Hybrid functionals with system‐dependent parameters: Conceptual foundations and methodological developments

Approximate density‐functional theory (DFT) has become the major workhorse of modern computational chemistry and materials science, but the most widely used DFT approaches, local‐density approximation (LDA) and generalized gradient approximation (GGA), suffer from some fundamental deficiencies, including, in particular, the band gap problem. As a relatively cheap way to overcome the difficulty confronted by LDA/GGA, hybrid functional methods have attracted tremendous interest, first in molecular quantum chemistry, and more recently also in computational materials science. While early hybrid functionals use fixed parameters that are determined either by fitting some standard experimental database or based on theoretical arguments, recent studies have clearly indicated that the hybridization parameters carry on the physical significance and therefore should be system‐dependent. Developing theoretical methods to evaluate those parameters in a first‐principles manner has become one of the most active frontiers in theoretical chemistry community, and various schemes have been proposed. In this article, we aim at giving a systematic overview on the main theoretical concepts underlying various strategies and review major methodological developments in the recent years.