Electron Correlation in the Ground State of Helium

Coulson, C. A.; Neilson, A. H.

doi:10.1088/0370-1328/78/5/328

Cited by 320 publications

(193 citation statements)

References 5 publications

Supporting

Mentioning

183

Contrasting

Order By: Relevance

“…This was the original intracule and was discussed in the seminal paper by Coulson and Neilson. 41 Unlike most of the others discussed in this article, it is a rigorous probability density and has been widely studied; see ref. 35 and 42 and references therein.…”

Section: Position Intracule P(u)mentioning

confidence: 99%

A family of intracules, a conjecture and the electron correlation problem

Gill

Crittenden

O’Neill

et al. 2006

Phys. Chem. Chem. Phys.

View full text Add to dashboard Cite

We present a radical approach to the calculation of electron correlation energies. Unlike conventional methods based on Hartree-Fock or density functional theory, it is based on the twoelectron phase-space information in the Omega intracule, a three-dimensional function derived from the Wigner distribution. Our formula for the correlation energy is isomorphic to the Hartree-Fock energy expression but requires a new type of four-index integral. Preliminary results, obtained using a model that is based on the known correlation energies of small atoms, are encouraging.

show abstract

Section: Position Intracule P(u)mentioning

confidence: 99%

A family of intracules, a conjecture and the electron correlation problem

Gill

Crittenden

O’Neill

et al. 2006

Phys. Chem. Chem. Phys.

View full text Add to dashboard Cite

show abstract

“…The benefit of calculation one -particle density distribution to evaluate the expectation value for oneparticle where n=(-1) [4,5] The inter-particle distribution function in position space is a measure of a probability of finding an electron on the distance between the two positions of the electrons in the same shell or in different shells and it is defined as [6]: (4) Inter-particle expectation value is given by the relation [7].…”

Section: Materials Methodsmentioning

confidence: 99%

Energy calculation for beryllium atom in different excited states (1s2 2s 3s), (1s 2s2 3s) and (1s 2s 3s2)

AL-Sharaa

Mahmood

Madhkoor³

et al. 2017

AIP Conference Proceedings

View full text Add to dashboard Cite

Abstract. The energy expectation value E has been evaluated for Beryllium different excited state and Be like ions such as B +1 and C +2 and the potential energy expectation value V has been evaluated too. The partitioning technique of Hartree-Fock (H-F) has been used for existing wave functions. The results show that the expectation values of and < r 12 -1 > of (1s2s 3s 2 ) ,(1s2s 2 3s) and (1s2s 3s 2 ) states increase when the atomic number (Z) increases for all shells for Be-like ions .All the studied properties are calculated using atomic units.

show abstract

“…In particular, the radial intracule density was used to study Fermi and Coulomb correlation by means of the corresponding density holes. 10,11 In the last years, several topological analyses of I(r) and E(R) densities and their Laplacian functions ٌ 2 I(r) and a͒ Electronic mail: quel@stark.udg.es b͒ Author to whom correspondence should be addressed. Electronic mail: j.mestres@organon.oss.akzonobel.nl…”

Section: ͑2͒mentioning

confidence: 99%

“…These kind of difference maps can be seen as a generalization of the Coulomb hole, originally defined as the difference between the radial intracule densities calculated with a given ab initio method and with the HF approximation. 10 The effect of Coulomb correlation can be better appreciated in the Laplacian difference maps. For instance, the Ϫٌ 2 ⌬I C͑CI-HF͒ map ͓Fig.…”

Section: The C 2 H 4 Moleculementioning

confidence: 99%

“…1 Recently, the analysis of the electron-pair density and related functions has also received increasing attention. [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] However, the fact that the electron-pair density ⌫(r 1 ,r 2 ) is a six-dimensional function, 2 makes it difficult to visualize and analyze directly. The analysis of electron intracule and extracule densities instead of the electron-pair density itself appears to be an interesting alternative.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The mapping of the local contributions of Fermi and Coulomb correlation into intracule and extracule density distributions

Fradera

Duran

Mestres³

2000

The Journal of Chemical Physics

View full text Add to dashboard Cite

The contributions of the correlated and uncorrelated components of the electron-pair density to atomic and molecular intracule I(r) and extracule E(R) densities and its Laplacian functions ٌ 2 I(r) and ٌ 2 E(R) are analyzed at the Hartree-Fock ͑HF͒ and configuration interaction ͑CI͒ levels of theory. The topologies of the uncorrelated components of these functions can be rationalized in terms of the corresponding one-electron densities. In contrast, by analyzing the correlated components of I(r) and E(R), namely, I C (r) and E C (R), the effect of electron Fermi and Coulomb correlation can be assessed at the HF and CI levels of theory. Moreover, the contribution of Coulomb correlation can be isolated by means of difference maps between I C (r) and E C (R) distributions calculated at the two levels of theory. As application examples, the He, Ne, and Ar atomic series, the C 2 Ϫ2 , N 2 , O 2 ϩ2 molecular series, and the C 2 H 4 molecule have been investigated. For these atoms and molecules, it is found that Fermi correlation accounts for the main characteristics of I C (r) and E C (R), with Coulomb correlation increasing slightly the locality of these functions at the CI level of theory. Furthermore, I C (r), E C (R), and the associated Laplacian functions, reveal the short-ranged nature and high isotropy of Fermi and Coulomb correlation in atoms and molecules.

show abstract

Electron Correlation in the Ground State of Helium

Cited by 320 publications

References 5 publications

A family of intracules, a conjecture and the electron correlation problem

A family of intracules, a conjecture and the electron correlation problem

Energy calculation for beryllium atom in different excited states (1s2 2s 3s), (1s 2s2 3s) and (1s 2s 3s2)

The mapping of the local contributions of Fermi and Coulomb correlation into intracule and extracule density distributions

Contact Info

Product

Resources

About