The coupling constant averaged exchange–correlation energy density

ABSTRACT

The exchange–correlation energy, central to density-functional theory, may be represented in terms of the coupling constant averaged (CCA) exchange–correlation energy density. We present an approach to calculate the CCA energy density using accurate ab initio methods and its application to simple atomic systems. This function provides a link between intrinsically non-local, many-body electronic structure methods and simple local and semi-local density-functional approximations (DFAs). The CCA energy density is resolved into separate exchange and correlation terms and the features of each compared with those of quantities commonly used to construct DFAs. In particular, the more complex structure of the correlation energy density is found to exhibit features that align well with those present in the Laplacian of the density, suggesting its role as a key variable to be used in the construction of improved semi-local correlation functionals. The accurate results presented in this work are also compared with those provided by the Laplacian-dependent Becke–Roussel model for the exchange energy.

KEYWORDS:

• Energy densities
• density-functional theory
• exchange–correlation
• adiabatic connection
• coupled-cluster theory

Acknowledgements

The authors thank P. Gori-Giorgi and A. Mirtschink for fruitful discussions during this work. Andrew M. Teale is grateful for support from the Royal Society University Research Fellowship scheme. They are also grateful for access to the University of Nottingham High Performance Computing Facility.

Disclosure statement

No potential conflict of interest was reported by the authors.