Physical Review A

Metric measures of interparticle interaction in an exactly solvable two-electron model atom

István Nagy, I. Aldazábal

Published Sep 26, 2011• 15 citations

Abstract

The exact ground-state solutions for the model of two particles in a confining harmonic oscillator potential interacting through a repulsive harmonic oscillator force are used from the standpoint of geometric distances [Phys. Rev. Lett. 106, 050401 (2011).] between wave functions and densities. The distances from the noninteracting reference state are calculated at a specified confinement by increasing the coupling of the interparticle interaction. Based on the analytic expressions for coupling-dependent geometric measures, a discussion of the Hohenberg-Kohn mapping is given.

DOI: 10.1103/physreva.84.032516

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Physical Review A

Metric measures of interparticle interaction in an exactly solvable two-electron model atom

István Nagy, I. Aldazábal

Published Sep 26, 2011• 15 citations

Publisher

Abstract

DOI: 10.1103/physreva.84.032516

Related papers

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r_{12}

). Here, we make a start on the dynamic generalization of the harmonic external potential, the motivation being the serious criticism levelled recently against the foundations of time-dependent density-functional theory (e.g. [J. Schirmer and A. Dreuw, Phys. Rev. A {\bf 75}, 022513 (2007)]). In this context, we derive a simplified expression for the time-dependent electron density for arbitrary interparticle interaction, which is fully determined by an one-dimensional non-interacting Hamiltonian. Moreover, a closed solution for the momentum space density in the Moshinsky model is obtained.

Using a Hartree-Fock-like partitioning of the two-matrix in terms of the true correlated one-matrix, the corresponding approximate ground-state energy

{E}_{0}

is calculated for an exactly solvable closed-shell system proposed earlier by Moshinsky [Am. J. Phys. 36, 52 (1968)]. Comparisons of

{E}_{0}

with the Hartree-Fock ground-state energy

{E}_{\mathrm{HF}}

and the exact ground-state energy

{E}_{\mathrm{ex}}

are made. These comparisons provide valuable insight into the usefulness of a Hartree-Fock-like partitioning of the two-matrix with repulsive interparticle potentials. In particular, an explicit quantification for the applicability limit of Lieb's [Phys. Rev. Lett. 46, 457 (1981)] bound ${E}_{0}\ensuremath{\geqslant}{E}_{\mathrm{HF}}$ with unbounded oscillator potentials is given.