Solutions of chain molecules are often coarse grained by finding a set of effective interaction potentials such that the effective system reproduces a set of correlations of the original system. This procedure requires the “inversion” of correlation functions to interaction potentials. In the simplest case a pair correlation function is inverted to an effective pair potential.

Here, we investigate the applicability and performance of various inversion techniques. As an example, an aqueous ethanol solution is employed, where in the effective system each ethanol molecule is represented by one bead and the water is coarse-grained out completely. At low ethanol concentrations, the effective potential is well represented by the potential of mean force (PMF). However, at higher (but still low) concentrations the PMF fails to reproduce the pair structure. Integral equations (e.g. HNC) can be used to compute effective potentials up to moderately high ethanol concentrations. In very concentrated ethanol solutions, however, we have to resort to an iterative inversion procedure to find the correct effective potentials. While the iterative method can be applied at any concentration, it is computationally very expensive since a simulation of the effective system is required at each step of the iterative process. Integral equations are much less demanding and should be preferred whenever possible. Even at very high concentrations they are very useful by providing a much better starting solution for the iteration than the potential of mean force does.

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