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Eigenvalues of saturated hydrocarbons

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Abstract

A simplified Hückel-type molecular-orbital (MO) model for the valence electrons of saturated hydrocarbons is proposed and the consequent eigenvalue spectrum considered. A first foundational result is obtained, which every chemist “knows”, namely that: alkanes are stable, with half their (Hückel-type MO) eigenvalues positive and half negative.

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Notes

  1. Amongst these “early mathematicians” one might also be tempted to include A. A. Cayley for his somewhat more widely recognized work on alkane enumeration [2]. But though he evidently learned of this matter from Sylvester [24], Cayley stuck with the ordinary molecular graph (as in Fig. 1), or yet more abbreviatedly with the H-deleted C-network graph.

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Authors and Affiliations

  1. Department of Marine Sciences, Texas A&M, Galveston, Galveston, TX, 77553, USA

    D. J. Klein

  2. Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA, 23284, USA

    C. E. Larson

Authors
  1. D. J. Klein
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  2. C. E. Larson
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Corresponding author

Correspondence to C. E. Larson.

Additional information

The authors acknowledge the Welch Foundation of Houston, Texas, for support for this research, via grant BD-0894.

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Klein, D.J., Larson, C.E. Eigenvalues of saturated hydrocarbons. J Math Chem 51, 1608–1618 (2013). https://doi.org/10.1007/s10910-013-0168-1

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  • DOI: https://doi.org/10.1007/s10910-013-0168-1

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