Section 13.2.6. Concluding remarks

Each formulation of the rotation function described above has its advantages and disadvantages. The direct-space formulation [equation (13.2.3.3)] offers the possibility of modifying the Patterson function or selecting the strongest peaks to be used in the overlap integral. Also, the domain of integration may have any shape, as in the reciprocal-space formulation [equation (13.2.3.5)]. However, in both formulations, the numerical results can be somewhat imprecise because of the approximations introduced to save computing time.

When the domain of integration is spherical, as is usually the case, then the fast rotation function [equation (13.2.3.15)] is faster, more accurate and allows for angular-resolution enhancement. Moreover, since most of the computing time is spent in the calculation of the coefficients , a library of these coefficients may be compiled to assess the models in a given molecular-replacement problem more rapidly.

The direct rotation [equation (13.2.5.5)] seems preferable to the cross-rotation function, as it includes all self-Patterson terms of the search model. However, when the order of the space group is high, the calculated intensity represents only a small fraction of the observed one, and the discriminative power of the function drops, as compared with the cross-rotation function.

Patterson searches now benefit from new supercomputers. The real problem of molecular replacement, split for convenience into rotation and translation searches, is beginning to be tackled by genuine six-dimensional searches where all orientations are tested. This may represent the end of cross-rotation and direct-rotation functions.