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.     

An extended rism equation for molecular polar fluids

The RISM integral equation is extended to molecules with charged sites via a renormalization of the Coulomb potentials and the introduction of appropriate closure relations. For a fluid of diatomics with atomic charges of ±0.2 e the equation yields site-site correlation functions in qualitative agreement with those from computer simulation.     

Optimized theory for simple and molecular fluids

An optimized closure approximation for both simple and molecular fluids is presented. A smooth interpolation between Perkus-Yevick and hypernetted chain closures is optimized by minimizing the free energy self-consistently with respect to the interpolation parameter(s). The molecular version is derived from a refinement of the method for simple fluids. In doing so, a method is proposed which appropriately couples an optimized closure with the variant of the diagrammatically proper integral equation recently introduced by this laboratory [K. M. Dyer et al., J. Chem. Phys. 123, 204512 (2005)]. The simplicity of the expressions involved in this proposed theory has allowed the authors to obtain an analytic expression for the approximate excess chemical potential. This is shown to be an efficient tool to estimate, from first principles, the numerical value of the interpolation parameters defining the aforementioned closure. As a preliminary test, representative models for simple fluids and homonuclear diatomic Lennard-Jones fluids were analyzed, obtaining site-site correlation functions in excellent agreement with simulation data.     

Self-consistent field equations in the distribution function theory of polymeric liquids

In the distribution function approach to the conformational and thermodynamic properties of polymeric liquids site-site (pair) distribution functions are essential components of the theory. These site-site pair distribution functions are basically mean fields obeying integral equations. In our recent works, a set of self-consistent field equations has been proposed for site-site pair correlation functions which allow us to study conformational and thermodynamic properties of polymeric liquids. In this article, we present a short review of the theory and its applications to a number of aspects of polymeric liquids we have made until now. We also present a self-consistent version of the polymer reference interaction site model where the integral equations for the intramolecular site-site correlation functions are obtained from the Kirkwood hierarchy on the basis of the present theory. The present theory is shown to predict correctly the scaling properties associated with swollen and collapsed polymers in good and poor solvents, respectively. At finite densities, self-consistent solutions of the intra- and intermolecular equations yield the structures and thermodynamics of polymer melts which are favorably compared with Monte Carlo simulation results. Self-consistent theory results are found to be more accurate than the non-self-consistent approaches that use an ideal Gaussian chain conformation distribution function. © 1995 John Wiley & Sons, Inc.     

Towards a more accurate reference interaction site model integral equation theory for molecular liquids

A systematic approach for increasing the accuracy of the reference interaction site model (RISM) theory is introduced that uses input from simulation results to produce very accurate site-site pair correlation functions for single component molecular liquids. The methodology allows the computation of the "RISM bridge function." Realistic molecular liquids such as water, alcohols, amides, and others are investigated, and the merits and limitations of the method for each of these liquids are examined in relation to the known deficiencies of the RISM theory.     

Applications of the RISM equation to diatomic fluids: the liquids nitrogen,oxygen and bromine

The reference interaction site model (RISM) integral equation is used to study the equilibrium pair correlation for one-component liquids composed of homonuclear diatomic molecules. The integral equation is first tested by comparing the results obtained from it with those of computer simulation calculations. An internal consistency test is developed which seems to provide an a priori measure of the accuracy of the RISM equation. Then the theory is used to interpret the neutron scattering structure factor data taken on the liquids nitrogen and oxygen. For both of these liquids, a satisfactory explanation of the data is obtained by assuming that the short ranged repulsive forces between molecules are mimicked by a two-site hard core model. However, this simple model does not provide a satisfactory explanation of the data taken from liquid bromine. But, it is shown that a slightly more sophisticated model for the short-ranged repulsion between Br₂ molecules does provide an adequate explanation. With the molecular models determined by fitting the neutron scattering data, the RISM equation provides a method for determining the atom, atom to center-of-mass, and center-of-mass to center-of-mass intermolecular distribution functions in the diatomic liquids. From these functions, the local structures in the three liquids are analyzed. While orientational pair correlations are nearly negligible in both the liquids nitrogen and oxygen, these correlations are fairly substantial in liquid bromine. Furthermore, even when the orientation of a molecule does not greatly influence the orientation of its neighbors, it is found that the orientation of a molecule does have an important effect on the location of its neighbors. Thus, the coupling of translational and orientational coordinates is significant, even in the liquids nitrogen and oxygen.     

An integral equation theory for inhomogeneous molecular fluids: the reference interaction site model approach

An integral equation theory which is applicable to inhomogeneous molecular liquids is proposed. The "inhomogeneous reference interaction site model (RISM)" equation derived here is a natural extension of the RISM equation to inhomogeneous systems. This theory makes it possible to calculate the pair correlation function between two molecules which are located at different density regions. We also propose approximations concerning the closure relation and the intramolecular susceptibility of inhomogeneous molecular liquids. As a preliminary application of the theory, the hydration structure around an ion is investigated. Lithium, sodium, and potassium cations are chosen as the solute. Using the Percus trick, the local density of solvent around an ion is expressed in terms of the solute-solvent pair correlation function calculated from the RISM theory. We then analyze the hydration structure around an ion through the triplet correlation function which is defined with the inhomogeneous pair correlation function and the local density of the solvent. The results of the triplet correlation functions for cations indicate that the thermal fluctuation of the hydration shell is closely related to the size of the solute ion. The triplet correlation function from the present theory is also compared with that from the Kirkwood superposition approximation, which substitutes the inhomogeneous pair correlation by the homogeneous one. For the lithium ion, the behavior of the triplet correlation functions from the present theory shows marked differences from the one calculated within the Kirkwood approximation.     

Theoretical and computational investigations on thermodynamic properties, effective site diameters, and molecular free volume of carbon disulfide fluid

A newly proposed theory [R. Laghaei et al., J. Chem. Phys. 124, 154502 (2006)] was extended to polyatomics and applied to compute the density and temperature dependence of the effective site diameters of carbon disulfide fluids. The generic van der Waals (GvdW) theory was also extended to polyatomics in order to calculate the GvdW parameters and the molecular free volume using the effective site diameters as the repulsion-attraction separation distance. A three-site Lennard-Jones potential available in the literature was slightly modified and used in Monte Carlo simulations to obtain the functions appearing in the effective site diameter and GvdW expressions. The interaction potential was examined to reproduce the fluid phase thermodynamic properties using Gibbs ensemble Monte Carlo simulations and also the equation of state in the liquid phase using NVT Monte Carlo (NVT-MC) simulations. Comparison between the simulation results and experimental data shows excellent agreement for the densities of the coexisting phases, the vapor pressure, properties of the predicted critical point, and the equation of state. NVT-MC simulations were performed over a wide range of densities and temperatures in sub- and supercritical regions to compute the effective site diameters, the GvdW parameters, and the molecular free volume. The molecular structure in terms of the site-site pair correlation functions, the density dependence of the effective site diameters, and the density and temperature dependence of the GvdW parameters and molecular free volume were studied and discussed. The GvdW parameters were fitted to empirical expressions as a function of density and temperature. The computed molecular free volume will be used in future investigations to study the transport properties of carbon disulfide.     

SSOZ-HNC and SSOZ-PY integral equation studies of the structure of three-site polar fluids

Structure factors and site-site distribution functions for models of liquid carbon disulphide (CS₂) and acetonitrile (CH₃CN) are obtained by using the site-site Ornstein-Zernike (SSOZ) integral equation with the Percus-Yevick (PY) and the hypernetted chain (HNC) closures. The calculated structure factors are found to be in good agreement with the neutron and X-ray diffraction data as well as with the simulation data. The site charges have a significant effect on the distribution functions but not on the structure factors of both the systems. There is very good qualitative agreement between the calculated distribution functions and the results from computer simulations. Distinctive shoulders found in the simulation results for the first peaks of the C-N and CH₃-CH₃ distribution functions are enhanced in the calculations using the integral equations.     

Wavelet algorithm for solving integral equations of molecular liquids. A test for the reference interaction site model

A new efficient method is developed for solving integral equations based on the reference interaction site model (RISM) of molecular liquids. The method proposes the expansion of site-site correlation functions into the wavelet series and further calculations of the approximating coefficients. To solve the integral equations we have applied the hybrid scheme in which the coarse part of the solution is calculated by wavelets with the use of the Newton-Raphson procedure, while the fine part is evaluated by the direct iterations. The Coifman 2 basis set is employed for the wavelet treatment of the coarse solution. This wavelet basis set provides compact and accurate approximation of site-site correlation functions so that the number of basis functions and the amplitude of the fine part of solution decrease sufficiently with respect to those obtained by the conventional scheme. The efficiency of the method is tested by calculations of SPC/E model of water. The results indicated that the total CPU time to obtain solution by the proposed procedure reduces to 20% of that required for the conventional hybrid method.     

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.     

Evaluation of site-site bridge diagrams for molecular fluids

The presence of bridge functions in formally exact integral equation theories is the primary obstacle preventing the extraction of exact fluid structure from these theories. The bridge functions are typically neglected but in many fluids their impact may be significant. Each bridge function can be subdivided into bridge diagrams, which are well defined but difficult to evaluate. The calculation of bridge diagrams for the Chandler-Silbey-Ladanyi (CSL) integral equation theory is the subject of this paper. In particular, we evaluate the diagrams required to yield an exact theory up to the first power in density [O(rho(1))] and provide algorithms that remain feasible for any molecule. Further, the bridge diagrams are evaluated and compared with the f-bond and h-bond formulations. Exact bridge diagrams are numerically evaluated for several chiral molecules, for two polar dimers, and for SPC/E water. The quality of the diagrams is assessed in two ways: First, the predicted interatomic distributions are compared with those obtained from Monte Carlo simulations. Second, the connectivity constraints are evaluated and the errors in satisfying these exact relationships are compared for the f-bond and h-bond formulations. For apolar fluids, a clear improvement in CSL theory is evident with the inclusion of O(rho(0)) and O(rho(1)) diagrams. In contrast, for polar fluids, the inclusion of bridge diagrams does not lead to improvement in the structural predictions.     

Bridge function for the dipolar fluid from simulation

The exact bridge function of the Lennard-Jones dipolar (Stockmayer) fluid is extracted from Monte Carlo simulation data. The projections g(mnl)(r) onto rotational invariants of the non-spherically symmetric pair distribution function g(r, Ω) are accumulated during simulation. Making intensive use of anisotropic integral equation techniques, the molecular Ornstein-Zernike equation is then inverted in order to derive the direct correlation function c(mnl)(r), the cavity function y(mnl)(r), the negative excess potential of mean force lny|(mnl)(r), and the bridge function b(mnl)(r) projections. b(r, Ω) presents strong, non-universal anisotropies at high dipolar coupling. This simulation data analysis may serve as reference and guide for approximated bridge function theories of dipolar fluids and is a valuable step towards the case of more refined, nonlinear water-like geometries.     

Local structure of solvation of nonpolar chains in nonpolar solvents at infinite dilution

The SSOZ (site-site Ornstein-Zernike) equation is used to study the local structure of solvation of linear nonpolar molecules in nonpolar solvents. The atom-atomic interaction potentials are described by the Lennard-Jones potential. The chain-solvent atom-atomic pair correlation functions are calculated in relation to the chain length (number of atoms), solvent density, and the ratio of the geometrical parameters of solvent and chain atoms. Institute of Theoretical and Experimental Biophysics, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 37, No. 4, pp. 742–749, July–August, 1996. Translated by L. Smolina     

"Up" versus "down" alignment and hydration structures of solutes at the air/water interface revealed by heterodyne-detected electronic sum frequency generation with classical molecular dynamics simulation

We unambiguously demonstrate the "up" versus "down" alignment of a pair of prototypical solute molecules adsorbed at the air/water interface for the first time using heterodyne-detected electronic sum frequency generation spectroscopy. This molecular alignment is also reproduced by classical molecular dynamics (MD) simulation theoretically. Furthermore, the MD simulation indicates distinctly different interface-specific hydration structures around the two solute molecules, which dictate the molecular alignment at the interface. It is concluded that the hydrophilicity difference between the terminal functional groups of the solute governs the molecular orientation and surrounding hydration structures at the interface.     

Pair structure of the hard-sphere Yukawa fluid: an improved analytic method versus simulations, Rogers-Young scheme, and experiment

We present a comprehensive study of the equilibrium pair structure in fluids of nonoverlapping spheres interacting by a repulsive Yukawa-like pair potential, with special focus on suspensions of charged colloidal particles. The accuracy of several integral equation schemes for the static structure factor, S(q), and radial distribution function, g(r), is investigated in comparison to computer simulation results and static light scattering data on charge-stabilized silica spheres. In particular, we show that an improved version of the so-called penetrating-background corrected rescaled mean spherical approximation (PB-RMSA) by Snook and Hayter [Langmuir 8, 2880 (1992)], referred to as the modified PB-RMSA (MPB-RMSA), gives pair structure functions which are in general in very good agreement with Monte Carlo simulations and results from the accurate but nonanalytical and therefore computationally more expensive Rogers-Young integral equation scheme. The MPB-RMSA preserves the analytic simplicity of the standard rescaled mean spherical (RMSA) solution. The combination of high accuracy and fast evaluation makes the MPB-RMSA ideally suited for extensive parameter scans and experimental data evaluation, and for providing the static input to dynamic theories. We discuss the results of extensive parameter scans probing the concentration scaling of the pair structure of strongly correlated Yukawa particles, and we determine the liquid-solid coexistence line using the Hansen-Verlet freezing rule.     

Shear viscosity of Stockmayer fluid: Application of integral equations method to Vesovic–Wakeham scheme

In our previous works, we applied the integral equations method to calculate transport properties of nonpolar fluids such as Lennard–Jones (12-6) fluid [R. Khordad, Physica A 387 (2008) 4519, M.M. Papari, R. Khordad, Z. Akbari, Physica A 388 (2009) 585]. The present work is a continuation of our studies on transport properties of polar fluids. We use the Stockmayer potential and examine theoretically the viscosity and pressure of several refrigerant mixtures such as R125 + R143a, HFC-125 + HFC-134a, HFC-125 + HFC-32, and HFC-134a + HFC-32. We solve numerically the Ornstein–Zernike (OZ) equation using the hypernetted-chain approximation (HNC) for binary fluid mixtures and obtain the pair correlation functions. Finally, the density and temperature dependence of shear viscosity and pressure are studied using Vesovic–Wakeham method and compared with experimental results. According to the results obtained from the present work reveals that the integral equations method is suitable for predicting the pressure and shear viscosity of this class of fluids.