Maximum-entropy and Padé-like approximations to atomic scattering factors

Abstract

Three different methods, namely maximum entropy, combination of Dirac deltas and two-point Padé approximants, are used to construct tight model-independent approximations to the atomic form factor F(k) in terms of a few quantities related to its inverse Fourier trnsform, i.e. the one-particle density ρ(r). The accuracy of these approximations is analyzed in a Hartree-Fock framework. These extrapolation techniques, being completely general and modelindependent, can be applied to other kind of physical systems, such as solids, molecules or nuclei.

Reciprocal form factors from momentum density magnitudes

“…they can be applied to other atomic magnitudes (e.g. form factors (Zarzo et al 1996)) and also to other kinds of systems, such as molecules, solids or nuclei (see e.g. Antolín et al 1996).…”

Minimum-cross-entropy estimation of atomic charge densities from scattering factors

“…The important role played by the elastic and inelastic components of the total scattering intensity in the analysis of chemical binding and correlation effects in those systems has enforced the separate measurements of its components (Duguet et al 1983, McClelland andFink 1985) as well as the obtention of highly accurate computations of scattering factors (Wang et al 1993(Wang et al , 1995. In this sense, the authors have obtained tight approximations to F (k) in atoms by means of few local values of the density ρ(r) and/or some radial expectation values (Zarzo et al 1997)…”

Computation of the Entropy of Polynomials Orthogonal on an Interval

“…atomic and molecular physics, condensed matter theories). For instance, several maximum entropy methods based on the position and momentum entropies, as well as on their sum, have been developed [16,21] and widely used [3,15,37] for determination of macroscopic quantities of natural systems. Nevertheless, the lack of a general theoretical methodology and of accurate numerical algorithms of computation these information entropies still prevents this approach from being more widely used.…”