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

© International Union of Crystallography 2006
International Tables for Crystallography (2006). Vol. F. ch. 16.1, p. 334   | 1 | 2 |

Section 16.1.2.1. SIR differences

G. M. Sheldrick,c H. A. Hauptman,b C. M. Weeks,b* R. Millerb and I. Usóna

a Institut für Anorganisch Chemie, Universität Göttingen, Tammannstrasse 4, D-37077 Göttingen, Germany,bHauptman–Woodward Medical Research Institute, Inc., 73 High Street, Buffalo, NY 14203-1196, USA, and cLehrstuhl für Strukturchemie, Universität Göttingen, Tammannstrasse 4, D-37077 Göttingen, Germany
Correspondence e-mail:  weeks@orion.hwi.buffalo.edu

16.1.2.1. SIR differences

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Given the individual normalized structure-factor magnitudes [(|E_{\rm nat}|, |E_{\rm der}|)] and the atomic scattering factors [|\;f_{j}| = |\;f_{j}^{0} + f_{j}^{'} + if_{j}^{''}| = [(\;f_{j}^{0} + f_{j}^{'})^{2} + (\;f_{j}^{''})^{2}]^{1/2}] which allow for the possibility of anomalous scattering, then greatest-lower-bound estimates of SIR difference-E magnitudes are [|E_{\Delta}| = {\left|\left(\textstyle\sum_{j=1}^{N_{\rm der}}\displaystyle \left|\;f_{j}\right|^{2}\right)^{1/2} |E_{\rm der}| - \left(\textstyle\sum_{j=1}^{N_{\rm nat}}\displaystyle \left|\;f_{j}\right|^{2}\right)^{1/2} |E_{\rm nat}|\right| \over q\left[\left(\textstyle\sum_{j=1}^{N_{\rm der}}\displaystyle |\;f_{j}|^{2}\right) - \left(\textstyle\sum_{j=1}^{N_{\rm nat}}\displaystyle |\;f_{j}|^{2}\right)\right]^{1/2}}, \eqno(16.1.2.2)] where [q = q_{0} \exp (q_{1}s^{2} + q_{2}s^{4})] is a least-squares-fitted empirical renormalization scaling function, dependent on [s = \sin (\theta)/\lambda], that imposes the condition [\langle|E_{\Delta}|^{2}\rangle = 1] and serves to define [q_{0},\ q_{1}] and [q_{2}].








































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