On representation of Coulomb integral by one‐electron functionals

A simple expression for the distance between two electrons, (δr12)ab, has been defined from one-electron expectation values. This value is calculated for triplet and singlet systems of two electrons, and closed-shell molecules of up to 58 electrons. When (δr12)ab is compared to the corresponding coulomb integral, Jab, an interesting relationship is observed. The relationship is followed extremely closely by all pairs of electrons, except for some deviations involving delocalized core–core electron pairs.

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Eine Beschreibung von Hückel-Parametern mit Hilfe von Kennzahlen / A Description of Hüchel Parameters by Use of Characterizing Indices

Zeitschrift für Naturforschung A ◽

10.1515/zna-1979-1211 ◽

1979 ◽

Vol 34 (12) ◽

pp. 1463-1466

Author(s):

J. Voitländer ◽

R. Brüggemann

Keyword(s):

General Expression ◽

Linear Equations ◽

Simple Graph ◽

Resonance Integral ◽

Effective Model ◽

Coulomb Integral ◽

Model Hamiltonian ◽

Non Linear ◽

Semiempirical Formula ◽

Non Linear Equations

Abstract In many cases simple graph theoretical eigenvalue methods suffice to explain properties of molecules. Introducing valuations or weights of graphs (e.g. Hückel-Coulomb-and Hückel-resonance integrals) one may ask how they are related to effective nuclear charges and bond distances.We are interested in whether such relations are bijective (injective and surjective) mappings. Injectivity and/or sujectivity can be characterized by indices, for instance “solution numbers” of non linear equations.Using as physically motivated starting points (I) a simple effective model Hamiltonian and (II) a semiempirical formula for β (resonance integral) and a general expression for α (Coulomb integral) we can show that the mappings resulting from (I) and (II) agree with respect to their indices. Therefore we conclude that omitted terms in (I) are immaterial with respect to the mapping properties.

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The electronic structure of conjugated systems II. Unsaturated hydrocarbons and their hetero-derivatives

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1947.0136 ◽

1947 ◽

Vol 192 (1028) ◽

pp. 16-32 ◽

Cited By ~ 280

Keyword(s):

Activation Energy ◽

Electronic Structure ◽

Theoretical Basis ◽

Electron Densities ◽

Unsaturated Hydrocarbons ◽

Conjugated Systems ◽

Coulomb Integral

The theory of Part I (Coulson & Longuet-Higgins 1947) is applied to hydrocarbons and their hetero-derivatives. An equation is given relating differences in activation energy to electron densities and atom polarizabilities (in the sense of Part I) for a heterolytic reaction at different positions in a conjugated system. The equations of Part I are then applied to hydrocarbons containing no odd-membered unsaturated rings. It has previously been shown that in such hydrocarbons all the electron densities are unity, and it is here proved that when one coulomb integral is altered slightly, the electron densities are alternately increased and decreased throughout the molecule. This fact is shown to provide a theoretical basis for the experimental law of alternating polarity in conjugated systems containing a hetero-atom.

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