A systematic analysis of weighting schemes for structure factors in macromolecular crystallography

The three weighting schemes for structure-factor amplitudes used in macromolecular crystallography, and the products of these weighting schemes, have been analysed by comparison of the figures of merit to the cosine of the phase difference between the current phase estimate and the true phase, and by computation of the linear correlation coefficient between these figures. The results of the analysis indicate that (i) the σ_A and Sim weighting schemes are superior to all others investigated (for the latter scheme, provided that Σ_L has been computed by the method of Henderson & Moffat [Acta Cryst. (1971), B27, 1414–1420]), (ii) all weighting schemes are an underestimate of the cosine of the phase difference, (iii) the correlation between the Rayment figures of merit and the cosine of the phase difference is quite low, indicating a poor weighting scheme, and (iv) for the figures of merit obtained by multiplication of weights, better results are obtained when the best weighting schemes, namely the σ_A and Sim figures of merit, are combined.