3,071 research outputs found
Atomic and molecular intracules for excited states
Intracules in position space, momentum space and phase space have been calculated for low-lying excited states of the He atom, Be atom, formaldehyde and butadiene. The phase-space intracules (Wigner intracules) provide significantly more information than the position- and momentum-space intracules, particularly for the Be atom. Exchange effects are investigated through the differences between corresponding singlet and triplet states.This work was supported by the Engineering and Physical
Sciences Research Council through the award of an Advanced
Research Fellowship (GR/R77636) to NAB and a
Joint Research Equipment Initiative grant (GR/R62052)
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
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.
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
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
Resolutions of the Coulomb operator: VI. Computation of auxiliary integrals
We discuss the efficient computation of the auxiliary integrals that arise
when resolutions of two-electron operators (specifically, the Coulomb and
long-range Ewald operators) are employed in quantum chemical calculations. We
derive a recurrence relation that facilitates the generation of auxiliary
integrals for Gaussian basis functions of arbitrary angular momentum and
propose a near-optimal algorithm for its use
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
A Remarkable Identity Involving Bessel Functions
We consider a new identity involving integrals and sums of Bessel functions.
The identity provides new ways to evaluate integrals of products of two Bessel
functions. The identity is remarkably simple and powerful since the summand and
integrand are of exactly the same form and the sum converges to the integral
relatively fast for most cases. A proof and numerical examples of the identity
are discussed.Comment: 10 pages, 2 figure
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