Nonlocal Functionals Inspired by the Strongly Interacting Limit of DFT: Exact Constraints and Implementation

Capturing
strong correlation effects remains a key challenge for
the development of improved exchange–correlation (XC) functionals
in density functional theory. The recently proposed multiple radii
functional (MRF) [J. Phys. Chem. Lett. 2017, 8, 2799; J. Chem. Theory Comput. 2019, 15, 3580] was designed to capture
strong correlation effects seamlessly, as its mathematical structure
draws from that of the exact XC functional in the limit of infinite
correlations. The MRF functional provides a framework for building
approximations along the density-fixed adiabatic connection, delivers
accurate XC energy densities in the standard DFT gauge (same as that
of the exact exchange energy density), and is free of one-electron
self-interaction errors. To facilitate the development of XC functionals
based on the MRF, we examine the behavior of the MRF functional when
applied to uniform and scaled densities and consider how it can be
made exact for the uniform electron gas. These theoretical insights
are then used to build improved forms for the fluctuation
function, an object that defines XC energy densities within
the MRF framework. We also show how the MRF fluctuation function for
physical correlation can be easily readjusted to accurately capture
the XC functional in the limit of infinite correlations, demonstrating
the versatility of MRF for building approximations for different correlation
regimes. We describe the implementation of MRF using densities expanded
on Gaussian basis sets, which improves the efficiency of previous
grid-based MRF implementations.