  Accurate approximation of the exchange-correlation (XC) energy in density
functional theory (DFT) calculations is essential for reliably modelling
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 LDA and 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, demonstrated in real-space for the series of spherically-symmetric
atoms.
