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<p>(Semi-)local density functional approximations (DFAs) are the workhorse electronic structure methods in
condensed matter theory and surface science. The correlation energy density εc(r) (a spatial function that
yields the correlation energy Ec upon integration) is central to defining such DFAs. Unlike Ec, εc(r) is not
uniquely defined, however. Indeed, there are infinitely many functions that integrate to the correct Ec for
a given electron density ρ. The challenge for constructing useful DFAs is thus to find a suitable connection
between εc(r) and ρ. Herein, we present a new such approach by deriving εc(r) directly from the coupled-
cluster (CC) energy expression. The corresponding energy densities are analyzed for prototypical two-electron
systems. To explore their usefulness for designing DFAs, we construct a semilocal functional to approximate
the numerical CC correlation energy densities. Importantly, the energy densities are not simply used as
reference data, but guide the choice of the functional form, leading to a remarkably simple and accurate
correlation functional for the Helium isoelectronic series.
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Power Laws Used to Extrapolate the Coupled Cluster Correlation Energy to the Thermodynamic Limit
