Abstract
The wave structure of the electron lends itself to the formulation of chemical phenomena in terms of number theory. Without a particle concept the behaviour of elementary units of matter, in the form of solitons, is described directly in the wave formalism originally proposed by Schrödinger and Madelung in hydrodynamic analogy. The quantum condition appears naturally as a minimum action principle. All atoms are alike with nuclei bathed in a uniform electronic fluid, the spherical wave structure of which is revealed by optimization on a logarithmic spiral. The density distribution pattern has much in common with the Bohr–de Broglie model of atomic structure and predicts a number of important atomic properties, including atomic size, ionization radius, electronegativity and atomic polarizability. The intimate connection between atomic properties and space-time curvature is convincingly demonstrated by derivation of atomic radii as a periodic function optimized on Fibonacci spirals. Details of covalent interaction are elucidated by the manipulation of ionization radii and the golden ratio as parameters to predict interatomic distance, bond order, dissociation energy, stretching force constant and dipole moments. Extended to molecules the matter-wave approach demonstrates that the concepts of structure and shape of a free molecule are strictly four-dimensional. Molecular structure observed and modelled in three dimensions only applies to condensed phases. Molecules involved in chemical change are essentially in the free state and their mode of interaction is not always obvious as a function of assumed three-dimensional structure. Proposed mechanisms for synthetic processes serve to rationalize the apparent discrepancies.
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Notes
- 1.
As understood in three-dimensional Euclidean space.
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Boeyens, J.C.A. (2013). Chemical Wave Structures. In: The Chemistry of Matter Waves. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7578-7_9
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