Scaling up accurate density functional theory calculations with the embedded cluster density approximation

The computational cost of Kohn-Sham density functional theory (KS-DFT) increases rapidly when advanced, orbital-based exchange-correlation (XC) energy functionals are used. To scale up such simulations, we have developed the embedded cluster density approximation (ECDA), which is a local correlation method formulated in the framework of DFT. In ECDA, for each atom, we select its nearby atoms to form a cluster. The rest of the system is the environment. The system's electron density is partitioned among the cluster and the environment, and the cluster's XC energy is calculated with an advanced XC energy functional. The cluster's XC energy is later projected onto its central atom. This procedure is performed for every atom in the system, and the total system's XC energy is obtained as the sum of these atomic XC energies. Since the clusters are defined by partitioning the electron density, rather than localizing the orbitals, ECDA is a nearly black-box local correlation method and is applicable to systems having various bond types, such as ionic, metallic, and covalent bonds. We demonstrate ECDA's performance on molecules, metals, and oxides. In these examples, the exact exchange is employed as the advanced XC energy functional. Another appealing feature of ECDA is that it is a variational method and the analytical forces can be derived. We expect ECDA to be a simple, yet effective local correlation method for scaling up advanced DFT simulations in the future.