Skip to main content
SpringerLink
Log in

A study of the relationships between unpaired electron density, spin-density and cumulant matrices

  • Regular Article
  • Published:
Theoretical Chemistry Accounts Aims and scope Submit manuscript

Abstract

This work describes the derivation of simple relationships between the density matrix of effectively unpaired electrons and the spin-density matrix in N-electron systems. The link between both devices turns out to be the one-electron matrix arising from the diagonal contraction of the cumulant matrix corresponding to the second-order reduced density matrix. We study some features of this contracted matrix, showing its usefulness to describe the electronic correlation. Numerical determinations performed in selected systems with different spin symmetries confirm the theoretical predictions.

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. Takatsuka K, Fueno T, Yamaguchi K (1978) Theor Chim Acta 48:175

    Article  CAS  Google Scholar 

  2. Takatsuka K, Fueno T (1978) J Chem Phys 69:661

    Article  CAS  Google Scholar 

  3. Bochicchio RC (1991) J Mol Struct (Theochem) 228:209

    Article  Google Scholar 

  4. Bochicchio RC (1998) J Mol Struct (Theochem) 429:229

    Article  CAS  Google Scholar 

  5. Lain L, Torre A, Bochicchio RC, Ponec R (2001) Chem Phys Lett 346:283

    Article  CAS  Google Scholar 

  6. Bochicchio RC, Lain L, Torre A (2003) Chem Phys Lett 375:45

    Article  CAS  Google Scholar 

  7. Torre A, Lain L, Bochicchio R (2003) J Phys Chem A 107:127

    Article  CAS  Google Scholar 

  8. Staroverov VN, Davidson ER (2000) Chem Phys Lett 330:161

    Article  CAS  Google Scholar 

  9. Staroverov VN, Davidson ER (2000) J Am Chem Soc 122:186

    Article  CAS  Google Scholar 

  10. Davidson ER, Clark AE (2007) Phys Chem Chem Phys 9:1881

    Article  CAS  Google Scholar 

  11. Bochicchio R, Lain L, Torre A (2003) J Comput Chem 24:1902

    Article  CAS  Google Scholar 

  12. Lain L, Torre A, Bochicchio R (2004) J Phys Chem A 108:4132

    Article  CAS  Google Scholar 

  13. Torre A, Alcoba DR, Lain L, Bochicchio RC (2005). J Phys Chem A 109:6587

    Article  CAS  Google Scholar 

  14. Head-Gordon M (2003) Chem Phys Lett 372:508

    Article  CAS  Google Scholar 

  15. Proynov EI (2006) J Mol Struct (Theochem) 762:159

    Article  CAS  Google Scholar 

  16. Alcoba DR, Bochicchio RC, Lain L, Torre A (2006) Chem Phys Lett 429:286

    Article  CAS  Google Scholar 

  17. Mazziotti DA (1998) Chem Phys Lett 289:419

    Article  CAS  Google Scholar 

  18. Kutzelnigg W, Mukherjee D (1997) J Chem Phys 107:432

    Article  CAS  Google Scholar 

  19. Kutzelnigg W, Mukherjee D (1999) J Chem Phys 110:2800

    Article  CAS  Google Scholar 

  20. Mazziotti DA (2000) Chem Phys Lett 326:212

    Article  CAS  Google Scholar 

  21. Harris FE (2002) Int J Quantum Chem 90:105

    Article  CAS  Google Scholar 

  22. Nooijen M, Wladyslawski M, Hazra A (2003) J Chem Phys 118:4832

    Article  CAS  Google Scholar 

  23. Herbert JM (2007) Int J Quantum Chem 107:703

    Article  CAS  Google Scholar 

  24. Harriman JE (2007) Phys Rev A 75:032513

    Article  Google Scholar 

  25. Mazziotti DA (ed) (2007) Advances in chemical physics, vol 134. Wiley, New York. See also references therein

  26. Bochicchio RC, Lain L, Torre A (2003) Chem Phys Lett 374:567

    Article  CAS  Google Scholar 

  27. Alcoba DR, Bochicchio RC, Lain L, Torre A (2008) Phys Chem Chem Phys 10:5144

    Article  CAS  Google Scholar 

  28. Vyboishchikov SF, Salvador P (2006) Chem Phys Lett 430:204

    Article  CAS  Google Scholar 

  29. Alcoba DR, Torre A, Lain L, Bochicchio RC (2007) J Chem Phys 127:104110

    Article  Google Scholar 

  30. Alcoba DR, Lain L, Torre A, Bochicchio RC (2009) Chem Phys Lett 470:136

    Article  CAS  Google Scholar 

  31. Torre A, Alcoba DR, Lain L, Bochicchio RC (2010) J Phys Chem A 114:2344

    Article  CAS  Google Scholar 

  32. Kutnelnigg W, Mukherjee D (2002) J Chem Phys 116:4787

    Article  Google Scholar 

  33. Lain L, Torre A, Bochicchio R (2002) J Chem Phys 117:5497

    Article  CAS  Google Scholar 

  34. Lain L, Torre A, Alcoba DR, Bochicchio RC (2009) Chem Phys Lett 476:101

    Article  CAS  Google Scholar 

  35. Staroverov VN, Davidson E (2000) Int J Quantum Chem 77:651

    Article  CAS  Google Scholar 

  36. Pauncz R (1979) Spin eigenfunctions—construction and use. Plenum Press, New York

    Google Scholar 

  37. Schmidt MW, Baldridge KK, Boatz JA, Elbert ST, Gordon MS, Jensen JH, Koseki S, Matsunaga N, Nguyen KA, Su S, Windus TL, Dupuis M, Montgomery JA (1993) J Comput Chem 14:1347

    Article  CAS  Google Scholar 

  38. Luzanov AV, Zhikol OA (2005) Int J Quantum Chem 104:167

    Article  CAS  Google Scholar 

  39. Alcoba DR, Bochicchio RC, Torre A, Lain L to be published

Download references

Acknowledgments

L.L. and A.T. acknowledge the Spanish Ministry of Science and Innovation for the grant No. CTQ2009-07459/BQU and the Universidad del País Vasco for the grant No. GIU09/43. D.R.A and R.C.B. acknowledge the support from the Projects X017 (Universidad de Buenos Aires) and PIP 11220090100061 (Consejo Nacional de Investigaciones Científicas y Técnicas). We thank the Universidad del País Vasco for allocation of computational resources.

Author information

Authors and Affiliations

  1. Departamento de Química Física, Facultad de Ciencia y Tecnología, Universidad del País, Vasco. Apdo. 644, 48080, Bilbao, Spain

    Luis Lain & Alicia Torre

  2. Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and Instituto de Física de Buenos Aires, Consejo Nacional de Investigaciones Científicas y Técnicas, Ciudad Universitaria, 1428, Buenos Aires, Argentina

    Diego R. Alcoba & Roberto C. Bochicchio

Authors
  1. Luis Lain
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alicia Torre
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Diego R. Alcoba
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Roberto C. Bochicchio
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Luis Lain.

Additional information

Published as part of the special issue celebrating theoretical and computational chemistry in Spain.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lain, L., Torre, A., Alcoba, D.R. et al. A study of the relationships between unpaired electron density, spin-density and cumulant matrices. Theor Chem Acc 128, 405–410 (2011). https://doi.org/10.1007/s00214-010-0795-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00214-010-0795-6

Keywords

Search

Navigation