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The golden jubilee of the Coulson-Rushbrooke pairing theorem

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Abstract

The year 1990 marks the fiftieth anniversary of the much celebrated Pairing Theorem of Coulson and Rushbrooke. In its original form, the Theorem stated that for any altemant hydrocarbon: (1) the π-electron energy levels are symmetrically distributed about the zero energy level; (2) the LCAO-MO associated with the energy levelɛ i is the same as that belonging to the energy level -ɛ i except for a difference of sign (only) in every other atomic orbital coefficient; (3) the totalπ-electron charge density at any carbon atom in the molecule equals unity. Here, we trace the origins of this Theorem, describe its subsequent development, and outline some of its more significant uses. We conclude by discussing recent applications of the Theorem to positive and negative hydrocarbon ions, Möbius systems, and high-spin hydrocarbon species.

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Authors and Affiliations

  1. The King's School, CT1 2ES, Canterbury, Kent, UK

    R. B. Mallion

  2. Department of Chemistry, University of Georgia, 30602, Athens, Georgia, USA

    D. H. Rouvray

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  1. R. B. Mallion
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  2. D. H. Rouvray
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Mallion, R.B., Rouvray, D.H. The golden jubilee of the Coulson-Rushbrooke pairing theorem. J Math Chem 5, 1–21 (1990). https://doi.org/10.1007/BF01166272

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