AN INTERESTING RELATIONSHIP BETWEEN INTERELECTRONIC DISTANCE AND THE CORRESPONDING COULOMB INTEGRAL

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.

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

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.

Electronegativity and Electron Affinity

Various consequences of the supposition that the value of the resonance integral βAB depends on the nature of the bond are evaluated within the framework of the simple Hückel method. The resulting equation for βAB in function of the polarity 1 of the AB bond is:βAB =(1-I2)-½ [C+(½) ∫ (αA-αB)dI] where αX is the Coulomb integral. A solution is proposed corresponding with βAB = βAA ·βBB)½. Further elaboration then suggests that the simple Hückel method in this form is in favour of the ionic approximation to chemical bonding. The Coulomb integral turns out to be the electron affinity, which must now be considered as the electronegativity of elements when forming chemical bonds.