Electron avoidance: A nonlocal radius for strong correlation

Abstract

We present here a model of the exchange-correlation hole for strongly correlated systems using a simple nonlocal generalization of the Wigner-Seitz radius. The model behaves similarly to the strictly correlated electron approach, which gives the infinitely correlated limit of density functional theory. Unlike the strictly correlated method, however, the energies and potentials of this model can be presently calculated for arbitrary geometries in three dimensions. We discuss how to evaluate the energies and potentials of the nonlocal model, and provide results for many systems where it is also possible to compare to the strictly correlated electron treatment.

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…”

“…18,19 More recently, new approximate functionals inspired to the SCE mathematical structure have been also proposed and tested. [25][26][27] They retain the nonlocality of SCE by using as key ingredient some integrals of the density, and their implementation in a self-consistent scheme is still the object of on-going work.…”

Exchange–Correlation Functionals via Local Interpolation along the Adiabatic Connection

“…In spite of the recent improvements, we still lack an algorithm that will solve the SCE problem for general 3D molecular geometries at low computational cost. However, a good candidate to approximate the SCE energy density in the gauge of the XC hole potential is the nonlocal radius functional (NLR), 43 which has been already implemented and used in ref (44). …”

“…A more practical way to proceed is to build approximations for the SCE functional inspired by its exact form, as it was done in the construction of the NLR functional. 43,44 …”

Functional derivative of the zero-point-energy functional from the strong-interaction limit of density-functional theory

“…The SCE solution unveils how the exact XC functional mathematically transforms the information on the electronic density into an expectation value of the electron-electron repulsion, even if only in the case of its λ → ∞ asymptotic expansion. Its investigation lead to the construction of new non-local density functionals, based on particular integrals of the density [15][16][17] rather than on the traditional ingredients of standard approximations (local density and gradients, occupied and unoccupied KS orbitals).…”