Abstract:
Molecular shape is recognized as an emergent property that complements
the projection fromfour-dimensional space-time to tangent Euclidean space. Projection
from hypercomplex algebra to real algebra necessitates the three-dimensional
definition of concepts such as chirality, quantum uncertainty and probability density
to compensate for errors of abstraction. The emergent alternative description
of extranuclear charge density as spherical standing waves, optimized by a golden
spiral, reveals atomic structure in line with the periodic table of the elements and
underpinning the concepts of bond order, interatomic distance and stretching force
constant, related to chemical interaction. The principles giving rise to molecular
structure are shown to depend, like bond order, on the constructive interference of
atomic wave fields, optimized by minimal adjustment to bond orders. The procedure
is shown to be equivalent to the philosophy of molecular mechanics. Arguments
based on the traditional interpretation of electronegativity, are presented to relate
the parameters of strain-free bond lengths, dissociation energies and harmonic force
constants, used in molecular mechanics, to quantum-mechanically defined ionization
radii of atoms. Atomic electron densities and a bond-order function, both obtained
by number-theory optimization, enable the direct calculation of interatomic
distance, dissociation energy and stretching force constant for all pairwise interactions
of any order. Torsional interaction determines the final shape of a molecule
and presumably can only be understood as a four-dimensional effect.
