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Methods of Electronic Structure Theory pp 79–127Cite as

The Self-Consistent Field Equations for Generalized Valence Bond and Open-Shell Hartree—Fock Wave Functions

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Part of the book series: Modern Theoretical Chemistry ((MTC,volume 3))

Abstract

The basic starting point for calculating ab initiowave functions of molecules is generally the Hartree—Fock (HF) wave function, which in the simplest case involves two electrons (one with each spin) in each orbital Φi with the total wave function antisymmetrized in order to satisfy the Pauli principle

$$ a[({\phi _{1}}\alpha )({\phi _{1}}\beta )({\phi _{2}}\alpha )({\phi _{2}}\beta )...({\phi _{n}}\alpha )({\phi _{n}}\beta )] = a[({\phi _{1}}{\phi _{1}}{\phi _{2}}{\phi _{2}}...{\phi _{n}}{\phi _{n}}\alpha \beta \alpha \beta ...\alpha \beta )] $$
((1))

Here a is the antisymmetrizer or determinant operator* and α and β are the usual spin functions. In Eq. (1) as elsewhere, we arrange products of spatial functions and spin functions in order of increasing electron numbers.

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Authors and Affiliations

  1. Arthur Amos Noyes Laboratory of Chemical Physics, California Institute of Technology, Pasadena, California, USA

    Frank W. Bobrowicz & William A. Goddard III

  2. Batelle Memorial Institute, Columbus, Ohio, USA

    Frank W. Bobrowicz

Authors
  1. Frank W. Bobrowicz
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  2. William A. Goddard III
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Editors and Affiliations

  1. University of California, Berkeley, USA

    Henry F. Schaefer III

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© 1977 Springer Science+Business Media New York

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Bobrowicz, F.W., Goddard, W.A. (1977). The Self-Consistent Field Equations for Generalized Valence Bond and Open-Shell Hartree—Fock Wave Functions. In: Schaefer, H.F. (eds) Methods of Electronic Structure Theory. Modern Theoretical Chemistry, vol 3. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0887-5_4

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  • DOI: https://doi.org/10.1007/978-1-4757-0887-5_4

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-0889-9

  • Online ISBN: 978-1-4757-0887-5

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