Simple Fully Nonlocal Density Functionals for Electronic Repulsion Energy

Abstract

From a simplified version of the mathematical structure of the strong coupling limit of the exact exchange-correlation functional, we construct an approximation for the electronic repulsion energy at physical coupling strength, which is fully nonlocal. This functional is self-interaction free and yields energy densities within the definition of the electrostatic potential of the exchange-correlation hole that are locally accurate and have the correct asymptotic behavior. The model is able to capture strong correlation effects that arise from chemical bond dissociation, without relying on error cancellation. These features, which are usually missed by standard density functional theory (DFT) functionals, are captured by the highly nonlocal structure, which goes beyond the “Jacob’s ladder” framework for functional construction, by using integrals of the density as the key ingredient. Possible routes for obtaining the full exchange-correlation functional by recovering the missing kinetic component of the correlation energy are also implemented and discussed.

Investigation of the Exchange-Correlation Potentials of Functionals Based on the Adiabatic Connection Interpolation

“…The functionals of Refs. [25][26][27] are already very good candidate, although they pose new technical problems at the implementation level due to their non-local density dependence. If one wants to stay within…”

Sum-rules of the response potential in the strongly-interacting limit of DFT

“…[8][9][10] The study of this limit has inspired new approximations, based on the spherically averaged electron density. [11][12][13] In contrast with the more common LDA or GGA models for the xc hole, these approximations are fully non-local density functionals.…”

Restoring Size Consistency of Approximate Functionals Constructed from the Adiabatic Connection

“…A promising route in this direction is the construction of approximations by interpolating energy densities along the adiabatic connection, which requires non-local functionals for the strong-interaction limit 35,57 and/or for the λ = 1 case . 58 The Supporting Information is available free of charge on the ACS Publications website at DOI:.…”