Theoretical Analysis of the Spin Hamiltonian Parameters in Co^(II)S₄ Complexes, Using Density Functional Theory and Correlated ab initio Methods

A systematic Density Functional Theory (DFT) and multiconfigurational ab initio computational analysis of the Spin Hamiltonian (SH) parameters of tetracoordinate S = 3/2 Co(II)S4–containing complexes has been performed. The complexes under study bear either arylthiolato, ArS–, or dithioimidodiphosphinato, [R2P(S)NP(S)R′2]− ligands. These complexes were chosen because accurate structural and spectroscopic data are available, including extensive Electron Paramagnetic Resonance (EPR)/Electron Nuclear Double Resonance (ENDOR) studies. For comparison purposes, the [Co(PPh3)2Cl2] complex, which was thoroughly studied in the past by High–Field and Frequency EPR and Variable Temperature, Variable Field Magnetic Circular Dichroism (MCD) spectroscopies, was included in the studied set. The magnitude of the computed axial zero-field splitting parameter D (ZFS), of the Co(II)S4 systems, was found to be within ∼10% of the experimental values, provided that the property calculation is taken beyond the accuracy obtained with a second-order treatment of the spin–orbit coupling interaction. This is achieved by quasi degenerate perturbation theory (QDPT), in conjunction with complete active space configuration interaction (CAS-CI). The accuracy was increased upon recovering dynamic correlation with multiconfigurational ab initio methods. Specifically, spectroscopy oriented configuration interaction (SORCI), and difference dedicated configuration interaction (DDCI) were employed for the calculation of the D-tensor. The sign and magnitude of parameter D was analyzed in the framework of Ligand Field Theory, to reveal the differences in the electronic structures of the investigated Co(II)S4 systems. For the axial complexes, accurate effective g′-tensors were obtained in the QDPT studies. These provide a diagnostic tool for the adopted ground state configuration (±3/2 or ±1/2) and are hence indicative of the sign of D. On the other hand, for the rhombic complexes, the determination of the sign of D required the SH parameters to be derived along suitably constructed symmetry interconversion pathways. This procedure, which introduces a dynamic perspective into the theoretical investigation, helped to shed some light on unresolved issues of the corresponding experimental studies. The metal hyperfine and ligand super-hyperfine A-tensors of the C2 [Co{(SPPh2)(SPiPr2)N}2] complex were estimated by DFT calculations. The theoretical data were shown to be in good agreement with the available experimental data. Decomposition of the metal A-tensor into individual contributions revealed that, despite the large ZFS, the observed significant anisotropy should be largely attributed to spin–dipolar contributions. The analysis of both, metal and ligand A-tensors, is consistent with a highly covalent character of the Co–S bonds.