As an example, Figure shows the distribution of the coordinate differences together with the proposed PDF, and the EDF with the proposed CDF. This have been plotted for two clusters where the first, (NTA) 1 (SA) 1 (EDA) 2 , has optimized to the same minimum as the reference, and the second, (FA) 1 (MSA) 1 (TMA) 1 , has optimized to a minimum different from the reference method. It is here quite clear to see that the first cluster decently follows the proposed distribution, while the second cluster deviates significantly. The two upper panels contain the histogram/distribution of the differences of the atomic positions for two molecular clusters. The geometries compared are optimized at the reference level (DF-MP2/aug-cc-pVQZ) and r 2 SCAN-3c. The proposed fit is obtained through sums of weighted order statistics for the cauchy PDF. In the two lower panels the EDF for the same data is plotted alongside the CDF for a cauchy distribution (using the same parameters as the PDF).