Multiscale Coarse-Graining and Structural Correlations:  Connections to Liquid-State Theory

Noid, W. G.; Chu, Jhih‐Wei; Ayton, Gary S.; Voth, Gregory A.

doi:10.1021/jp068549t

Cited by 198 publications

(287 citation statements)

References 49 publications

Supporting

Mentioning

283

Contrasting

Order By: Relevance

“…28,29,[45][46][47][48][49][50][51]63 This suggests that nonbonded interactions between CG sites are often well represented, at least to a good first approximation, as pairwise additive. A recent analysis 30 has also demonstrated that the MS-CG equations for these pair potentials are related to well-known exact kinetic equations for the liquid state 67 and systematically incorporate critical three-body correlations present in the underlying atomistic model, which may be a key feature in the previous successes of the MS-CG method.…”

Section: Discussionmentioning

confidence: 99%

The multiscale coarse-graining method. I. A rigorous bridge between atomistic and coarse-grained models

Noid

Chu

Ayton

et al. 2008

The Journal of Chemical Physics

Self Cite

753

1,165

View full text Add to dashboard Cite

Coarse-grained ͑CG͒ models provide a computationally efficient method for rapidly investigating the long time-and length-scale processes that play a critical role in many important biological and soft matter processes. Recently, Izvekov and Voth introduced a new multiscale coarse-graining ͑MS-CG͒ method ͓J. Phys. Chem. B 109, 2469 ͑2005͒; J. Chem. Phys. 123, 134105 ͑2005͔͒ for determining the effective interactions between CG sites using information from simulations of atomically detailed models. The present work develops a formal statistical mechanical framework for the MS-CG method and demonstrates that the variational principle underlying the method may, in principle, be employed to determine the many-body potential of mean force ͑PMF͒ that governs the equilibrium distribution of positions of the CG sites for the MS-CG models. A CG model that employs such a PMF as a "potential energy function" will generate an equilibrium probability distribution of CG sites that is consistent with the atomically detailed model from which the PMF is derived. Consequently, the MS-CG method provides a formal multiscale bridge rigorously connecting the equilibrium ensembles generated with atomistic and CG models. The variational principle also suggests a class of practical algorithms for calculating approximations to this many-body PMF that are optimal. These algorithms use computer simulation data from the atomically detailed model. Finally, important generalizations of the MS-CG method are introduced for treating systems with rigid intramolecular constraints and for developing CG models whose equilibrium momentum distribution is consistent with that of an atomically detailed model.

show abstract

Section: Discussionmentioning

confidence: 99%

The multiscale coarse-graining method. I. A rigorous bridge between atomistic and coarse-grained models

Noid

Chu

Ayton

et al. 2008

The Journal of Chemical Physics

Self Cite

753

1,165

View full text Add to dashboard Cite

show abstract

“…There are two methods belonging to the force-based methods: the force-matching method [168] and the multiscale coarse-graining method [169,170]. The latter was validated through rigorous statistical thermodynamic formulations by Noid et al [171][172][173]. Rühle et al [174] implemented the IBI, IMC and force-matching methods into a toolkit and compared them by coarse-graining water molecules, liquid methanol, liquid propane and a single molecule of hexane.…”

Section: Iterative Boltzmann Inversion Methodsmentioning

confidence: 99%

Challenges in Multiscale Modeling of Polymer Dynamics

et al. 2013

View full text Add to dashboard Cite

The mechanical and physical properties of polymeric materials originate from the interplay of phenomena at different spatial and temporal scales. As such, it is necessary to adopt multiscale techniques when modeling polymeric materials in order to account for all important mechanisms. Over the past two decades, a number of different multiscale computational techniques have been developed that can be divided into three categories: (i) coarse-graining methods for generic polymers; (ii) systematic coarse-graining methods and (iii) multiple-scale-bridging methods. In this work, we discuss and compare eleven different multiscale computational techniques falling under these categories and assess them critically according to their ability to provide a rigorous link between polymer chemistry and rheological material properties. For each technique, the fundamental ideas and equations are introduced, and the most important results or predictions are shown and discussed. On the one hand, this review provides a comprehensive tutorial on multiscale computational techniques, which will be of interest to readers newly entering this field; on the other, it presents a critical discussion of the future opportunities and key challenges in the multiscale geometric mapping matrix between all-atomistic and coarse-grained models N number of monomers per chain N e entanglement length, which is the number of monomers between two entanglements n v number of polymer chains per unit volume n ij (n 0 (r ij )) entanglement number (at equilibrium) between particle pairs i and j p r , P R configurational probability distributions in all-atomistic and coarse-grained models, respectively R ee end-to-end distance of polymer chain R G radius of gyration of polymer chain s segment index/contour length variable along primitive chain S(q) single chain coherent dynamic scattering function Z number of entanglements per chain, defined as Z = N/N e α exponent in standard Mittag-Leffler function σ

show abstract

“…[17]. Furthermore, there is recent interest in developing coarse-graining methods based on this theory, see for example [29,33,34].…”

Section: Introductionmentioning

confidence: 99%

Convergence of Density Expansions of Correlation Functions and the Ornstein–Zernike Equation

Kuna

Tsagkarogiannis

2018

Ann. Henri Poincaré

View full text Add to dashboard Cite

Abstract.We prove absolute convergence of the multi-body correlation functions as a power series in the density uniformly in their arguments. This is done by working in the context of the cluster expansion in the canonical ensemble and by expressing the correlation functions as the derivative of the logarithm of an appropriately extended partition function. In the thermodynamic limit, due to combinatorial cancellations, we show that the coefficients of the above series are expressed by sums over some class of two-connected graphs. Furthermore, we prove the convergence of the density expansion of the "direct correlation function" which is based on a completely different approach and it is valid only for some integral norm. Precisely, this integral norm is suitable to derive the OrnsteinZernike equation. As a further outcome, we obtain a rigorous quantification of the error in the Percus-Yevick approximation.

show abstract

Multiscale Coarse-Graining and Structural Correlations: Connections to Liquid-State Theory

Cited by 198 publications

References 49 publications

The multiscale coarse-graining method. I. A rigorous bridge between atomistic and coarse-grained models

The multiscale coarse-graining method. I. A rigorous bridge between atomistic and coarse-grained models

Challenges in Multiscale Modeling of Polymer Dynamics

Convergence of Density Expansions of Correlation Functions and the Ornstein–Zernike Equation

Contact Info

Product

Resources

About