A site-renormalized molecular fluid theory

Dyer, Kippi M.; Perkyns, John S.; Pettitt, B. Montgomery

doi:10.1063/1.2785188

Cited by 21 publications

(57 citation statements)

References 33 publications

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“…The numerical methods that have emerged in the second part of the last century from liquid-state theories [1,2], including integral equation theory in the interactionsite [3][4][5][6][7][8] or molecular [9][10][11][12][13][14] picture, classical density functional theory (DFT) [15][16][17], or classical fields theory [18][19][20][21], have become methods of choice for many physical chemistry or chemical engineering applications [22][23][24][25]. They can yield reliable predictions for both the microscopic structure and the thermodynamic properties of molecular fluids in bulk, interfacial, or confined conditions at a much more modest computational cost than molecular-dynamics or Monte-Carlo simulations.…”

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confidence: 99%

Molecular Density Functional Theory of Water

Jeanmairet

Levesque

Vuilleumier

et al. 2013

J. Phys. Chem. Lett.

135

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Three dimensional implementations of liquid state theories offer an efficient alternative to computer simulations for the atomic-level description of aqueous solutions in complex environments. In this context, we present a (classical) molecular density functional theory (MDFT) of water that is derived from first principles and is based on two classical density fields, a scalar one, the particle density, and a vectorial one, the multipolar polarization density. Its implementation requires as input the partial charge distribution of a water molecule and three measurable bulk properties, namely the structure factor and the k-dependent longitudinal and transverse dielectric constants. It has to be complemented by a solute-solvent three-body term that reinforces tetrahedral order at short range.The approach is shown to provide the correct three-dimensional microscopic solvation profile around various molecular solutes, possibly possessing H-bonding sites, at a computer cost two-three orders of magnitude lower than with explicit simulations. [22][23][24][25]. They can yield reliable predictions for both the microscopic structure and the thermodynamic properties of molecular fluids in bulk, interfacial, or confined conditions at a much more modest computational cost than molecular-dynamics or Monte-Carlo simulations. A current challenge concerns their implementation in three dimensions in order to describe molecular liquids, solutions, and mixtures in complex environments such as atomistically-resolved solid interfaces or biomolecular media. There have been a number of recent efforts in that direction using 3D-RISM [26][27][28][29][30][31], lattice field [32,33] or Gaussian field [20,34] theories. Recently, a molecular density functional theory (MDFT) approach to solvation has been introduced. [35][36][37][38][39][40] It relies on the definition of a free-energy functional depending on the full six-dimensional position and orientation solvent density. In the so-called homogeneous reference fluid (HRF) approximation, the (unknown) excess free energy can be inferred from the angular-dependent direct correlation function of the bulk solvent, that can be predetermined from molecular simulations of the pure solvent. Compared to reference molecular dynamics calculations, such approximation was shown to be accurate for polar, non-hydrogen bonded fluids [35,[38][39][40][41], but to require some corrections for water [39,[42][43][44].In this paper we introduce a simplified version of MDFT that can be derived rigorously for SPC-or TIPnP-like representations of water, involving a single LennardJones interaction site and distributed partial charges. In that case we will seek a simpler functional form expressed in terms of the particle density n(r) and site-distributed polarisation density P(r), and requiring as input simpler physical quantities than the full position and orientation-dependent direct correlation function. This functional may be considered as a multipolar generalization of the generic dipolar fluid free-ene...

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confidence: 99%

Molecular Density Functional Theory of Water

Jeanmairet

Levesque

Vuilleumier

et al. 2013

J. Phys. Chem. Lett.

135

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“…As such, there is a general set of site-generated proximal distribution functions that follow the same left, right, and both hierarchy of terms as do the full, angularly dependent molecular pair distribution functions. 14 In turn, each type of generalized proximal distribution function is uniquely generated from an average of its related angular correlation function over the familiar r, 1 , 2 molecular coordinates within the proximal ordering of the complete set of r ij site-site vectors unique to a given configuration of a pair of molecules.…”

Section: Discussionmentioning

confidence: 99%

Proximal distributions from angular correlations: A measure of the onset of coarse-graining

Dyer

Pettitt²

2013

The Journal of Chemical Physics

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In this work we examine and extend the theory of proximal radial distribution functions for molecules in solution. We point out two formal extensions, the first of which generalizes the proximal distribution function hierarchy approach to the complete, angularly dependent molecular pair distribution function. Second, we generalize from the traditional right-handed solute-solvent proximal distribution functions to the left-handed distributions. The resulting neighbor hierarchy convergence is shown to provide a measure of the coarse-graining of the internal solute sites with respect to the solvent. Simulation of the test case of a deca-alanine peptide shows that this coarse-graining measure converges at a length scale of approximately 5 amino acids for the system considered.

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“…If we follow the diagrammatic analysis of Ladanyi, Chandler, and Richardson [18, 19, 21], then we find [27] that, if we choose the molecular displacement vector, R ij = r ij , so that it coincides with one of the site–site displacement vectors, then the potential naturally decomposes into the none,left,right,both terms of the diagrammatically proper theory [19]. In that case, the full molecular potential is of the general form

U_{i j} = u_{i j}^{o} + u_{i j}^{l} + u_{i j}^{r} + u_{i j}^{b},

where, if i labels an arbitrary site on molecule 1, j an arbitrary site on molecule 2,

u_{i j}^{o} = u_{i j} false(r false)

u_{i j}^{l} = \sum_{normalγ \neq i} u false(false| r_{i j} - d_{γ} false| false)

u_{i j}^{r} = \sum_{ν \neq j} u false(false| r_{i j} + d_{ν} false| false)

u_{i j}^{b} = \sum_{normalγ \neq i} \sum_{ν \neq j} u false(false| r_{i j} - d_{γ} + d_{ν} false| false),

and we have assumed that the potential between sites displaced by r ij is radially symmetric, d γ is the displacement of site γ from the molecular center now made with reference to r ij , and the o , l , r , b are the conventional labels for the none, left, right, both decomposition referring to the absence or presence of intervening intramolecular bonds or correlations.…”

Section: Theorymentioning

confidence: 99%

“…Here we truncate the expansion of the re-summed indirect correlation function at first order,

τ ~ τ_{00}^{000} false(r false)

, and the closure equations take [27] the relatively simple form

c_{i j}^{o} false(r false) = g_{i j}^{o} false(r false) - t_{i j}^{o} false(r false) - 1

c_{i j}^{l} false(r false) = g_{i j}^{o} false(r false) false(g_{i j}^{l} false(r false) false[exp false(t_{i j}^{l} false(r false) false) false] - 1 false) - t_{i j}^{l} false(r false)

c_{i j}^{r} false(r false) = g_{i j}^{o} false(r false) false(g_{i j}^{r} false(r false) false[exp false(t_{i j}^{r} false(r false) false) false] - 1 false) - t_{i j}^{r} false(r false)

c_{i j}^{b} false(r false) = g_{i j}^{o} false(r false) false{g_{i j}^{b} false(r false) false[exp false(t_{i j}^{b} false(r false) + t_{i j}^{l} false(r false) + t_{i j}^{r} false(r false) false) false] - g_{i j}^{l} false(r false) false[exp false(t_{i j}^{l} false(r false) false) false] g_{i j}^{r} false(r false) false[exp false(t_{i j}^{r} false(r false) false) false] + 1 false} - t_{}

…”

Section: Theoryunclassified

“…In prior work, we used diagrammatic analysis [18, 21, 26] as a guide to diatomic model liquids [27], finding both that the diagrammatically proper equations can be extended beyond the first closures [20] to the complete ISM hypernetted-chain (HNC) approximation equivalent to the multipole case [28], and that the results for diatomic, polar liquids [29], the related electrolytes [30], and the isomorphic problem of n -butane in a simple fluid [31], could all be reliably obtained by the resulting theory, including the structure, solution thermodynamics, and the dielectric constant.…”

Section: Introductionmentioning

confidence: 99%

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Dielectric behavior for saline solutions from renormalized diagrammatically proper interaction site model theory

Dyer¹,

Perkyns²,

Pettitt³

2016

J. Phys.: Condens. Matter

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We consider the dielectric response of angularly dependent site–site theories for models of aqueous saline solutions. We find that we can use relatively low order approximations of the angularly dependent correlation functions with correct long ranged behavior to obtain good estimates of the dielectric constant for three site water models and simple 1–1 salts. We find that the solution thermodynamics results for this level of theory, as measured by the Kirkwood G integrals and the excess chemical potentials, are in good quantitative agreement with simulation even when the details of the short ranged structure is not as accurately determined. We find that the dielectric constant predictions of both the pure fluid and the salt-water mixtures are similarly predictive, in comparison to both simulation and experiment.

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A site-renormalized molecular fluid theory

Cited by 21 publications

References 33 publications

Molecular Density Functional Theory of Water

Molecular Density Functional Theory of Water

Proximal distributions from angular correlations: A measure of the onset of coarse-graining

Dielectric behavior for saline solutions from renormalized diagrammatically proper interaction site model theory

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