Helium dimer dispersion forces and correlation potentials in density functional theory

Abstract

The dispersion interaction in the helium dimer is considered from the viewpoint of the force on a nucleus. At large internuclear separations, Brueckner coupled cluster BD(T) forces agree well with near-exact dispersion forces. The atomic density distortion associated with the dispersion force is quantified by comparing the BD(T) dimer density with a superposition of atomic densities. For density functional theory calculations in the Hartree–Fock–Kohn–Sham (HFKS) formalism, the accuracy of the dispersion force is governed by the correlation potential. Calculations using the conventional Lee–Yang–Parr [Phys. Rev. B 37, 785 (1988)] potential only generate a small density distortion, giving forces significantly smaller than BD(T). The BD(T) electron densities are therefore used to determine improved correlation potentials using a modified Zhao–Morrison–Parr (ZMP) approach [Phys. Rev. A 50, 2138 (1994)]. HFKS calculations using these ZMP potentials quantitatively reproduce the distortion, giving dispersion forces in good agreement with BD(T). The dimer ZMP correlation potential is partitioned into two parts, one equal to the sum of two unperturbed spherical atomic correlation potentials and the other representing an interaction potential. HFKS calculations using the former do not generate the distortion; forces are close to Hartree–Fock. Calculations using the latter do generate the distortion, giving forces essentially identical to those from the full dimer potential. The origin of the distortion is traced to the asymmetric structure of the interaction correlation potential in the vicinity of each nucleus.