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Chemistry by Number Theory

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Electronic Structure and Number Theory

Part of the book series: Structure and Bonding ((STRUCTURE,volume 148))

Abstract

Aspects of elementary number theory pertaining to the golden ratio and the golden spiral are shown to be related to and therefore of importance in the simulation of chemical phenomena. Readily derived concepts include atomic structure, electronegativity, bond order, the theory of covalent interaction and aspects of molecular chirality. The physical interpretation of the results implicates the 4D structure of space–time as a fundamental consideration. The implied classical nature of 3D molecular structure identifies molecular mechanics as an ideal method for structure optimization, based on parameters obtained by number theory. All results point at a 4D wave structure of electrostatic charge.

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Notes

  1. 1.

    Three hundred isotopes of 100 elements with \(Z/N = 1\) are synthesized by α-particle addition in massive stellar objects. In interstellar space radioactive decay terminates at 264 stable isotopes of 81 elements.

  2. 2.

    On release into interstellar space, radioactive decay results in the survival of only 264 stable nuclides as two sets of 81 with A = 2n and two sets of 51 with odd A.

  3. 3.

    Bond order, assumed to stipulate the number of electron pairs in covalent interaction, although a poor measure of bond strength [19–21], is a convenient general working model.

  4. 4.

    For the sake of simplicity, we do not consider degrees of chirality as distinguished e.g. by chirality functions [26–28].

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Acknowledgements

Financial support by the Alexander von Humboldt Foundation is gratefully acknowledged. We acknowledge the input of Casper Schutte during many informative discussions.

Author information

Authors and Affiliations

  1. Unit for Advanced Scholarship, University of Pretoria, Lynnwood Road, 0002, Pretoria, South Africa

    Jan C. A. Boeyens

  2. Anorganisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 270, 69120, Heidelberg, Germany

    Peter Comba

Authors
  1. Jan C. A. Boeyens
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  2. Peter Comba
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Corresponding author

Correspondence to Jan C. A. Boeyens .

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Editors and Affiliations

  1. , Unit for Advanced Scholarship, University of Pretoria, Lynnwood Road, Pretoria, 5100, South Africa

    Jan C.A. Boeyens

  2. Anorganisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 270, Heidelberg, 69120, Germany

    Peter Comba

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Boeyens, J.C.A., Comba, P. (2013). Chemistry by Number Theory. In: Boeyens, J., Comba, P. (eds) Electronic Structure and Number Theory. Structure and Bonding, vol 148. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31977-8_1

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