18,261 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)
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
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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