Development of density functionals based on the exact-exchange energy density for wide application in chemistry, biophysics, and material sciences

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The development, implementation and evaluation of improved density functionals based on the exact-exchange energy density, carried out in the first funding period, shall be extended. For local hybrid functionals (LHs) improved local mixing functions will be optimized, which improve the exact-exchange admixture near the nuclei as well as asymptotically. Improved calibration functions to deal with the “gauge problem” of LHs will be implemented, and the optimization procedures will be improved. Range-separated local hybrids (RSLHs) will be implemented for the first time with full functionality in an efficient computer code, for ground-state energy and gradients as well as TDDFT excitation energies. The first competitive RSLHs will be optimized and evaluated in detail. Improved strong-correlation-corrected LHs and RSLHs (scLHs and scRSLHs) will also be implemented and optimized. In this context routines for automatic differentiation will be integrated, and novel TDDFT routines will be constructed to deal with functionals containing non-linear forms of the exact-exchange energy density. The new methods will be evaluated for a large number of data sets and will be applied to core-excitation spectra and to many other questions. The main goal of this project is to establish new, practical DFT methods for wide variety of applications.