Abstract
We strengthen the connection between information theory and quantum mechanical systems using a recently developed dequantization procedure which results in a decomposition of the kinetic energy as the sum of a classical term and a purely quantum term. For the nearly uniform electron gas, we thereby approximate the noninteracting kinetic energy as the sum of the Thomas-Fermi term, which is exact for the uniform electron gas, and the Weizsäcker term, which is proportional to the Fisher information. Electron correlation is included via a nonlocal analytical expression which is a functional of the (N-1)-conditional probability density. This expression is evaluated via a statistically rigorous Monte-Carlo procedure to obtain the correlation energy as a functional of the electron density. We show that this functional is well aproximated by a term which is proportional to the Shannon entropy. Thus the kinetic energy is expressed as the standard Thomas-Fermi term plus terms which are proportional to two of the cornerstones of information theory: the Fisher information, which is a measure of localization, and the Shannon entropy, which is a measure of delocalization.
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References
Vedral V.: Introduction to Quantum Information Science. Oxford University Press, Oxford (2006)
Fisher R.A.: Proc. Camb. Philos. Soc. 22, 700–725 (1925)
Nagy A.: J. Chem. Phys. 119, 9401–9405 (2003)
C.E. Shannon, Bell Syst. Tech. J. 27, 379–423, 623–656 (1948)
Romera E., Dehesa J.S.: J. Chem. Phys. 120, 8906–8912 (2004)
Sen K.D., Antolín J., Angulo J.C.: Phys. Rev. A 76, 032502 (2007) (7 pages)
I.P. Hamilton, R.A. Mosna, J. Comput. Appl. Math. (in press)
Parr R.G., Yang W.: Density Functional Theory of Atoms and Molecules. Oxford University Press, Oxford (1989)
Thomas L.H.: Proc. Cambridge Philos. Soc. 23, 542–548 (1927)
Fermi E.: Rend. Accad. Lincei 6, 602–607 (1927)
von Weizsäcker C.F.: Z. Phys. 96, 431–458 (1935)
Mosna R.A., Hamilton I.P., Delle Site L.: J. Phys. A 38, 3869–3878 (2005)
Mosna R.A., Hamilton I.P., Delle Site L.: J. Phys. A 39, L229–L235 (2006)
Hamilton I.P., Mosna R.A., Delle Site L.: Theor. Chem. Acct. 118, 407–415 (2007)
Delle Site L.: J. Phys. A 40, 2787–2792 (2007)
Ghiringhelli L.M., Delle Site L.: Phys. Rev. B 77, 073104 (2008) (4 pages)
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Ghiringhelli, L.M., Delle Site, L., Mosna, R.A. et al. Information-theoretic approach to kinetic-energy functionals: the nearly uniform electron gas. J Math Chem 48, 78–82 (2010). https://doi.org/10.1007/s10910-010-9690-6
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DOI: https://doi.org/10.1007/s10910-010-9690-6