Covalent Interaction

Abstract

Reviewed in historical context, bond order emerges as a vaguely defined concept without a clear theoretical basis. As an alternative, the spherical standing-wave model of the extranuclear electronic distribution on an atom provides a simple explanation of covalent bond order as arising from the constructive and destructive interference of wave patterns. A quantitative measure derives from a number pattern that relates integer and half-integer bond orders through series of Fibonacci numbers, consistent with golden-spiral optimization. Unlike any previous definition of bond order, this approach is shown to predict covalent bond length, dissociation energy and stretching force constants for homonuclear interactions that are quantitatively correct. The analysis is supported by elementary number theory and involves atomic number and the golden ratio as the only parameters. Validity of the algorithm is demonstrated for heteronuclear interactions of any order. An exhaustive comparison of calculated dissociation energies and interatomic distance in homonuclear diatomic interaction, with experimental data from critical review, is tabulated. A more limited survey of heteronuclear interactions confirms that the numerical algorithms are generally valid. The large group of heteronuclear hydrides is of particular importance to demonstrate the utility of the method, and molecular hydrogen is treated as a special case. A simple formula that describes the mutual polarization of heteronuclear pairs of atoms, in terms of valence densities derived from a spherical-wave structure of extranuclear electronic charge, is used to calculate the dipole moments of diatomic molecules. Valence density depends on the volume of the valence sphere as determined by the atomic ionization radius, and the interatomic distance is determined by the bond order of the diatomic interaction. The results are in satisfactory agreement with literature data and should provide a basis for the calculation of more complex molecular dipole moments. The diatomic CO is treated as a special case, characteristic of all interactions traditionally identified as dative bonds.