Correcting electron-density resolution bias in reciprocal space

Fourier syntheses are always affected by series-termination errors, which generate sets of positive and negative ripples around each main peak in the map. The interaction among the ripples distorts the profile of the map and moves peaks away from their correct positions. In a previous paper [Altomare et al. (2008). Acta Cryst. A64, 326-336] an algorithm was described which reduces the resolution bias by removing the effects of the ripples in direct space. In this paper the correction is performed in reciprocal space: the effect of the ripples on the atomic scattering factors is calculated and subtracted from the usual atomic scattering factors. The modified scattering factors are used to calculate new structure factors, from which more accurate electron-density maps may be obtained. The experimental tests show that the procedure minimizes the effects of the resolution bias and provides atomic positions that are more accurate than those provided by traditional approaches.