Molecular Binding in Post-Kohn-Sham Orbital-Free DFT

Abstract

Molecular binding in post-Kohn–Sham orbital-free DFT is investigated, using noninteracting kinetic energy functionals that satisfy the uniform electron gas condition and which are inhomogeneous under density scaling. A parameter is introduced that quantifies binding, and a series of functionals are determined from fits to near-exact effective homogeneities and/or Kohn–Sham noninteracting kinetic energies. These are then used to investigate the relationship between binding and the accuracy of the effective homogeneity and noninteracting kinetic energy at the equilibrium geometry. For a series of 11 molecules, the binding broadly improves as the effective homogeneity improves, although the extent to which it improves is dependent on the accuracy of the noninteracting kinetic energy; optimal binding appears to require both to be accurate simultaneously. The use of a Thomas–Fermi–von Weizsäcker form, augmented with a second gradient correction, goes some way toward achieving this, exhibiting molecular binding on average. The findings are discussed in terms of the noninteracting kinetic potential and the Hellmann–Feynman theorem. The extent to which the functionals can reproduce the system-dependence of the near-exact effective homogeneity is quantified, and potential energy curves are presented for selected molecules. The study provides impetus for including density scaling homogeneity considerations in the design of noninteracting kinetic energy functionals.