Skip to main content
Log in

Entanglement of electrons in interacting molecules

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

We use the concept of quantum entanglement to give a physical meaning to the electron correlation energy in systems of interacting electrons. The electron correlation is not directly observable, being defined as the difference between the exact ground state energy of the many-electron Schrödinger equation and the Hartree-Fock energy. Using the configuration interaction method for the hydrogen molecule, we calculate the correlation energy and compare it with the entanglement as a function of the nucleus-nucleus separation. In the same spirit, we analyze a dimer of ethylene, which represents the simplest organic conjugate system, changing the relative orientation and distance of the molecules to obtain the configuration corresponding to maximum entanglement.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge Univ. Press, Cambridge (2000).

    MATH  Google Scholar 

  2. C. H. Bennet et al., Phys. Rev. Lett., 70, 1895 (1993).

    Article  ADS  Google Scholar 

  3. C. H. Bennet and S. J. Wiesner, Phys. Rev. Lett., 69, 2881 (1992).

    Article  ADS  Google Scholar 

  4. A. K. Ekert, Phys. Rev. Lett., 67, 661 (1991).

    Article  MATH  ADS  Google Scholar 

  5. C. A. Fuchs, Phys. Rev. Lett., 79, 1162 (1997).

    Article  ADS  Google Scholar 

  6. S. Ghosh, T. F. Rosenbaum, G. Aeppli, and S. N. Coppersmith, Nature, 425, 48 (2003).

    Article  ADS  Google Scholar 

  7. Y. Chen, P. Zanardi, Z. D. Wang, and F. C. Zhang, New J. Phys., 8, 97 (2006); arXiv: quant-ph/0407228v4 (2004).

    Article  ADS  Google Scholar 

  8. L. He, G. Bester, and A. Zunger, Phys. Rev. B, 72, 195307 (2005); arXiv:cond-mat/0503492v4 (2005).

  9. F. Buscemi, P. Bordone, and A. Bertoni, Phys. Rev. A, 73, 052312 (2006); arXiv: quant-ph/0602127v1 (2006).

  10. J. Schliemann et al., Phys. Rev. A, 64, 022303 (2001).

  11. G. C. Ghirardi and L. Marinatto, Phys. Rev. A, 70, 012109 (2004).

    Google Scholar 

  12. Z. Huang and S. Kais, Chem. Phys. Lett., 413, 1 (2005).

    Article  ADS  Google Scholar 

  13. W. Harneit, Phys. Rev. A, 65, 032322 (2002).

    Google Scholar 

  14. D. M. Collin, Z. Naturforsch. A, 48, 68 (1993).

    Google Scholar 

  15. J. C. Ramírez et al., Phys. Rev. A, 56, 4477 (1997).

    Article  ADS  Google Scholar 

  16. A. Szabo and N. S. Ostlund, Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory, McGraw-Hill, New York (1989).

    Google Scholar 

  17. E. Schrödinger, Naturwissenschaften, 23, 807 (1935).

    Article  Google Scholar 

  18. A. C. Doherty, P. A. Parrilo, and F. M. Spedalieri, Phys. Rev. Lett., 88, 187904 (2002).

    Google Scholar 

  19. B. d’Espagnat, Conceptual Foundations of Quantum Mechanics (Math. Phys. Monogr. Ser., Vol. 20, 2nd ed.), Benjamin, Reading, Mass. (1976).

    Google Scholar 

  20. J. von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton Univ. Press, Princeton, N. J. (1955).

    MATH  Google Scholar 

  21. J. R. Gittings and A. J. Fisher, Phys. Rev. A, 66, 032305 (2002).

    Google Scholar 

  22. J. Paldus, P. E. S. Wormer, F. Visser, and A. van der Avoird, J. Chem. Phys., 76, 2458 (1982).

    Article  ADS  Google Scholar 

  23. G. E. Scuseria et al., J. Chem. Phys., 86, 2881 (1987).

    Article  ADS  Google Scholar 

  24. P. Zanardi, Phys. Rev. A, 65, 042101 (2002).

    Google Scholar 

  25. C. H. Bennett, H. Bernstein, S. Popescu, and B. Schumacher, Phys. Rev. A, 53, 2046 (1996).

    Article  ADS  Google Scholar 

  26. A. D. Gottlieb and N. J. Mauser, Phys. Rev. Lett., 95, 123003 (2005).

    Google Scholar 

  27. R. Grobe, K. Rzazewski, and J. H. Eberly, J. Phys. B, 27, L503 (1994).

    Article  ADS  Google Scholar 

  28. P. Gersdorf, W. John, J. P. Perdew, and P. Ziesche, Internat. J. Quantum Chem., 61, 935 (1997).

    Article  Google Scholar 

  29. M. J. Frisch et al., Gaussian98 (Revision A.11.3), Gaussian, Pittsburgh, Pa. (1998).

    Google Scholar 

  30. J. Čížek, J. Chem. Phys., 45, 4256 (1966).

    Article  Google Scholar 

  31. G. E. Scuseria, C. L. Janssen, and H. F. Schaefer III, J. Chem. Phys., 89, 7382 (1988).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to T. A. C. Maiolo.

Additional information

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 2, pp. 321–338, August, 2007.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Maiolo, T.A.C., Della Sala, F., Martina, L. et al. Entanglement of electrons in interacting molecules. Theor Math Phys 152, 1146–1159 (2007). https://doi.org/10.1007/s11232-007-0098-9

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11232-007-0098-9

Keywords

Navigation