N-derivative of Shannon entropy of shape function for atoms

The Shannon entropy of the ratio of electron density and the number of electrons, shape function entropy, is reported for the atoms He-Ac within the non-relativistic exchange-only optimized effective potential model. The derivative of the shape function entropy with electron number at constant external potential is related to an integral containing the difference between the average Fukui function and the shape function weighted by the logarithm of electron density. The trends in the shape function entropy, its spin analogue and the corresponding derivatives with electron number reveal interesting periodic behaviour.

[1]  R. Parr,et al.  Fukui function from a gradient expansion formula, and estimate of hardness and covalent radius for an atom , 1995 .

[2]  L. Pacios.  Study of a gradient expansion approach to compute the Fukui function in atoms , 1997 .

[3]  Casida.  Generalization of the optimized-effective-potential model to include electron correlation: A variational derivation of the Sham-Schlüter equation for the exact exchange-correlation potential. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[4]  P. Ayers,et al.  On the importance of the "density per particle" (shape function) in the density functional theory. , 2004, The Journal of chemical physics.

[5]  W. Kohn,et al.  Self-Consistent Equations Including Exchange and Correlation Effects , 1965 .

[6]  R. T. Sharp,et al.  A Variational Approach to the Unipotential Many-Electron Problem , 1953 .

[7]  R. Parr,et al.  Statistical atomic models with piecewise exponentially decaying electron densities , 1977 .

[8]  R. P. Sagar,et al.  Information uncertainty-type inequalities in atomic systems , 2003 .

[9]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[10]  Görling,et al.  Density-functional theory for excited states. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[11]  J. D. Talman,et al.  Optimized effective atomic central potential , 1976 .

[12]  From explicit to implicit density functionals , 1999 .

[13]  Sears,et al.  Some novel characteristics of atomic information entropies. , 1985, Physical review. A, General physics.

[14]  P. Geerlings,et al.  Quantum similarity of atoms: a numerical Hartree-Fock and Information Theory approach , 2004 .

[15]  P. Geerlings,et al.  Conceptual density functional theory. , 2003, Chemical reviews.

[16]  R. Dreizler,et al.  Relativistic spin-density-functional theory: Robust solution of single-particle equations for open-subshell atoms , 2001 .

[17]  K. Fukui,et al.  Role of frontier orbitals in chemical reactions. , 1982, Science.

[18]  Engel,et al.  Accurate optimized-potential-model solutions for spherical spin-polarized atoms: Evidence for limitations of the exchange-only local spin-density and generalized-gradient approximations. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[19]  P. Hohenberg,et al.  Inhomogeneous Electron Gas , 1964 .

[20]  Rodolfo O. Esquivel,et al.  Molecular similarity based on information entropies and distances , 1998 .

[21]  Paul Geerlings,et al.  Density functional theory and quantum similarity , 2005 .

[22]  J. D. Talman.  A program to compute variationally optimized effective atomic potentials , 1989 .

[23]  P. Fuentealba,et al.  Atomic spin-density polarization index and atomic spin-density information entropy distance , 2002 .

[24]  R. P. Sagar,et al.  Shannon-information entropy sum as a correlation measure in atomic systems , 2003 .

[25]  Robert G. Parr,et al.  Density functional approach to the frontier-electron theory of chemical reactivity , 1984 .

[26]  P. Ayers.  Density per particle as a descriptor of Coulombic systems. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[27]  A numerical study of molecular information entropies , 1994 .

[28]  P. Geerlings,et al.  The use of density functional theory-based reactivity descriptors in molecular similarity calculations , 1998 .

[29]  J. Perdew,et al.  Density-Functional Theory for Fractional Particle Number: Derivative Discontinuities of the Energy , 1982 .

[30]  Mel Levy,et al.  DFT ionization formulas and a DFT perturbation theory for exchange and correlation, through adiabatic connection , 1995 .

[31]  J. D. Talman,et al.  Optimized central potentials for atomic ground-state wavefunctions , 1978 .

[32]  M. Levy,et al.  Connections between ground-state energies from optimized-effective potential exchange-only and Hartree-Fock methods , 2003 .