Coulson–Fischer theory

In theoretical chemistry and molecular physics, Coulson–Fischer theory provides a quantum mechanical description of the electronic structure of molecules. The 1949 seminal work of Coulson and Fischer[1] established a theory of molecular electronic structure which combines the strengths of the two rival theories which emerged soon after the advent of quantum chemistry - valence bond theory and molecular orbital theory, whilst avoiding many of their weaknesses. For example, unlike the widely used Hartree–Fock molecular orbital method, Coulson–Fischer theory provides a qualitatively correct description of molecular dissociative processes.[2] The Coulson–Fischer wave function has been said to provide a third way in quantum chemistry.[3] Modern valence bond theory is often seen as an extension of the Coulson–Fischer method.

Theory

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Coulson–Fischer theory is an extension of modern valence bond theory that uses localized atomic orbitals as the basis for VBT structures.[4] In Coulson-Fischer Theory, orbitals are delocalized towards nearby atoms. This is described for H2 as follows:[1]

where a and b are atomic 1s orbitals, that are used as the basis functions for VBT, and λ is a delocalization parameter from 0 to 1. The VB structures then use and as the basis functions to describe the total electronic wavefunction as

in obvious analogy to the Heitler-London wavefunction.[5] However, an expansion of the Coulson-Fischer description of the wavefunction in terms of a and b gives:

A full VBT description of H2 that includes both ionic and covalent contributions is

where ε and μ are constants between 0 and 1.

As a result, the CF description gives the same description as a full valence bond description, but with just one VB structure.[4]

References

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  1. ^ a b C.A. Coulson and I. Fischer, Notes on the Molecular Orbital Treatment of the Hydrogen Molecule, Phil. Mag. 40, 386 (1949)
  2. ^ S. Wilson and J. Gerratt, Calculation of potential energy curves for the ground state of the hydrogen molecule, Molec. Phys. 30, 777 (1975) https://doi.org/10.1080/14786444908521726
  3. ^ S. Wilson, On the Wave Function of Coulson and Fischer: A Third Way in Quantum Chemistry, in Advances in the Theory of Atomic and Molecular Systems, ed. P. Piecuch, J. Maruani, G. Delgado-Barrio and S. Wilson, Progress in Theoretical Chemistry and Physics 19, Springer (2009)
  4. ^ a b Shaik, Sason; Hiberty, Philippe C. (2007-11-16). A Chemist's Guide to Valence Bond Theory. Hoboken, NJ, USA: John Wiley & Sons, Inc. doi:10.1002/9780470192597. ISBN 978-0-470-19259-7.
  5. ^ "Heitler, W., & London, F. (1927). Wechselwirkung neutraler Atome und homopolare Bindung nach der Quantenmechanik. Zeitschrift für Physik, 44, 455-472. - References - Scientific Research Publishing"
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