Reinvestigation of the Use of Patterson Maps to Extrapolate Data to Higher Resolution

Many years ago, Karle & Hauptman proposed that the Patterson function could be used for data extrapolation beyond the observed range of the actual measured data. Few people have subsequently attempted to exploit this interesting idea, which might suggest possible limitations of this method, even in structural applications of modest complexity. This appears not to be the case, however, but the original ideas for implementing the extrapolation can be significantly improved. New calculation protocols indicate that Patterson maps may be used to extend observed data sets from 1.0 to ~ 0.5 Å resolution with reasonably good precision. Correlation coefficients between the extrapolated F(hkl)'s and their structure-computed expected values typically range between 0.40 and 0.70 across the unobserved range, even for structures containing as many as 600 non-H light atoms in the asymmetric unit. The method is equally good at extrapolating F values for small zones of data that may not have been recorded within the observed resolution range of the diffraction experiment. Furthermore, triplet phase invariants that incorporate one or two extrapolated terms are nearly as reliable as those formed using only the observed data.