Exchange-Correlation Energy Densities from Coupled Cluster Theory
Johannes T. Margraf
Chair of Theoretical Chemistry, Technical University of Munich
(Semi-)local density functional approximations (DFAs) are the workhorse electronic
structure methods in condensed matter theory and surface science. Central to defining
such DFAs is the exchange-correlation energy density exc , a spatial function that
yields the exchange-correlation energy Exc upon integration.
Unlike Exc , exc is not uniquely defined. Indeed, there are infinitely many functions
that integrate to the correct Exc for a given electron density p . The challenge for
constructing a useful DFA is to find a systematic connection between p and εxc . While several empirical and rigorous approaches to this problem are known, there has
been little innovation with respect to the fundamental functional forms of DFAs in
recent years.
Herein, we discuss a less explored route to constructing DFAs. Specifically, a recipe
for deriving exc directly from many-body wavefunctions is presented. The
corresponding energy densities are analyzed and (semi-)local approximations are
presented. The extension to non-local DFAs will be discussed.