InternationalReciprocal spaceTables for Crystallography Volume B Edited by U. Shmueli © International Union of Crystallography 2010 |
International Tables for Crystallography (2010). Vol. B, ch. 2.2, p. 215
## Section 2.2.2. Introduction |

Direct methods are today the most widely used tool for solving small crystal structures. They work well both for equal-atom molecules and when a few heavy atoms exist in the structure. In recent years the theoretical background of direct methods has been improved to take into account a large variety of prior information (the form of the molecule, its orientation, a partial structure, the presence of pseudosymmetry or of a superstructure, the availability of isomorphous data or of data affected by anomalous-dispersion effects, …). Owing to this progress and to the increasing availability of powerful computers, the phase problem for small molecules has been solved in practice: a number of effective, highly automated packages are today available to the scientific community.

The combination of direct methods with so-called direct-space methods have recently allowed the *ab initio* crystal structure solution of proteins. The present limit of complexity is about 2500 non-hydrogen atoms in the asymmetric unit, but diffraction data at atomic resolution (~1 Å) are required. Trials are under way to bring this limit to 1.5 Å and have shown some success.

The theoretical background and tables useful for origin specification are given in Section 2.2.3; in Section 2.2.4 the procedures for normalizing structure factors are summarized. Phase-determining formulae (inequalities, probabilistic formulae for triplet, quartet and quintet invariants, and for one- and two-phase s.s.'s, determinantal formulae) are given in Section 2.2.5. In Section 2.2.6 the connection between direct methods and related techniques in real space is discussed. Practical procedures for solving small-molecule crystal structures are described in Sections 2.2.7 and 2.2.8, and references to the most extensively used packages are given in Section 2.2.9. The integration of direct methods, isomorphous replacement and anomalous-dispersion techniques is briefly discussed in Section 2.2.10.

The reader interested in a more detailed description of the topic is referred to a recent textbook (Giacovazzo, 1998).

### References

Giacovazzo, C. (1998).*Direct Phasing in Crystallography*. New York: IUCr, Oxford University Press.