Van der Waals Perspective on Coarse-Graining: Progress toward Solving Representability and Transferability Problems

Nicholas J.H. Dunn, Thomas T. Foley, William G. Noid

Research output: Contribution to journalArticlepeer-review

80 Scopus citations


Conspectus Low-resolution coarse-grained (CG) models provide the necessary efficiency for simulating phenomena that are inaccessible to more detailed models. However, in order to realize their considerable promise, CG models must accurately describe the relevant physical forces and provide useful predictions. By formally integrating out the unnecessary details from an all-atom (AA) model, “bottom-up” approaches can, at least in principle, quantitatively reproduce the structural and thermodynamic properties of the AA model that are observable at the CG resolution. In practice, though, bottom-up approaches only approximate this “exact coarse-graining” procedure. The resulting models typically reproduce the intermolecular structure of AA models at a single thermodynamic state point but often describe other state points less accurately and, moreover, tend to provide a poor description of thermodynamic properties. These two limitations have been coined the “transferability” and “representability” problems, respectively. Perhaps, the simplest and most commonly discussed manifestation of the representability problem regards the tendency of structure-based CG models to dramatically overestimate the pressure. Furthermore, when these models are adjusted to reproduce the pressure, they provide a poor description of the compressibility. More generally, it is sometimes suggested that CG models are fundamentally incapable of reproducing both structural and thermodynamic properties. After all, there is no such thing as a “free lunch”; any significant gain in computational efficiency should come at the cost of significant model limitations. At least in the case of structural and thermodynamic properties, though, we optimistically propose that this may be a false dichotomy. Accordingly, we have recently re-examined the “exact coarse-graining” procedure and investigated the intrinsic consequences of representing an AA model in reduced resolution. These studies clarify the origin and inter-relationship of representability and transferability problems. Both arise as consequences of transferring thermodynamic information from the high resolution configuration space and encoding this information into the many-body potential of mean force (PMF), that is, the potential that emerges from an exact coarse-graining procedure. At least in principle, both representability and transferability problems can be resolved by properly addressing this thermodynamic information. In particular, we have demonstrated that “pressure-matching” provides a practical and rigorous means for addressing the density dependence of the PMF. The resulting bottom-up models accurately reproduce the structure, equilibrium density, compressibility, and pressure equation of state for AA models of molecular liquids. Additionally, we have extended this approach to develop transferable potentials that provide similar accuracy for heptane-toluene mixtures. Moreover, these potentials provide predictive accuracy for modeling concentrations that were not considered in their parametrization. More generally, this work suggests a “van der Waals” perspective on coarse-graining, in which conventional structure-based methods accurately describe the configuration dependence of the PMF, while independent variational principles infer the thermodynamic information that is necessary to resolve representability and transferability problems.

Original languageEnglish (US)
Pages (from-to)2832-2840
Number of pages9
JournalAccounts of Chemical Research
Issue number12
StatePublished - Dec 20 2016
Externally publishedYes

Bibliographical note

Funding Information:
W.G.N. gratefully acknowledges very productive collaborations with M. Scott Shell that contributed to part of the work reviewed herein, as well as very helpful comments on this manuscript from Markus Deserno, Lasse Jensen, Ard Louis, and Christine Peter. This work has been financially supported by the National Science Foundation (NSF Grant Nos. MCB-1053970, CHE-1565631), by the Alfred P. Sloan Foundation, and by a Camille Dreyfus Teacher-Scholar Award. This work was also supported by ACS PRF under Grant No. 52100-ND6. We gratefully acknowledge the Donors of the American Chemical Society Petroleum Research fund for support of this research. This work was partially supported by funding from the Penn State Materials Computation Center. Portions of this research were conducted with Advanced CyberInfrastructure computational resources provided by The Institute for CyberScience at The Pennsylvania State University (http://ics.

Publisher Copyright:
© 2016 American Chemical Society.


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