Intracule functional models: I. Angle-corrected correlation kernels

Dumont, Élise; Crittenden, Deborah L.; Gill, Peter M. W.

doi:10.1039/b709513a

Cited by 23 publications

(22 citation statements)

References 18 publications

(23 reference statements)

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“…We believe that our results will be useful in the future development of accurate correlation functionals within density-functional theory [42,43] and intracule functional theory [44][45][46][47][48][49].…”

Section: Resultsmentioning

confidence: 99%

Ground state of two electrons on a sphere

Loos

Gill²

2009

Phys. Rev. A

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We have performed a comprehensive study of the singlet ground state of two electrons on the surface of a sphere of radius R. We have used electronic structure models ranging from restricted and unrestricted Hartree-Fock theory to explicitly correlated treatments, the last of which lead to near-exact wavefunctions and energies for any value of R. Møller-Plesset energy corrections (up to fifth-order) are also considered, as well as the asymptotic solution in the large-R regime.

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Section: Resultsmentioning

confidence: 99%

Ground state of two electrons on a sphere

Loos

Gill²

2009

Phys. Rev. A

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“…This kind of relation could be useful in the future development of intracule functional theory [43][44][45][46][47][48].…”

Section: Position Intraculementioning

confidence: 99%

Hooke’s law correlation in two-electron systems

Loos

2010

Phys. Rev. A

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We study the properties of the Hooke's law correlation energy (Ec), defined as the correlation energy when two electrons interact via a harmonic potential in a D-dimensional space. More precisely, we investigate the 1 S ground state properties of two model systems: the Moshinsky atom (in which the electrons move in a quadratic potential) and the spherium model (in which they move on the surface of a sphere). A comparison with their Coulombic counterparts is made, which highlights the main differences of the Ec in both the weakly and strongly correlated limits. Moreover, we show that the Schrödinger equation of the spherium model is exactly solvable for two values of the dimension (D = 1 and 3), and that the exact wave function is based on Mathieu functions.

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“…The Angle intracule of two non-interacting particles is entirely determined by the Jacobian factor and is [28] Υ 0 (ω) = 1 2 sin ω.…”

Section: Angle Intraculementioning

confidence: 99%

“…Based on the observation of Rassolov [26] that both relative position and relative momentum are important to describe the correlation between pairs of electrons, and because the Omega intracule contains information on both quantities, Ω(u, v, ω) has been extensively used in Intracule Functional Theory (IFT) [16,17,[27][28][29][30][31][32][33]. Appropriate integrations [16] reduce the Omega intracule to lower-order intracules such as P (u), M (v) and the Angle intracule [27,28] …”

Section: Introductionmentioning

confidence: 99%

Distribution of r₁₂· p₁₂in quantum systems

2013

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We introduce the two-particle probability density X(x) of x = r12 · p12 = (r1 − r2) · (p1 − p2). We show how to derive X(x), which we call the Posmom intracule, from the many-particle wavefunction. We contrast it with the Dot intracule [Y. A. Bernard, D. L. Crittenden, P. M. W. Gill, Phys. Chem. Chem. Phys., 10, 3447 (2008)] which can be derived from the Wigner distribution and show the relationships between the Posmom intracule and the one-particle Posmom density [Y. A. Bernard, D. L. Crittenden, P. M. W. Gill, J. Phys. Chem. A, 114, 11984 (2010)]. To illustrate the usefulness of X(x), we construct and discuss it for a number of two-electron systems.

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Intracule functional models: I. Angle-corrected correlation kernels

Cited by 23 publications

References 18 publications

Ground state of two electrons on a sphere

Ground state of two electrons on a sphere

Hooke’s law correlation in two-electron systems

Distribution of r₁₂· p₁₂in quantum systems

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Intracule functional models: I. Angle-corrected correlation kernels

Cited by 23 publications

References 18 publications

Ground state of two electrons on a sphere

Ground state of two electrons on a sphere

Hooke’s law correlation in two-electron systems

Distribution of r12· p12in quantum systems

Contact Info

Product

Resources

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Distribution of r₁₂· p₁₂in quantum systems