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.
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References
M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge Univ. Press, Cambridge (2000).
C. H. Bennet et al., Phys. Rev. Lett., 70, 1895 (1993).
C. H. Bennet and S. J. Wiesner, Phys. Rev. Lett., 69, 2881 (1992).
A. K. Ekert, Phys. Rev. Lett., 67, 661 (1991).
C. A. Fuchs, Phys. Rev. Lett., 79, 1162 (1997).
S. Ghosh, T. F. Rosenbaum, G. Aeppli, and S. N. Coppersmith, Nature, 425, 48 (2003).
Y. Chen, P. Zanardi, Z. D. Wang, and F. C. Zhang, New J. Phys., 8, 97 (2006); arXiv: quant-ph/0407228v4 (2004).
L. He, G. Bester, and A. Zunger, Phys. Rev. B, 72, 195307 (2005); arXiv:cond-mat/0503492v4 (2005).
F. Buscemi, P. Bordone, and A. Bertoni, Phys. Rev. A, 73, 052312 (2006); arXiv: quant-ph/0602127v1 (2006).
J. Schliemann et al., Phys. Rev. A, 64, 022303 (2001).
G. C. Ghirardi and L. Marinatto, Phys. Rev. A, 70, 012109 (2004).
Z. Huang and S. Kais, Chem. Phys. Lett., 413, 1 (2005).
W. Harneit, Phys. Rev. A, 65, 032322 (2002).
D. M. Collin, Z. Naturforsch. A, 48, 68 (1993).
J. C. Ramírez et al., Phys. Rev. A, 56, 4477 (1997).
A. Szabo and N. S. Ostlund, Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory, McGraw-Hill, New York (1989).
E. Schrödinger, Naturwissenschaften, 23, 807 (1935).
A. C. Doherty, P. A. Parrilo, and F. M. Spedalieri, Phys. Rev. Lett., 88, 187904 (2002).
B. d’Espagnat, Conceptual Foundations of Quantum Mechanics (Math. Phys. Monogr. Ser., Vol. 20, 2nd ed.), Benjamin, Reading, Mass. (1976).
J. von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton Univ. Press, Princeton, N. J. (1955).
J. R. Gittings and A. J. Fisher, Phys. Rev. A, 66, 032305 (2002).
J. Paldus, P. E. S. Wormer, F. Visser, and A. van der Avoird, J. Chem. Phys., 76, 2458 (1982).
G. E. Scuseria et al., J. Chem. Phys., 86, 2881 (1987).
P. Zanardi, Phys. Rev. A, 65, 042101 (2002).
C. H. Bennett, H. Bernstein, S. Popescu, and B. Schumacher, Phys. Rev. A, 53, 2046 (1996).
A. D. Gottlieb and N. J. Mauser, Phys. Rev. Lett., 95, 123003 (2005).
R. Grobe, K. Rzazewski, and J. H. Eberly, J. Phys. B, 27, L503 (1994).
P. Gersdorf, W. John, J. P. Perdew, and P. Ziesche, Internat. J. Quantum Chem., 61, 935 (1997).
M. J. Frisch et al., Gaussian98 (Revision A.11.3), Gaussian, Pittsburgh, Pa. (1998).
J. Čížek, J. Chem. Phys., 45, 4256 (1966).
G. E. Scuseria, C. L. Janssen, and H. F. Schaefer III, J. Chem. Phys., 89, 7382 (1988).
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 2, pp. 321–338, August, 2007.
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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
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DOI: https://doi.org/10.1007/s11232-007-0098-9