Ab Initio Calculation of Coupling-Constant Averaged Exchange–Correlation Holes for Spherically Symmetric Atoms

Accurate approximation of the exchange-correlation (XC) energy in density functional theory (DFT) calculations is essential for reliably modeling electronic systems. Many such approximations are developed from models of the XC hole; accurate reference XC holes for real electronic systems are crucial for evaluating the accuracy of these models however the availability of reliable reference data is limited to a few systems. In this study, we employ the Lieb optimization with a coupled cluster singles and doubles (CCSD) reference to construct accurate coupling-constant averaged XC holes, resolved into individual exchange and correlation components, for five spherically symmetric atoms: He, Li, Be, N, and Ne. Alongside providing a new set of reference data for the construction and evaluation of model XC holes, we compare our data against the exchange and correlation hole models of the established local density approximation (LDA) and Perdew-Burke-Ernzerhof (PBE) density functional approximations. Our analysis confirms the established rationalization for the limitations of LDA and the improvement observed with PBE in terms of the hole depth and its long-range decay, which is demonstrated in real-space for this series of spherically symmetric atoms.