Patching the Exchange-Correlation Potential in Density Functional Theory.

Abstract

A method for directly patching exchange-correlation (XC) potentials in materials is derived. The electron density of a system is partitioned into subsystem densities by dividing its Kohn-Sham (KS) potential among the subsystems. Inside each subsystem, its projected KS potential is required to become the total system's KS potential. This requirement, together with the nearsightedness principle of electronic matters, ensures that the electronic structures inside subsystems can be good approximations to the total system's electronic structure. The nearsightedness principle also ensures that subsystem densities could be well localized in their regions, making it possible to use high-level methods to invert the XC potentials for subsystem densities. Two XC patching methods are developed. In the local XC patching method, the total system's XC potential is improved in the cluster region. We show that the coupling between a cluster and its environment is important for achieving a fast convergence of the electronic structure in the cluster region. In the global XC patching method, we discuss how to patch the subsystem XC potentials to construct the XC potential in the total system, aiming to scale up high-level quantum mechanics simulations of materials. Proof-of-principle examples are given.