SAS differences

Sheldrick, G. M.; Hauptman, H. A.; Weeks, C. M.; Miller, R.; Usón, I.

doi:10.1107/97809553602060000689

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

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

Section 16.1.2.2. SAS differences

G. M. Sheldrick,^c H. A. Hauptman,^b C. M. Weeks,^b ^* R. Miller^b and I. Usón^a

^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

16.1.2.2. SAS differences

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Given Friedel pairs of normalized structure-factor magnitudes $[(|E_{+{\bf H}}|, |E_{-{\bf H}}|)]$ and the atomic scattering factors, then the greatest-lower-bound estimates of SAS difference [|E|] 's are $[{|E_{\Delta}| = {\left[\textstyle\sum_{j=1}^{N}\displaystyle (\;f_{j}^{0} + f_{j}^{'})^{2} + (\;f_{j}^{''})^{2}\right]^{1/2} \|E_{+{\bf H}}| - |E_{-{\bf H}}\| \over 2q\left[\textstyle\sum_{j=1}^{N}\displaystyle (\;f_{j}^{''})^{2}\right]^{1/2}}}, \eqno(16.1.2.3)]$ where, again, q is an empirical renormalization scaling function that imposes the condition $[\langle |E_{\Delta}|^{2}\rangle = 1]$ .

References

International Tables for Crystallography (2006). Vol. F. ch. 16.1, p. 334