Reference state for the generalized Yvon-Born-Green theory: Application for coarse-grained model of hydrophobic hydration

Coarse-grained (CG) models provide a computationally efficient means for investigating phenomena that remain beyond the scope of atomically detailed models. Although CG models are often parametrized to reproduce the results of atomistic simulations, it is highly desirable to determine accurate CG models from experimental data. Recently, we have introduced a generalized Yvon-Born-Green (g-YBG) theory for directly (i.e., noniteratively) determining variationally optimized CG potentials from structural correlation functions. In principle, these correlation functions can be determined from experiment. In the present work, we introduce a reference state potential into the g-YBG framework. The reference state defines a fixed contribution to the CG potential. The remaining terms in the potential are then determined, such that the combined potential provides an optimal approximation to the many-body potential of mean force. By specifying a fixed contribution to the potential, the reference state significantly reduces the computational complexity and structural information necessary for determining the remaining potentials. We also validate the quantitative accuracy of the proposed method and numerically demonstrate that the reference state provides a convenient framework for transferring CG potentials from neat liquids to more complex systems. The resulting CG model provides a surprisingly accurate description of the two- and three-particle solvation structures of a hydrophobic solute in methanol. This work represents a significant step in developing the g-YBG theory as a useful computational framework for determining accurate CG models from limited experimental data.