Embedded cluster density approximation for scalable high-level exchange-correlation calculations in periodic systems

Accurate prediction of electronic properties generally requires high-level electronic-structure methods, whose computational cost often scales steeply with system sizes. One way to extend high-level methods to large systems is to calculate electronic structures in local regions using high-level methods and then assemble these results across the system. Recently, we developed a method, termed embedded cluster density approximation (ECDA), to scale up high-level exchange-correlation (XC) calculations in finite systems. In this work, we extend ECDA to periodic systems. With ECDA, a cluster's electron density is defined based on the density functional embedding theory, which ensures that the cluster's density is seamlessly embedded in the system. The cluster's XC energy density is then calculated using a high-level XC functional and projected to its central atom. The system's XC energy is constructed by patching these atom-centered XC energies over the entire system. Using a hybrid XC functional as the high-level method, we demonstrate that ECDA is a nearly black-box method that can be applied to systems with various bond types. In general, good accuracy can be achieved with modest cluster sizes. It is also straightforward for ECDA to calculate energy differences and produce smooth energy surfaces. All these appealing features are due to the use of density partitioning for defining local active spaces. However, we also note that, for covalent systems, density partitioning produces unsaturated bonds at cluster boundaries, which may make the convergence of ECDA against cluster size zigzag.