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. 25.2, p. 735   | 1 | 2 |

## Section 25.2.10.3.1. The Patterson map interpretation algorithm in SHELXS

G. M. Sheldricku*

#### 25.2.10.3.1. The Patterson map interpretation algorithm in SHELXS

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Space-group-general automatic Patterson map interpretation was introduced in the program SHELXS86 (Sheldrick, 1985); completely different algorithms are employed in the current version of SHELXS, based on the Patterson superposition minimum function (Buerger, 1959, 1964; Richardson & Jacobson, 1987; Sheldrick, 1991, 1998a; Sheldrick et al., 1993). The algorithm used in SHELXS is as follows:

 (1) A single Patterson peak, v, is selected automatically (or input by the user) and used as a superposition vector. A sharpened Patterson map [with coefficients instead of , where E is a normalized structure factor] is calculated twice, once with the origin shifted to −v/2 and once with the origin shifted to +v/2. At each grid point, the minimum of the two Patterson function values is stored, and this superposition minimum function is searched for peaks. If a true single-weight heavy atom-to-heavy atom vector has been chosen as the superposition vector, this function should consist ideally of one image of the heavy-atom structure and one inverted image, with two atoms (the ones corresponding to the superposition vector) in common. There are thus about 2N peaks in the map, compared with in the original Patterson map, a considerable simplification. The only symmetry element of the superposition function is the inversion centre at the origin relating the two images. (2) Possible origin shifts are found so that the full space-group symmetry is obeyed by one of the two images, i.e., for about half the peaks, most of the symmetry equivalents are present in the map. This enables the peaks belonging to the other image to be eliminated and, in principle, solves the heavy-atom substructure. In the space group P1, the double image cannot be resolved in this way. (3) For each plausible origin shift, the potential atoms are displayed as a triangular table that gives the minimum distance and the Patterson superposition minimum function value for all vectors linking each pair of atoms, taking all symmetry equivalents into account. This table enables spurious atoms to be eliminated and occupancies to be estimated, and also in some cases reveals the presence of noncrystallographic symmetry. (4) The whole procedure is then repeated for further superposition vectors as required. The program gives preference to general vectors (multiple vectors will lead to multiple images), and it is advisable to specify a minimum distance of (say) 8 Å for the superposition vector (3.5 Å for selenomethionine MAD data) to increase the chance of finding a true heavy atom-to-heavy atom vector.

### References

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Richardson, J. W. & Jacobson, R. A. (1987). Computer-aided analysis of multi-solution Patterson superpositions. In Patterson and Pattersons, edited by J. P. Glusker, B. Patterson & M. Rossi, pp. 311–317. Oxford: IUCr and Oxford University Press.Google Scholar
Sheldrick, G. M. (1985). Computing aspects of crystal structure determination. J. Mol. Struct. 130, 9–16.Google Scholar
Sheldrick, G. M. (1991). Tutorial on automated Patterson interpretation to find heavy atoms. In Crystallographic computing 5. From chemistry to biology, edited by D. Moras, A. D. Podjarny & J. C. Thierry, pp. 145–157. Oxford: IUCr and Oxford University Press.Google Scholar
Sheldrick, G. M. (1998a). Location of heavy atoms by automated Patterson interpretation. In Direct methods for solving macromolecular structures, edited by S. Fortier, pp. 131–141. Dordrecht: Kluwer Academic Publishers.Google Scholar
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