Efficient Semi-numerical Implementation of Global and Local Hybrid Functionals for Time-Dependent Density Functional Theory

Local hybrid functionals with position-dependent exactexchange admixture offer increased flexibility compared to global hybrids. For sufficiently advanced functionals of this type, this is expected to hold also for a wide range of electronic excitations within time-dependent density functional theory (TDDFT). Following a recent semi-numerical implementation of local hybrid functionals for ground-state selfconsistent-field calculations (Bahmann, H.; Kaupp, M. J. Chem. Theory Comput. 2015, 11, 1540-1548), the first linear-response TDDFT implementation of local hybrids is reported, using a semi-numerical integration technique. The timings and accuracy of the semi-numerical implementation are evaluated by comparison with analytical schemes for time-dependent Hartree Fock (TDHF) and for the TPSSh global hybrid. In combination with the RI approximation to the Coulomb part of the kernel, the semi-numerical implementation is faster than the existing analytical TDDFT/TDHF implementation of global hybrid functionals in the TURBOMOLE code, even for small systems and moderate basis sets. Moreover, timings for global and local hybrids are practically equal for the semi-numerical scheme. The way to TDDFT calculations with local hybrid functionals for large systems is thus now open, and more sophisticated parametrizations of local hybrids may be evaluated.