as it approaches the Dirac delta function when the scale parameter, γ, approaches zero. This is an appropriate limit, because if the two clusters are exactly the same geometry then the coordinate difference distribution would exactly be the Dirac-delta function. In reality the two geometries are not exactly the same when optimized at two different levels of theory, but assuming the differences between the two compared geometries is small, the differences should be able to be described well using the Cauchy distribution. Whereas, if the differences between the two geometries are large, fx. if one or more monomers have been significantly rotated, the data should not follow the cauchy distribution.