Molecular Shape

Abstract

Molecular shape is recognized as an emergent property that complements the projection from four-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 define 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.