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Summary and Prospects

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Brillouin-Wigner Methods for Many-Body Systems

Part of the book series: Progress in Theoretical Chemistry and Physics ((PTCP,volume 21))

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Abstract

A summary of the present status of Brillouin–Wigner many-body methodology is given. Future prospects are assessed.

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Notes

  1. 1.

    The use of ‘Møller–Plesset’ or ‘Hartree–Fock model’ to label particular choices of zero-order Hamiltonian in many-body perturbation theory dates from the work of Pople et al. [2] and of Wilson and Silver [3]. In their original publication of 1934, Møller and Plesset [4] did not recognize the “many-body” character of the theory in the modern (post-Brueckner) sense.

  2. 2.

    See, for example, the monograph Electron correlation in molecules [5, 6] published by one of us in 1984 for an account of the then current thinking on the problems associated with quasi-degenerate diagrammatic perturbation theory.

  3. 3.

    In the monograph Electron correlation in molecules [5, 6] published by one of us in 1984, three solutions to the intruder state problem were offered:

  4. 4.

    See, for example, C.J. Cramer in his book Essentials of Computational Chemistry [33] writes

    “... ccsd(t)... has come to be the effective gold standard for single-reference calculations.” p. 226.

  5. 5.

    Even for molecules containing light atoms, properties depending on the wave function close to the nuclear region can require the use of a relativistic formalism.

  6. 6.

    There are many quantum chemistry packages available to the contemporary researcher. For a review of some of theses see reference [45].

  7. 7.

    Pople’s Nobel citation reads “for his development of computational methods in quantum chemistry”.

  8. 8.

    For a brief overview of the many applications of mp2 in contemporary molecular electronic structure studies see the recent report by one of us [45] which continues earlier reports on the subject [46–49].

  9. 9.

    When the electron group functions are associated with electron pairs this approach becomes the well known generalized valence bond method (gvb) [54].

  10. 10.

    Some algorithms exploit the relation between the modern valence bond wavefunction and the complete active space self-consistent field (cas-scf) functions. This leads to the so-called cas-vb approach [58–60].

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Authors and Affiliations

  1. Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynska Dolina F 1, 842 48, Bratislava, Solvakia

    Ivan Hubač

  2. Institute of Physics, Silesian University, 74601, Opava, Czech Republic

    Ivan Hubač

  3. Theoretical Chemistry Group Physical & Theoretical Chemistry Laboratory, University of Oxford, South Parks Road, Oxford, OX1 3QZ, United Kingdom

    Stephen Wilson

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Hubač, I., Wilson, S. (2010). Summary and Prospects. In: Brillouin-Wigner Methods for Many-Body Systems. Progress in Theoretical Chemistry and Physics, vol 21. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3373-4_5

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