Dual approach for effective potentials that accurately model structure and energetics.

Because they eliminate unnecessary degrees of freedom, coarse-grained (CG) models enable studies of phenomena that are intractable with more detailed models. For the same reason, the effective potentials that govern CG degrees of freedom incorporate entropic contributions from the eliminated degrees of freedom. Consequently, these effective potentials demonstrate limited transferability and provide a poor estimate of atomic energetics. Here, we propose a simple dual-potential approach that combines "structure-based" and "energy-based" variational principles to determine effective potentials that model free energies and potential energies, respectively, as a function of the CG configuration. We demonstrate this approach for 1-site CG models of water and methanol. We accurately sample configuration space by performing simulations with the structure-based potential. We accurately estimate average atomic energies by postprocessing the sampled configurations with the energy-based potential. Finally, the difference between the two potentials predicts a qualitatively accurate estimate for the temperature dependence of the structure-based potential.