New approaches for incorporating the exact exchange energy density into density functional approximations

In the last ten years, hybrid density functional approximations have become the most widely used method in modern quantum chemistry. Hybrid functionals combine the semi-local exchange-correlation and a fraction of the exact-exchange energy. The most common are global hybrid functionals, with a constant fraction of the exact exchange determined emprirically. Recently, two complementary strategies have been proposed to improve the performance of hybrid functionals. In range-separated hybrid functionals, the fraction of exact exchange depends on the interelectronic distance. In local hybrid functionals, the fraction of exact exchange is position-dependent. In this work, we propose two approaches that combine range-separated and local hybrid functionals together, providing a promising route to more accurate results.\nMost previous implementations of range-separated hybrid functionals use a universal, system-independent screening parameter, fitted to experimental data. However, the screening parameter proves to depend strongly on the choice of the training set. Moreover, such functionals violate the exact high-density limit. In this work, we argue that the separation between short-range (SR) and long-range (LR) interactions should depend on the local density. We propose an approximation that uses a position-dependent screening function o( r) defining a local range separation (LRS) for mixing exact (HF-type) and LSDA exchange. This method adds a substantial flexibility to describe diverse chemical compounds. Moreover, the new model satisfies a high-density limit better than the approximation with fixed screening parameter.\nWe have also developed an alternative strategy to improve the range-separated functionals by combining them together with local hybrid functionals. We consider two limiting cases: screened local hybrids with short-range exact exchange, and long-range corrected hybrids with long-range exact exchange. The former approach can treat metals and narrow-gap semiconductors much more efficiently than standard local hybrids do. The latter method provides the correct asymptotic behavior, which is important for the treatment of charge transfer and Rydberg excitations in finite systems.