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

We develop 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 over the system in an atom-by-atom manner. We derive the relationship between the embedding potential and system's KS potential. We show how to efficiently compute the system's XC potential which is the functional derivative of the patched XC energy with respect to the system's electron density. The accuracy of ECDA is examined by patching the exact exchange (EXX) and the random phase approximation (RPA) correlation energy densities in a one-dimensional hydrogen chain, as well as by patching EXX energy densities in several molecules. The agreement between ECDA and KS-DFT on total energies, dipole moments, XC potentials, and KS eigenvalues is good in general as the clusters are made larger. Based on these encouraging results, we expect ECDA to be a simple, yet effective method to scale up high-level KS-DFT simulations in large systems.