Embedded cluster density approximation for exchange-correlation energy: a natural extension of the local density approximation

We developed a local correlation method in the framework of Kohn-Sham density functional theory (KS-DFT). The method is termed embedded cluster density approximation (ECDA) and is a logical extension of the local density approximation. In ECDA, an embedded cluster is defined for each atom based on the finite-temperature density-functional embedding theory. The clusters' XC energy densities are calculated using high-level XC functionals. The system's XC energy is then constructed by patching these locally computed, high-level XC energy densities in the system in an atom-by-atom manner. A key result is the derivation of the relationship between the embedding potential and system's KS potential, based on which we show how to efficiently compute the system's XC potential following the optimized effective potential procedure. The accuracy of ECDA is examined by patching the exact exchange (EXX) and the random phase approximation (RPA) correlation energies in a one-dimensional hydrogen chain, as well as by patching EXX energies in several molecules. We expect ECDA to be a simple, yet effective method to scale up high-level KS-DFT calculations in large-scale strongly correlated systems.