Lessons from the Spin-Polarization/Spin-Contamination Dilemma of Transition-Metal Hyperfine Couplings for the Construction of Exchange-Correlation Functionals.

Hyperfine couplings (HFCs) of open-shell transition-metal centers are known to often depend crucially on core-shell spin polarization (CSSP). The latter is typically underestimated by semilocal density functionals, while admixture of exact exchange (EXX) in (global) hybrid functionals enhances CSSP. Unfortunately, a metal-ligand antibonding character of one or more of the singly occupied molecular orbitals of the complex will cause substantial valence-shell spin polarization (VSSP), which for global hybrids with higher EXX admixtures may lead to substantial spin contamination, thereby deteriorating the overall electronic structure and the dipolar couplings. In view of this known dilemma, we use a subset of 3d complexes from an earlier study (M. Munzarová, M. Kaupp J. Phys. Chem. A 1999, 103, 9966-9983) to examine systematically a wide range of exchange-correlation functionals for metal HFCs, including highly parametrized (meta-)GGAs, global, and range-separated hybrid functionals not yet available in earlier studies, as well as for the first time local hybrids with real-space position-dependent EXX admixture. Both CSSP and VSSP have been carefully analyzed in terms of their orbital contributions, both for cases dominated only by CSSP and for systems influenced crucially by VSSP and spin contamination. While some more parametrized meta-GGA functionals (τ-HCTH, VSXC, partially M06-L) provide surprisingly realistic CSSP, some others (MN12-L, MN15-L) and some global hybrids (M05, M06, partly MN15) exhibit dramatic shortcomings in describing the CSSP contributions. Local hybrid functionals provide a promising way of enhancing CSSP by high EXX admixture in the core region while avoiding excessive VSSP and thus spin contamination. These analyses provide important insights that may help to construct improved functionals for HFCs and related properties (e.g., contact NMR shifts).