Implementation of Molecular Gradients for Local Hybrid Density Functionals Using Seminumerical Integration Techniques

We present the first implementation of the derivative of the local hybrid exchange-correlation energy with respect to the displacement of nuclei in a Gaussian-type atomic basis set. This extends a recent efficient implementation of local hybrid functionals for self-consistent Kohn-Sham and linear-response TDDFT calculations into the TURBOMOLE program package. In contrast to seminumerical schemes for global exact-exchange admixtures and to the related SCF and TDDFT implementations of local hybrid functionals, additional analytical integrals have to be evaluated at each grid point in the case of molecular gradients. The overall efficiency of the present scheme is improved through prescreening with the density matrix (P-junctions), as well as with spherical overlap estimates (S-junctions). Comparative timings for structure optimizations with local vs global hybrid functionals are discussed while gauging the accuracy for S- and P-junctions using varying thresholds. Local hybrids are furthermore assessed for structure optimization and harmonic vibrational frequency calculations (using numerical second derivatives) of a selection of test systems, comparing with experimental data and some widely used density functionals.