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Structure determination without Fourier inversion. Part I. Unique results for centrosymmetric examples by Karl F. Fischer; Armin Kirfel; Helmuth Zimmermann is a Chemistry article available to read on EtoBox.

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## Abstract A concept is presented for determining a one-dimensional structure of__m__independent point scatterers by mapping into an__m__-dimensional space**P**^m^at least__m__observations as (__m__– 1)-dimensional so-called “isosurfaces” defined by__s__(__h__) ·__g__(__h__) or__g__(__h__) alone, where__s__(__h__) and__g__(__h__) are sign and modulus, respectively, of the geometrical structure factor. Values of__g__(__h__) are derived from the observed |__F__(__h__)|. The “solution vector(s)”, (__x__~1~, ...,__x__~m~), representing the coordinates__x__~j~of the point scatterers is (are) found from the “common” intersection(s) of__n__≥__m__different isosurfaces. Homometric and quasi-homometric structures can thus safely be detected from multiple solutions, the latter mainly arising from the experimental uncertainties of the__g__(__h__). Spatial resolution is by far higher than that offered by a corresponding Fourier transform. Computer time can be drastically reduced upon consideration of both the symmetry of**P**^m^and the anti-symmetry and self-similarity properties of the isosurfaces, which allow for tayloring of the intersection search routines and/or applying linear approximat

Who reads Structure determination without Fourier inversion. Part I. Unique results for centrosymmetric examples?

Author

Karl F. Fischer; Armin Kirfel; Helmuth Zimmermann

Publisher

Oldenbourg Wissenschaftsverlag; Walter de Gruyter GmbH (ISSN 2194-4946)

Published

2005

Language

EN

Field

Chemistry (Physical Sciences)