Information-theoretic approach to kinetic-energy functionals: The nearly uniform electron gas - Ghiringhelli, Luca M.; Site, Luigi Delle; Mosna, Ricardo A.; Hamilton, I. P. (Journal of Mathematical Chemistry, 2010)
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. © 2010 Springer Science+Business Media, LLC.
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Keywords: Fisher information; Kinetic-energy functionals; Shannon entropy