Locally Range-Separated Local Hybrid Functionals – The Next Level on the Hybrid Functional Ladder

In this work, the new class of locally range-separated local hybrid (LRSLH) functionals is presented. LRSLH functionals combine the concepts of a local exact-exchange admixture as in local hybrids with a locally range-separated exact-exchange admixture as in locally range-separated hybrid functionals. The satisfiability of important theoretical constraints on hybrid functionals by the LRSLH approach is discussed in comparison to existing hybrid functional classes by proposing a new categorization scheme for hybrid functionals, labeled as hybrid functional ladder. In particular, this concerns the iso-orbital and asymptotic potential limits as well as the high-density limit with respect to uniform coordinate scaling and the gradient expansion of the exchange energy density, which in contrast to existing hybrid schemes can be simultaneously satisfied by LRSLH functionals. Furthermore, this work provides a first explorative study regarding the performance of the new LRSLH approach. Despite featuring only up to two empirical parameters, the optimized LRSLH functionals exhibit a similar performance for atomization energies and transition barrier heights as some of the more recent hybrid functionals. In particular, this highlights the great potential of the new LRSLH approach.