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

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.

Solubility Limits in Lennard-Jones Mixtures: Effects of Disparate Molecule Geometries.

In order to better understand general effects of the size and energy disparities between macromolecules and solvent molecules in solution, especially for macromolecular constructs self-assembled from smaller molecules, we use the first- and second-order exact bridge diagram extensions of the HNC integral equation theory to investigate single-component, binary, ternary, and quaternary mixtures of Lennard-Jones fluids. For pure fluids, we find that the HNCH3 bridge function integral equation (i.e., exact to third order in density) is necessary to quantitatively predict the pure gas and pure liquid sides of the coexistence region of the phase diagram of the Lennard-Jones fluid. For the mixtures, we find that the HNCH2 bridge function integral equation is sufficient to qualitatively predict solubility in the binary, ternary, and quaternary mixtures, up to the nominal solubility limit. The results, as limiting cases, should be useful to several problems, including accurate phase diagram predictions for complex mixtures, design of self-assembling nanostructures via solvent controls, and the solvent contributions to the conformational behavior of macromolecules in complex fluids.

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

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.

Site-renormalised molecular fluid theory: on the utility of a two-site model of water.

We propose a simple, two-site model of water, using the familiar three-site Simple Point Charge (SPC) model as a guide. We briefly examine the resulting dielectric and solvation properties of the bulk fluid, both pure and in a three component mixture of apolar or ionic simple fluid solutes, using integral equation methods. The results confirm a practical utility of this simplified model, and the essential predictive properties of the site-renormalised molecular fluid theory.

A molecular site-site integral equation that yields the dielectric constant.

Our recent derivation [K. M. Dyer et al., J. Chem. Phys. 127, 194506 (2007)] of a diagrammatically proper, site-site, integral equation theory using molecular angular expansions is extended to polar fluids. With the addition of atomic site charges we take advantage of the formal long-ranged potential field cancellations before renormalization to generate a set of numerically stable equations. Results for calculations in a minimal (spherical) angular basis set are presented for the radial distribution function, the first dipolar (110) projection, and the dielectric constant for two model diatomic systems. All results, when compared to experiment and simulation, are a significant quantitative and qualitative improvement over previous site-site theories. More importantly, the dielectric constant is not trivial and close to simulation and experiment.

A site-renormalized molecular fluid theory.

The orientation-dependent pair distribution function for molecular fluids on site-site potentials is expanded in a topological analog of the diagrammatically proper site-site theory of liquids [D. Chandler et al., Mol. Phys. 46, 1335 (1982)]. The resulting functions are then used to diagrammatically renormalize the molecular fluid theory. A result is that the diagrammatically proper interaction site model theory is shown to be a linearized, minimal angular basis set approximation to this site-renormalized molecular theory. This framework is used to propose a new, exact, and proper closure to the diagrammatically proper interaction site model theory. The resulting equation system contains a bridge function expansion in the proper site-site theory. In addition, the construction of the theory is such that the molecular pair distribution function, in full dimensionality, is intrinsic to the theory. Furthermore, the theory is equivalent to the molecular Ornstein-Zernike treatment of site-site molecules in the basis set expansion of Blum and Torruella [J. Chem. Phys. 56, 303 (1971)]. A significant formal result of the theory is the demonstration that certain classes of diagrams which would otherwise be considered improper in the interaction site model formalism are included in the angular expansion of molecular interactions. Numerical results for several apolar homonuclear models and an apolar heteronuclear model are shown to quantitatively improve upon those of reference interaction site model and our recent proper variant with respect to simulation. Significant numerical results are that the various thermodynamic quantities obey the exact symmetries and sum rules within numerical error for the different sites in the heteronuclear case, even for the low order approximation used in this work, and the theory is independent of the so-called auxiliary site problem common to previous site-site theories.

Systematic investigation of theories of transport in the Lennard-Jones fluid.

Three kinetic theories of transport are investigated for the single-species Lennard-Jones model fluid. Transport coefficients, including diffusion, shear, and bulk viscosity, are calculated from these theories for the Lennard-Jones fluid across the fluid regions of the phase diagram. The results are systematically compared against simulation. It is found that for each transport property considered, there is at least one theoretical result based on approximations that have been systematically derived from a first-principles starting point that is quantitatively useful over a wide range of densities and temperatures. To the authors' knowledge, this article constitutes the first such compendium of results for the Lennard-Jones model fluid that has been assembled.

Effective density terms in proper integral equations.

Two complementary routes to a new integral equation theory for site-site molecular fluids are presented. First, a simple approximation to a subset of the atomic site bridge functions in the diagrammatically proper integral equation theory is presented. This in turn leads to a form analogous to the reactive fluid theory, in which the normalization of the intramolecular distribution function and the value of the off-diagonal elements in the density matrix of the proper integral equations are the means of propagating the bridge function approximation. Second, a derivation from a topological expansion of a model for the single-site activity followed by a topological reduction and low-order truncation is given. This leads to an approximate numerical value for the new density coefficient. The resulting equations give a substantial improvement over the standard construction as shown with a series of simple diatomic model calculations.

Simple bond length dependence: a correspondence between reactive fluid theories.

Two elementary models of reactive fluids are examined, the first being a standard construction assuming molecular dissociation at infinite separation; the second is an open mixture of nondissociative molecules and free atoms in which the densities of free atoms and molecules are coupled. An approximation to the density of molecules, to low order in site density, is derived in terms of the classical associating fluid theory variously described by Wertheim [J. Chem. Phys. 87, 7323 (1987)] and Stell [Physica A 231, 1 (1996)]. The results are derived for a fluid of dimerizing hard spheres, and predict dependence of the molecular density on the total site density, the hard sphere diameter, and the bond length of the dimer. The results for the two reactive models are shown to be qualitatively similar, and lead to equivalent predictions of the molecular density for the infinitely short and infinitely long bond lengths.