The Calculation of Intermolecular Potential Energy Surfaces

  • A. J. Stone
Part of the NATO ASI Series book series (NSSB, volume 227)


It is now possible to carry out accurate ab initio calculations on molecular complexes by a variety of techniques. The supermolecule approach is widely used, and is capable of high absolute accuracy, but it is subject to Basis Set Superposition Error, especially when electron correlation is taken into account, and this is a difficulty when accurate calculations of small interaction energies are required. Perturbation theory is not subject to BSSE, but perturbation methods as currently implemented are ‘uncoupled’; that is, the response of the electrons to the perturbation is not treated self-consistently. Nevertheless this method gives a more detailed description of the interaction than the supermolecule approach, and consequently provides more physical insight into the nature of the interaction. Both of these methods require calculations to be carried out at a wide range of dimer geometries if a full description of the potential energy surface is needed, and this is extremely time-consuming.

A useful alternative approach is to isolate the components of the perturbation expansion, namely the repulsion, electrostatic interaction, induction, and dispersion terms, and to calculate each of them independently by the most appropriate technique. Thus the electrostatic interaction can be calculated accurately from distributed multipole descriptions of the individual molecules, while the induction and dispersion contributions may be derived from molecular polarizabilities. This approach has the advantage that the properties of the monomers have to be calculated only once, after which the interactions may be evaluated easily and efficiently at as many dimer geometries as required. The repulsion is not so amenable, but it can be fitted by suitable analytic functions much more satisfactorily than the complete potential. The result is a model of the intermolecular potential that is capable of describing properties to a high level of accuracy.


Multipole Moment Multipole Expansion Penetration Effect Induction Energy Dispersion Integral 


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  1. 1.
    Price, S. L.; Stone, A. J. Molec. Phys. 40: 805 (1980).ADSCrossRefGoogle Scholar
  2. 2.
    Bartlett, R. J. J. Phys. Chem 93: 1697 (1989).CrossRefGoogle Scholar
  3. 3.
    Pople, J. A.; Head-Gordon, M.; Raghavachari, K. J. Chem. Phys. 87: 5968 (1988).ADSCrossRefGoogle Scholar
  4. 4.
    Boys, S. F.; Bernardi, F. Molec. Phys. 19: 553 (1970).ADSCrossRefGoogle Scholar
  5. 5.
    van Lenthe, J. H.; van Duijneveldt-Van der Rijdt, J. G. C. M.; van Duijneveldt, F. B. Adv. Chem. Phys. 69: 521 (1987).Google Scholar
  6. 6.
    Knowles, P. J. private communication.Google Scholar
  7. 7.
    Szalewicz, K.; Cole, S. J.; Kolos, W.; Bartlett, R. J. J. Chem. Phys. 89: 3662 (1988).ADSCrossRefGoogle Scholar
  8. 8.
    Stone, A. J. in Theoretical Models of Chemical Bonding, vol. 4, Z. B. Maksie, ed., Springer (1989).Google Scholar
  9. 9.
    Stone, A. J.; Tough, R. J. A. Chem. Phys. Lett. 110: 123 (1984).ADSCrossRefGoogle Scholar
  10. 10.
    Price, S. L.; Stone, A. J.; Alderton, M. Molec. Phys. 52: 987 (1984).ADSCrossRefGoogle Scholar
  11. 11.
    Buckingham, A. D. Adv. Chem. Phys. 12: 107 (1967).Google Scholar
  12. 12.
    Stone, A. J. Chem. Phys. Lett. 83:233 (1981); Stone, A. J.; Alderton, M. Molec. Phys. 56: 1047 (1985).ADSCrossRefGoogle Scholar
  13. 13.
    Pullman, A.; Perahia, D. Theor. Chim. Acta 48: 29 (1978).CrossRefGoogle Scholar
  14. 14.
    Rico, J. F.; Alvarez-Collado, J. R.; Paniagua, M. Molec. Phys. 56: 1145 (1985).ADSCrossRefGoogle Scholar
  15. 15.
    Cooper, D. L.; Stutchbury, N. C. J. Chem. Phys. Lett. 120: 167 (1985).ADSCrossRefGoogle Scholar
  16. 16.
    Sokalski, W. A.; Sawaryn, A. J. Chem. Phys. 87: 526 (1987).ADSCrossRefGoogle Scholar
  17. 17.
    Vigné-Maeder, F.; Claverie, P. J. Chem. Phys. 88: 4934 (1988).ADSCrossRefGoogle Scholar
  18. 18.
    Hayes, I. C.; Stone, A. J. Molec. Phys. 53: 69 (1984)ADSCrossRefGoogle Scholar
  19. Hayes, I. C.; Stone, A. J. Molec. Phys. 53: 83 (1984)ADSCrossRefGoogle Scholar
  20. Hurst, G. J. B.; Hayes, I. C.; Stone, A. J. Molec. Phys. 53: 107 (1984).ADSCrossRefGoogle Scholar
  21. 19.
    Amos, R. D.; Rice, J. E. CADPAC: The Cambridge Analytical Derivatives Package, issue 4.0, Cambridge, 1987.Google Scholar
  22. 20.
    Stone, A. J.; Price, S. L. J. Phys. Chem 92: 3325 (1988).CrossRefGoogle Scholar
  23. 21.
    Hall, G. G.;. Tsujinaga, K. Theor. Chim. Acta 69:425 (1986); Tsujinaga, K.; Hall, G. G. Theor. Chim. Acta 70: 257 (1986).CrossRefGoogle Scholar
  24. 22.
    Rijks, W.; Gerritsen, M.; Wormer, P. E. S. Molec. Phys. 66: 929 (1989).ADSCrossRefGoogle Scholar
  25. 23.
    Stone, A. J.; Tong, C.-S. in preparation.Google Scholar
  26. 24.
    Wheatley, R. J.; Price, S. L., submitted for publication.Google Scholar
  27. 25.
    Kita, S.; Noda, K.; Inouye, H. J. Chem. Phys. 64: 3346 (1976).CrossRefGoogle Scholar
  28. 26.
    Kim, Y. S.; Kim, S. K.; Lee, W. D. Chem. Phys. Lett. 80: 574 (1981).ADSCrossRefGoogle Scholar
  29. 27.
    Gellert, P. D.Phil. thesis, University of Oxford.Google Scholar
  30. 28.
    Stone, A. J. Molec. Phys. 56: 1065 (1985).ADSCrossRefGoogle Scholar
  31. 29.
    Wormer, P. E. S.; Rijks, W. Phys. Rev. A33: 2928 (1986)ADSCrossRefGoogle Scholar
  32. Rijks, W.; Wormer, P. E. S. J. Chem. Phys. 88: 5704 (1988).ADSCrossRefGoogle Scholar
  33. 30.
    Stone, A. J. Chem. Phys. Lett. 155: 102 (1989).ADSCrossRefGoogle Scholar
  34. 31.
    Dalgarno, A.; Stewart, A. L. Proc. Roy. Soc. A 238: 276 (1956)MathSciNetADSCrossRefGoogle Scholar
  35. Dalgarno, A.; Lynn, N. Proc. Phys. Soc. London, A 70: 223 (1957).ADSCrossRefGoogle Scholar
  36. 32.
    Buckingham, A. D.; Pople, J. A. Trans. Faraday Soc. 51: 1173 (1955).CrossRefGoogle Scholar
  37. 33.
    Stone, A. J. Chem. Phys. Lett. 155: 111 (1989).ADSCrossRefGoogle Scholar
  38. 34.
    Casimir, H. B. G.; Polder, D. Phys. Rev. 73: 360 (1948).ADSMATHCrossRefGoogle Scholar
  39. 35.
    Stone, A. J.; Tong, C.-S. Chem. Phys.,in press.Google Scholar
  40. 36.
    Visser, F.; Wormer, P. E. S.; Stam, P. J. Chem. Phys. 79: 4973 (1983)ADSCrossRefGoogle Scholar
  41. Visser, F.; Wormer, P. E. S.; Jacobs, W. P. J. H. J. Chem. Phys. 82: 3753 (1984)ADSCrossRefGoogle Scholar
  42. Visser, F.; Wormer, P. E. S. Molec. Phys. 52: 723 (1984).CrossRefGoogle Scholar
  43. 37.
    Douketis, C.; Scoles, G.; Marchetti, S.; Thakkar, A. J. J. Chem. Phys. 76: 3057 (1982).ADSCrossRefGoogle Scholar
  44. 38.
    Tang, K. T.; Toennies, J. P. Chem. Phys. 80: 3276 (1984).Google Scholar
  45. 39.
    Knowles, P. J.; Meath, W. J. Chem. Phys. Lett. 124:164 (1986); Molec. Phys. 59:965 (1986); Molec. Phys. 60: 1143 (1987).ADSCrossRefGoogle Scholar
  46. 40.
    Clary, D. C.; Lovejoy, C, M.; ONeil, S. V.; Nesbitt, D. J. Phys. Rev. Letters 61: 1576 (1988);ADSCrossRefGoogle Scholar
  47. Clary, D. C.; Nesbitt, D. J. J. Chen. Phys. 90: 7000 (1989)ADSCrossRefGoogle Scholar
  48. Nesbitt, D. J.; Lovejoy, C. M.; Lindeman, T. G.; ONeil, S. V.; Clary, D. C. J. Chem. Phys. 91: 722 (1989)ADSCrossRefGoogle Scholar
  49. ONeil, S. V.; Nesbitt, D. J.; Rosmus, P; Werner, H.-J.; Clary, D. C. J. Chem. Phys. 91:711 (1989); Clary, D. C. this volume.Google Scholar
  50. 41.
    Nesbitt, D. J.; Child, M. S.; Clary, D. C. J. Chem. Phys. 90: 4855 (1989).ADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1990

Authors and Affiliations

  • A. J. Stone
    • 1
  1. 1.University Chemical LaboratoryCambridgeEngland

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