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Sheldrick's 1.2 Å rule and beyond

Acta Cryst. (2003). D59, 615–617

In 1990 George Sheldrick summarised his experience in solving crystal structures of small organic molecules by the rule that at least half the number of possible reflections between 1.1 and 1.2 Å resolution had to be well measured [F > 4σ(F)] for direct methods to succeed (Acta Cryst. A46, 467–473). The present authors investigate the expectation value |E|2 of the squared normalized structure-factor amplitude as a function of resolution for numerous organic molecules, including 700 proteins. Direct methods assume that atoms are statistically independent and predict |E|2 = 1 at all resolutions. However, the authors observe a consistent peak with a value of about 1.3 around a resolution of 1.1 Å, and trace its origin to not only the existence of individual bonding distances, but to the occurrence in these molecules of numerous families of inter-atomic distances which differ by 1.1–1.2 Å. They conclude that incorporating data in this critical resolution range contributes not only to resolving atoms, but also to introducing some of the structural information that is missing from the stereochemistry-free foundations of direct methods. Finally, they argue that a 'stereochemically aware' extension of direct methods proposed by the senior author should significantly relax the data resolution requirements embodied in Sheldrick’s rule.

Richard J. Morris and Gérard Bricogne