On the nature of the correction to the Weizsacker term

Abstract

It is shown that the reduced first-order density matrix may be written as γ1(1, 2) = ρ1/2(1) ρ1/2(2)[1+B(1, 2)/ρ(1) ρ(2)]1/2. The function B(1, 2) is equal to −2γ2(1, 2; 1, 2) for the Hartree–Fock case so that the quotient inside the brackets is, in fact, the statistical correlation function, which describes the Fermi hole. For the general case (when correlation is included), it is shown that B(1, 2)≠−2γ2(1, 2; 1, 2); the quotient, however, is a function which describes Fermi and Coulomb correlation. It is shown that the kinetic energy density may be written as the Weizsacker term plus a correlation term given by 1/4 ρ(1)∇1 ∇2[B(1, 2)/ρ(1) (ρ(2)]2 → 1. In view of the relationship between B(1, 2) and the correlation function, the nature of the non-Weizsacker term is discussed.