Theoretica chimica acta

, Volume 38, Issue 4, pp 311–326 | Cite as

The evaluation of two-centre molecular integrals involving one-electron green's functions

  • Michael Blakemore
  • Gwynne A. Evans
  • John Hyslop


The numerical evaluation of certain two-centre molecular integrals involving one-electron Green's functions is considered. Considerable improvement is realized over earlier calculations when semi-analytic methods are employed using Fourier transforms to reduce the order of the multiple quadratures. The resulting triple integrals are evaluated using improved polar grids which yield almost machine accuracy on utilizing Gaussian quadrature prescriptions. For illustration, integrals arising from two alternative variational functionals are evaluated and the corresponding energy curves compared for the H2 + ion, thus providing an assessment of the validity of the Born-Oppenheimer separation embodied in one of the functionals.

Key words

Numerical integration Two-centre molecular integrals Green's functions 


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  1. 1.
    Hall,G.G., Hyslop,J., Rees,D.: Intern. J. Quantum Chem.4, 5 (1970)Google Scholar
  2. 2.
    Davis,P.J., Rabinowitz,P.:Numerical integration. Waltham, Mass.: Blaisdell 1967Google Scholar
  3. 3.
    Hyslop,J.: Theoret. Chim. Acta (Berl.)31, 189 (1973)Google Scholar
  4. 4.
    Stroud,A.H., Secrest,D.:Gaussian quadrature formulas. Englewood Cliffs, New Jersey: Prentice-Hall 1966Google Scholar
  5. 5.
    Harris,F.E., Michels,H.H.: Advan. Chem. Phys.13, 205 (1967)Google Scholar
  6. 6.
    Shanks,D.: J. Math. Phys.34, 1 (1955)Google Scholar
  7. 7.
    Alaylioglu,A., Evans,G.A., Hyslop,J.: J. Comp. Phys.13, 433 (1973)Google Scholar
  8. 8.
    Chisholm,J.S.R., Genz, A., Rowlands,G.: J. Comp. Phys.10, 284 (1972)Google Scholar
  9. 9.
    Levin,D.: Intern. J. Computer Math.3, 371 (1973)Google Scholar
  10. 10.
    Prosser,F.R., Blanchard,C.H.: J, Chem. Phys.36, 1112 (1962)Google Scholar
  11. 11.
    Geller,M.: J. Chem. Phys.36, 2424 (1962)Google Scholar
  12. 12.
    Laurenzi,B.J.: Intern. J. Quantum Chem.3, 489 (1969)Google Scholar
  13. 13.
    Gradshteyn,I.S., Ryzhik,I.M.:Tables of integrals, series and products. New York: Academic Press 1965Google Scholar
  14. 14.
    Abramowitz,M., Stegun,I.A.: Handbook of Mathematical Functions. New York: Dover Publications 1965Google Scholar
  15. 15.
    Powell,M.J.: Computer J.7, 155 (1964)Google Scholar
  16. 16.
    Wind,H.: J. Chem. Phys.42, 2371 (1965)Google Scholar

Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • Michael Blakemore
    • 1
  • Gwynne A. Evans
    • 1
  • John Hyslop
    • 1
  1. 1.Department of MathematicsUniversity of TechnologyLoughboroughEngland

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