Abstract: Systems and methods are disclosed for a new approach to the rare-event Monte Carlo sampling problem. This technique utilizes a symmetrization strategy to create probability distributions that are more highly connected and thus more easily sampled than their original, potentially sparse counterparts. The methods can be applied to Lennard-Jones clusters of varying complexity and rare-event character. In one embodiment, a system is disclosed comprising a grouping module for dividing a control variable range into a first set of groups and a second set of groups, an analysis module for computing data representative of the physical system over the set of control values in each group in the first and second set of groups and for accelerating the flow of information by simultaneously exchanging information between all of the control values within a group; and a swapping module for communicating data.