Iteratively reweighted least squares in crystalstructure refinements

The use of robust techniques in crystal structure multipole refinements of smallmolecules as an alternative to the commonly adopted weighted least squares ispresented and discussed. As is well known, the main disadvantage of leastsquaresfitting is its sensitivity to outliers. The elimination from the data set ofthe most aberrant reflections (due to both experimental errors and incompletenessof the model) is an effective practice that could yield satisfactory results,but it is often complicated in the presence of a great number of bad data points,whose one-by-one elimination could become unattainable. This problem can becircumvented by means of a robust least-squares regression that minimizes theinfluence of outliers. This work is aimed at showing the capability of a robustregression to achieve an higher reliability of the least-squares estimates withrespect to the traditional weighted least-squares crystal structure refinement interms of both accuracy and precision. The results can be considered encouragingand represent a starting point for future developments.