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Local approximation for the hartree–fock exchange potential: a deformation approach
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In this paper, a method for deriving local approximations of the exchange term in the Hartree-Fock equation for a system of fermions interacting with a Coulomb-force is presented.Abstract:
We present a method for deriving local approximations of the exchange-term in the Hartree–Fock equation for a system of fermions interacting with a Coulomb-force. Within our model, we give a justification of the Slater-approximation where the exchange-term is replaced by the third root of the local density. Our approach is based on deformations, i.e. local scaling transformations of a constant density, combined with the "high density limit" of infinite number of particles.read more
Citations
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Multiple bound states for the Schroedinger-Poisson problem
Antonio Ambrosetti,David Ruiz +1 more
TL;DR: In this paper, the authors studied the problem where u, V : Ω3 → ℝ are radial functions, λ > 0 and 1 < p < 5, and gave multiplicity results depending on p and on the parameter λ.
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On the Schrödinger–Poisson–Slater System: Behavior of Minimizers, Radial and Nonradial Cases
TL;DR: In this paper, a lower bound for Coulomb energy was obtained for the static case ω = 0, where ω ∈ (2,3) for both radial and non-radial cases.
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Existence of least energy nodal solution for a Schrödinger–Poisson system in bounded domains
TL;DR: In this paper, the existence of least energy nodal solution for a class of Schrodinger-Poisson systems with nonlinearity having a subcritical growth was proved for a bounded domain.
Journal ArticleDOI
Infinitely many positive solutions for the nonlinear schrödinger–poisson system
TL;DR: In this paper, it was shown that (0.1) has infinitely many nonradial positive solutions if b < 0, or if b ≥ 0 and 2m < n.
Journal ArticleDOI
Existence of least energy nodal solution for a Schr\"odinger-Poisson system in bounded domains
TL;DR: In this article, the existence of least energy nodal solution for a class of Schrodinger-Poisson systems in a bounded domain with nonlinearity having a subcritical growth was proved.
References
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Journal ArticleDOI
Self-Consistent Equations Including Exchange and Correlation Effects
Walter Kohn,L. J. Sham +1 more
TL;DR: In this paper, the Hartree and Hartree-Fock equations are applied to a uniform electron gas, where the exchange and correlation portions of the chemical potential of the gas are used as additional effective potentials.
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Density-functional exchange-energy approximation with correct asymptotic behavior.
TL;DR: This work reports a gradient-corrected exchange-energy functional, containing only one parameter, that fits the exact Hartree-Fock exchange energies of a wide variety of atomic systems with remarkable accuracy, surpassing the performance of previous functionals containing two parameters or more.
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A Simplification of the Hartree-Fock Method
TL;DR: In this article, the Hartree-Fock equations can be regarded as ordinary Schrodinger equations for the motion of electrons, each electron moving in a slightly different potential field, which is computed by electrostatics from all the charges of the system, positive and negative, corrected by the removal of an exchange charge, equal in magnitude to one electron, surrounding the electron whose motion is being investigated.
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Note on Exchange Phenomena in the Thomas Atom
TL;DR: In this paper, the electrons are regarded as forming a perfect gas satisfying the Fermi statistics and occupying the region of phase space of lowest energy, with two opposite spins in each volume (2πh)3, and the remainder is assumed to be empty.
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Correlation Energy of an Electron Gas at High Density
TL;DR: In this paper, the correlation energy per particle of an electron gas expressed in rydbergs is computed for small values of rs (high density) and found to be given by ec=Alnrs+C+O(rs).