Local hybrid functionals: Theory, implementation, and performance of an emerging new tool in quantum chemistry and beyond

The state of the art in the development, implementation, validation, and application of local hybrid functionals with position-dependent exact-exchange admixture is reviewed comprehensively. Starting from the general formulation of a local hybrid functional, possible constructions of local mixing functions to determine the position dependence are scrutinized in terms of their exact properties as well as their desirable features. The gauge problem pertaining to the ambiguity of exchange-energy densities is discussed. Smoking guns for the gauge problem are identified, and the first calibration functions to improve the match of the exact and semi-local exchange-energy densities are compared. In view of the appearance of nonstandard exact-exchange integrals, a crucial aspect is the efficient implementation of local hybrid functionals. This has been achieved recently using a resolution of the identity and/or semi-numerical techniques, both for ground-state energies and gradients, and for linear-response time-dependent density functional theory. The validation and early applications of local hybrids are reviewed, including thermochemistry, reaction barriers, structures and vibrational frequencies, electric and magnetic properties, as well as electronic excitation spectra. This article is categorized under: Electronic Structure Theory > Density Functional Theory Electronic Structure Theory > Ab Initio Electronic Structure Methods Software > Quantum Chemistry