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Problems

While real space refinement has a glorious history, it does not have a very sound mathematical basis. The problem has to do with error analysis. Least squares optimization has built into it the assumption that every observation is independant and its uncertainty follows a Normal distribution. When each density point in the map is considered an ``observation" they certainly are not independant - neigboring points tend to have very similar densities.

The real errors of the observations follow a strange distribution. The errors assoicated with the amplitudes are usually much smaller than those associated with the phases. This asymmetry cannot be expressed in real space.

Due to these, or other unknown problems, a cycle of refinement with the real space module usually requires more short loops than expected.



Dale Edwin Tronrud
Thu Jul 6 23:24:57 PDT 2000