  In a recent study [J. Chem. Theory Comput. 2021, 17, 1457-1468], some of us
examined the accuracy of magnetizabilities calculated with density functionals
representing the local density approximation (LDA), generalized gradient
approximation (GGA), meta-GGA (mGGA) as well as global hybrid (GH) and
range-separated (RS) hybrid functionals by assessment against accurate
reference values obtained with coupled-cluster theory with singles, doubles and
perturbative triples [CCSD(T)]. Our study was later extended to local-hybrid
(LH) functionals by Holzer et al. [J. Chem. Theory Comput. 2021, 17,
2928-2947]; in this work, we examine a larger selection of LH functionals, also
including range-separated LH (RSLH) functionals and strong-correlation LH
(scLH) functionals. Holzer et al also studied the importance of the physically
correct handling of the magnetic gauge dependence of the kinetic energy density
$(\tau)$ in mGGA calculations by comparing the Maximoff--Scuseria formulation
of $\tau$ used in our aforementioned study to the more physical current-density
extension derived by Dobson. In this work, we also revisit this comparison with
a larger selection of mGGA functionals. We find that the newly tested LH, RSLH
and scLH functionals outperform all the functionals considered in the previous
studies. The various LH functionals afford the seven lowest mean absolute
errors, while also showing remarkably small standard deviations and mean
errors. Most strikingly, the best two functionals are scLHs that also perform
remarkably well in cases with significant multiconfigurational character such
as the ozone molecule, which is traditionally excluded from the statistical
error evaluation due to its large errors with common density functionals.
