On the adiabatic connection method, and scaling of electron–electron interactions in the Thomas–Fermi limit

In this paper we examine three aspects of electron–electron scaling: (i) the electron–electron repulsions are only scaled in Thomas–Fermi theory; (ii) the electron–electron repulsions are scaled, and the one electron potential is adjusted to give a prescribed density, in Thomas–Fermi–Dirac theory; and (iii) new approaches to the adiabatic connection formulas are presented to help improve the exchange–correlation functional. A new generalized two-point expression is presented. Models (i) and (ii) are solved exactly.