Force matching (FM) is a multiscale method that can be used to develop CG models from all-atom (or fine-grained) simulations. Recently, it has been shown that the FM approach is equivalent to the theory of simple liquids, namely the Yvon-Born-Green (YBG) equation. In this work, the FM approach is extended as a way to solve the YBG equation self-consistently. As a result, given any pair-wise distribution function, the underlying pair potential that gives rise to such a distribution can be computed via this approach. The SCFM is applied to develop the CG force fields of liquid water and liquid hexane. In applying the SCFM method to liquid hexane, both the bonded and nonbonded terms are included in the self-consistent iteration without separate treatments. Compared to the other technique that may also be used to extract pair potentials from pair distribution functions, i.e., the inverse Monte Carlo method, the SCFM method is shown to require much fewer interaction steps to achieve a converged result. The issue of transferability for CG force fields to different thermodynamic states will also be discussed.

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