Some Remarks on Exchange Inhomogeneity Corrections in Many-Electron Systems

  • Irene B. Ortenburger
  • Frank Herman
Part of the The IBM Research Symposia Series book series (IRSS)


In the preceding paper Sham pointed out that a number of people have by now calculated the first principles value of the second order exchange inhomogeneity parameter β. Ma and Ortenburger1 find a value of 0.0011 (in the units of HVDO), Liberman2 finds 0.0016, while the nomencal work of Gel dart and Taylor3 would seem to support the smaller value. In any case the theoretical value for β is considerably smaller than the values obtained empirically by Herman, Van Dyke, and Ortenburger4,5 from self-consistent calculations for a number of representative atomic systems. In the work of HVDO the optimum value of β is found to be about 0.005; the inclusion of exchange inhomogeneity corrections with this coefficient leads to a considerable improvement in the total energy: this is lowered about half of the distance between the best energy obtained ignoring these corrections. and the exact Hartree-Fock total energy.


Order Term Atomic System Gradient Expansion Inhomogeneity Correction Atomic Krypton 
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  1. [1]
    S. Ma and I.B. Ortenburger, unpublished.Google Scholar
  2. [2]
    D.A. Liberman, private communication.Google Scholar
  3. [3]
    D.J.W. Gel dart and R. Taylor, Can. J. Phys. 48, 155 (1970).CrossRefGoogle Scholar
  4. [4]
    F. Herman, J.P. Van Dyke, and I.B. Ortenburqer, Phys. Rev. Letters 22, 807 (1969).CrossRefGoogle Scholar
  5. [5]
    F. Herman, I.B. Ortenburger, and J.P. Van Dyke, Intern J. Quantum Chem. IIIS, 827 (1970).Google Scholar

Copyright information

© Plenum Press, New York 1971

Authors and Affiliations

  • Irene B. Ortenburger
    • 1
  • Frank Herman
    • 1
  1. 1.IBM CorporationSan JoseUSA

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