Iteratively reweighted least squares in crystal structure refinements

The use of robust techniques in crystal structure multipole refinements of small molecules as an alternative to the commonly adopted weighted least squares is presented and discussed. As is well known, the main disadvantage of least-squares fitting is its sensitivity to outliers. The elimination from the data set of the most aberrant reflections (due to both experimental errors and incompleteness of 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 be circumvented by means of a robust least-squares regression that minimizes the influence of outliers. This work is aimed at showing the capability of a robust regression to achieve an higher reliability of the least-squares estimates with respect to the traditional weighted least-squares crystal structure refinement in terms of both accuracy and precision. The results can be considered encouraging and represent a starting point for future developments.