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.