Abstract:
Reviewed in historical context, bond order emerges as a vaguely defined
concept without a clear theoretical basis. As an alternative, the spherical standingwave
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.
