An Efficient Coupled-Perturbed KohnSham Implementation of NMR Chemical Shift Computations with Local Hybrid Functionals and Gauge-Including Atomic Orbitals

Nuclear shielding calculations for local hybrid (LH) functionals with position-dependent exact-exchange admixtures within a coupled-perturbed Kohn-Sham (CPKS) framework have been implemented into the Turbomole code using efficient seminumerical integration techniques to deal with two-electron integrals. When using gauge-including atomic orbitals, LHs generate additional terms within the pre-loop section of the CPKS scheme compared to global hybrid (GH) functionals, related to perturbed electron-repulsion integrals. These terms have been implemented and tested in detail, together with dependencies on grid sizes and integral screening procedures. Even with relatively small grids, a seminumerical treatment of GHs reproduces analytical GH results with high accuracy while improving scaling with system and basis-set sizes significantly. The extra terms generated by LHs in the pre-loop part increase the scaling of that contribution slightly, but the advantages compared to the analytical scheme are largely retained, in particular for the typically large basis sets used in NMR shift calculations, allowing for a very efficient computational scheme. An initial comparison of four first-generation LHs based on LDA exchange for a shielding test set of 15 small main-group molecules against high-level CCSD(T) benchmark data indicates a substantial reduction of the systematically underestimated shieldings compared to semilocal functionals or GHs for non-hydrogen nuclei when a so-called t-LMF is used to control the position dependence of the exact-exchange admixture. In contrast, proton shieldings are underestimated with this LMF, while an LH with a so-called s-LMF performs much better. These results are discussed in the context of experience for other properties, and they suggest directions for further improvements of LHs regarding nuclear shieldings.