The vectors in the Patterson map can be divided into two categories. Intermolecular vectors depend both on the orientation of the molecule and on its position so, once the orientation is known, these can be exploited in the translation function. Crystal Patterson map Intramolecular vectors before rotation Colour-coded Patterson map Intramolecular vectors after rotation On average, the intramolecular vectors will be shorter than the intermolecular vectors, so the rotation function can be computed using only the part of the Patterson map near the origin. We won't go into detail here, but it turns out that if you assume that a crystal is made up of similarly-shaped atoms that all have positive electron density, then there are statistical relationships between sets of structure factors. These statistical relationships can be used to deduce possible values for the phases.
Direct methods exploit such relationships, and can be used to solve small molecule structures.
Unfortunately, the statistical relationships become weaker as the number of atoms increases, and direct methods are limited to structures with, at most, a few hundred atoms in the unit cell. However, they do become useful in the context of experimental phasing methods, such as isomorphous replacement and anomalous dispersion, as discussed below. Multiple isomorphous replacement In isomorphous replacement, the idea is to make a change to the crystal that will perturb the structure factors and, by the way that they are perturbed, to make some deductions about possible phase values. The figure below illustrates the effect of adding a heavy atom to the structure considered above. The introduction of a heavy atom will change the scattered intensity significantly.