view article

Figure 1
This figure illustrates some of the difficulties involved in rotating the Patterson map calculated from a search molecule instead of rotating the search molecule directly. Each of the four figures shows nine (3 × 3) unit cells. Since the unit-cell parameters of crystal space and Patterson space are identical, they are superimposed in (a), (b) and (c) for convenience. (a) shows a simple molecule with four atoms (black) and the corresponding Patterson peaks (red) associated with one lattice point. (b) shows the molecule and the corresponding configuration of Patterson peaks translated to each lattice point. An alternating red–blue coloring scheme is used to distinguish the groups of Patterson peaks associated with each lattice translation. It can be seen that the groups are not spatially separated. Therefore, as the search model is rotated, vectors in the map that are close to each other rotate around different origins. In order to be able to consistently rotate the search pattern present in the map, the two types of vectors must be spatially separated. (c) shows the molecule and the corresponding Patterson peaks in an artificially enlarged unit cell. (For the purpose of this illustration, the molecule is scaled down instead of enlarging the entire drawing.) By making the unit cell sufficiently large, the groups of Patterson peaks associated with each lattice point are spatially separated. In (d) the molecule is omitted and the observed Patterson map superimposed. (Note that the observed Patterson map has the true unit-cell parameters of the crystal, while the model Patterson map is artificially enlarged.) The rotation function is computed by rotating the Patterson maps with respect to each other. For each sampling point in angular space, the correlation integral (1) is computed in the yellow integration shell.

Journal logoBIOLOGICAL
ISSN: 1399-0047
Follow Acta Cryst. D
Sign up for e-alerts
Follow Acta Cryst. on Twitter
Follow us on facebook
Sign up for RSS feeds