Theoretical Chemistry Accounts

, Volume 127, Issue 3, pp 211–221 | Cite as

Orbital relaxation and the third-order induction energy in symmetry-adapted perturbation theory

  • Konrad Patkowski
  • Krzysztof Szalewicz
  • Bogumil Jeziorski
Regular Article


Theoretical investigations of the induction interaction between closed-shell molecules which fully account for the orbital relaxation effects are presented. Explicit expressions for the third-order induction energy in terms of molecular integrals and orbital energies are given and implemented within the sapt2008 program for symmetry-adapted perturbation theory (SAPT) calculations. Numerical investigations for the He–He, He–LiH, Ar–Ar, H2–CO, H2O–H2O, and H2O–NH3 model dimers show that the orbital relaxation increases the third-order induction interaction by 15 to 50% at near-equilibrium geometries, with the largest effect observed for complexes involving highly polar monomers. At large intermonomer separations, the relaxed third-order induction energy perfectly recovers the difference \(\delta E^{\rm HF}_{\rm int}\) between the Hartree–Fock interaction energy and the sum of the uncorrelated SAPT contributions through second order in the intermolecular interaction operator. At the near-equilibrium geometries, the sum of the relaxed third-order induction and exchange-induction energies reproduces, however, only a small fraction (6 to 15%) of \(\delta E^{\rm HF}_{\rm int}\) for the nonpolar systems and about 40 to 60% for the polar ones. A comparison of the complete SAPT calculations with the coupled-cluster treatment with single, double, and noniterative triple excitations [CCSD(T)] suggests that the pure SAPT approach with all the available third-order corrections is more accurate for nonpolar systems while for the polar ones the hybrid approach including \(\delta E^{\rm HF}_{\rm int}\) gives better results.


Intermolecular interactions Symmetry-adapted perturbation theory Induction energy 


  1. 1.
    Jeziorski B, Moszyński R, Szalewicz K (1994) Chem Rev 94:1887CrossRefGoogle Scholar
  2. 2.
    Jeziorski B, Szalewicz K (1998) In: von Ragué Schleyer P, Allinger NL, Clark T, Gasteiger J, Kollman PA, Schaefer HF III, Schreiner PR (eds) Encyclopedia of computational chemistry, vol 2. Wiley, Chichester, pp 1376–1398Google Scholar
  3. 3.
    Jeziorski B, Szalewicz K (2003) In: Wilson S (ed) Handbook of molecular physics and quantum chemistry, vol 3, part 2, chap. 9. Wiley, New York, pp 232–279Google Scholar
  4. 4.
    Szalewicz K, Patkowski K, Jeziorski B (2005) Struct Bonding 116:43CrossRefGoogle Scholar
  5. 5.
    Korona T, Moszyński R, Jeziorski B (2002) Mol Phys 100:1723CrossRefGoogle Scholar
  6. 6.
    Korona T, Przybytek M, Jeziorski B (2006) Mol Phys 104:2303CrossRefGoogle Scholar
  7. 7.
    Korona T (2008) J Chem Phys 128:224104CrossRefGoogle Scholar
  8. 8.
    Korona T (2007) Phys Chem Chem Phys 9:6004CrossRefGoogle Scholar
  9. 9.
    Korona T, Jeziorski B (2008) J Chem Phys 128:144107CrossRefGoogle Scholar
  10. 10.
    Misquitta AJ, Szalewicz K (2002) Chem Phys Lett 357:301CrossRefGoogle Scholar
  11. 11.
    Misquitta AJ, Jeziorski B, Szalewicz K (2003) Phys Rev Lett 91:033201CrossRefGoogle Scholar
  12. 12.
    Misquitta AJ, Szalewicz K (2005) J Chem Phys 122:214109CrossRefGoogle Scholar
  13. 13.
    Misquitta AJ, Podeszwa R, Jeziorski B, Szalewicz K (2005) J Chem Phys 123:214103CrossRefGoogle Scholar
  14. 14.
    Hesselmann A, Jansen G (2002) Chem Phys Lett 357:464CrossRefGoogle Scholar
  15. 15.
    Hesselmann A, Jansen G (2002) Chem Phys Lett 362:319CrossRefGoogle Scholar
  16. 16.
    Hesselmann A, Jansen G (2003) Chem Phys Lett 367:778CrossRefGoogle Scholar
  17. 17.
    Hesselmann A, Jansen G, Schütz M (2005) J Chem Phys 122:014103CrossRefGoogle Scholar
  18. 18.
    Jeziorska M, Cencek W, Patkowski K, Jeziorski B, Szalewicz K (2007) J Chem Phys 127:124303CrossRefGoogle Scholar
  19. 19.
    Korona T, Moszyński R, Jeziorski B (1997) Adv Quantum Chem 28:171CrossRefGoogle Scholar
  20. 20.
    Patkowski K, Jeziorski B, Korona T, Szalewicz K (2002) J Chem Phys 117:5124CrossRefGoogle Scholar
  21. 21.
    Patkowski K, Jeziorski B, Szalewicz K (2004) J Chem Phys 120:6849CrossRefGoogle Scholar
  22. 22.
    Przybytek M, Patkowski K, Jeziorski B (2004) Collect Czech Chem Commun 69:141CrossRefGoogle Scholar
  23. 23.
    Jeziorska M, Jeziorski B, Cizek J (1987) Int J Quantum Chem 32:149CrossRefGoogle Scholar
  24. 24.
    Moszyński R, Heijmen TGA, Jeziorski B (1996) Mol Phys 88:741Google Scholar
  25. 25.
    Moszyński R, Cybulski SM, Chałasiński G (1994) J Chem Phys 100:4998CrossRefGoogle Scholar
  26. 26.
    Sadlej AJ (1980) Mol Phys 39:1249CrossRefGoogle Scholar
  27. 27.
    Conway A, Murrell JN (1972) Mol Phys 23:1143CrossRefGoogle Scholar
  28. 28.
    Jeziorski B, Bulski M, Piela L (1976) Int J Quantum Chem 10:281CrossRefGoogle Scholar
  29. 29.
    Gutowski M, Chałasiński G, van Duijneveldt-van de Rijdt JGCM (1984) Int J Quantum Chem 26:971CrossRefGoogle Scholar
  30. 30.
    Chałasiński G, Jeziorski B, Szalewicz K (1977) Int J Quantum Chem 11:247CrossRefGoogle Scholar
  31. 31.
    Jeziorski B, Chałasiński G, Szalewicz K (1978) Int J Quantum Chem 14:271CrossRefGoogle Scholar
  32. 32.
    Jeziorski B, Schwalm WA, Szalewicz K (1980) J Chem Phys 73:6215CrossRefGoogle Scholar
  33. 33.
    Ćwiok T, Jeziorski B, Kołos W, Moszyński R, Szalewicz K (1992) J Chem Phys 97:7555CrossRefGoogle Scholar
  34. 34.
    Patkowski K, Korona T, Jeziorski B (2001) J Chem Phys 115:1137CrossRefGoogle Scholar
  35. 35.
    Rybak S, Jeziorski B, Szalewicz K (1991) J Chem Phys 95:6579CrossRefGoogle Scholar
  36. 36.
    Patkowski K, Szalewicz K, Jeziorski B (2006) J Chem Phys 125:154107CrossRefGoogle Scholar
  37. 37.
    Bukowski R, Cencek W, Jankowski P, Jeziorska M, Jeziorski B, Kucharski SA, Lotrich VF, Misquitta AJ, Moszyński R, Patkowski K, Podeszwa R, Rybak S, Szalewicz K, Williams HL, Wheatley RJ, Wormer PES, Żuchowski PS. SAPT2008: An ab initio program for many-body symmetry-adapted perturbation theory calculations of intermolecular interaction energies. University of Delaware and University of Warsaw (
  38. 38.
    Gutowski M, Piela L (1988) Mol Phys 64:337CrossRefGoogle Scholar
  39. 39.
    Rowe DJ, Ryman A, Rosensteel G (1980) Phys Rev A 22:2362CrossRefGoogle Scholar
  40. 40.
    Caves T, Karplus M (1969) J Chem Phys 50:3649CrossRefGoogle Scholar
  41. 41.
    Jeziorski B, Moszyński R, Ratkiewicz A, Rybak S, Szalewicz K, Williams HL (1993) In: Clementi E (ed) Methods and techniques in computational chemistry: METECC-94, vol B. STEF, Cagliari, p 79Google Scholar
  42. 42.
    Monkhorst HJ, Jeziorski B, Harris FE (1981) Phys Rev A 23:1639CrossRefGoogle Scholar
  43. 43.
    Kutzelnigg W (1980) J Chem Phys 73:343CrossRefGoogle Scholar
  44. 44.
    Adams WH (1996) Int J Quantum Chem 60: 273CrossRefGoogle Scholar
  45. 45.
    Saunders V, Guest M. atmol program package. SERC Daresbury Laboratory, Daresbury, Great BritainGoogle Scholar
  46. 46.
    Dalton, a molecular electronic structure program, Release 2.0 (2005), see
  47. 47.
    van Mourik T, Wilson AK, Dunning TH Jr (1999) Mol Phys 96:529CrossRefGoogle Scholar
  48. 48.
    Werner H-J, Knowles PJ, Lindh R, Schütz M, Celani P, Korona T, Manby FR, Rauhut G, Amos RD, Bernhardsson A et al (2009) Molpro, version 2009.1, a package of ab initio programs, see
  49. 49.
    Moszyński R, Jeziorski B, Ratkiewicz A, Rybak S (1993) J Chem Phys 99:8856CrossRefGoogle Scholar
  50. 50.
    Moszyński R, Jeziorski B, Rybak S, Szalewicz K, Williams HL (1994) J Chem Phys 100:5080CrossRefGoogle Scholar
  51. 51.
    Szalewicz K, Jeziorski B (1997) In: Scheiner S (ed) Molecular interactions—from van der Waals to strongly bound complexes. Wiley, New York, p. 3Google Scholar
  52. 52.
    Bukowski R, Cencek W, Patkowski K, Jankowski P, Jeziorska M, Kolaski M, Szalewicz K (2006) Mol Phys 104:2241CrossRefGoogle Scholar
  53. 53.
    Williams HL, Szalewicz K, Moszyński R, Jeziorski B (1995) J Chem Phys 103:4586CrossRefGoogle Scholar
  54. 54.
    Korona T, Williams HL, Bukowski R, Jeziorski B, Szalewicz K (1997) J Chem Phys 106:5109CrossRefGoogle Scholar
  55. 55.
    Zhao Y, Truhlar DG (2005) J Chem Theory Comput 1:415CrossRefGoogle Scholar
  56. 56.
    Pernal K, Podeszwa R, Patkowski K, Szalewicz K (2009) Phys Rev Lett 103:263201CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Konrad Patkowski
    • 1
  • Krzysztof Szalewicz
    • 1
  • Bogumil Jeziorski
    • 2
  1. 1.Department of Physics and AstronomyUniversity of DelawareNewarkUSA
  2. 2.Faculty of ChemistryUniversity of WarsawWarsawPoland

Personalised recommendations