Extended Huckel Theory and Molecular Hartree-fock Scf Theory.

نویسندگان

  • F P Boer
  • M D Newton
  • W N Lipscomb
چکیده

In the past several years a wide variety of molecules has been studied by means of the extended Htickel theory, which explicitly includes all overlaps between atomic orbitals and systematic guesses for the elements of the Hamiltonian matrix.1 These studies, in spite of their very approximate nature, have yielded a wealth of chemical information in terms of eigenvalues and eigenvectors: charge distributions and reactive sites, ionization potentials, rotational barriers, relative stabilities of isomers, stable molecular configurations, binding energies, etc. Unfortunately, a theoretical understanding of the extended Huckel method has lagged behind its often spectacular success. In this brief paper we address ourselves initially to understanding a small fragment of this success: ability to approximate binding energies. We also try to enumerate the serious errors involved in obtaining the eigenvalues, and come to the conclusion that in the present form of the method several large errors more or less cancel. We suggest that the extended Hfickel theory1 may be regarded as a method of simulating Hartree-Fock (HF) calculations by guessing the elements of the HF Hamiltonian matrix through the use of the Wolfsberg-Helmholz approximation. A critical examination of this method has been made possible by the availability of a diatomic wave function package.3 A sounder theoretical basis for the extended Huckel theory is obtained because nuclear repulsions N in the HF theory are shown to cancel approximately against half of the difference between molecular and atomic core energies, not, as expected,4 against electron-electron repulsions which are counted twice when eigenvalues are summed over electrons. This new observation is fortunate since the electron-electron term of the HF method is often a few times larger than the nuclear term.5' Define Eim as the core (kinetic plus electron-nuclear attraction) energy of an electron in the ith molecular orbital, 2(2Jij K1j) as the electron-electron interij action energy, A as the energy of atomization (negative for stable molecules), Eim as the eigenvalues of the one-electron HF Hamiltonian, and the new quantity A as (Eim E a) + N (where a refers to atoms). Now the HF closed-shell

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عنوان ژورنال:
  • Proceedings of the National Academy of Sciences of the United States of America

دوره 52 4  شماره 

صفحات  -

تاریخ انتشار 1964