Intracule densities in the strong-interaction limit of density functional theory.
The correlation energy in density functional theory can be expressed exactly in terms of the change in the probability of finding two electrons at a given distance r(12) (intracule density) when the electron-electron interaction is multiplied by a real parameter lambda varying between 0 (Kohn-Sham system) and 1 (physical system). In this process, usually called adiabatic connection, the one-electron density is (ideally) kept fixed by a suitable local one-body potential. While an accurate intracule density of the physical system can only be obtained from expensive wavefunction-based calculations, being able to construct good models starting from Kohn-Sham ingredients would highly improve the accuracy of density functional calculations. To this purpose, we investigate the intracule density in the lambda --> infinity limit of the adiabatic connection. This strong-interaction limit of density functional theory turns out to be, like the opposite non-interacting Kohn-Sham limit, mathematically simple and can be entirely constructed from the knowledge of the one-electron density. We develop here the theoretical framework and, using accurate correlated one-electron densities, we calculate the intracule densities in the strong interaction limit for few atoms. Comparison of our results with the corresponding Kohn-Sham and physical quantities provides useful hints for building approximate intracule densities along the adiabatic connection of density functional theory.
Laboratoire de Chimie Théorique, CNRS, Université Pierre et Marie Curie, 4 Place Jussieu, F-75252 Paris, France. paola.gori-giorgi@lct.jussieu.fr
Paola
P
Gori-Giorgi
Michael
M
Seidl
Andreas
A
Savin
D000465:Algorithms; D001608:Beryllium / Q000737:chemistry*; D004583:Electrons; D006371:Helium / Q000737:chemistry*; D008958:Models, Molecular; D009010:Monte Carlo Method; D009356:Neon / Q000737:chemistry*; D011789:Quantum Theory
D006371:Helium; D009356:Neon; D001608:Beryllium