3,474 research outputs found
Leading-order behavior of the correlation energy in the uniform electron gas
We show that, in the high-density limit, restricted M{\o}ller-Plesset (RMP)
perturbation theory yields for the correlation energy per electron in the uniform electron gas,
where is the Seitz radius. This contradicts an earlier derivation which
yielded . The reason for the
discrepancy is explained.Comment: 4 pages, accepted for publication in Int. J. Quantum Che
Exact energy of the spin-polarized two-dimensional electron gas at high density
We derive the exact expansion, to , of the energy of the high-density
spin-polarized two-dimensional uniform electron gas, where is the Seitz
radius.Comment: 7 pages, 1 figure and 1 table, submitted to Phys. Rev.
The uniform electron gas
The uniform electron gas or UEG (also known as jellium) is one of the most
fundamental models in condensed-matter physics and the cornerstone of the most
popular approximation --- the local-density approximation --- within
density-functional theory. In this article, we provide a detailed review on the
energetics of the UEG at high, intermediate and low densities, and in one, two
and three dimensions. We also report the best quantum Monte Carlo and
symmetry-broken Hartree-Fock calculations available in the literature for the
UEG and discuss the phase diagrams of jellium.Comment: 37 pages, 8 figures, 8 tables, accepted for publication in WIRES
Computational Molecular Scienc
Correlation energy of two electrons in a ball
We study the ground-state correlation energy of two electrons of
opposite spin confined within a -dimensional ball () of radius .
In the high-density regime, we report accurate results for the exact and
restricted Hartree-Fock energy, using a Hylleraas-type expansion for the former
and a simple polynomial basis set for the latter. By investigating the exact
limiting correlation energy E_{\rm c}^{(0)} = \lim_{R \to 0} \Ec for various
values of , we test our recent conjecture [J. Chem. Phys. {\bf 131} (2009)
241101] that, in the large- limit, for
any spherically-symmetric confining external potential, where .Comment: 6 pages, 2 figure
Correlation energy of two electrons in the high-density limit
We consider the high-density-limit correlation energy \Ec in
dimensions for the ground states of three two-electron systems: helium
(in which the electrons move in a Coulombic field), spherium (in which they
move on the surface of a sphere), and hookium (in which they move in a
quadratic potential). We find that the \Ec values are strikingly similar,
depending strongly on but only weakly on the external potential. We
conjecture that, for large , the limiting correlation energy \Ec \sim
-\delta^2/8 in any confining external potential, where .Comment: 4 pages, 0 figur
Chemistry in One Dimension
We report benchmark results for one-dimensional (1D) atomic and molecular
systems interacting via the Coulomb operator . Using various
wavefunction-type approaches, such as Hartree-Fock theory, second- and
third-order M{\o}ller-Plesset perturbation theory and explicitly correlated
calculations, we study the ground state of atoms with up to ten electrons as
well as small diatomic and triatomic molecules containing up to two electrons.
A detailed analysis of the 1D helium-like ions is given and the expression of
the high-density correlation energy is reported. We report the total energies,
ionization energies, electron affinities and other interesting properties of
the many-electron 1D atoms and, based on these results, we construct the 1D
analog of Mendeleev's periodic table. We find that the 1D periodic table
contains only two groups: the alkali metals and the noble gases. We also
calculate the dissociation curves of various 1D diatomics and study the
chemical bond in H, HeH, He, H, HeH and
He. We find that, unlike their 3D counterparts, 1D molecules are
primarily bound by one-electron bonds. Finally, we study the chemistry of
H and we discuss the stability of the 1D polymer resulting from an
infinite chain of hydrogen atoms.Comment: 27 pages, 7 figure
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