Section 13.1.5.1. Relevant parameters: standard case

A poorly determined structure, if known at sufficient resolution and accuracy, can be improved by structural refinement of an atomic model to fit the observations. These methods often use existing structural knowledge (of bond lengths and angles, for example) to improve the convergence of the refinement process.

The most important contributions of noncrystallographic symmetry arise before this point of structure determination is reached. In this stage of structural analysis, the distribution of scattering density may be constrained by the requirements of noncrystallographic symmetry. The density may be improved by imposing noncrystallographic symmetry on poorly defined scattering density, and, in favourable cases, cyclical improvement leads to a unique corrected structure. To avoid any confusion with refinement of the atomic structure, this process will be referred to as `symmetry correction' or `correction' (Hoppe & Gassmann, 1968).

Noncrystallographic symmetry can also be used to improve the accuracy and convergence of atomic structural refinement by increasing the number of observations to a given resolution (Section 13.1.5.5).

The power of correction methods in improving an unknown structure in the standard case (Section 13.1.2.1) depends on:

The first three parameters are expressed in quantitative terms; parameter (4) might be true or false, but more often lies between these; and parameters (5) and (6) are not easily expressed in measurable form.

The resolution d should ideally be matched to the level of similarity of the subunits. The root-mean-square displacement between an atom in one subunit and the rotated and translated position of the corresponding atom from another subunit (or model subunit) provides an order of magnitude for the resolution d which can be used effectively. In many cases, the resolution is worse than this for practical reasons of crystal disorder and data collection.

This limit was encountered by Huber et al. (1974) working at 1.9 Å resolution. They found that a model structure with a mean coordinate difference of 1.9 Å was not usable for molecular replacement, while another model agreeing to 0.75 Å gave results which allowed the structure to be refined. This suggests that agreement significantly better than the resolution is required.