Theoretica Chimica Acta

, Volume 95, Issue 3–4, pp 131–150 | Cite as

Symmetry adaptation and the utilization of point group symmetry in valence bond calculations, including CASVB

  • Thorstein Thorsteinsson
  • David L. Cooper
  • Joseph Gerratt
  • Mario Raimondi


We present practical approaches for symmetry-adapting valence bond wave functions, with emphasis on the CASVB method. Significant savings in the computational effort become available, both in relation to the application of the Hamiltonian operator and to the reduced number of variational parameters. Results are presented for modern VB representations of CASSCF descriptions of benzene and diborane.

Key words

CASVB CASSCF VB Symmetry adaptation Spin-coupled 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Karadakov PB, Gerratt J, Raimondi M, Cooper DL (1992) J Chem Phys 97:7635CrossRefGoogle Scholar
  2. 2.
    Thorsteinsson T (1995) Development of methods in spin-coupled theory. PhD thesis, University of Liverpool, UKGoogle Scholar
  3. 3.
    Thorsteinsson T, Cooper DL, Gerratt J, Karadakov PB, Raimondi M (1996) Theor Chim Acta 93:343CrossRefGoogle Scholar
  4. 4.
    Thorsteinsson T, Cooper DL (1996) Theor Chim Acta 94:233Google Scholar
  5. 5.
    MOLPRO is a package ofab initio programs written by Werner H-J, Knowles PJ with contributions from Almlöf J, Amos RD, Berning A, Deegan MJO, Eckert F, Elbert ST, Hampel C, Lindh R, Meyer W, Nicklaß A, Peterson K, Pitzer R, Stone AJ, Taylor PR, Mara ME, Pulay P, Schütz M, Stoll H, Thorsteinsson T, Cooper DLGoogle Scholar
  6. 6.
    Werner H-J, Knowles PJ (1985) J Chem Phys 82:5053; Knowles PJ, Werner H-J (1985) Chem Phys Lett 115:259CrossRefGoogle Scholar
  7. 7.
    Malmqvist PÅ (1986) Int J Quant Chem 30:479CrossRefGoogle Scholar
  8. 8.
    For a review of applications see, for example: Cooper DL, Gerratt J, Raimondi M (1991) Chem Rev 91:929CrossRefGoogle Scholar
  9. 9.
    Karadakov PB, Gerratt J, Cooper DL, Raimondi M (1995) Theor Chim Acta 90:51CrossRefGoogle Scholar
  10. 10.
    Hamermesh G (1962) Group theory and its application to physical problems. Addison-Wesley, Reading, MA, Sect. 3-18Google Scholar
  11. 11.
    Gerratt J (1971) Adv Atom Mol Phys 7:141; See also: Wright SC, Cooper DL, Gerratt J, Raimondi M (1992) J Phys Chem 96:7943CrossRefGoogle Scholar
  12. 12.
    Cooper DL, Gerratt J, Raimondi M, Sironi M, Thorsteinsson T (1993) Theor Chim Acta 85:261CrossRefGoogle Scholar
  13. 13.
    Dunning TH (1989) J Chem Phys 90:1007CrossRefGoogle Scholar
  14. 14.
    Cooper DL, Gerratt J, Raimondi M (1986) Nature 323:699; Cooper DL, Wright SC, Gerratt J, Hyams PA, Raimondi M (1989) J Chem Soc, Perkin Trans 2:719; da Silva EC, Gerratt J, Cooper DL, Raimondi M (1994) J Chem Phys 101:3866CrossRefGoogle Scholar
  15. 15.
    Wilson S, Gerratt J (1975) J Mol Phys 30:765CrossRefGoogle Scholar
  16. 16.
    Cooper DL, Gerratt J, Raimondi M (1991) J Mol Struc (THEOCHEM) 229:155; Sironi M, Raimondi M, Cooper DL, Gerratt J (1991) J Phys Chem 95:10617CrossRefGoogle Scholar
  17. 17.
    Gerratt J, Cooper DL, Raimondi M (1990) In: Klein DJ, Trinastic N (eds) Valence bond theory and Chemical Structure. Elsevier, AmsterdamGoogle Scholar
  18. 18.
    Siegbahn PEM (1984) Chem Phys Lett 109:417CrossRefGoogle Scholar
  19. 19.
    Olsen J, Roos BO, Jørgensen P, Jensen HJAa (1988) J Chem Phys 89:2185; Zarrabian S, Sarma CR, Paldus J (1989) Chem Phys Lett 155:183; Harrison RJ, Zarrabian S (1989) Chem Phys Lett 158:393CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Thorstein Thorsteinsson
    • 1
  • David L. Cooper
    • 1
  • Joseph Gerratt
    • 2
  • Mario Raimondi
    • 3
  1. 1.Department of ChemistryUniversity of LiverpoolLiverpoolUK
  2. 2.School of ChemistryUniversity of BristolCantocks CloseUK
  3. 3.Dipartimento di Chimica Fisica ed ElettrochimicaUniversità di MilanoMilanoItaly

Personalised recommendations