Gauge effects in local hybrid functionals evaluated for weak interactions and the GMTKN30 test set

<p>The so-called ‘gauge problem’, due to the non-uniqueness of exchange-energy densities, is a fundamental challenge for density functionals depending on these energy densities, such as local hybrid functionals. We have recently demonstrated how gauge effects influence the potential-energy curves of the argon dimer, and other quantities depending on ‘non-physical’ Pauli repulsions introduced by incompatible gauges of (semi-)local and exact-exchange energy densities . Introduction of suitable calibration functions depending only on semi-local quantities allowed to correct for these deficiencies and suggested ways to obtain more accurate local hybrid functionals beyond the local spin density approximation (LSDA) exchange-energy density. Here we extend the study of the gauge problem by comparing a number of uncalibrated and calibrated local hybrids for (1) the potential-energy curves of further noble-gas dimers and (2) for the entire GMTKN30 test set and its individual subsets. We find that DFT-D3 dispersion corrections fitted to be compatible with uncalibrated local hybrids have to correct not only for missing London dispersion but also for gauge artefacts that make weak interactions too repulsive. This burden is taken away when using properly calibrated local hybrids, which perform much better for dispersion-sensitive quantities already without D3 corrections, and which require only the physically relevant dispersion to be corrected for. The present results suggest directions for further improvement of calibration functions for local hybrids.</p

A Relativistic Quantum-Chemical Analysis of the trans Influence on ¹H NMR Hydride Shifts in Square-Planar Platinum(II) Complexes

Empirical correlations between characteristic ¹H NMR shifts in Pt­(II) hydrides with trans ligand influence series, Pt–H distances, and ¹⁹⁵Pt shifts are analyzed at various levels of including relativistic effects into density-functional calculations. A close examination of the trans ligand effects on hydride NMR shifts is shown to be dominated by spin–orbit shielding σ^SO. A rather complete understanding of the trends has been obtained by detailed molecular orbital (MO)-by-MO and localized MO analyses of the paramagnetic and spin–orbit (SO) contributions to the chemical shifts, noting that it is the perpendicular shift-tensor components that determine the trend of the ¹H hydride shifts. In contrast to previous assumptions, the change of the Pt–H distance in given complexes does not allow correlations between hydride shifts and metal–hydrogen bond length to be understood. Instead, variations in the polarization of metal 5d orbitals by the trans ligand affects the SO (and partly paramagnetic) shift contributions, as well as the Pt–H distances and the covalency of the metal–hydrogen bond (quantified, e.g., by natural atomic charges and delocalization indices from quantum theory atoms-in-molecules), resulting in a reasonable correlation of these structural/electronic quantities with hydride σ^SO shieldings. Our analysis also shows that specific σ^p- and σ^SO-active MOs are not equally important across the entire series. This explains some outliers in the correlation for limited ranges of trans-influence ligands. Additionally, SO effects from heavy-halide ligands may further complicate trends, indicating some limitations of the simple one-parameter correlations. Strikingly, σ-donating/π-accepting ligands with a very strong trans influence are shown to invert the sign of the usually shielding σ^SO contribution to the ¹H shifts, by a substantial reduction of the metal 5d orbital involvement in Pt–H bonding, and by involvement of metal 6p-type orbitals in the magnetic couplings, in violation of the Buckingham–Stephens “off-center ring-current” picture