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Spherical-Harmonic Expansion Techniques for Multicenter Integrals over STO’s. A Re-Examination for Vector Processing Computers

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ETO Multicenter Molecular Integrals
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Abstract

In multicenter integral calculations, it is useful to express an atomic orbital as a spherical-harmonic expansion about a point displaced from the orbital’s center. Through judicious choice of these expansion points, it is possible to calculate the general electron-repulsion integral for orbitals displaced at most by distances of the order of the bond lengths.

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References

  1. Coolidge, A.S.: 1932, Phys. Rev. 42, p. 189.

    Article  CAS  Google Scholar 

  2. Landshoff, R.: 1936, Z. Physik 102, p. 201.

    Article  CAS  Google Scholar 

  3. Barnett, M.P. and Coulson, C.A.: 1951, Phil. Tran. Soc. (London) 243, p. 221.

    Article  Google Scholar 

  4. Harris, F.E. and Michels, H.H.: 1965, J. Chem. Phys. 43, p. 165.

    Article  Google Scholar 

  5. Harris, F.E. and Michels, H.H.: 1966, J. Chem. Phys. 45, p. 116.

    Article  CAS  Google Scholar 

  6. Harris, F.E. and Michels, H.H.: 1967, Adv. Chem. Phys. 13, Prigogine, I. (Ed.), Interscience.

    Google Scholar 

  7. Shavitt, I. and Karplus, M.: 1962, J. Chem. Phys. 36, p. 550.

    Article  CAS  Google Scholar 

  8. Shavitt, I.: 1963, Meth. in Compt. Physics 2, B. Adler, et. al. (Eds.), Academic Press.

    Google Scholar 

  9. Shavitt, I. and Karplus, M.: 1965, J. Chem. Phys. 43, p. 398.

    Article  CAS  Google Scholar 

  10. Bonham, R.A., Peacher, J.L. and Cox, H.L.: 1964, J. Chem. Phys. 40, p. 3083.

    Article  CAS  Google Scholar 

  11. Monkhorst, H.J. and Harris, F.E.: 1972, Int. J. Quantum Chem. 6, p. 601.

    Article  CAS  Google Scholar 

  12. Graovac, A., Monkhorst, H.J. and Zivkovic, T.: 1973, Int. J. Quantum Chem. 7, p. 233.

    Article  Google Scholar 

  13. Silverstone, H.J.: 1968, J. Chem. Phys. 48, p.4098, 4106, 4108.

    Google Scholar 

  14. Silverstone, H.J.: 1969, J. Chem. Phys. 51, p. 956, 4287.

    Article  Google Scholar 

  15. Silverstone, H.J.: 1970, J. Chem. Phys. 53, p. 4169.

    Google Scholar 

  16. Silverstone, H.J. and Kay, K.G.: 1969, J. Chem. Phys. 50, p. 5045.

    Article  CAS  Google Scholar 

  17. Boys, S.F.: 1950, Proc. Roy. Soc. A (London) 200, p. 542.

    Article  CAS  Google Scholar 

  18. Boys, S.F.: 1960, Proc. Roy. Soc. A (London) 258, p. 402.

    Article  Google Scholar 

  19. Browne, J.C. and Poshusta, R.D.: 1962, J. Chem. Phys. 36, p. 1933.

    Article  CAS  Google Scholar 

  20. Harris, F.E.: 1963, Rev. Mod. Phys. 35, p. 558.

    Article  CAS  Google Scholar 

  21. Krauss, M.: 1963, J. Chem. Phys. 38, p. 564.

    Article  CAS  Google Scholar 

  22. Dunning, Jr., T.H. and Hay, P.J.: 1977, Methods of Electronic Structure Theory III, Schaefer, H.F. (Ed.), Plenum Press.

    Google Scholar 

  23. Krishnan, R., Hinkley, J.S. and Pople, J.A.: 1980, J. Chem. Phys. 72, p. 650. (Also see previous papers in this series.)

    Google Scholar 

  24. Harris, F.E.: 1963, Rev. Mod. Phys. 35, p. 558.

    Article  CAS  Google Scholar 

  25. Löwdin, P.O.: 1956, Adv. Phys. 5, p.l.

    Article  Google Scholar 

  26. Sharma, R.R.: 1976, Phys. Rev. A 13, p. 517.

    Article  Google Scholar 

  27. Jones, H.W. and Weatherford, C.A.: 1978, Int. J. Quantum Chem. Symp. 12, p. 483.

    CAS  Google Scholar 

  28. Johnson, P.: Feb., 1978, Comp. Design, 89.

    Google Scholar 

  29. Ruedenberg, K.: 1967, Theor. Chin. Acta 7, p. 359.

    Article  Google Scholar 

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© 1982 D. Reidel Publishing Company, Dordrecht, Holland

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Michels, H.H. (1982). Spherical-Harmonic Expansion Techniques for Multicenter Integrals over STO’s. A Re-Examination for Vector Processing Computers. In: Weatherford, C.A., Jones, H.W. (eds) ETO Multicenter Molecular Integrals. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-7921-5_10

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  • DOI: https://doi.org/10.1007/978-94-009-7921-5_10

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-009-7923-9

  • Online ISBN: 978-94-009-7921-5

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