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Computational Bottlenecks in Molecular Orbital Calculations

  • H. Bernhard Schlegel
  • Michael J. Frisch
Part of the NATO ASI Series book series (ASIC, volume 339)

Abstract

This Chapter examines some of the major steps in molecular orbital calculations, such as energies and gradients at SCF, MCSCF, MPn, CI, CC and QCI levels and SCF second derivatives. The emphasis is on the computational requirements rather than the details of the theory. Specifically cpu times, memory size and disk usage are considered for integral evaluation and transformation, solution of the SCF, CPHF and configuration interaction problems, and calculation of energy derivatives. Conventional, direct and semi-direct algorithms are compared and some guidelines for choosing between them are given.

Keywords

Configuration Interaction Spin Orbital Self Consistent Field Molecular Orbital Calculation Electron Integral 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Hehre, W. J., Radom, L., Schleyer, P. vR., and Pople, J. A., Ab Initio Molecular Orbital Theory, Wiley-Interscience, New York, 1986.Google Scholar
  2. 2.
    Szabo, A. and Ostlund, N. S., Modem Quantum Chemistry: Introduction to Advanced Electronic Structure Theory, Macmillan, New York, 1982.Google Scholar
  3. 3.
    R. McWeeny and Craig, D. P., Methods of Molecular Quantum Mechanics, Academic Press, London, 1989.Google Scholar
  4. 4.
    Wilson, S., Electron Correlation in Molecules, Clarendon Press, Oxford, 1984.Google Scholar
  5. 5.
    Daudel, R., Leroy, G., Peeters, D. and Sana, M., Quantum Chemistry, WileyInterscience, Chichester, 1983.Google Scholar
  6. 6.
    Jørgensen, P. and Simons, J., Second Quantization -Based Methods in Quantum Chemistry, Academic Press, New York, 1981.Google Scholar
  7. 7.
    Born, M. and Oppenheimer, J. R., Ann. Physik, 84, 457 (1927).CrossRefGoogle Scholar
  8. 8.
    Hartree, D. R. Proc. Cambridge Phil. Soc., 24, 89, 11, 426 (1928); Fock, V. Z. Phys., 61, 126, (1930); 62, 795, (1930); 75, 622, (1932).Google Scholar
  9. 9.
    Slater, J. C., Phys. Rev., 34, 1293 (1929); 35, 509 (1930).Google Scholar
  10. 10.
    Boys, S. F., Proc. Roy. Soc. (London), A200 542 (1950); for a discussion of the utility of gaussians in quantum chemistry see Shavitt,I.,Methods in Computational Physics, vol 2, Wiley, New York, 1962.Google Scholar
  11. 11.
    Slater, J. C., Phys. Rev., 36, 57 (19309)Google Scholar
  12. 12.
    Head-Gordon, M. and Pople, J. A., J. Chem. Phys., 89, 5777 (1988) and references therein.CrossRefGoogle Scholar
  13. 13.
    Bauschlicher, C. W. Theor. Chim. Acta, 76, 187 (1989).CrossRefGoogle Scholar
  14. 14.
    Roothaan, C. C. J., Rev. Mod. Phys., 23, 69 (1951); Hall, G. G., Proc. Roy. Soc. (London), A205, 541 (1951).Google Scholar
  15. 15.
    For a discussion of SCF stability and convergence see Schlegel, H. B.; McDouall, J. J. W. in Computational Advances in Organic Reactions, Ögretir, C. Csizmadia, I. G., eds., (Kluwer Academic, the Netherlands), 1990.Google Scholar
  16. 16.
    For a review of MCSCF methods see Werner, H. -J. Adv. Chem. Phys., 69, 1 (1987); Shepard, R. Adv. Chem. Phys., 69, 63 (1987); Roos, B. O., Adv. Chem. Phys., 69, 399 (1987).Google Scholar
  17. 17.
    Almlöf, J.; Korsell, K.; Faegri, K., Jr. J. Comput. Chem., 3, 385 (1982).CrossRefGoogle Scholar
  18. 18.
    Frisch, M. J.; Head-Gordon, M.; Trucks, G.; Foresman, J. B.; Schlegel, H. B.; Raghavachari, K.; Robb, M. A.; Binkley, J. S.; Gonzalez, C.; DeFrees, D. J.; Fox, D. J.; Whiteside, R. A.; Seeger, R.; Melius, C. F.; Baker, J.; Martin, L. R.;Kahn, L. R.; Stewart, J. J. P.; Fluder, E. M.; Topiol, S.; Pople, J. A. GAUSSIAN 90, Gaussian, Inc., Pittsburgh PA, 1990.Google Scholar
  19. 19.
    For some reviews of analytical gradients see Pulay, P., Adv. Chem. Phys., 69, 241 (1987); Jørgensen, P., and Simons, J. (Eds.), Geometrical Derivatives of Energy Surfaces and Molecular Properties,Reidel, Dordrecht, 1986; Gaw, J. F., and Handy, N. C., Annu. Rep. Prog. Chem. Sec. C, 81, 291 (1985); Fogarasi, G., and Pulay, P., Annu. Rev. Phys. Chem., 35, 191 (1984).Google Scholar
  20. 20.
    Schlegel, H. B., Adv. Chem. Phys., 67, 249 (1987).CrossRefGoogle Scholar
  21. 21.
    Kato, S.; Morokuma, K. Chem. Phys. Lett., 65, 19 (1979); Dupuis, M. J. Chem. Phys., 74, 5758 (1981); Osamura, Y.; Yamagichi, Y.; Schaefer III, H. F. J. Chem. Phys., 75, 2919 (1981); 77, 383 (1982); Schlegel, H. B.; Robb, M. A. Chem. Phys. Lett., 93, 43 (1982).Google Scholar
  22. 22.
    Pople, J. A.; Krishnan, R.; Schlegel, H. B.; Binkley, J. S. Int. J. Quantum Chem., Quantum Chem. Symp., 13, 225 (1979).Google Scholar
  23. 23.
    Gerratt, J.; Mills, I. M. J. Chem. Phys., 49, 1719, 1730 (1968).CrossRefGoogle Scholar
  24. 24.
    Osamura, Y.; Yamagichi, Y.; Schaefer III, H. F. J. Chem. Phys., 77, 383 (1982).CrossRefGoogle Scholar
  25. 25.
    Frisch, M. J.; Head-Gordon, M.; Pople, J. A. Chem. Phys. Lett., 141, 189 (1990).Google Scholar
  26. 26.
    Møller, C.; Plesset, M. S. Phys. Rev., 46, 618 (1934).CrossRefGoogle Scholar
  27. 27.
    For a review of MBPT and coupled cluster methods see Bartlett, R. J. Annu. Rev. Phys. Chem., 32 359 (1981).CrossRefGoogle Scholar
  28. 28.
    Brillouin, L., Actualities Sci, Ind., 71, 159 (1934).Google Scholar
  29. 29.
    Taylor, P. R. Int. J. Quantum Chem., 31, 521 (1987); Saebo, S.; Almlöf, J. Chem. Phys. Lett., 154, 83 (1989); Head-Gordon, M.; Pople, J. A.; Frisch, M. J. Chem. Phys. Lett., 153, 503 (1989).Google Scholar
  30. 30.
    Frisch, M. J.; Head-Gordon, M.; Pople, J. A. Chem. Phys. Lett., 166, 275, 281 (1990).CrossRefGoogle Scholar
  31. 31.
    Rice, J. E.; Amos, R. D. Chem. Phys. Lett., 122, 585 (1985); Simandiras, E. D.; Amos, R. D.; Handy, N. C. Chem. Phys., 114, 9 (1987)Google Scholar
  32. 32.
    Handy, N. C., and Schaefer, H. F., J. Chem. Phys., 81, 5031 (1984).CrossRefGoogle Scholar
  33. 33.
    Krishnan, R.; Pople, J. A. Int. J. Quantum Chem., 14, 91 (1978); Krishnan, R.; Frisch, M. J.; Pople, J. A. J. Chem. Phys., 72, 4244 (1980).Google Scholar
  34. 34.
    Pople, J. A.; Seeger, R.; Krishnan, R. Int. J. Quantum Chem., Quantum Chem. Symp., 11, 149 (1977).CrossRefGoogle Scholar
  35. 35.
    Cizek, J. Adv. Chem. Phys., 14, 35 (1969).CrossRefGoogle Scholar
  36. 36.
    Pople, J. A.; Head-Gordon, M.; Raghavachari, K. J. Chem. Phys., 87, 5968 (1987).CrossRefGoogle Scholar
  37. 37.
    Hurley, A. C. Electron Correlation in Molecules, Academic, New York, 1976; Pople, J. A.; Krishnan, R.; Schlegel, H. B.; Binkley, J. S. Int. J. Quantum Chem., 14, 545 (1978).Google Scholar
  38. 38.
    Raghavachari, K. J. Chem. Phys., 82, 4607 (1985); Raghavachari, K.; Trucks, G. W.; Pople,J. A.; Head-Gordon, M. Chem. Phys. Lett., 157, 479 (1989).Google Scholar
  39. 39.
    Urban, M.; Noga, J.; Cole, S. J.; Bartlett, R. J. J. Chem. Phys., 83, 4041 (1985); Noga, J.; Bartlett, R. J. J. Chem. Phys., 86, 7041 (1987) and references therein.Google Scholar
  40. 40.
    Fitzgerald, G.; Harrison, R.; Laidig, W. D.; Bartlett, R. J. J. Chem. Phys., 82 4375 (1985).CrossRefGoogle Scholar
  41. 41.
    Gauss, J.; Cremer, D. Chem. Phys. Lett., 138, 131 (1987); 153, 303 (1988).Google Scholar
  42. 42.
    Krishnan, R.; Schlegel, H. B.; Pople, J. A. J. Chem. Phys., 72, 4654 (1980); Brooks, B. R.; Laidig, W. D.; Saxe, P.; Goddard, J. D.; Yamagichi, Y.; Schaefer II, H. F. J. Chem. Phys., 72, 4652 (1980).Google Scholar
  43. 43.
    Scheiner, A. C.; Scuseria, G. E.; Rice, J. E.; Lee, T. J.; Schaefer II, H. F. J. Chem. Phys., 87, 5361 (1987); Salter, E. A.; Trucks, G. W.; Bartlett, R. J. J. Chem. Phys., 90, 1752 (1989).Google Scholar
  44. 44.
    Gauss, J.; Cremer, D. Chem. Phys. Lett., 150, 280 (1988); ibid,163, 549 (1989).Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1991

Authors and Affiliations

  • H. Bernhard Schlegel
    • 1
  • Michael J. Frisch
    • 2
  1. 1.Dept. of ChemistryWayne State UniversityDetroitUSA
  2. 2.Lorentzian, Inc.North HavenUSA

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