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Keywords:

  • Rüdenberg's Integral Approximations;
  • Roothaan's “Restricted Hartree–Fock” Theory;
  • Implicit Multi-Center Integrations;
  • non-empirical Extended-Hückel Theory

Abstract

After having reviewed some pioneer integral approximations closely related to Rüdenberg's expansions of one- and two-electron orbital products, we apply the previously described “Implicit Multi-Center Integration” techniques on Roothaan's “restricted” Fock-matrix components over standard atomic orbital bases. The resulting compact forms are very similar to the well-known “Wolfsberg–Helmholz Conjecture” of “Extended-Hückel Theory,” which relates the various off-diagonal matrix elements of “restricted” Fock-type to their corresponding diagonal counterparts. In this way, a “nonempirical Extended-Hückel Theory” can be created. © 2012 Wiley Periodicals, Inc.