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

Gill, Peter M. W.; Crittenden, Deborah L.; O’Neill, Darragh P.; Besley, Nicholas A.

doi:10.1039/b511472a

Cited by 68 publications

(101 citation statements)

References 50 publications

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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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“…We have conjectured 9 that an Omega correlation energy functional exists, i.e. E c ¼ F½Oðu; v; oÞ ð3:10Þ…”

Section: Intracule-based Correlation Modelsmentioning

confidence: 99%

“…9 We and others have explored the two-parameter correlation kernel Gðu; v; oÞ ¼ C s j 0 ðzsÞ ð 3:15Þ…”

Section: Intracule-based Correlation Modelsmentioning

confidence: 99%

Intracule functional models: I. Angle-corrected correlation kernels

Dumont

Crittenden

Gill

2007

Phys. Chem. Chem. Phys.

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“…35 The approach was also extended to describing bond dissociation through separation of long and short range correlation effects, 36 a scheme which has been previously applied to conventional density functionals. Gill has suggested several forms of intracule functionals, 33 among them is the Wigner intracule which was subsequently tested on a set of light atom diatomics. 37 Investigations continue into various intracule forms and their applicability.…”

Section: ( ) _ Jexc[p(r)]mentioning

confidence: 99%

“…Gill, 33 Giorgi, of two electrons. An analogous approach was suggested by Rassolov when he derived an expression for a Hartree-Fock electron correlation operator from the correlation energy of two-electron ions in the high density limit and the dense homogeneous electron gas.…”

Section: ( ) _ Jexc[p(r)]mentioning

confidence: 99%

Properties and applications of the average interparticle distance

Hollett

Poirier

2008

J Mol Model

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ewfoundland AbstractThe first and second moment operators are used to define the origin invariant shape and size of a molecule or functional group, as well as expressions for the distance between two electrons and the distance between an electron and a nucleus.The measure of molecular size correlates quite well with an existing theoretical measure of molecular volume calculated from isodensity contours. Also, the measure of size is effective in predicting steric effects of substituents which have been measured experimentally. The electron-electron and electron-nuclear distances are related to components of the Hartree-Fock energy. The average distance between two electrons models the Coulomb energy quite well, especially in the case of localized molecular orbitals. The average distance between an electron and a nucleus is closely related to the electron-nuclear attraction energy of a molecule.The relationships discovered between the average interparticle distances and molecular energy components have led to the development of a new empirical approach to modelling the electronic structure of molecules. The general energy expression for a simulated electronic structure theory is defined, along with the functional form of t he interatomic distance dependent energy functions. The theory is used to model the hydrogen molecule, the first-row hydrides, and ethane. The models, which have the correct RHF/6-31G(d) optimized geometries, also fit the RHF/6-31G(d) energy at equilibrium and the UHF /6-31G( d) energy at the bond dissociation limit, as well as some vibrational frequencies.Also directly related to the interelectronic distance, is the issue of electron correlation. Several new approaches to the electron correlation problem have emerged 11 in recent years. Among the new methods is orbital functional theory, in which the correlation energy is a functional of the molecular orbitals. The correlation energy of different isoelectronic series as a function of nuclear charge is investigated in an effort to design a correlation operator. Insight is also gained by examining the explicit CISD energy expression.Ill

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

Cited by 68 publications

References 50 publications

Ground state of two electrons on a sphere

Ground state of two electrons on a sphere

Intracule functional models: I. Angle-corrected correlation kernels

Properties and applications of the average interparticle distance

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