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Information entropies of many‐electron systems
Author(s) -
Yáñez R. J.,
Angulo J. C.,
Dehesa J. S.
Publication year - 1995
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560560507
Subject(s) - electron , position and momentum space , kinetic energy , physics , entropy (arrow of time) , electron density , quantum mechanics , harmonic oscillator , statistical physics , excited state , position (finance) , boltzmann constant , density functional theory , finance , economics
The Boltzmann–Shannon ( BS ) information entropy S ρ = ∫ ρ( r )log ρ( r ) dr measures the spread or extent of the one‐electron density ρ( r ), which is the basic variable of the density function theory of the many electron systems. This quantity cannot be analytically computed, not even for simple quantum mechanical systems such as, e.g., the harmonic oscillator ( HO ) and the hydrogen atom ( HA ) in arbitrary excited states. Here, we first review (i) the present knowledge and open problems in the analytical determination of the BS entropies for the HO and HA systems in both position and momentum spaces and (ii) the known rigorous lower and upper bounds to the position and momentum BS entropies of many‐electron systems in terms of the radial expectation values in the corresponding space. Then, we find general inequalities which relate the BS entropies and various density functionals. Particular cases of these results are rigorous relationships of the BS entropies and some relevant density functionals (e.g., the Thomas–Fermi kinetic energy, the Dirac–Slater exchange energy, the average electron density) for finite many‐electron systems. © 1995 John Wiley & Sons, Inc.