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Chemistry as a “Manifestation of Quantum Phenomena” and the Born–Oppenheimer Approximation?

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Molecular Electronic Structures of Transition Metal Complexes II

Part of the book series: Structure and Bonding ((STRUCTURE,volume 143))

Abstract

When considering the work of Carl Ballhausen on vibrational spectra, it is suggested that his use of the Born–Oppenheimer approximation is capable of some refinement and extension in the light of later developments. A consideration of the potential energy surface in the context of a full Coulomb Schrödinger Hamiltonian in which translational and rotational motions are explicitly considered would seem to require a reformulation of the Born–Oppenheimer approach. The resulting potential surface for vibrational motion should be treated, allowing for the rotational motion and the nuclear permutational symmetry of the molecule.

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Notes

  1. 1.

    This Hamiltonian results from the standard canonical quantization of electrodynamics if it is assumed that particle speeds are negligible compared to the speed of light, and all charge–photon interactions are discarded; the Coulomb gauge condition must also be imposed [8].

  2. 2.

    The work was completed in 1944 and was actually received by the journal in October 1948.

  3. 3.

    The discussion below is aimed at the general polyatomic case. The cases A = 1, A = 2, A = 3 (the nuclear configurations that define, respectively, a point, a line, and a plane) may be dealt with by special techniques that are not considered here as it would deflect the main thrust of the argument.

  4. 4.

    The eigenfunctions expand in integer powers of κ; most of the eigenvalues expand in even powers of κ.

  5. 5.

    Although it seems very likely that the special case of this approach, called in [2] the Longuet–Higgins approach, in which the nuclei are regarded as fixed in the electronic problem and as variables in the nuclear motion problem could be treated as above.

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Acknowledgments

Some of this work developed as part of ESA contract 21790/08/NL/HE and was carried out at the Universite Libre de Bruxelles. I thank the Fonds National de la Recherche Scientifique (F.R.S.-FNRS, contracts FRFC and IISN), the Universite libre de Bruxelles, and the “Action de Recherches Concertees de la Communaute francaise de Belgique” for accommodation and the provision of library and computing facilities.

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Authors and Affiliations

  1. Service de Chimie Quantique et Photophysique, Université Libre de Bruxelles, 1050, Bruxelles, Belgium

    Brian T. Sutcliffe

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  1. Brian T. Sutcliffe
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Correspondence to Brian T. Sutcliffe .

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Editors and Affiliations

  1. St. Edmund Hall, Oxford, OX1 4AR, United Kingdom

    David Michael P. Mingos

  2. The Royal Institution of Great Britain, Albermarle Street 21, London, W1X 4BS, United Kingdom

    Peter Day

  3. , Department of Chemistry, Technical University of Denmark, Building 207, Lyngby, 2800, Denmark

    Jens Peder Dahl

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Sutcliffe, B.T. (2011). Chemistry as a “Manifestation of Quantum Phenomena” and the Born–Oppenheimer Approximation?. In: Mingos, D., Day, P., Dahl, J. (eds) Molecular Electronic Structures of Transition Metal Complexes II. Structure and Bonding, vol 143. Springer, Berlin, Heidelberg. https://doi.org/10.1007/430_2011_44

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