The Map Correlation Coefficient for Optimally Superposed Maps

In judging the effectiveness of methods of solving crystal structures, it is customary to use the mean phase error or the map correlation coefficient as a measure of success. When methods for ab initio phase determination are being developed, it is necessary to take into account that the solutions found may correspond to different origin and enantiomorph choices, so a procedure of map alignment must be performed prior to calculation of a phase-similarity measure. A fast-Fourier-transform-based algorithm for map alignment is proposed for different space groups. The possibility of additional alignment by map `overturning' is discussed for very low resolution protein syntheses. Simple analytical equations defining the permitted origin shift are included.