Relationship between local molecular field theory and density functional theory for non-uniform liquids

Archer, Andrew J.; Evans, Robert

doi:10.1063/1.4771976

Cited by 21 publications

(65 citation statements)

References 40 publications

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“…This argument matches the results of Rodgers and Weeks [55] in the several instances they considered. Derivations that emphasize alternative (electrostatic) interactions are available elsewhere [56][57][58]. Though the statistical mechanical theory of Eq.…”

Section: Local Molecular Field Theorymentioning

confidence: 99%

Molecular Theory and the Effects of Solute Attractive Forces on Hydrophobic Interactions

et al. 2016

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The role of solute attractive forces on hydrophobic interactions is studied by coordinated development of theory and simulation results for Ar atoms in water. We present a concise derivation of the local molecular field (LMF) theory for the effects of solute attractive forces on hydrophobic interactions, a derivation that clarifies the close relation of LMF theory to the EXP approximation applied to this problem long ago. The simulation results show that change from purely repulsive atomic solute interactions to include realistic attractive interactions diminishes the strength of hydrophobic bonds. For the Ar-Ar rdfs considered pointwise, the numerical results for the effects of solute attractive forces on hydrophobic interactions are of opposite sign and larger in magnitude than predicted by LMF theory. That comparison is discussed from the point of view of quasi-chemical theory, and it is suggested that the first reason for this difference is the incomplete evaluation within LMF theory of the hydration energy of the Ar pair. With a recent suggestion for the system-size extrapolation of the required correlation function integrals, the Ar-Ar rdfs permit evaluation of osmotic second virial coefficients B2. Those B2 also show that incorporation of attractive interactions leads to more positive (repulsive) values. With attractive interactions in play, B2 can change from positive to negative values with increasing temperatures. This is consistent with the historical work of Watanabe, et al., that B2 ≈ 0 for intermediate cases. In all cases here, B2 becomes more attractive with increasing temperature.

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Section: Local Molecular Field Theorymentioning

confidence: 99%

Molecular Theory and the Effects of Solute Attractive Forces on Hydrophobic Interactions

et al. 2016

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“…, are expected to be more accurate than those of the form 3 . Likewise, the approximations of the form [1 (α 1 ) 2 (α 2 ) 3 (α 3 ) ] a are expected to be better than those of the form [1 (α 1 ) 2 (α 2 ) 3 (α 3 ) ] b or, even more, of the form…”

Section: Radial Distribution Functionmentioning

confidence: 99%

“…It is well known that equilibrium systems confined in one-dimensional geometries with interactions restricted to first nearest neighbors (1st nn) admit a full exact statistical-mechanical solution [5, 15, 26, 27, 29-38, 42, 43, 52, 53]. Apart from its undoubtful pedagogical and illustrative values [6,8,11,12,25,[44][45][46][47], this exact solution can also be exploited as a benchmark for approximations [2,3,7,10,13,14,16,43,51] or simulation methods [9].…”

Section: Introductionmentioning

confidence: 99%

One-Dimensional Fluids with Second Nearest–Neighbor Interactions

Fantoni

Santos

2017

J Stat Phys

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As is well known, one-dimensional systems with interactions restricted to first nearest neighbors admit a full analytically exact statistical-mechanical solution. This is essentially due to the fact that the knowledge of the first nearest-neighbor probability distribution function, p 1 (r), is enough to determine the structural and thermodynamic properties of the system. On the other hand, if the interaction between second nearestneighbor particles is turned on, the analytically exact solution is lost. Not only the knowledge of p 1 (r) is not sufficient anymore, but even its determination becomes a complex many-body problem. In this work we systematically explore different approximate solutions for one-dimensional second nearest-neighbor fluid models. We apply those approximations to the square-well and the attractive two-step pair potentials and compare them with Monte Carlo simulations, finding an excellent agreement.

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“…We verify our numerical method in Sec. 4 and validate it with thermodynamic sum-rules in 1D and 2D settings, for single-fluid and multiple-species equilibrium and dynamic settings. Furthermore, we also include a comparison with stochastic sampling techniques.…”

Section: Introductionmentioning

confidence: 98%

Pseudospectral methods for density functional theory in bounded and unbounded domains

Nold

Goddard

Yatsyshin

et al. 2017

Journal of Computational Physics

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Classical Density Functional Theory (DFT) is a statistical–mechanical framework to analyse fluids, which accounts for nanoscale fluid inhomogeneities and non-local intermolecular interactions. DFT can be applied to a wide range of interfacial phenomena, as well as problems in adsorption, colloidal science and phase transitions in fluids. Typical DFT equations are highly non-linear, stiff and contain several convolution terms. We propose a novel, efficient pseudo-spectral collocation scheme for computing the non-local terms in real space with the help of a specialised Gauss quadrature. Due to the exponential accuracy of the quadrature and a convenient choice of collocation points near interfaces, we can use grids with a significantly lower number of nodes than most other reported methods. We demonstrate the capabilities of our numerical methodology by studying equilibrium and dynamic two-dimensional test cases with single- and multispecies hard-sphere and hard-disc particles modelled with fundamental measure theory, with and without van der Waals attractive forces, in bounded and unbounded physical domains. We show that our results satisfy statistical mechanical sum rules

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Relationship between local molecular field theory and density functional theory for non-uniform liquids

Cited by 21 publications

References 40 publications

Molecular Theory and the Effects of Solute Attractive Forces on Hydrophobic Interactions

Molecular Theory and the Effects of Solute Attractive Forces on Hydrophobic Interactions

One-Dimensional Fluids with Second Nearest–Neighbor Interactions

Pseudospectral methods for density functional theory in bounded and unbounded domains

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