The first systematic evaluation of local hybrid functionals for the calculation of electronic excitation energies within linear-response time-dependent density functional theory (TDDFT) is reported. Using our recent efficient semi-numerical TDDFT implementation [T. M. Maier et al., J. Chem. Theory Comput. 11, 4226 (2015)], four simple, thermochemically optimized one-parameter local hybrid functionals based on local spin-density exchange are evaluated against a database of singlet and triplet valence excitations of organic molecules, and against a mixed database including also Rydberg, intramolecular charge-transfer (CT) and core excitations. The four local hybrids exhibit comparable performance to standard global or range-separated hybrid functionals for common singlet valence excitations, but several local hybrids outperform all other functionals tested for the triplet excitations of the first test set, as well as for relative energies of excited states. Evaluation for the combined second test set shows that local hybrids can also provide excellent Rydberg and core excitations, in the latter case rivaling specialized functionals optimized specifically for such excitations. This good performance of local hybrids for different excitation types could be traced to relatively large exact-exchange (EXX) admixtures in a spatial region intermediate between valence and asymptotics, as well as close to the nucleus, and lower EXX admixtures in the valence region. In contrast, the tested local hybrids cannot compete with the best range-separated hybrids for intra- and intermolecular CT excitation energies. Possible directions for improvement in the latter category are discussed. As the used efficient TDDFT implementation requires essentially the same computational effort for global and local hybrids, applications of local hybrid functionals to excited-state problems appear promising in a wide range of fields. Influences of current-density dependence of local kinetic-energy dependent local hybrids, differences between spin-resolved and "common" local mixing functions in local hybrids, and the effects of the Tamm-Dancoff approximation on the excitation energies are also discussed.

Following the suggestion of local hybrid functionals with position-dependent exact-exchange admixture [J. Jaramillo, G. E. Scuseria, and M. Ernzerhof, J. Chem. Phys. 118, 1068 (2003)], a functional that mixes only local and exact exchange plus local correlation has been constructed. With a simple local mixing function for the position dependence, this Lh-SVWN functional provides atomization energies for the G2-1 set that are competitive with currently available state-of-the-art functionals like, e.g., B3LYP. This is achieved without generalized gradient approximations for exchange or correlation.

Local hybrid functionals with position-dependent exact-exchange admixture are a new class of exchange-correlation functionals in density functional theory that promise to advance the available accuracy in many areas of application. Local hybrids with different local mixing functions (LMFs) governing the position dependence are validated for the heats of formation of the extended G3/99 set, and for two sets of barriers of hydrogen-transfer and heavy-atom transfer reactions (HTBH38 and NHTBH38 databases). A simple local hybrid Lh-SVWN with only Slater and exact exchange plus local correlation and a one-parameter LMF, g(r)=b(tau(W)(r)tau(r)), performs best and provides overall mean absolute errors for thermochemistry and kinetics that are a significant improvement over standard state-of-the-art global hybrid functionals. In particular, this local hybrid functional does not suffer from the systematic deterioration that standard functionals exhibit for larger molecules. In contrast, local hybrids based on generalized gradient approximation exchange tend to give rise to nonintuitive LMFs, and no improved functionals have been obtained along this route. The LMF is a real-space function and thus can be analyzed in detail. We use, in particular, graphical analyses to rationalize the performance of different local hybrids for thermochemistry and reaction barriers.

Local hybrid density functionals, with position-dependent exact-exchange admixture, are an important extension to the popular global hybrid functionals, promising improved accuracy for many properties. An efficient implementation is crucial to make local hybrids available for widespread application. The resolution-of-the-identity approach used in previous implementations to compute nonstandard two-electron integrals has been found to require large uncontracted basis sets, rendering the cost of local hybrid calculations impractical for large-scale systems. On the basis of recently promoted seminumerical implementations of exact exchange in global hybrid functionals, we present an efficient, self-consistent implementation of local hybrid functionals within the generalized Kohn-Sham scheme. The final cost of a local hybrid calculation is equal to that of a meta-GGA global hybrid using the seminumerical algorithm. Since seminumerical schemes exhibit superior scaling with respect to system and basis set size over analytical exact exchange, and this advantage is not affected by a position-dependent admixture of exact exchange, local hybrid calculations for large systems are now possible.

Local hybrid functionals with position-dependent exact-exchange 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 self-consistent-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.

We present a model for the exchange-correlation hole and the exchange-correlation energy in the strong-correlation (SC) limit of density functional theory. The SC limit is useful in the construction of exchange-correlation functionals through interpolation of the adiabatic connection. The new approximation (referred to as shell model) is an improvement of the non-local radius (NLR) model recently proposed by Wagner and Gori-Giorgi [Phys. Rev. A 90, 052512 (2014)]. The NLR model does not correctly reproduce the limit of the strongly correlated homogeneous electron gas and this shortcoming is remedied by the shell model. As in the case of the NLR model, the spherically averaged electron density ρ(r,u)=∫dΩ4πρ(r+u) is the starting point for the construction of the shell model and it is also its computational bottleneck. We show how ρ(r, u), the NLR, and the shell model can be implemented efficiently. For this purpose, analytical integrals for the normalization and the energy density of the underlying holes are provided. Employing the shell model, we illustrate how improved adiabatic connection interpolations can be constructed.

A prominent feature of aromatic compounds is the ring current that can be observed indirectly in nuclear magnetic resonance experiments. This current is generated by an external magnetic field. In molecular electronics, molecules serve as conductors, and they are connected to metallic contacts that act as electron sources and electron sinks. We show that ring currents can also be found in molecular electronic devices containing cyclic π-electron systems. The circular currents are related to interference phenomena that can render the molecule impenetrable to electrons. While only small currents pass through the molecule, large internal circular currents are stimulated. We conjecture that the internal currents should result in experimentally observable magnetic moments.

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.