Robust/Resistant Technique for Crystal-Structure Refinement

摘要

A refinement technique is robust if it works well over a broad class of error distributions in the data, and resistant if it is not strongly influenced by any small subset of the data. Least squares possesses neither property. A more robust/resistant procedure is to minimize, instead of a simple sum of squared differences, a sum of terms of the form (x exp 2 /2)(1 - (x/a) exp 2 + (1/3) (x/a) exp 4 ) for absolute value x absolute value less than or equal to a and a exp 2 /6 for absolute value x absolute value > a. Here x = w/sup 1/2/(absolute value F sub 0 absolute value - absolute value F/sub c/ absolute value)/S. S is a measure of the width of the error distribution based on the results of the previous cycle, and a is a constant chosen so that extreme data do not influence the solution. This function behaves like the sum of squares for small absolute value x absolute value, but is constant for large abolute value x absolute value, so that the effect of large differences is deemphasized. A least-squares program can easily be modified to perform this more robust/resistant procedure. The modified procedure has been used in a reanalysis of D(+)-tartaric acid data. Results show that the technique provides an efficient means for automatic screening of least-squares results for good data sets. If the results don't agree with least squares it suggests systematic effects. (ERA citation 07:022689)