We have developed the embedded cluster density approximation (ECDA) method which aims to scale up high-level Kohn-Sham density functional theory (KS-DFT) simulations in large systems [JCTC, 14, 6211  (2018)]. ECDA is a local correlation method formulated in the framework of KS-DFT. It is a logical extension of the local density approximation (LDA). The idea of ECDA is demonstrated in the following figure. For each atom, a cluster is defined to enclose that atom. The remaining atoms are considered as the environment. The system's electron density is then partitioned among the cluster and its environment. In the figure, clusters' electron densities are yellow and environments' electron densities are blue. For each cluster, its central atoms are circled. 

The cluster's XC energy density is then calculated using advanced exchange-correlation functionals. The system's XC energy is then constructed by patching these locally computed XC energy densities over the entire system in an atom-by-atom manner.  ECDA is a fully self-consistent method, with which we can investigate charge transfer/reorganization in heterogeneous materials (such as, oxide interfaces). ECDA is currently being developed in the ABINIT program and will be released in the future. 

To demonstrate ECDA's performance, in what follows we apply ECDA to three molecules given below. (The extension of ECDA to solids is in progress).

Energies for stretching Cl-C bond predicted by self-consistent ECDA calculations. 

ECDA can reasonably produce the exact exchange potentials for several molecules. We show the convergence of ester's EXX potential with respect to cluster size. Nb=1, 2, and 3 denote that 1st, 2nd, and 3rd nearest neighbors are included for defining clusters. The interval between the contour lines is 0.1 a.u..

For Cl-tetracene and tripeptide, ECDA also well produces their EXX potentials. The interval between contour lines is 0.1 a.u..

Kohn-Sham eigenvalues predicted by self-consistent ECDA calculations. Self-consistent KS-DFT-EXX results are the benchmark