Theoretica chimica acta

, Volume 83, Issue 1–2, pp 69–103 | Cite as

Orthogonally spin-adapted multi-reference Hilbert space coupled-cluster formalism: diagrammatic formulation

  • Piotr Piecuch
  • Josef Paldus


The problem of spin-adaptation of the multi-reference (MR) coupled-cluster (CC) formalism, employing Jeziorski-Monkhorst ansatz, is addressed. The diagrammatic technique based on graphical methods of spin algebras is generalized to the MR case, so that both direct and coupling terms can be determined. Usefulness of this fully diagrammatic spin-adaptation approach is illustrated on a derivation of explicit expressions for the linear and bilinear coupling terms that are required in the special two-reference MR-CC theory involving singly and doubly excited states (MR-CCSD formalism). Results obtained with the diagrammatic approach are compared with those derived earlier using the algebraic technique and relative advantages of both procedures are compared.

Key words

Many-electron correlation problem Coupled-cluster approach Multi-reference formalism Spin-adaptation Graphical methods of spin algebras 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Jeziorski B, Monkhorst HJ (1981) Phys Rev A24:1668Google Scholar
  2. 2.
    Jeziorski B, Paldus J (1988) J Chem Phys 88:5673Google Scholar
  3. 3.
    Paldus J, Pylypow L, Jeziorski B (1989) In: Kaldor U (ed) Many-body methods in quantum chemistry. (Lect Notes Chem 52) Springer, Berlin Heidelberg New York, p 151Google Scholar
  4. 4.
    Paldus J, Jeziorski B (1988) Theor Chim Acta 73:81Google Scholar
  5. 5.
    Meissner L (1987) Size extensive methods for the description of electron correlation effects in quasidegenerate states. PhD Thesis, Nicholas Copernicus University, Torun, Poland (in Polish)Google Scholar
  6. 6.
    Meissner L, Jankowski K, Wasilewski J (1988) Int J Quantum Chem 34:535; Meissner L, Jankowski K (1989) ibid 36:705Google Scholar
  7. 7.
    Balková A, Kucharski SA, Meissner L, Bartlett RJ (1991) Theor Chim Acta 80:335Google Scholar
  8. 8.
    Paldus J, Piecuch P, Pylypow L, Jeziorski B, unpublished resultsGoogle Scholar
  9. 9.
    Meissner L, Kucharski SA, Bartlett RJ (1989) J Chem Phys 91:6187; Meissner L, Bartlett RJ (1990) J Chem Phys 92:561Google Scholar
  10. 10.
    Paldus J (1983) In: Löwdin PO, Pullman B (eds) New horizons of quantum chemistry. Reidel, Dordrecht, p 31Google Scholar
  11. 11.
    Paldus J (1977) J Chem Phys 67:303; Adams BG, Paldus J (1979) Phys Rev A20:1Google Scholar
  12. 12.
    Jucys AP, Levinson IB, Vanagas VV (1960) Mathematical apparatus of the theory of angular momentum. Institute of Physics and Mathematics of the Academy of Sciences of the Lithuanian S.S.R, Mintis, Vilnius (in Russian); English translations: (1962) Israel Program for Scientific Translations, Jerusalem; (1964) Gordon and Breach, New York; Jucys AP, Bandzaitis AA (1977) The theory of angular momentum in quantum mechanics, 2nd edn. Mokslas, Vilnius (in Russian); Brink DM, Satchler GR (1968) Angular momentum, 2nd edn. Clarendon Press, Oxford; El Baz E, Castel B (1972) Graphical methods of spin algebras in atomic, nuclear and particle physics. Marcel Dekker, New York; for a brief review of these methods, see, e.g., Lindgren I, Morrison J (1982) Atomic many-body theory. Springer, Berlin Heidelberg New York; see also Appendix of Piecuch P (1988) In: Maruani J (ed) Molecules in physics, chemistry and biology, vol 2, Physical aspects of molecular systems. Kluwer, Dordrecht, p 417Google Scholar
  13. 13. (a)
    Čížek J (1966) Theor Chim Acta 6:292;Google Scholar
  14. 13. (b)
    Paldus J, Adams BG, Čížek J (1977) Int J Quantum Chem 11:813Google Scholar
  15. 14.
    Paldus J, Čížek J (1975) Advan Quantum Chem 9:105Google Scholar
  16. 15.
    Harris FE, Jeziorski B, Monkhorst HJ (1981) Phys Rev A23:1632Google Scholar
  17. 16.
    Piecuch P, Paldus J (1989) Int J Quantum Chem 36:429Google Scholar
  18. 17.
    Piecuch P, Paldus J (1990) Theor Chim Acta 78:65Google Scholar
  19. 18.
    Kucharski SA, Bartlett RJ (1991) Theor Chim Acta 80:387Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Piotr Piecuch
    • 1
  • Josef Paldus
    • 1
    • 3
  1. 1.Department of Applied MathematicsUniversity of WaterlooWaterlooCanada
  2. 2.Institute of ChemistryUniversity of WroclawWroclawPoland
  3. 3.the Department of Chemistry, and Guelph-Waterloo Center for Graduate Work in Chemistry, Waterloo CampusUniversity of WaterlooWaterlooCanada

Personalised recommendations