Revisiting Gauge-Independent Kinetic Energy Densities in Meta-GGAs and Local Hybrid Calculations of Magnetizabilities

Abstract

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 (τ) in mGGA calculations by comparing the Maximoff–Scuseria formulation of τ 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 of 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 statistical error evaluations due to its large errors with common density functionals.

Toward the Next Generation of Density Functionals: Escaping the Zero-Sum Game by Using the Exact-Exchange Energy Density

“…The scLHs and the ωLH22t RSLH have now been implemented for NMR nuclear shieldings and the related molecular magnetizabilities . For the latter case LHs dominate the overall best-performing functionals in a larger evaluation against CCSD­(T) benchmark data.…”

Spin-Symmetry Breaking and Hyperfine Couplings in Transition-Metal Complexes Revisited Using Density Functionals Based on the Exact-Exchange Energy Density

“…These show substantial improvements over the underlying LHs and RSLHs regarding spin-restricted bond-disssociation curves and the closely related FSEs of open-shell atoms. While we have also already found appreciable improvements for more “real-world” systems, including the magnetizabillities of molecules like ozone, further evaluations of these new functionals are mandatory to judge their overall usability in challenging chemical systems. Naturally, this should also be done for open-shell transition-metal complexes.…”

Implementation and First Evaluation of Strong-Correlation-Corrected Local Hybrid Functionals for the Calculation of NMR Shieldings and Shifts

“…Additionally, we have also implemented and will evaluate for the first time for nuclear shieldings the recent successful range-separated LH (RSLH) ωLH22t, which has been shown to perform excellently for a wide variety of questions and which exhibits the correct long-range asymptotic potential. , We note in passing that recent scRSLH extensions of ωLH22t are not yet covered here and will be reported elsewhere. A related, first successful implementation and evaluation of scLHs and RSLHs for a benchmark set of magnetizabilities has just been reported . The implementation shares parts of the code with the shielding code; here, we will give more of the theoretical background.…”

“…A related, first successful implementation and evaluation of scLHs and RSLHs for a benchmark set of magnetizabilities has just been reported. 49 The implementation shares parts of the code with the shielding code; here, we will give more of the theoretical background.…”