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Ergodicity and Rapid Electron Delocalization - The Dynamical Mechanism of Atomic Reactivity and Covalent Bonding

Journal article
Authors Sture Nordholm
William Eek
Volume 111
Issue 9
Pages 2072-2088
ISSN 0020-7608
Publication year 2011
Published at Department of Chemistry
Pages 2072-2088
Language en
Keywords covalent bonding, atomic reactivity, ergodicity, thomas-fermi theory
Subject categories Chemical Sciences


Surprisingly, the historical development of the understanding of the concept of covalent bonding is incomplete and the physical mechanism responsible for bonding is still the subject of debate among chemists. We argue that this is primarily due to the key role played by quantum mechanics and the peculiarity of the Coulomb interaction operating between the electrons and nuclei in molecules. A study of the simplest molecules H and H2 as well as the π-electron structure of planar conjugated hydrocarbon molecules leads to the conclusion that delocalization of electron dynamics is the key mechanism of covalent bonding. We find that the new concept of quantum ergodicity defined in terms of the globality of the energy eigenfunctions relates directly to covalent bonding. This is illustrated in the Höckel model of the π-electrons in polyene molecules. An understanding results associating covalent bonding most fundamentally with the relaxation of nonergodic dynamical constraints upon the electron dynamics in atoms and molecules. The strain energy present due to these constraints can be crudely estimated by the comparison of the results of Thomas-Fermi (TF) density functional calculations, which can be carried out both with and without these constraints. We present results for the light atoms H through Ar indicating that there is a very considerable strain in most atoms with the exception of the inert gas atoms. For the atoms H through Ne, we can verify this picture by direct comparison of ergodic TF and self-consistent field-molecular orbital (SCF-MO) results. Comparison with atomization energies for some small molecules shows that due to repulsive mechanisms only a small fraction of the covalent strain energy is actually realized as binding energy in most molecules. The hydride molecules appear to be most efficient in utilizing the strain energy.

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