Showing papers on "Thomas–Fermi model published in 1975"

Density functional theory of interacting closed shell systems. II. The determination of charge densities and the Hellman–Feynman theorem

Abstract: The density functional formalism and the additive density approximation are used to obtain the nonadditive contribution to the electron density of a set of closed shell atoms in the absence of external fields It is shown that due to the additive density approximation, the Hellman–Feynman theorem is violated when the force on the nucleus is examined The reason for this violation is discussed

Charge distribution in heterovalent alloys

Abstract: The selfconsistent charge density is calculated by means of the density functional formalism using a local exchange-correlation potential for a simple jellium model of a divalent impurity and a vacancy in a monovalent host. The resulting charge density around the impurity does not lend itself to an interpretation in terms of a surface dipole layer, though the dependence of the total charge transfer on the density is as predicted by the dipole model. The charge density inside a vacancy is found to be higher than that obtained by folding over a free surface; the calculated formation energy is an order of magnitude lower than typical experimental values. The validity of the Thomas-Fermi approximation for this model is discussed.

Linear response theory and molecular vibrations: The Thomas–Fermi model

Abstract: Instead of treating the density change Δρ (r) associated with molecular vibrations via a many electron response function and the change ΔV (r) in the nuclear potential due to the displacements, single‐particle potential theory is used to write Δρ (r) = Fdr′ F (r,r′) ΔV (r′). The linear response function F may be constructed exactly from the orbitals and eigenvalues Ei of the (unique) single‐particle potential that generates the exact single particle density V (r) in the equilibrium configuration. The argument that F is a functional of V implies F = F[ρ]. This in turn suggests extracting F from the Thomas–Fermi (TF) model and its refinements. The explicit form of F is given from (a) lowest order TF theory and (b) a theory that incorporates elements of higher order treatments. The linear response function found is formally similar to that derived from the free‐particle density matrix with suitable redefinition of the Fermi energy.