InternationalCrystallography of biological macromoleculesTables for Crystallography Volume F Edited by M. G. Rossmann and E. Arnold © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. F, ch. 13.2, p. 273
## Section 13.2.5. Other rotation functions |

The rotation function was hitherto described in terms of self- and cross-Patterson vectors. This is perhaps inevitable in the self-rotation case, but the problem of determining the absolute orientation of the subunits when a model structure is available may be formulated in a different way. We may try to compare directly the observed and calculated intensities or structure factors by using any criterion analogous to those employed in refinement procedures, *e.g.*, the crystallographic *R* factor or correlation coefficients.

When the space-group symmetry is explicitly exhibited, the structure factor corresponding to a crystal with *M* independent molecules in the unit cell takes the form where and denote, respectively, the transformation matrix and the translation associated with the *g*th symmetry operation of the crystal space group. The corresponding intensity is

For criteria based on amplitudes, the calculated structure factor will contain only the contribution of the rotated model, *i.e.*, the Fourier transform of a single molecule in the crystal cell, assuming *P*1 symmetry. For criteria based on intensities, some symmetry information may be introduced, A criterion often considered is the correlation coefficient on intensities, where means `average over reflections'. It may be calculated within reasonable computing time provided that

is referred to as the direct-rotation function (DeLano & Brünger, 1995). A major advantage of this formulation is that the information stemming from already-positioned subunits may be taken into account, just by adding their contribution to the calculated intensities.

### References

DeLano, W. L. & Brünger, A. T. (1995).*The direct rotation function: rotational Patterson correlation search applied to molecular replacement*.

*Acta Cryst.*D

**51**, 740–748.Google Scholar