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 have been evaluated systematically for a set of experimental
3d transition-metal NMR shifts of 70 complexes encompassing 12 × 49Ti, 10 × 51V, 10 × 53Cr,
11 × 55Mn, 9 × 57Fe, 9 × 59Co, and 9 × 61Ni shift values, as well as
a diverse range of electronic structure characteristics. The overall
39 functionals evaluated include one LDA, eight GGAs, seven meta-GGAs
(including their current-density-functionalCDFTversions),
nine global hybrids, four range-separated hybrids, eight local hybrids,
and two 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 and 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 parametrized
global hybrids also are unsuitable. For many functionals depending
on local kinetic energy τ, their CDFT variants perform much
better than their “non-CDFT” versions. This holds notably
also for the above-mentioned 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 specific nuclei
and specific types of complexes that are challenges for a given functional.