Analytical energy gradient for the embedded cluster density approximation.

Abstract

We recently developed the embedded cluster density approximation (ECDA), which is a local correlation method for scaling up Kohn-Sham (KS) density functional theory calculations using high-level exchange-correlation (XC) functionals. In ECDA, a system's XC energy is obtained by patching locally calculated, high-level XC energy densities over the entire system. Our previous formulation of ECDA is not variational, making it difficult to derive the analytical energy gradient. In this work, we present a fully variational formulation of ECDA and derive the analytical energy gradient. The challenge for making ECDA a variational method is that both partitioning the system's density and solving the system's XC potential are the optimized effective potential (OEP) problems. Simply regularizing these two OEP equations makes ECDA a nonvariational method. We show how to regularize these two OEP problems while still keeping ECDA variational. KS linear responses are involved in the calculations of the system's XC potential and the analytical energy gradients, but are not explicitly constructed. The terms involving the KS linear responses are calculated by solving the Sternheimer equation. The analytical energy gradients are validated with a Si2H6 molecule and are used to relax the geometry of Si6H10. In both examples, the exact exchange is used as the high-level XC functional and is patched over the molecules.