Effect of the Current Dependence of Tau-Dependent Exchange-Correlation Functionals on Nuclear Shielding Calculations

Exchange-correlation functionals that depend on the local kinetic energy τ are widely used in many fields. This includes meta-generalized gradient approximation (GGA) functionals and their global hybrid versions as well as local hybrid functionals with τ-dependent local mixing functions to determine position-dependent exact-exchange admixture. Under the influence of an external magnetic field, τ becomes dependent on the gauge of the magnetic vector potential and should thus be extended to a gauge-invariant formulation. The currently most widely used extension for nuclear shielding calculations is that suggested by Maximoff and Scuseria (Maximoff, S. N.; Scuseria, G. E. Chem. Phys. Lett. 2004, 390, 408). Using the recent first implementation of local hybrids in this framework, we have found unphysical paramagnetic contributions, which are most clearly identified for atoms but are also present in molecules. These τ_MS artifacts are small for the TPSS or TPSSh functionals, significantly deshielding in the case of nonhydrogen nuclei for the M06-L and M06 functionals and significantly shielding in those cases for the first-generation τ-dependent local hybrids LH07t-SVWN and LH12ct-SsifPW92. We have therefore implemented an extension of a linear-response nuclear shielding code to the proper current-density functional version of τ suggested by Dobson (Dobson, J. F. J. Chem. Phys. 1993, 98, 8870). Using τ_D eliminates the gauge dependence as well as the unphysical contributions introduced by τ_MS. A first evaluation of this implementation for a set of main-group nuclear shieldings against CCSD(T) benchmark data indicates rather small effects for the TPSS and TPSSh functionals but significant changes for the other functionals studied: the previously observed remarkable performance of the highly parameterized meta-GGA functional M06-L is found to be the result of error compensation with the lack of an explicit current dependence. Results for the M06 functional are improved somewhat but are still overall of relatively low accuracy. In contrast, too low proton shieldings found recently for τ-dependent local hybrids are improved significantly within the τ_D current-density functional framework while preserving the outstanding performance of these functionals for other nuclei.