ electronic configurations, the D^SO(NOB-PK) values are considerably underestimated in the absolute magnitude, compared with the experimental ones. The D^SO tensor analysis based on the orbital region partitioning technique (ORPT) revealed that the D^SO 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 d³ and d⁵ configurations, the (SOR → UOR) excitations contribute in a nearly isotropic manner, which causes fortuitous error cancellations in the DFT-based D^SO values. These results indicate that more efforts to develop DFT frameworks should be directed towards the reproduction of quantitative D^SO tensors of transition metal complexes with various electronic configurations and local symmetries around metal ions.