Some novel characteristics of atomic information entropies

Abstract

Near--Hartree-Fock information entropies ${S}_{\ensuremath{\rho}}$=-F\ensuremath{\rho}(r)ln\ensuremath{\rho}(r)dr and ${S}_{\ensuremath{\gamma}}$=-F \ensuremath{\gamma}(p)ln\ensuremath{\gamma}(p)dp, where \ensuremath{\rho}(r) and \ensuremath{\gamma}(p) are one-electron densities in coordinate and momentum space, respectively, have been computed for atoms in their ground and excited states. The information entropies for the harmonic oscillator and hydrogen atom as prototype systems are also discussed. The result of this exercise is a numerical discovery that for the ground state, ${S}_{\ensuremath{\rho}}$+${S}_{\ensuremath{\gamma}}$ shows its minimum value. This study for atoms in their ground states, using wave functions of single-zeta, double-zeta, and near--Hartree-Fock quality, also unearths a startling feature that the entropy sum, ${S}_{\ensuremath{\rho}}$+${S}_{\ensuremath{\gamma}}$, increases with an enhancement in the ground-state wave-function quality.