Abstract
Coarse-graining is a systematic reduction of the number of degrees of freedom used to describe a system of interest. Coarse-graining can be thought of as a projection on the coarse-grained degrees of freedom and is therefore dependent on the number and type of basis functions used to represent the coarse-grained force field. We show that many-body extensions of the coarse-grained force field can result in substantial changes of the two-body interactions, making them much more attractive at short distances. This interplay can be alleviated by first parametrizing the two-body potential and then fitting the additional three-body contribution to the residual forces. The approach is illustrated on liquid water where three-body interactions are essential to reproduce the structural properties, and liquid methanol where two-body interactions are sufficient to reproduce the main structural features of the atomistic system. Furthermore, we demonstrate that the structural and thermodynamic accuracy of the coarse-grained models can be controlled by varying the magnitude of the three-body interactions. Our findings motivate basis set extensions which separate the many-body contributions of different order.
Highlights
Coarse-graining (CG) is a systematic way to reduce the number of degrees of freedom describing a specific physical system
Consistency between the coarse-grained and the fine-grained models can be defined in terms of consistency of the equilibrium probability densities resulting in unique expressions for the CG masses and interaction potential, i.e. the many-body potential of mean force (PMF).[1]
This approach corresponds to projecting the many-body mean force, i.e., the negative gradient of the many-body PMF, into the space of force fields defined by the CG basis set
Summary
Coarse-graining (CG) is a systematic way to reduce the number of degrees of freedom describing a specific physical system. It can be shown that these methods minimize the relative entropy between the CG and atomistic ensembles.[4] An alternative route is to match the forces of the CG system to those of the atomistic description, employing force-matching (FM) or multiscale coarse-graining (MS-CG).[1,5,6] This approach corresponds to projecting the many-body mean force, i.e., the negative gradient of the many-body PMF, into the space of force fields defined by the CG basis set It allows to systematically increase the accuracy of the approximation of the many-body PMF by expanding the basis set. FM and structural coarse-graining can be connected via Yvon–Born–Green theory.[7,8]
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