Connecting Systems with Short and Long Ranged Interactions:  Local Molecular Field Theory for Ionic Fluids

Chen, Yng-Gwei; Kaur, Charanbir; Weeks, John D.

doi:10.1021/jp0469261

Cited by 59 publications

(189 citation statements)

References 32 publications

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“…If both molecules carry a net charge, we find u 1,ij (r) ϭ q i q j erf(r͞ )͞ r. The associated Coulomb core component is w q0,ij ϭ q i q j erfc(r͞ )͞ r. Thus, the results of Fig. 1, scaled by q i q j ͞ , give examples of possible u 1,ij and w q0,ij for ionic solution models (6). For a monopole and a dipole, we find u 1,ij …”

Section: [3]mentioning

confidence: 79%

“…1, sets the range of w q0,ij and thus determines an effective Coulomb core size (6). The external potential from fixed charged solutes or walls fi (r i ) ϵ 0,fi (r i ) ϩ 1,fi (r i ) can similarly be separated into short-and long-ranged parts, as illustrated below.…”

Section: [3]mentioning

confidence: 99%

“…Thus, we can ensure that all of the u 1,ji will slowly vary over the length scales of relevant local pair correlations in the system by choosing larger than some state-dependent minimum value min . This choice permits a consistent and controlled use of the mean field approximation in computing the average, and we anticipate very accurate results from the LMF theory for any Ն min if we properly describe the resulting density in the mimic system (6).…”

Section: Local Molecular Field Approximationmentioning

confidence: 99%

“…Crudely assuming all counterions are found within l G of the wall and using a simple cubic lattice to estimate the characteristic counterion spacing in this volume, we now have a Ӎ a 3D ϵ (l w 2 l G ) 1/3 ϭ l w ͞(2 ) 1/6 . There is weak coupling between the counterions, with ⌫ a 3D ϵ l B ͞a 3D ϭ 2/3 ͞ (2 ) 1/2 Ͻ Ͻ 1, and here it is natural to take min Ӎ l B ϭ l w ( ͞2 ) 1/2 as an estimate for the effective Coulomb core size (6). The crossover to strong coupling with essentially 2D packing and min Ӎ a 2D ϭ l w occurs for on the order of unity, and the 2D packing indeed provides a larger average spacing at large .…”

Section: Charged Walls With Point Counterionsmentioning

confidence: 99%

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Local molecular field theory for effective attractions between like charged objects in systems with strong Coulomb interactions

Chen

Weeks

2006

Proc. Natl. Acad. Sci. U.S.A.

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103

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Strong, short-ranged positional correlations involving counterions can induce a net attractive force between negatively charged strands of DNA and lead to the formation of ion pairs in dilute ionic solutions. However, the long range of the Coulomb interactions impedes the development of a simple local picture. We address this general problem by mapping the properties of a nonuniform system with Coulomb interactions onto those of a simpler system with short-ranged intermolecular interactions in an effective external field that accounts for the averaged effects of appropriately chosen long-ranged and slowly varying components of the Coulomb interactions. The remaining short-ranged components combine with the other molecular core interactions and strongly affect pair correlations in dense or strongly coupled systems. We show that pair correlation functions in the effective short-ranged system closely resemble those in the uniform primitive model of ionic solutions and illustrate the formation of ion pairs and clusters at low densities. The theory accurately describes detailed features of the effective attraction between two equally charged walls at strong coupling and intermediate separations of the walls. Analytical results for the minimal coupling strength needed to get any attraction and for the separation at which the attractive force is a maximum are presented.effective short-ranged model ͉ ion pairing ͉ mean field theory ͉ Poission-Boltzmann S trong Coulomb interactions in crowded, nonuniform environments have important experimental consequences in a wide variety of biophysical applications ranging from DNA packaging in viruses to transport in ion channels (1-4). These interactions present major challenges to theory and computer simulations not only because of their characteristic long range but also because they can be very strong at short distances. Here, we present a local molecular field (LMF) theory (5) that averages over particular long-ranged and slowly varying components of the Coulomb interactions (6) while still maintaining an accurate description of the short-ranged components. Our model provides a general and physically suggestive theory for strongly coupled Coulomb systems and reduces exactly to the classical Poisson-Boltzmann (PB) approximation for dilute, weakly coupled systems.We consider a general starting point where a molecule of species i, described by a rigid body frame with center at r i , interacts with an external field, fi (r i ), that comes from fixed charged solutes, or walls, or particular fixed molecules of a mobile species, as illustrated below. The subscript f indicates the source of the field, which we treat as a special fixed species f. The interaction between a pair of molecules of species i and j is assumed to have the general form w ij (r ij ) ϭ w s,ij (r ij ) ϩ w q,ij (r ij ), where r ij ϵ r j Ϫ r i . The w s,ij (r ij ) denote general (repulsive core and other), short-ranged intermolecular interactions. There are angular coordinates expressing orientations of the body fram...

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Section: [3]mentioning

confidence: 79%

Section: [3]mentioning

confidence: 99%

Section: Local Molecular Field Approximationmentioning

confidence: 99%

Section: Charged Walls With Point Counterionsmentioning

confidence: 99%

See 2 more Smart Citations

Local molecular field theory for effective attractions between like charged objects in systems with strong Coulomb interactions

Chen

Weeks

2006

Proc. Natl. Acad. Sci. U.S.A.

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103

142

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“…We show that local molecular field (LMF) theory (20)(21)(22)(23) offers exactly that opportunity. LMF theory corrects naive truncation schemes by introducing an effective electrostatic potential V R (r) that accounts for the remaining effects of the long-ranged interactions.…”

mentioning

confidence: 94%

Interplay of local hydrogen-bonding and long-ranged dipolar forces in simulations of confined water

Rodgers

Weeks

2008

Proc. Natl. Acad. Sci. U.S.A.

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145

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Spherical truncations of Coulomb interactions in standard models for water permit efficient molecular simulations and can give remarkably accurate results for the structure of the uniform liquid. However, truncations are known to produce significant errors in nonuniform systems, particularly for electrostatic properties. Local molecular field (LMF) theory corrects such truncations by use of an effective or restructured electrostatic potential that accounts for effects of the remaining long-ranged interactions through a density-weighted mean field average and satisfies a modified Poisson's equation defined with a Gaussian-smoothed charge density. We apply LMF theory to 3 simple molecular systems that exhibit different aspects of the failure of a naïve application of spherical truncations-water confined between hydrophobic walls, water confined between atomically corrugated hydrophilic walls, and water confined between hydrophobic walls with an applied electric field. Spherical truncations of 1/r fail spectacularly for the final system, in particular, and LMF theory corrects the failings for all three. Further, LMF theory provides a more intuitive way to understand the balance between local hydrogen bonding and longer-ranged electrostatics in molecular simulations involving water.effective short-ranged model | spherical truncation | confinement | hydrophobic walls | electric field A n accurate and efficient treatment of Coulomb interactions in molecular simulations represents an important and ongoing challenge. Standard biomolecular simulation packages like CHARMM (1) and AMBER (2), in general, assign effective point charges to interaction sites even in neutral molecules to approximate the charge separation of the electron cloud along polar bonds. Effective point charges are also found in most standard water models such as the extended simple point charge (SPC/E) model (3) shown in Fig. 1A, and water molecules are increasingly being included explicitly in biomolecular simulations.To minimize edge effects in necessarily finite simulation cells, these simulations use periodic boundary conditions (4). Researchers have long sought to devise spherical truncations of the Coulomb 1/r potential so that the truncated potential accurately describes the strong Coulomb forces between closely spaced charges that lead to hydrogen bonding in water but then vanish quickly beyond some properly chosen cutoff radius. Then, only the minimum (closest) image of an interacting charge needs to be accounted for and fast and efficient simulations that scale linearly with system size are possible. In bulk-like systems these spherical truncation approaches can be surprisingly accurate, but standard estimates of thermodynamic properties in the bulk liquid are less satisfactory (5-12).However, it has long been established (13) that when these spherical truncations are employed in nonuniform geometries, such as near a lipid bilayer, there can be pronounced errors in structure, thermodynamics, and particularly electrostatic properties. In those ...

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Systematic Methods for Structurally Consistent Coarse-Grained Models

Noid

2012

Methods in Molecular Biology

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This chapter provides a primer on theories for coarse-grained (CG) modeling and, in particular, reviews several systematic methods for determining effective potentials for CG models. The chapter first reviews a statistical mechanics framework for relating atomistic and CG models. This framework naturally leads to a quantitative criterion for CG models that are "consistent" with a particular atomistic model for the same system. This consistency criterion is equivalent to minimizing the relative entropy between the two models. This criterion implies that a many-body PMF is the appropriate potential for a CG model that is consistent with a particular atomistic model. This chapter then presents a unified exposition of the theory and numerical methods for several approaches for approximating this many-body PMF. Finally, this chapter closes with a brief discussion of a few of the outstanding challenges facing the field of systematic coarse-graining.

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Connecting Systems with Short and Long Ranged Interactions: Local Molecular Field Theory for Ionic Fluids

Cited by 59 publications

References 32 publications

Local molecular field theory for effective attractions between like charged objects in systems with strong Coulomb interactions

Local molecular field theory for effective attractions between like charged objects in systems with strong Coulomb interactions

Interplay of local hydrogen-bonding and long-ranged dipolar forces in simulations of confined water

Systematic Methods for Structurally Consistent Coarse-Grained Models

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