Phase combination and cross validation in iterated density-modification calculations

A variety of density-modification techniques are now available for improving electron-density maps in accordance with known chemical information. This modification must, however, always be constrained by consistency with the experimental data. This is conventionally achieved by alternating cycles of map modification in real space with recombination with the experimental data in reciprocal space. The phase recombination is based upon the assumption that the density-modified map may be treated as a partial model of the structure which contains information independent of the experimentally derived phases. This assumption is shown to be incorrect, and an alternative procedure is investigated which as a side effect allows calculation of a free R factor.