Ornstein-Zernike Integral Equation Theory Research Articles

Applicability of a central force water model to study adsorption in disordered hydrophobic matrices—replica Ornstein–Zernike theory

A simple central force water model to study adsorption in random Lennard-Jones-like matrices has been studied using the replica Ornstein–Zernike integral equation theory in hypernetted-chain (HNC) approximation and in HNC+bridge approximation. The structure of water in obstacle matrices of different sizes was studied, showing that the model appropriately accounts for the hydrophobic hydration. By calculating the chemical potential of water in the model adsorbent, we have constructed the adsorption isotherm. Except for the cases of highly dispersed matrices, water gets excluded from the crowded hydrophobic environment, as expected experimentally.

Integral equation theory of thermodynamics, pair structure, and growing static length scale in metastable hard sphere and Weeks-Chandler-Andersen fluids.

We employ the Ornstein-Zernike integral equation theory with the Percus-Yevick (PY) and modified-Verlet (MV) closures to study the equilibrium structural and thermodynamic properties of metastable monodisperse hard sphere and continuous repulsion Weeks-Chandler-Andersen (WCA) fluids under density and temperature conditions where the system is strongly overcompressed or supercooled, respectively. The theoretical results are compared to crystal-avoiding simulations of these dense monodisperse model one-component fluids. The equation of state (EOS) and dimensionless compressibility are computed using both the virial and compressibility routes. For hard spheres, the MV-based virial route EOS and dimensionless compressibility are in very good agreement with simulation for all packing fractions, much better than the PY analogs. The corresponding MV-based predictions for the static structure factor are also very good. The amplitude of density fluctuations on the local cage scale and in the long wavelength limit, and three technically different measures of the density correlation length, are studied with both closures. All five properties grow in a roughly exponential manner with density in the metastable regime up to packing fractions of 58% with no sign of saturation. The MV-based results are in good agreement with our crystal-avoiding simulations. Interestingly, the density dependences of long and short wavelength quantities are closely related. The MV-based theory is also quite accurate for the thermodynamics and structure of supercooled monodisperse WCA fluids. Overall our findings are also relevant as critical input to microscopic theories that relate the equilibrium pair correlation function or static structure factor to dynamical constraints, barriers, and activated relaxation in glass-forming liquids.

Closure for the Ornstein-Zernike equation with pressure and free energy consistency.

The Ornstein-Zernike (OZ) integral equation theory is a powerful approach to simple liquids due to its low computational cost and the fact that, when combined with an appropriate closure equation, the theory is thermodynamically complete. However, approximate closures proposed to date exhibit pressure or free energy inconsistencies that produce inaccurate or ambiguous results, limiting the usefulness of the Ornstein-Zernike approach. To address this problem, we combine methods to enforce both pressure and free energy consistency to create a new closure approximation and test it for a single-component Lennard-Jones fluid. The closure is a simple power series in the direct and total correlation functions for which we have derived analytical formulas for the excess Helmholtz free energy and chemical potential. These expressions contain a partial molar volumelike term, similar to excess chemical potential correction terms recently developed. Using our bridge approximation, we have calculated the pressure, Helmholtz free energy, and chemical potential for the Lennard-Jones fluid using the Kirkwood charging, thermodynamic integration techniques, and analytic expressions. These results are compared with those from the hypernetted chain equation and the Verlet-modified closure against Monte Carlo and equations-of-state data for reduced densities of ρ^{*}<1 and temperatures of T^{*}=1.5, 2.74, and 5. Our closure shows consistency among all thermodynamic paths, except for one expression of the Gibbs-Duhem relation, whereas the hypernetted chain equation and the Verlet-modified closure exhibit consistency between only a few relations. Accuracy of the closure is comparable to the Verlet-modified closure and a significant improvement to results obtained from the hypernetted chain equation.

Integral equation theory based direct and accelerated systematic coarse-graining approaches.

Coarse-grained (CG) molecular dynamics (MD) simulations have become popular for investigating systems on multiple length and time scales ranging from atomistic to mesoscales. In CGMD, several atoms are mapped onto a single CG bead and the effective interactions between CG beads are determined. Iterative coarse-graining methods, such as iterative Boltzmann inversion (IBI), are computationally expensive and can have convergence issues. In this paper, we present a direct and computationally efficient theoretical procedure for coarse-graining based on the Ornstein-Zernike (OZ) and hypernetted chain (HNC) integral equation theory. We demonstrate the OZ-HNC-based CG method by coarse-graining a bulk water system, a water-methanol mixture system, and an electrolyte system. We show that the accuracy of the CG potentials obtained from the OZ-HNC-based coarse-graining is comparable to iterative systematic coarse-graining methods. Furthermore, we show that the CG potentials from OZ-HNC can be used to reduce the number of iterations and hence the computational cost of the iterative systematic coarse-graining approaches, like IBI and relative entropy minimization.

Correction of Kovalenko-Hirata closure in Ornstein-Zernike integral equation theory for Lennard-Jones fluids

We have studied the accuracy of Ornstein-Zernike (OZ) integral equation theory in terms of the solvation free energy (SFE) for a two-component Lennard-Jones system at the infinite dilution limit. We have employed the hypernetted chain (HNC), Kovalenko-Hirata (KH), Kobryn-Gusarov-Kovalenko (KGK), and Percus-Yevick (PY) closure equations. Further, we have extended the Verlet-modified (VM) closure to the two-component system to examine the accuracy of this method in terms of the SFE. Molecular dynamics simulations were employed to compare the results with the above mentioned OZ theories. The HNC and KH approximations significantly overestimate the SFE, whereas the PY approximation tends to underestimate it. The overestimation of the SFE by the KGK approximation becomes significant when the solvent density is relatively high. In contrast, the VM approximation is found to be rather accurate at all studied conditions. An analysis of the integrand for the SFE reveals that, to improve the SFE, the first rising (FR) region in the radial distribution function (RDF) must be corrected. We have also tested the sigma-enlarging-bridge (SEB) function that we proposed previously [T. Miyata and Y. Ebato, J. Mol. Liq. 217 (2016) 75] for the correction of the FR region of the RDF. In this study, we applied the SEB function to both HNC-type and KH-type closures and found that these combinations (SEB-HNC and SEB-KH) improve the SFE significantly.

Competition between excluded-volume and electrostatic interactions for nanogel swelling: effects of the counterion valence and nanogel charge.

In this work the equilibrium distribution of ions around a thermo-responsive charged nanogel particle in an electrolyte aqueous suspension is explored using coarse-grained Monte Carlo computer simulations and the Ornstein-Zernike integral equation theory. We explicitly consider the ionic size in both methods and study the interplay between electrostatic and excluded-volume effects for swollen and shrunken nanogels, monovalent and trivalent counterions, and for two different nanogel charges. We find good quantitative agreement between the ionic density profiles obtained using both methods when the excluded repulsive force exerted by the cross-linked polymer network is taken into account. For the shrunken conformation, the electrostatic repulsion between the charged groups provokes a heterogeneous polymer density profile, leading to a nanogel structure with an internal low density hole surrounded by a dense corona. The results show that the excluded-volume repulsion strongly hinders the ion permeation for shrunken nanogels, where volume exclusion is able to significantly reduce the concentration of counterions in the more dense regions of the nanogel. In general, we demonstrate that the thermosensitive behaviour of nanogels, as well as their internal structure, is strongly influenced by the valence of the counterions and also by the charge of the particles. On the one hand, an increase of the counterion valence moves the swelling transition to lower temperatures, and induces a major structuring of the charged monomers into internal and external layers around the crown for shrunken nanogels. On the other hand, increasing the particle charge shifts the swelling curve to larger values of the effective radius of the nanogel.

A pressure consistent bridge correction of Kovalenko-Hirata closure in Ornstein-Zernike theory for Lennard-Jones fluids by apparently adjusting sigma parameter

Ornstein-Zernike (OZ) integral equation theory is known to overestimate the excess internal energy, Uex, pressure through the virial route, Pv, and excess chemical potential, μex, for one-component Lennard-Jones (LJ) fluids under hypernetted chain (HNC) and Kovalenko-Hirata (KH) approximatons. As one of the bridge correction methods to improve the precision of these thermodynamic quantities, it was shown in our previous paper that the method to apparently adjust σ parameter in the LJ potential is effective [T. Miyata and Y. Ebato, J. Molec. Liquids. 217, 75 (2016)]. In our previous paper, we evaluated the actual variation in the σ parameter by using a fitting procedure to molecular dynamics (MD) results. In this article, we propose an alternative method to determine the actual variation in the σ parameter. The proposed method utilizes a condition that the virial and compressibility pressures coincide with each other. This method can correct OZ theory without a fitting procedure to MD results, and possesses characteristics of keeping a form of HNC and/or KH closure. We calculate the radial distribution function, pressure, excess internal energy, and excess chemical potential for one-component LJ fluids to check the performance of our proposed bridge function. We discuss the precision of these thermodynamic quantities by comparing with MD results. In addition, we also calculate a corrected gas-liquid coexistence curve based on a corrected KH-type closure and compare it with MD results.

Molecular Solvation Theory of Liquid Interfaces and Electric Interfacial Layers in Nanosystems

Solvation is critical for a broad range of chemistry, renewable energy, and bionanomaterials. At present, there is a need of theoretical solvation models that adequately include solvent molecular structure and predict solvation effects, in particular, in local confinement of nanosystems. Such theoretical models are of great demand to extend the capabilities of molecular simulations by far not sufficient to address the whole spectrum of scales from fast to very slow in large nanosystems of interest. Ornstein-Zernike type integral equation theory of liquids which is based on the first principles of statistical mechanics enables predictive microscopic modelling of chemical species, nanoparticles, and biomolecules in solution. In particular, the 3D-RISM-KH molecular theory of solvation1-3 yields 3D maps of correlation functions of solvent molecules site at a solute (supra)molecule or nanoparticle and then solvation free energy (SFE) analytically. With an input of a classical molecular force field of interaction potentials between explicit solute and solvent molecules (same as in molecular simulation), it accurately predicts the solvation structure, SFE, and electrochemistry of chemical and biomolecular species in solution and soft matter.1-5 3D-RISM-KH consistently accounts for effects of chemical specificities on solvation properties in complex nanosystems, problematic for molecular simulations and continuum solvation models. Analytical route to the solvation free energy allows multiscale coupling of the 3D-RISM-KH molecular theory of solvation with the KS-DFT, CASSCF, and FMO methods of quantum chemistry, MM, MD, and DPD simulations.1-3 The 3D-RISM-KH theory has been applied to evaluate the solvation structure, thermodynamics, and electric interfacial layer of modified cellulose nanocrystals (CNC) in ambient aqueous NaCl solution at concentration 0.0–0.25 mol/kg.4 Analysis of the 3D maps of Na+ density distributions shows the molecular structure and effect of the electric interfacial layer on effective interactions between charged CNC particles. The method readily treats provides structural models and modeling procedure to study effective forces and phase ordering of CNC suspensions in electrolyte solution. The 3D-RISM-KH theory was employed to study and validate against experiment the molecular recognition between kaolinite clay and a series of heterocyclic aromatic compounds (HAC) representative of N- and S-containing moieties in bitumen asphaltene macromolecules in toluene solvent.5 From the 3D site density distributions, SFE, and 3D-SFE density, 3D-RISM-KH predicts the arrangement and thermodynamics of adsorption of HAC and toluene on the kaolinite surface. The calculated adsorption enthalpy and loading ratio of phenanthridine-acridine were correlated to experimental Langmuir constant and adsorption loading. This provides insights into the specific interactions of clays, bitumen, and solvents components. Finally, the replica RISM-KH-VM molecular theory of solvation in nanoporous material reveals the mechanism of sorption and electrochemistry of electrolyte solution in nanoporous electrodes.2,3 The latter is drastically different from a planar electrode interface due to substantial distortion electric interfacial layer of electrolyte ions and solvent molecules by nanoporous confinement and surface functionalities. This interplay of nanoporous confinement and chemical specificities results in solvent-specific wetting and water depletion in hydrophobic nanopores, asymmetry in solvation and adsorption of cations and anions, desalination in hydrophobic nanopores and its reversal with external voltage, and specific adsorption in functionalized nanopores. The method reveals that specific capacitance of nanoporous electrodes is determined by a chemical balance in the Nernst-Planck equation comprising 4 electric interfacial layers, rather than 2 layers for a planar electrochemical capacitor. This includes the potential drop across the Stern layer at the surface of nanopores and the Gouy-Chapman layer averaged thermally and statistically over the nanoporous material, the osmotic term due to a difference in the ionic concentration in the electrodes and bulk solution, and the chemical potentials of sorbed solvated ions statistically averaged over the nanoporous material. [1] Molecular Theory of Solvation. Hirata, F., ed. Kluwer, Dordrecht, 2003. [2] (a) Kovalenko, A. Pure Appl . Chem . 2013, 85, 159. (b) Kovalenko, A. Condens. Matter Phys. 2015, 18, 32601. [3] Kovalenko, A. Multiscale modeling of solvation. In: Springer Handbook of Electrochemistry, Breitkopf, C.; Swider-Lyons, K., Eds. Springer, 2016. [4] Lyubimova, O.; Stoyanov, S. R.; Gusarov, S.; Kovalenko, A. Langmuir, 2015, 31, 7106. [5] Huang, W.-J.; et al. J. Phys. Chem. C 2014, 118, 23821.

Solvation Structure and Quasidynamics of Biomolecules Steered with Effective Solvation Forces Obtained From Molecular Theory of Solvation

Three-dimensional reference interaction site model with Kovalenko-Hirata closure (3D-RISM-KH molecular theory of solvation) is Ornstein-Zernike type integral equation theory of liquids. Based on first principles of statistical mechanics, 3D-RISM-KH consistently accounts for effect of chemical specificities of solvent, co-solvent, ions, and ligands on biomolecules solvation structure and thermodynamics, including steric forces, hydrophobicity, hydrogen bonding, and other effective interactions. 3D-RISM-KH supplemented with the partial molar volume correction, a.k.a. “Universal Correction” (UC), provides an excellent agreement with experimental data on a large set of small compounds for solvation free energies in octanol and water, and octanol-water partition coefficients. 3D-RISM-KH structural water detection and placement are implemented in Amber Tools and Molecular Operating Environment (MOE) packages. Structural water plays critical role in protein interactions and functions; case studies include HET-s prion, Aβ oligomer and fibril formation, folding promotion in GroEL chaperonin, and ligand binding to maltose-binding protein. Multi-time-step MD of biomolecules steered with mean solvation forces obtained from 3D-RISM-KH at outer steps and treated with generalized solvation force extrapolation (GSFE) at inner steps is efficiently stabilized with the optimized isokinetic Nose-Hoover chain (OIN) thermostat. The accuracy of GSFE and efficiency of OIN allow picoseconds outer steps while accurately reproducing conformational properties, as validated on hydrated alanine dipeptide, miniprotein 1L2Y, and protein G. Due to 3D-RISM-KH statistical averaging over rare events of solvent exchange and localization in biomolecular spaces, this quasidynamics results in time scale compression of protein conformational changes coupled with solvent and so in huge acceleration of conformational sampling. This provides up to 1000-fold effective speedup of sampling, compared to conventional MD with explicit solvent, and enables to fold the miniprotein from a fully denatured state in 60ns quasidynamics, cf. 4-9μs folding time in experiment.

Thermodynamic significance to correct the location of first rising region in radial distribution function approximately estimated from Ornstein–Zernike integral equation theory for Lennard–Jones fluids

We have calculated the excess internal energy, Uex, pressure through the virial route, pv, and excess chemical potential, μex, for one-component Lennard–Jones (LJ) fluids by using hypernetted chain (HNC), Kovalenko–Hirata (KH), Percus–Yevick (PY) and Verlet modified (VM) approximations in an Ornstein–Zernike (OZ) integral equation theory. The results have been compared with molecular dynamics simulation to examine the accuracy of each approximation at relatively high density region. HNC and KH approximations significantly overestimate the above three thermodynamic quantities, whereas PY and VM approximations give relatively accurate results. The analysis upon the integrand to evaluate Uex, pv and μex has revealed that the precise location of the first rising (FR) region in radial distribution function is the most important for the accurate evaluation of these quantities. We have applied an approximate bridge function pretending to adjust σ parameter in the LJ potential both to HNC and KH approximations, to obtain satisfactorily corrected results regarding Uex, pv and μex. Thus, we propose one of the necessary conditions for accurately evaluating thermodynamic quantities by using some approximated OZ theories: it is the proper location of the FR region in radial distribution functions.

Accuracy of solvation free energy calculated by hypernetted chain and Kovalenko–Hirata approximations for two-component system of Lennard-Jones liquid

The accuracy of both hypernetted chain (HNC) and Kovalenko–Hirata (KH) approximations assumed in an Ornstein–Zernike integral equation theory has been studied in terms of the solvation free energy (SFE) by comparing with molecular dynamics simulation for Lennard-Jones liquid. The Lennard-Jones parameters for the solute, ɛu and σu, were systematically varied. ɛu-dependence of the relative SFE is found to be hardly dependent on the approximations. However, σu-dependences of the SFE obtained both from HNC and KH approximations considerably differ from those by molecular dynamics simulation. The source of the error in the SFE from both approximations is also discussed.

Fluctuations and micro-heterogeneity in mixtures of complex liquids

The role of concentration fluctuation and micro-heterogeneity in aqueous methanol mixtures are examined by two different methods: computer simulations of two systems with sizes of 2048 and 16 384 molecules, and site-site Ornstein-Zernike integral equation theory with two different closures. The focus is on the short and long range behaviour of the correlation functions, their running integrals and the structure factors. It is found that the micro-heterogeneous nature of these mixtures does not allow a proper stabilisation of the long range tail of the correlations as obtained through computer simulations, even over 6 ns runs. Similarly, approximate closures provide poor estimates of the concentration fluctuations and micro-structure of the mixtures. Interestingly, the analysis of the inadequacies of both these studies provide interesting insights about the nature and interplay of the concentration fluctuations and the micro-heterogeneity in these mixtures.

Liquid theory with high accuracy and broad applicability: Coupling parameter series expansion and non hard sphere perturbation strategy

Thermodynamic and structural properties of liquids are of fundamental interest in physics, chemistry, and biology, and perturbation approach has been fundamental to liquid theoretical approaches since the dawn of modern statistical mechanics and remains so to this day. Although thermodynamic perturbation theory (TPT) is widely used in the chemical physics community, one of the most popular versions of the TPT, i.e. Zwanzig (Zwanzig, R. W. J. Chem. Phys. 1954, 22, 1420-1426) 1st-order high temperature series expansion (HTSE) TPT and its 2nd-order counterpart under a macroscopic compressibility approximation of Barker-Henderson (Barker, J. A.; Henderson, D. J. Chem. Phys. 1967, 47, 2856-2861), have some serious shortcomings: (i) the nth-order term of the HTSE is involved with reference fluid distribution functions of order up to 2n, and the higher-order terms hence progressively become more complicated and numerically inaccessible; (ii) the performance of the HTSE rapidly deteriorates and the calculated results become even qualitatively incorrect as the temperature of interest decreases. This account deals with the developments that we have made over the last five years or so to advance a coupling parameter series expansion (CPSE) and a non hard sphere (HS) perturbation strategy that has scored some of its greatest successes in overcoming the above-mentioned difficulties. In this account (i) we expatiate on implementation details of our schemes: how input information indispensable to high-order truncation of the CPSE in both the HS and non HS perturbation schemes is calculated by an Ornstein-Zernike integral equation theory; how high-order thermodynamic quantities, such as critical parameters and excess constant volume heat capacity, are extracted from the resulting excess Helmholtz free energy with irregular and inevitable numerical errors; how to select reference potential in the non HS perturbation scheme. (ii) We give a quantitative analysis on why convergence speed of the CPSE in both the HS and non HS perturbation schemes is certainly faster than that of the HTSE and the HS perturbation scheme. (iii) We illustrate applications of the CPSE TPT in both the HS and non HS perturbation schemes in calculating thermodynamic properties of various coarse-grained potential function models and as input information of other liquid state theories such as a classical density functional theory (DFT), and also discuss, in the framework of classical DFT, the potential of our CPSE scheme in several typical problems of chemical physics interest. (iv) Finally, we consider several topics which are possibly expected to be settled in the immediate future and possible integration with other liquid state theory frameworks aiming to solve problems in complex fluids in both bulk and inhomogeneous states.

Structural and thermodynamic properties of the restricted primitive model electrolyte in a mixture with uncharged hard spheres: a grand canonical Monte Carlo simulation and integral equation study

A restricted primitive model electrolyte in a mixture with uncharged hard spheres was studied at room temperature using grand canonical Monte Carlo computer simulation and Ornstein–Zernike integral equation theory in the hypernetted chain approximation (HNC). The mean spherical approximation results are also presented for a few cases. We obtained the pair distribution functions of species of the system, the dependencies of the total fluid density and the ionic fraction on the chemical potentials, the excess internal energy and the heat capacity at constant volume for a wide range of chemical potentials of the species from the simulations and HNC theory. In the majority of cases, good agreement between the theoretical predictions and simulation data is obtained. The composition of the mixture is determined by the chemical potentials of both species. The pair distribution functions have a Debye-like shape at low densities for various values of the ion fraction. By increasing the chemical potential of the uncharged component, weak trends for structuring of the solution are observed with the formation of ion-hard sphere-ion complexes. At high densities, a tendency for in-phase oscillations of ion–ion functions is observed similar to the pure electrolyte in the restricted primitive model. We analysed the chemical potential–density and the chemical potential–ion fraction projections of the equation of state in detail. Also, the heat capacity at constant volume has been calculated for the first time. The model and the results are useful for the development of the theory of inhomogeneous fluid mixtures.

STRINGENT VERIFICATION OF THIRD ORDER + SECOND ORDER PERTURBATION DENSITY FUNCTION THEORY: BASED ON SHORT-RANGE SQUARE WELL POTENTIAL

A recently proposed third order + second order perturbation density functional theory (DFT) approach is made self-contained by using a virial pressure from the Ornstein–Zernike integral equation theory as input to determine the numerical value of an associated physical parameter. An exacting examination is formulated by applying the self-contained perturbation DFT approach to a short-range square well fluid of low temperatures subject to various external fields and comparing the theoretical results for density profiles to the corresponding grand canonical ensemble Monte Carlo simulation results. The comparison seems favorable for the third order + second order perturbation DFT approach as a self-contained and accurate predictive approach. It is surprisingly found that this self-contained third order + second order perturbation DFT approach is displayed outstandingly even if a deep SW perturbation term is being accounted for by a second order perturbation expansion. A discussion is presented about potential opportunity for this perturbation scheme.

Going beyond the mean field approximation in classical density functional theory andapplication to one attractive core-softened model fluid

A novel scheme is advanced for an excess Helmholtz free energy density functional. Thepresent scheme is isomorphic to one frequently used mean field approximation (MFA)methodology, but goes beyond the latter in that the present scheme contains a bulksecond-order direct correlation function (DCF) which can be obtained by numericallysolving a bulk Ornstein–Zernike (OZ) integral equation theory (IET), and is therefore ingeneral more accurate than the bulk second-order DCF expected from MFA methodology.The scheme is applied in the framework of classical density functional theory (DFT) toone so-called attractive core-softened model potential with a double square wellattraction in homogeneous conditions. Quantitatively it is found that the presentscheme is in general more accurate than two previously confirmed third-order + second-order perturbation DFT and non-uniform fifth-order thermodynamic perturbation theory,even if the present scheme is implemented in a purely predictive manner and the third-order + second-order perturbation DFT is implemented in a partially predictive manner. Qualitatively thepresent scheme is characterized by several desirable features not possessed by previousmethodologies: (i) It is not concerned with any adjustable parameters, and this allows forhandy applications. (ii) It does not deal with problems of determining self-consistently bothan effective hard sphere diameter and a tail contribution to the full pair potentialunder consideration. (iii) Although the present scheme uses OZ IET to supplyinput information, it is safely applicable to subcritical regions of the bulk phasediagram.

Structural properties of effective potential model by liquid state theories

This paper investigates the structural properties of a model fluid dictated by an effective inter-particle oscillatory potential by grand canonical ensemble Monte Carlo (GCEMC) simulation and classical liquid state theories. The chosen oscillatory potential incorporates basic interaction terms used in modeling of various complex fluids which is composed of mesoscopic particles dispersed in a solvent bath, the studied structural properties include radial distribution function in bulk and inhomogeneous density distribution profile due to influence of several external fields. The GCEMC results are employed to test the validity of two recently proposed theoretical approaches in the field of atomic fluids. One is an Ornstein-Zernike integral equation theory approach; the other is a third order + second order perturbation density functional theory. Satisfactory agreement between the GCEMC simulation and the pure theories fully indicates the ready adaptability of the atomic fluid theories to effective model potentials in complex fluids, and classifies the proposed theoretical approaches as convenient tools for the investigation of complex fluids under the single component macro-fluid approximation.

A theoretical investigation on the honeycomb potential fluid

A local self-consistent Ornstein-Zernike (OZ) integral equation theory (IET) is proposed to provide a rapid route for obtaining thermodynamic and structural information for any thermodynamically stable or metastable state points in the bulk phase diagram without recourse to traditional thermodynamic integration, and extensive NVT-Monte Carlo simulations are performed on a recently proposed honeycomb potential in three dimensions to test the theory's reliability. The simulated quantities include radial distribution function (rdf) and excess internal energy, pressure, excess chemical potential, and excess Helmholtz free energy. It is demonstrated that (i) the theory reproduces the rdf very satisfactorily only if the bulk state does not enter deep into a two phases coexistence region; (ii) the excess internal energy is the only one of the four thermodynamic quantities investigated amenable to the most accurate prediction by the present theory, and the simulated pressure is somewhat overestimated by the theoretical calculations, but the deviation tends to vanish along with rising of the temperature; (iii) using the structural functions from the present local self-consistent OZ IET, a previously derived local expression, due to the present author, achieves even a higher accuracy in calculating for the excess chemical potential than the exact virial pressure formula for the pressure, and the resulting excess Helmholtz free energy is in surprisingly same with the simulation results due to offset of the errors. Based on the above observations, it is suggested that it may be a good procedure to integrate the theoretical excess internal energy along the isochors to get the excess Helmholtz free energy, which is then fitted to a polynomial to be used for calculation of all of other thermodynamic quantities in the framework of the OZ IET.

Local Self-Consistent Ornstein−Zernike Integral Equation Theory and Application to a Generalized Lennard-Jones Potential

Local self-consistent Ornstein-Zernike (OZ) integral equation theory (IET) provides a rapid and easy route for obtaining independently thermodynamic and structural information for a single state point. Because of neglect of information of neighboring state points in determining a self-consistent adjustable parameter performance of the local self-consistent OZ IET is somewhat vulnerable and worthy of intensive investigation. For this reason, we have performed Monte Carlo simulations to obtain thermodynamic and structural properties of fluid with a generalized Lennard-Jones potential, and the present simulation results are employed to verify the quality of a local version of a recently developed global self-consistent OZ IET and a local expression for computation of excess chemical potential directly from the structural functions of the state point of interest. Comprehensive comparison and analysis demonstrate the following (i) the present local self-consistent OZ IET performs quite well for calculation of pressure and excess internal energy; (ii) using the same structural functions from the present local self-consistent OZ IET, the previously derived local expression by the present author has by and large the same accuracy in calculating the excess chemical potential as an exact virial formula for the pressure; (iii) although the excellent performance exhibited for the above thermodynamic quantities persists to very low temperature and very short-ranged potential and remains even in the liquid-solid coexistence region, the excess Helmholtz free energy calculated from the pressure and excess chemical potential shows evident inaccuracy for a density-temperature combination deep in the liquid-solid coexistence region, and this makes it necessary to derive a local formulation for the excess free energy.

New free energy density functional and application to core-softened fluid

A new free energy density functional is advanced for general nonhard sphere potentials characterized by a repulsive core with a singular point at zero separation. The present functional is characterized by several features. (i) It does not involve with dividing the potentials into hard-sphere-like contribution and tail contribution in sharp contrast with usual effective hard sphere model+mean field approximation for tail contribution. (ii) It has no recourse to the use of weighted density and is computationally modest; it also does not resort to an equation of state and/or an excess Helmholtz free energy of bulk fluid over a range of density as input. Consequently, all of input information can be obtained by numerical solution of a bulk Ornstein-Zernike integral equation theory (OZ IET). Correspondingly, despite the use of bulk second-order direct correlation function (DCF) as input, the functional is applicable to the subcritical region. (iii) There is no any adjustable parameter associated with the present functional, and an effective hard sphere diameter entering the functional can be determined self-consistently and analytically once the input information, i.e., the second-order DCF and pressure of the coexistence bulk fluid, are obtained by the OZ IET. The present functional is applied to a core-softened fluid subject to varying external fields, and the density distributions predicted by the present functional are more self-consistent with available simulation results than a previous third-order+second-order perturbation density functional theory.