Directly patching high-level exchange-correlation potential based on fully determined optimized effective potentials.

The key element in Kohn-Sham (KS) density functional theory is the exchange-correlation (XC) potential. We recently proposed the exchange-correlation potential patching (XCPP) method with the aim of directly constructing high-level XC potential in a large system by patching the locally computed, high-level XC potentials throughout the system. In this work, we investigate the patching of the exact exchange (EXX) and the random phase approximation (RPA) correlation potentials. A major challenge of XCPP is that a cluster's XC potential, obtained by solving the optimized effective potential equation, is only determined up to an unknown constant. Without fully determining the clusters' XC potentials, the patched system's XC potential is "uneven" in the real space and may cause non-physical results. Here, we developed a simple method to determine this unknown constant. The performance of XCPP-RPA is investigated on three one-dimensional systems: H, HLi, and the stretching of the H-H bond. We investigated two definitions of EXX: (i) the definition based on the adiabatic connection and fluctuation dissipation theorem (ACFDT) and (ii) the Hartree-Fock (HF) definition. With ACFDT-type EXX, effective error cancellations were observed between the patched EXX and the patched RPA correlation potentials. Such error cancellations were absent for the HF-type EXX, which was attributed to the fact that for systems with fractional occupation numbers, the integral of the HF-type EXX hole is not -1. The KS spectra and band gaps from XCPP agree reasonably well with the benchmarks as we make the clusters large.