Conceptual Insights into DFT Spin-State Energetics of Octahedral Transition-Metal Complexes through a Density Difference Analysis

In this study, an intuitive concept is derived, which explains the characteristic dependence of spin-state energetics on the exact exchange admixture of DFT functionals in the case of octahedral transition metal complexes. The change in electron density distributions upon varying the admixture, c(3), in the B3LYP functional is analyzed for archetype ionic and covalent systems as well as for the Fe2+ ion in an ideal octahedral field. An understanding of how the DFT description of the electronic structure of octahedral complexes changes as a function of c(3) is sought. A systematic spin-state energy analysis of 50 octahedral complexes of various metals and ligands with consistent experimental data is presented, allowing the derivation, in theory, of an optimal c(3) value for each system. The notion that the admixture dependence of DFT spin-state energetics stems from the treatment of nondynamic electrons arising from the mixing of (M-Lz2)(0)(dz2)(2) and (M-Lx2-y2)(0)(dx2-y2)(2) configurations into the dominant (M-Lx2-y2)(2)(dx2-y2)(0) and (M-Lx2-y2)(2)(dx2-y2)(0) ones in the low(er) spin states is put forward. That is, in the effort to mimic such electron-electron interactions, E-x(LDA) overestimates, whereas exact exchange downplays the contribution of this type of electron correlation to the stability of low(er) spin states, leading to the widespread practical observation that the higher the exact exchange admixture, the more stable the high-spin-state configuration.