Finite-temperature full configuration interaction

  • Zhuangfei Kou
  • So Hirata
Regular Article
Part of the following topical collections:
  1. Shavitt Memorial Festschrift Collection


The exact basis-set values of various thermodynamic potentials of a molecule are evaluated by the finite-temperature full configuration-interaction (FCI) method using ab initio molecular integrals over Gaussian-type orbitals. The thermodynamic potentials considered are the grand partition function, grand potential, internal energy, entropy, and chemical potential in the grand canonical ensemble as well as the partition function, Helmholtz energy, internal energy, and entropy in canonical ensemble. Approximations to FCI that are accurate at low and high temperatures are proposed, implemented, and tested. The results of finite-temperature FCI and its approximations are compared with one another as well as with the results of finite-temperature zeroth-order many-body perturbation theory, in which the Fermi–Dirac statistics is exact. Analytical asymptotic properties in the low- or high-temperature limits of some of these thermodynamic potentials are also given.


Configuration interaction Thermodynamics Partition function Temperature Canonical ensemble Grand canonical ensemble Fermi–Dirac statistics 



We thank U.S. Department of Energy Scientific Discovery through Advanced Computing (SciDAC) program (DE-FG02-12ER46875) for financial support. S. H. is a Camille Dreyfus Teacher-Scholar and a Scialog Fellow of Research Corporation for Science Advancement.


  1. 1.
    Shavitt I (1977) Methods of electronic structure theory. Plenum, New York, p 189CrossRefGoogle Scholar
  2. 2.
    Lischka H, Shepard R, Brown FB, Shavitt I (1981) Int J Quantum Chem S15:91Google Scholar
  3. 3.
    Shavitt I (1998) Mol. Phys. 94:3CrossRefGoogle Scholar
  4. 4.
    Lischka H, Müller T, Szalay PG, Shavitt I, Pitzer RM, Shepard R (2011) Wiley Interdiscip Rev Comput Mol Sci 1:191CrossRefGoogle Scholar
  5. 5.
    Shavitt I, Bartlett RJ (2009) Many-body methods in chemistry and physics. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  6. 6.
    Shavitt I (1985) Tetrahedron 41:1531CrossRefGoogle Scholar
  7. 7.
    Schaefer HF (1986) Science 231:1100CrossRefGoogle Scholar
  8. 8.
    Sherrill CD, Schaefer HF (1999) Adv Quantum Chem 34:143CrossRefGoogle Scholar
  9. 9.
    Roos B (1972) Chem Phys Lett 15:153CrossRefGoogle Scholar
  10. 10.
    Shavitt I, Bender CF, Pipano A, Hosteny RP (1973) J Comput Phys 11:90CrossRefGoogle Scholar
  11. 11.
    Davidson ER (1975) J Comput Phys 17:87CrossRefGoogle Scholar
  12. 12.
    Siegbahn PEM (1979) J Chem Phys 70:5391CrossRefGoogle Scholar
  13. 13.
    Siegbahn PEM (1980) J Chem Phys 72:1647CrossRefGoogle Scholar
  14. 14.
    Handy NC (1980) Chem Phys Lett 74:280CrossRefGoogle Scholar
  15. 15.
    Knowles PJ, Handy NC (1984) Chem Phys Lett 111:315CrossRefGoogle Scholar
  16. 16.
    Olsen J, Roos BO, Jørgensen P, Jensen HJA (1988) J Chem Phys 89:2185CrossRefGoogle Scholar
  17. 17.
    Knowles PJ (1989) Chem Phys Lett 155:513CrossRefGoogle Scholar
  18. 18.
    Olsen J, Jørgensen P, Simons J (1990) Chem Phys Lett 169:463CrossRefGoogle Scholar
  19. 19.
    Harrison RJ (1991) J Chem Phys 94:5021CrossRefGoogle Scholar
  20. 20.
    Martinez TJ, Mehta A, Carter EA (1992) J Chem Phys 97:1876CrossRefGoogle Scholar
  21. 21.
    Gan ZT, Alexeev Y, Gordon MS, Kendall RA (2003) J Chem Phys 119:47CrossRefGoogle Scholar
  22. 22.
    Bytautas L, Ruedenberg K (2004) J Chem Phys 121:10905CrossRefGoogle Scholar
  23. 23.
    Shepard R (2005) J Phys Chem A 109:11629CrossRefGoogle Scholar
  24. 24.
    Ohtsuka Y, Nagase S (2008) Chem Phys Lett 463:431CrossRefGoogle Scholar
  25. 25.
    Booth GH, Thom AJW, Alavi A (2009) J Chem Phys 131:054106CrossRefGoogle Scholar
  26. 26.
    Bytautas L, Henderson TM, Jiménez-Hoyos CA, Ellis JK, Scuseria GE (2011) J Chem Phys 135:044119CrossRefGoogle Scholar
  27. 27.
    Bauschlicher CW, Langhoff SR, Taylor PR, Handy NC, Knowles PJ (1986) J Chem Phys 85:1469CrossRefGoogle Scholar
  28. 28.
    Bauschlicher CW, Taylor PR (1986) J Chem Phys 85:6510CrossRefGoogle Scholar
  29. 29.
    Bauschlicher CW, Langhoff SR (1988) J Chem Phys 89:4246CrossRefGoogle Scholar
  30. 30.
    Evangelisti S, Bendazzoli GL, Gagliardi L (1994) Chem Phys 185:47CrossRefGoogle Scholar
  31. 31.
    Olsen J, Jørgensen P, Koch H, Balkova A, Bartlett RJ (1996) J Chem Phys 104:8007CrossRefGoogle Scholar
  32. 32.
    Christiansen O, Koch H, Jørgensen P, Olsen J (1996) Chem Phys Lett 256:185CrossRefGoogle Scholar
  33. 33.
    Dutta A, Sherrill CD (2003) J Chem Phys 118:1610CrossRefGoogle Scholar
  34. 34.
    Thøgersen L, Olsen J (2004) Chem Phys Lett 393:36CrossRefGoogle Scholar
  35. 35.
    Sherrill CD, Piecuch P (2005) J Chem Phys 122:124104CrossRefGoogle Scholar
  36. 36.
    Verdicchio M, Bendazzoli GL, Evangelisti S, Leininger T (2013) J Phys Chem A 117:192CrossRefGoogle Scholar
  37. 37.
    Giner E, Bendazzoli GL, Evangelisti S, Monari A (2013) J Chem Phys 138:074315CrossRefGoogle Scholar
  38. 38.
    Šimová L, Řezáč J, Hobza P (2013) J Chem Theor Comput 9:3420CrossRefGoogle Scholar
  39. 39.
    Matsubara T (1955) Prog Theor Phys 14:351CrossRefGoogle Scholar
  40. 40.
    Thouless DJ (1957) Phys Rev 107:1162CrossRefGoogle Scholar
  41. 41.
    Bloch C, de Dominicus C (1958) Nucl Phys 7:459CrossRefGoogle Scholar
  42. 42.
    Kohn W, Luttinger JM (1960) Phys Rev 118:41CrossRefGoogle Scholar
  43. 43.
    Luttinger JM, Ward JC (1960) Phys Rev 118:1417CrossRefGoogle Scholar
  44. 44.
    Balian R, Bloch C, de Dominicus C (1961) Nucl Phys 25:529CrossRefGoogle Scholar
  45. 45.
    Sanyal G, Mandal SH, Guha S, Mukherjee D (1993) Phys Rev E 48:3373CrossRefGoogle Scholar
  46. 46.
    March NH, Young WH, Sampanthar S (1967) The many-body problem in quantum mechanics. Cambridge University Press, LondonGoogle Scholar
  47. 47.
    Fetter AL, Walecka JD (1971) Quantum theory of many-particle systems. McGraw Hill, New YorkGoogle Scholar
  48. 48.
    Mattuck RD (1992) A guide to Feynman diagrams in the many-body problem. Dover, New YorkGoogle Scholar
  49. 49.
    Hirata S, He X (2013) J Chem Phys 138:204112CrossRefGoogle Scholar
  50. 50.
    He X, Ryu S, Hirata S (2014) J Chem Phys 140:024702CrossRefGoogle Scholar
  51. 51.
    Hirata S, Bartlett RJ (2000) Chem Phys Lett 321:216CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of ChemistryUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  2. 2.CRESTJapan Science and Technology AgencyKawaguchiJapan

Personalised recommendations