Systematic evaluation of modern density functional methods for the computation of NMR shifts of 3d transition-metal nuclei

A wide range of density functionals from all rungs of Jacob's ladder has been evaluated systematically for a set of experimental 3d transition-metal NMR shifts of 70 complexes encompassing 12 x ⁴⁹Ti, 10 x ⁵¹V, 10 x ⁵³Cr, 11 x ⁵⁵Mn, 9 x ⁵⁷Fe, 9 x ⁵⁹Co, and 9 x ⁶¹Ni shift values, as well as a diverse range of electronic-structure characteristics. The overall 39 functionals evaluated include one LDA, 8 GGAs, 7 meta-GGAs (including their current-density-functional - CDFT - versions), 9 global hybrids, 4 range-separated hybrids, 8 local hybrids, and 2 double hybrids, and we also include Hartree-Fock and MP2 calculations. While recent evaluations of the same functionals for a very large coupled cluster-based benchmark of main-group shieldings and shifts achieved in some cases aggregate percentage mean absolute errors clearly below 2%, the best results for the present 3d nuclei set are in the range between 4-5%. Strikingly, the overall best-performing functionals are the recently implemented CDFT versions of two meta-GGAs, namely cM06-L (4.0%) and cVSXC (4.3%), followed by cLH14t-calPBE (4.9%), B3LYP (5.0%), and cLH07t-SVWN (5.1%), i.e. the previously best-performing global hybrid and two local hybrids. A number of further functionals achieve aggregate deviations in the range 5-6%. Range-separated hybrids offer no particular advantage over global hybrids. Due to the overall poor performance of Hartree-Fock theory for all systems except the titanium complexes, MP2 and double-hybrid functionals are unsuitable for these 3d-nucleus shifts and provide large errors. Global hybrid functionals with larger EXX admixtures, such as BHLYP or M06-2X, also perform poorly, and some other highly parameterized global hybrids also are unsuitable. For many functionals depending on local kinetic energy tau , their CDFT variants perform much better than their "non-CDFT" versions. This holds notably also for the abovementioned M06-L and VSXC, while the effect is small for τ-dependent local hybrids and can even be somewhat detrimental to the agreement with experiment for a few other cases. The separation between well-performing and more poorly performing functionals is mainly determined by their results for the most critical nuclei ⁵⁵Mn, ⁵⁷Fe, and ⁵⁹Co. Here either moderate exact-exchange admixtures or CDFT versions of meta-GGAs are beneficial for the accuracy. The overall deviations of the better-performing global or local hybrids are then typically dominated by the ⁵³Cr shifts, where triplet instabilities appear to disfavor exact exchange admixture. Further detailed analyses help to pinpoint specfic nuclei and specific types of complexes that are challenges for a given functional.