INFORMATION ENTROPIES OF MANY-ELECTRON SYSTEMS

The Boltzmann-Shannon (BS) information entropy S-rho = -integral rho(r )log rho(r) dr measures the spread or extent of the one-electron densi ty rho(r), which is the basic variable of the density function theory of the many electron systems. This quantity cannot be analytically com puted, not even for simple quantum mechanical systems such as, e.g., t he harmonic oscillator (HO) and the hydrogen atom (HA) in arbitrary ex cited 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 kn own rigorous lower and upper bounds to the position and momentum ss en tropies of many-electron systems in terms of the radial expectation va lues in the corresponding space. Then, we find general inequalities wh ich relate the ss entropies and various density functionals. Particula r cases of these results are rigorous relationships of the ss entropie s and some relevant density functionals (e.g., the Thomas-Fermi kineti c energy, the Dirac-Slater exchange energy, the average electron densi ty) for finite many-electron systems. (C) 1995 John Wiley & Sons, Inc.