Skip to main content
SpringerLink
Log in

Symmetry-adapted formulation of the G-particle-hole hypervirial equation method

  • Original Paper
  • Published:
Journal of Mathematical Chemistry Aims and scope Submit manuscript

Abstract

Highly accurate 2-body reduced density matrices of atoms and molecules have been directly determined without calculation of their wave functions with the use of the G-particle-hole hypervirial (GHV) equation method (Alcoba et al. in Int. J. Quantum Chem. 109:3178, 2009). Very recently, the computational efficiency of the GHV method has been significantly enhanced through the use of sum factorization and matrix-matrix multiplication (Alcoba et al. in Int. J. Quantum Chem 111:937, 2011). In this paper, a detailed analysis of the matrix contractions involved in GHV calculations is carried out. The analysis leads to a convenient strategy for exploiting point group symmetry, by which the computational efficiency of the GHV method is further improved. Implementation of the symmetry-adapted formulation of the method is reported. Computer timings and hardware requirements are illustrated for several representative chemical systems. Finally, the method is applied to the well-known challenging calculation of the torsional potential in ethylene.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Davidson E.R.: Reduced Density Matrices in Quantum Chemistry. Academic Press, New York (1976)

    Google Scholar 

  2. R.M. Erdahl, V. Smith (eds.), Density Matrices and Density Functionals, Proceedings of the A.J. Coleman Symposium, Kingston, ON, 1985 (Reidel, Dordrecht, 1987)

  3. Cioslowski, J. (ed.): Many-electron Densities and Reduced Density Matrices. Kluwer, Dordrecht (2000)

    Google Scholar 

  4. Coleman A.J., Yukalov V.I.: Reduced Density Matrices: Coulson’s Challenge. Springer, New York (2000)

    Book  Google Scholar 

  5. D.A. Mazziotti (ed.), Reduced-Density-matrix Mechanics with Applications to Many-Electron Atoms and Molecules. Adv. Chem. Phys. 134 (Wiley, New York, 2007) and references therein

  6. Husimi K.: Proc. Soc. Japan 22, 264 (1940)

    Google Scholar 

  7. Löwdin P.O.: Phys. Rev. 97, 1474 (1955)

    Article  Google Scholar 

  8. Mayer J.E.: Phys. Rev. 100, 1579 (1955)

    Article  CAS  Google Scholar 

  9. McWeeny R.: Proc. R. Soc. A 235, 496 (1956)

    Article  CAS  Google Scholar 

  10. Coleman A.J.: Rev. Mod. Phys. 35, 668 (1963)

    Article  Google Scholar 

  11. Garrod C., Percus J.K.: J. Math. Phys. 5, 1756 (1964)

    Article  CAS  Google Scholar 

  12. Beste A., Runge K., Bartlett R.: Chem. Phys. Lett. 355, 263 (2002)

    Article  CAS  Google Scholar 

  13. Cho S.: Sci. Rep. Gumma Univ. 11, 1 (1962)

    Google Scholar 

  14. Cohen L., Frishberg C.: Phys. Rev. A 13, 927 (1976)

    Article  Google Scholar 

  15. Nakatsuji H.: Phys. Rev. A 14, 41 (1976)

    Article  CAS  Google Scholar 

  16. C. Valdemoro, in Density Matrices and Density Functionals. Proceedings of the A.J. Coleman Symposium, Kingston, ON, 1985, ed. by R.M. Erdahl, V. Smith (Reidel, Dordrecht, 1987)

  17. Harriman J.E.: Phys. Rev. A 19, 1893 (1979)

    Article  Google Scholar 

  18. Colmenero F., Valdemoro C.: Int. J. Quantum Chem. 51, 369 (1994)

    Article  CAS  Google Scholar 

  19. Nakatsuji H., Yasuda K.: Phys. Rev. Lett. 76, 1039 (1996)

    Article  CAS  Google Scholar 

  20. Yasuda K., Nakatsuji H.: Phys. Rev. A 56, 2648 (1997)

    Article  CAS  Google Scholar 

  21. Valdemoro C., Tel L.M., Pérez-Romero E.: Adv. Quantum Chem. 28, 33 (1997)

    Article  CAS  Google Scholar 

  22. Mazziotti D.A.: Phys. Rev. A 57, 4219 (1998)

    Article  CAS  Google Scholar 

  23. Valdemoro C.: Phys. Rev. A 45, 4462 (1992)

    Article  Google Scholar 

  24. Colmenero F., Pérez del Valle C., Valdemoro C.: Phys. Rev. A 47, 971 (1993)

    Article  CAS  Google Scholar 

  25. Colmenero F., Valdemoro C.: Phys. Rev. A 47, 979 (1993)

    Article  CAS  Google Scholar 

  26. Mazziotti D.A.: Chem. Phys. Lett. 289, 419 (1998)

    Article  CAS  Google Scholar 

  27. C. Valdemoro, L.M. Tel, E. Pérez-Romero, in Many-Electron Densities and Reduced Density Matrices, ed. by J. Cioslowski (Kluwer, Dordrecht, 2000)

  28. C. Valdemoro, in Reduced-Density-Matrix Mechanics with Applications to Many-electron Atoms and Molecules. Adv. Chem. Phys. vol. 134, ed. by D.A. Mazziotti (wiley, New York, 2007)

  29. DePrince A.E. III, Mazziotti D.A.: J. Chem. Phys. 127, 104104 (2007)

    Article  Google Scholar 

  30. Valdemoro C., Tel L.M., Alcoba D.R., Pérez-Romero E.: Theor. Chem. Acc. 118, 503 (2007)

    Article  CAS  Google Scholar 

  31. Mazziotti D.A.: Phys. Rev. Lett. 97, 143002 (2006)

    Article  Google Scholar 

  32. Mazziotti D.A.: Phys. Rev. A 75, 022505 (2007)

    Article  Google Scholar 

  33. Valdemoro C., Alcoba D.R., Tel L.M., Pérez-Romero E.: Prog. Theor. Chem. Phys. 18, 175 (2008)

    Article  Google Scholar 

  34. Mazziotti D.A.: J. Chem. Phys. 126, 184101 (2007)

    Article  Google Scholar 

  35. Mazziotti D.A.: Phys. Rev. A 76, 052502 (2007)

    Article  Google Scholar 

  36. Mazziotti D.A.: J. Phys. Chem. A 112, 13684 (2008)

    Article  CAS  Google Scholar 

  37. Foley J.J. IV, Rothman A.E., Mazziotti D.A.: J. Chem. Phys. 130, 184112 (2009)

    Article  Google Scholar 

  38. Rothman A.E., Foley J.J. IV, Mazziotti D.A.: Phys. Rev. A 80, 052508 (2009)

    Article  Google Scholar 

  39. Snyder J.W., Rothman A.E., Foley J.J. IV, Mazziotti D.A.: J. Chem. Phys. 132, 154109 (2010)

    Article  Google Scholar 

  40. Alcoba D.R., Valdemoro C., Tel L.M., Pérez-Romero E.: Int. J. Quantum Chem. 109, 3178 (2009)

    Article  CAS  Google Scholar 

  41. Valdemoro C., Alcoba D.R., Tel L.M., Pérez-Romero E.: Int. J. Quantum Chem. 109, 2622 (2009)

    Article  CAS  Google Scholar 

  42. Alcoba D.R., Tel L.M., Pérez-Romero E., Valdemoro C.: Int. J. Quantum Chem. 111, 937 (2011)

    Article  CAS  Google Scholar 

  43. Valdemoro C., Alcoba D.R., Tel L.M., Pérez-Romero E.: Int. J. Quantum Chem. 111, 245 (2011)

    Article  CAS  Google Scholar 

  44. Alcoba D.R., Valdemoro C., Tel L.M., Pérez-Romero E., Oña O.B.: J. Phys. Chem. A 115, 2599 (2011)

    Article  CAS  Google Scholar 

  45. Valdemoro C., Alcoba D.R., Oña O.B., Tel L.M., Pérez-Romero E.: J. Math. Chem. 50, 492 (2012)

    Article  CAS  Google Scholar 

  46. Surjan P.R.: Second Quantized Approach to Quantum Chemistry: An Elementary Introduction. Springer, Berlin (1989)

    Book  Google Scholar 

  47. Kutzelnigg W.: Chem. Phys. Lett. 64, 383 (1979)

    Article  CAS  Google Scholar 

  48. Reitz H., Kutzelnigg W.: Chem. Phys. Lett. 66, 111 (1979)

    Article  CAS  Google Scholar 

  49. Kutzelnigg W.: Int. J. Quantum Chem. 18, 3 (1980)

    Article  CAS  Google Scholar 

  50. Valdemoro C., De Lara-Castells M.P., Pérez-Romero E., Tel L.M.: Adv. Quantum Chem. 31, 37 (1999)

    Article  Google Scholar 

  51. Valdemoro C., Tel L.M., Pérez-Romero E.: Phys. Rev. A 61, 032507 (2000)

    Article  Google Scholar 

  52. Valdemoro C., Alcoba D.R., Tel L.M., Pérez-Romero E.: Int. J. Quantum Chem. 85, 214 (2001)

    Article  CAS  Google Scholar 

  53. Valdemoro C., Tel L.M., Pérez-Romero E., Torre A.: J. Mol. Struct. (Theochem) 537, 1 (2001)

    Article  CAS  Google Scholar 

  54. Alcoba D.R., Valdemoro C.: Phys. Rev. A 64, 062105 (2001)

    Article  Google Scholar 

  55. Alcoba D.R.: Phys. Rev. A 65, 032519 (2002)

    Article  Google Scholar 

  56. Valdemoro C., Tel L.M., Alcoba D.R., Pérez-Romero E., Casquero F.J.: Int. J. Quantum Chem. 90, 1555 (2002)

    Article  CAS  Google Scholar 

  57. Valdemoro C., Alcoba D.R., Tel L.M.: Int. J. Quantum Chem. 93, 212 (2003)

    Article  CAS  Google Scholar 

  58. D.R. Alcoba, in Reduced-Density-matrix Mechanics with Applications to Many-electron Atoms and Molecules, Adv. Chem. Phys. vol. 134, ed. by D.A. Mazziotti (Wiley, New York, 2007)

  59. D.R. Alcoba, C. Valdemoro, Int. J. Quantum Chem. 102, 629 (2005); ibid. 106, 2999 (2006)

  60. C. Valdemoro, L.M. Tel, E. Pérez-Romero, in Quantum Systems in Chemistry and Physics I, ed. by A. Hernández-Laguna, J. Maruani, R. McWeeny, S. Wilson (Kluwer, Dordrecht, 2000)

  61. E. Fehlberg, NASA Technical Report R287 (1968); ibid, NASA Technical Report R315 (1969)

  62. A.D. McLean, in Proceedings of the Conference on Potential Energy Surfaces in Chemistry, ed. by W.A. Lester, Jr. (IBM San Jose, 1971), p. 87

  63. I. Shavitt, in Methods of Electronic Structure Theory, ed. by H.F. Schaefer, III (Plenum, New York, 1977)

  64. Crawford T.D., Schaefer H.F. III: Rev. Comput. Chem. 14, 33 (2000)

    Article  CAS  Google Scholar 

  65. Tel L.M., Pérez-Romero E., Casquero F.J., Valdemoro C.: Phys. Rev. A 67, 052504 (2003)

    Article  Google Scholar 

  66. R.D. Johnson III (ed.), NIST Computational Chemistry Comparison and Benchmark Database. NIST Standard Reference Database No. 101, National Institute of Standard and Technology, 2006. http://srdata.nist.gov/cccbdb

  67. Crawford T.D., Sherrill C.D., Valeev E.F., Fermann J.T., King R.A., Leininger M.L., Brown S.T., Janssen C.L., Seidl E.T., Kenny J.P., Allen W.D.: J. Comput. Chem. 28, 1610 (2007)

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Ciencias Exactas, Ciclo Básico Común, Universidad de Buenos Aires, Ciudad Universitaria, 1428, Buenos Aires, Argentina

    Gustavo E. Massaccesi

  2. Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428, Buenos Aires, Argentina

    Gustavo E. Massaccesi

  3. Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428, Buenos Aires, Argentina

    Diego R. Alcoba

  4. Instituto de Física de Buenos Aires, Consejo Nacional de Investigaciones Científicas y Técnicas, Ciudad Universitaria, 1428, Buenos Aires, Argentina

    Diego R. Alcoba

  5. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas, CCT La Plata, Consejo Nacional de Investigaciones Científicas y Técnicas, Universidad Nacional de La Plata, Diag. 113 y 64 (S/N), Sucursal 4, CC 16, 1900, La Plata, Argentina

    Ofelia B. Oña

Authors
  1. Gustavo E. Massaccesi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Diego R. Alcoba
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ofelia B. Oña
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Diego R. Alcoba.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Massaccesi, G.E., Alcoba, D.R. & Oña, O.B. Symmetry-adapted formulation of the G-particle-hole hypervirial equation method. J Math Chem 50, 2155–2167 (2012). https://doi.org/10.1007/s10910-012-0023-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10910-012-0023-9

Keywords

Search

Navigation