Fig. 1. Illustration of implicit mediated global correlations and effective larger cutoff in GSFE-refinement. Two dashed circles are two “local” region for LFEL centered at solute unit B and D respectively. As a comprising unit of LFELs centered on both unit B and D, unit C experience effective force from unit A as mediated by B, and effective force from E as mediated by D. In fact, each unit experience effective forces mediated by LFELs defined by all of its solvent unit, resulting in an effective large cutoff that is approximately two times the radius of dashed circle for defining LFEL as shown. All mediated global correlations in essence is the equality of shared states for overlapping DOFs belong to different LFELs, since only one set of coordinates is used in the whole optimization process, these correlations are naturally maintained.