INFORMATION ENTROPIES OF MANY-ELECTRON SYSTEMS

摘要

The Boltzmann-Shannon (BS) information entropy S-rho = -integral rho(r)log rho(r) dr measures the spread or extent of the one-electron density rho(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 ss 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 ss entropies of many-electron systems in terms of the radial expectation values in the corresponding space. Then, we find general inequalities which relate the ss entropies and various density functionals. Particular cases of these results are rigorous relationships of the ss 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. (C) 1995 John Wiley & Sons, Inc. [References: 31]