International
Tables for
Crystallography
Volume F
Crystallography of biological macromolecules
Edited by M. G. Rossmann and E. Arnold

International Tables for Crystallography (2006). Vol. F. ch. 19.5, p. 445   | 1 | 2 |

Section 19.5.3.4. Fourier–Bessel syntheses

R. Chandrasekarana* and G. Stubbsb

aWhistler Center for Carbohydrate Research, Purdue University, West Lafayette, IN 47907, USA, and  bDepartment of Molecular Biology, Vanderbilt University, Nashville, TN 37235, USA
Correspondence e-mail:  [email protected]

19.5.3.4. Fourier–Bessel syntheses

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Electron densities may be calculated for crystalline fibres, as they are in crystallography, using Fourier syntheses with coefficients determined for the crystalline reflections.

For noncrystalline fibres, it is more convenient to use Fourier–Bessel syntheses: the electron density ρ at point [(r, \varphi, z)] is [{\rho (r, \varphi, z) = (1/c) \textstyle\sum\limits_{l}\displaystyle \textstyle\sum\limits_{n}\displaystyle \hbox{{\bf g}}_{n, \, l} (r) \exp [i(n\varphi - 2\pi lz/c)],}\hfill\!\!\! \eqno(19.5.3.5)] where [\hbox{{\bf g}}_{n, \, l} (r) = \textstyle\int\limits_{0}^{\infty}\displaystyle \hbox{{\bf G}}_{n, \, l} (R) J_{n} (2\pi Rr)2\pi R \kern3pt\hbox{d}R. \eqno(19.5.3.6)]








































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