First-principles paramagnetic NMR of a challenging Fe(V) bis(imido) complex: a case for novel density functionals beyond the zero-sum game.

We investigate computationally the hyperfine couplings (HFCs) and the consequent paramagnetic nuclear magnetic resonance (pNMR) chemical shifts of a recently synthesised doublet Fe(V) bis(imido) complex. Using conventional global hybrid density-functional theory (DFT) methods with varying exact-exchange admixture, a significant spin contamination problem is observed, leading to a massive spin-density spill-over to the strongly bound imido ligands and to the BH group of the carbene framework. As a result, the computed paramagnetic NMR shifts, which are based on a combination of calculated -tensor, DFT-calculated orbital shielding and DFT-based HFCs, disagree strongly with the available experimental H NMR chemical shifts and predict unrealistic C shifts in the spill-over region. While semi-local functionals like PBE do not suffer from the spin-contamination problem, their inherent delocalisation errors also lead to a too spread-out spin-density distribution. We demonstrate that, by applying novel local hybrid and range-separated local hybrid functionals with correction terms for strong-correlation and/or delocalisation errors to the HFC computations, the spin contamination problem is significantly reduced, while keeping delocalisation errors small. This results in more realistic pNMR shifts obtained for this system, also when compared to data obtained using correlated HFCs. Problems with the use of a global hybrid functional are already observed at the level of the underlying optimised structure, and employing a semi-local functional in structure optimisation is found to improve the situation. With that, the combined /DFT method with the latest (range-separated) local hybrid functionals is seen to reasonably reproduce the H experiment and enable plausible predictions for the hitherto unreported C shifts in this challenging iron complex.