Application of a new least-squares method to structure refinement

Abstract

A new least-squares-type refinement algorithm which updates the parameter values after processing each reflection is tried in comparison with a standard block-diagonal least-squares refinement procedure. A ten-atom problem (C9S) in space group Fdd2, and a 30-atom problem (C26N4) in space group P21/c with varying-quality starting coordinate sets and choices of reflection/parameter ratios were used as test cases. With starting atomic coordinates off by at least ± 0.2 A from the correct values, the new method gives rapid convergence with considerable saving in computation time. The method also gives rapid convergence for both the good and poor starting coordinate sets when the reflection data set for the 30-atom problem was restricted to d > 2 A. For this restricted data set the traditional block-diagonal least-squares method diverged. Computer storage requirements are essentially the same for the new method as for the traditional least-squares methods.