The accuracy of atomic coordinates derived by least-squares or Fourier methods

Abstract

Recent work by Cruickshank on the accuracy of atomic co-ordinates obtained in Fourier syntheses is here related to that of Cochran on the connexions between the least-squares and Fourier methods. Except when the atomic peaks are not resolved, it is shown that the same co-ordinates and estimated errors are obtained by the method of least squares and by appropriately weighted Fourier series (corrected for finite summation). An expression is obtained for the relative accuracies of the weighted and unweighted Fourier methods.