In Molecular Replacement the orientation of a fragment of known structure is determined by searching for a peak in the ``Rotation Function''. Search methods are very useful for avoiding the problems of local minima but are not particularly efficient for getting the exact result. With a solution ``close enough'' to the peak one can perform least-squares refinement to home in on its center (Yates, T.O., Rini, J.M., Acta Cryst (1990) A46, 352-359). This module allows the user to refine the parameters of a model against a rotation function.
Refining with this module is more complicated than the other modules. The data required for the calculation of the function value, gradient, and curvature are different. In addition the space group of the calculation changes from one part of the calculation to another. This module is only implemented under the VMS operating system.
The function minimized with this module is
Minimizing this function means that the parameters of the model will be varied to achieve a match between the Patterson coefficients calculated from the model and the observed Patterson coefficients. This function is relatively insensitive to the position of the molecule in the unit cell so the model will not shift in space, it will only rotate. To achieve the magnitude of shifts which are expected for this type of refinement one will usually refine the model as a small number of rigid groups.
There is a complication in the manner in which the space group symmetry is included. Because we do not know the location of the fragment in the unit cell we cannot calculate the Patterson coefficients for the whole unit cell. We must calculate the Patterson coefficients for the model orientated as it would be in each asymmetric unit, with its center at the origin, and sum them. This calculation will eliminate any cross vectors between asymmetric units which is good because we know they are wrong. We then must calculate the gradient of the function for each asymmetric unit in space group P1 and combine the gradients.
The actual procedure is simpler than this explanation sounds because the observed Patterson contains the Patterson group symmetry so the gradient from each asymmetric unit will be equal. We only have to calculate one of them.
An analysis of the function which must be minimized by this module shows that the gradient can be calculated using a variation of the Agarwal method. The program Rfactor can be used to perform the calculation, only it must be use an alternate set of difference coefficients. These coefficients are
The calculation of the predicted scattering from your model is done
in two steps. First the Fourier transform of the model in P1 is calculated.
Then the Patterson coefficients ( 
) are calculated in
a fashion which excludes
contributions from the ``cross vectors''. These coefficients are calculated
with the program Averager_I. The Patterson coefficients are used to calculate
the function value and are involved in the gradient calculation.
The function value is calculated by comparing the observed Patterson coefficients with those calculated from the current model. This must be done in the Patterson space group.
The curvature is calculated by comparing the Fobs's with the Fcalc's of the model. Because the model, itself, is in space group P1 the Fobs's must be expanded by its symmetry to P1 so that the reflections can be matched. You must have a copy of your Fobs which has been expanded to space group P1. The atomic parameters are also required for curvature calculation. This module is usually used to perform rigid body refinement. Since one should not use a minimization method which requires the curvatures in rigid body refinement it is not likely that you will need to calculate curvatures.
The gradient is especially complicated to calculate because the coefficients
required (the C( 
) above) depend upon the Fobs's, the Fcalc's, and the
Patterson coefficients ( ).
The gradient coefficients must be calculated separately
and ran back through Rfactor using the AGARWAL command.
In a short loop all that need be done is to recalculate the Patterson coefficients of the new model, and run RFACTOR again.