An Efficient Coupled-Perturbed Kohn–Sham 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 reta...