Calculation of the point-by-point error in protein crystallographic electron-density functions

In protein crystallographic studies, the mean-square error at each point in the electron-density function is given, in space group P1, by [formula: see text] Here, Fo is the observed structure-factor amplitude; m(h) exp [i alpha B(h)] = P[alpha(h)] exp (i alpha) d alpha is the weighted phase factor in the 'best' Fourier coefficient of Blow & Crick; m2(h) exp (i alpha 2) = P[alpha(h)] exp (2i alpha) d alpha is similar to a traditional second moment. P[alpha(h)] d alpha is the probability that the phase angle for a given reflection has value between alpha and alpha + d alpha.