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Provide an better form of pairwise interaction potential that can be used for free energy calculations which produce lower variance compare to the traditional ``soft core'' form.
This work exploits the relatetionship between the radial distribution function (RDF) and the variance of free energy pathways for any pairwise potential to identify low variance pathways for free energy calculations. Low variance pathways are identified by searching for forms of pairwise interaction potential through its parameters space via optimizion with moderately accurate estimation of the RDF approximation methods.
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Provide the code for identifying pairwise interaction potential that produce low variance using two-body and three-body approximation for the radial distribution function. This code can be extended to add and test your own algorithms.
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