Distribution of r<sub>12</sub>· p<sub>12</sub>in quantum systems

Bernard, Yves; Loos, Pierre‐François; Gill, Peter M. W.

doi:10.1080/00268976.2013.811302

Cited by 7 publications

(7 citation statements)

References 65 publications

(87 reference statements)

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“…The correlation energy, E corr , is also provided in table 4, where we have assumed E FC ≈ E exact . The data presented are in excellent agreement with previously reported correlation energies where available [4,27,28]. The correlation energy, as a fraction of the total energy, increases monotonically as Z decreases.…”

Section: (B) Hartree-fock Energy and Electron Correlationsupporting

confidence: 91%

Hartree–Fock implementation using a Laguerre-based wave function for the ground state and correlation energies of two-electron atoms

King¹,

Baskerville²,

Cox³

2018

Phil. Trans. R. Soc. A.

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An implementation of the Hartree-Fock (HF) method using a Laguerre-based wave function is described and used to accurately study the ground state of two-electron atoms in the fixed nucleus approximation, and by comparison with fully correlated (FC) energies, used to determine accurate electron correlation energies. A variational parameter is included in the wave function and is shown to rapidly increase the convergence of the energy. The one-electron integrals are solved by series solution and an analytical form is found for the two-electron integrals. This methodology is used to produce accurate wave functions, energies and expectation values for the helium isoelectronic sequence, including at low nuclear charge just prior to electron detachment. Additionally, the critical nuclear charge for binding two electrons within the HF approach is calculated and determined to be=1.031 177 528.This article is part of the theme issue 'Modern theoretical chemistry'.

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Section: (B) Hartree-fock Energy and Electron Correlationsupporting

confidence: 91%

Hartree–Fock implementation using a Laguerre-based wave function for the ground state and correlation energies of two-electron atoms

King¹,

Baskerville²,

Cox³

2018

Phil. Trans. R. Soc. A.

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“…45 Constructed from the Nelectron wave function (approximate or exact), these reduced probability densities reveal information regarding the relative position, 1,4,7,24,38 momentum, 4,6,24,38 or position and momentum of electrons. 39,46 The analyses often involve the calculation of intracule holes, 1,47 which are the difference between the exact and the Hartree-Fock intracule. An intracule hole explicitly describes the effects of Coulomb correlation 48 on that particular intracule, and subsequent inferences are made regarding the correlated motion of the electrons.…”

Section: Introductionmentioning

confidence: 99%

Measuring correlated electron motion in atoms with the momentum-balance density

Todd,

Hollett

2020

Preprint

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Three new measures of relative electron motion are introduced: equimomentum, antimomentum, and momentum-balance. The equimomentum is the probability that two electrons have the exact same momentum, whereas the antimomentum is the probability their momenta are the exact opposite. Momentum-balance (MB) is the difference between the equimomentum and antimomentum, and therefore indicates if equal or opposite momentum is more probably in a system of electrons. The equimomentum, antimomentum and MB densities are also introduced, which are the local contribution to each quantity. The MB and MB density of the extrapolated-Full Configuration Interaction wave functions of atoms of the first three rows of the periodic table are analyzed, with a particular focus on contrasting the correlated motion of electrons with opposite and parallel spin. Coulomb correlation between opposite-spin electrons leads to a higher probability of equimomentum, whereas Fermi correlation between parallel-spin electrons leads to a higher probability of antimomentum. The local contribution to MB, given an electron is present, is a minimum at the nucleus and generally increases as the distance from the nucleus increases. There are also interesting similarities between the effects of Fermi correlation and Coulomb correlation (of opposite-spin electrons) on MB.

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“…9−17 Intracules are two-electron probability distribution functions. 10,13,16 The most common of which are the position, 18 P(u), and momentum intracules, 19 M(v)…”

Section: ■ Introductionmentioning

confidence: 99%

“…However, whether and how the electric field affects the relative momenta between two electrons has not yet been investigated. Theoretically, information regarding the relative momenta of electrons preionization can be obtained from intracules of the ground state electronic wave function. − …”

Section: Introductionmentioning

confidence: 99%

The Relative Alignment of Electron Momenta in Atoms and Molecules and the Effect of a Static Electric Field

Hollett

2017

J. Phys. Chem. A

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The relative momentum of electron pairs in atoms and small molecules is examined through calculation of the p · p probability distribution. The likelihood of aligned or antialigned momenta between paired electrons is determined from the calculated distributions. Coulomb correlation aligns the momenta of electron pairs, and the amount of alignment varies when considering momenta in specific directions in three-dimensional space. A static electric field is found to have competing effects on momentum alignment parallel and perpendicular to the electric field. However, the net effect of the electric field on alignment is significantly smaller than the effect of Coulomb correlation. Recent experimental advances suggest that such a correlation of electron momenta can now be measured directly using attosecond spectroscopic tools.

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Distribution of r₁₂· p₁₂in quantum systems

Cited by 7 publications

References 65 publications

Hartree–Fock implementation using a Laguerre-based wave function for the ground state and correlation energies of two-electron atoms

Hartree–Fock implementation using a Laguerre-based wave function for the ground state and correlation energies of two-electron atoms

Measuring correlated electron motion in atoms with the momentum-balance density

The Relative Alignment of Electron Momenta in Atoms and Molecules and the Effect of a Static Electric Field

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Distribution of r12· p12in quantum systems

Cited by 7 publications

References 65 publications

Hartree–Fock implementation using a Laguerre-based wave function for the ground state and correlation energies of two-electron atoms

Hartree–Fock implementation using a Laguerre-based wave function for the ground state and correlation energies of two-electron atoms

Measuring correlated electron motion in atoms with the momentum-balance density

The Relative Alignment of Electron Momenta in Atoms and Molecules and the Effect of a Static Electric Field

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Distribution of r₁₂· p₁₂in quantum systems