Integral equation theory for charged liquids: Model 2–2 electrolytes and the bridge function

Structure and thermodynamics of a 2D Lennard-Jones hexagonal fluid

The thermodynamic and structural properties of the 2D hexagonal soft-sites fluid are examined by integral equation theory benchmarked against extensive Monte Carlo simulations. Hexamers are built of six equal Lennard-Jones segments. Site-site integral equation theory is used to compute site-site correlation functions, excess internal energies and isotherms over a wide range of conditions and compared with results obtained from Monte Carlo simulations. Various approaches for computing the pressure are discussed as well. Satisfactory qualitative agreement between theory and simulations is found with details depending on the applied closure relation.

Bridge functions of classical one-component plasmas

In a recent paper, Lucco Castello et al. [arXiv:2107.03537] performed systematic extractions of classical one-component plasma bridge functions from molecular dynamics simulations and provided an accurate parametrization that was incorporated in their isomorph-based empirically modified hypernetted chain approach for Yukawa one-component plasmas. Here the extraction technique and parametrization strategy are described in detail, while the deficiencies of earlier efforts are discussed. The structural and thermodynamic predictions of the updated version of the integral equation theory approach are compared with extensive available simulation results revealing a truly unprecedented level of accuracy in the entire dense liquid region of the Yukawa phase diagram.

Testing the isomorph invariance of the bridge functions of Yukawa one-component plasmas

It has been recently conjectured that bridge functions remain nearly invariant along phase diagram lines of constant excess entropy for the broad class of R-simple liquids. To test this hypothesis, the bridge functions of Yukawa systems are computed outside the correlation void with the Ornstein-Zernike inversion method employing structural input from ultra-accurate molecular dynamics simulations and inside the correlation void with the cavity distribution method employing structural input from ultra-long specially designed molecular dynamics simulations featuring a tagged particle pair. Yukawa bridge functions are revealed to be isomorph invariant to a very high degree. The observed invariance is not exact, however, since isomorphic deviations exceed the overall uncertainties.

A multiple decay-length extension of the Debye-Hückel theory: to achieve high accuracy also for concentrated solutions and explain under-screening in dilute symmetric electrolytes

The Poisson-Boltzmann and Debye-Hückel approximations for the pair distributions and mean electrostatic potential in electrolytes predict that these entities have one single decay mode with a decay length equal to the Debye length 1/κD, that is, they have a characteristic contribution that decays with distance r like e-κDr/r. However, in reality, electrolytes have several decay modes e-κr/r, e-κ'r/r etc. with different decay lengths, 1/κ, 1/κ' etc., that in general are different from the Debye length. As an illustration of the significance of multiple decay modes in electrolytes, the present work uses a very simple extension of the Debye-Hückel approximation with two decay lengths, which predicts oscillatory modes when appropriate. This approach gives very accurate results for radial distribution functions and thermodynamic properties of aqueous solutions of monovalent electrolytes for all concentrations investigated, including high ones. It is designed to satisfy necessary statistical mechanical conditions for the distributions. The effective dielectric permittivity of the electrolyte plays an important role in the theory and each mode has its own value of this entity. Electrolytes with high electrostatic coupling, like those with multivalent ions and/or with solvent of low dielectric constant, have decay lengths in dilute solutions that substantially deviate from the Debye length. It is shown that this is caused by nonlinear ion-ion correlation effects and the origin of under-screening, i.e., 1/κ > 1/κD, in dilute symmetric electrolytes is analyzed. The under-screening is accompanied by an increase in the effective dielectric permittivity that is also caused by these correlations. The theoretical results for the decay length are successfully compared with recent experimental data for simple electrolytes in various solvents. The paper includes background material on electrolyte theory and screening in order to be accessible for nonexperts in the field.

Closure-based perturbative density-functional theory of hard-sphere freezing: properties of the bridge functional

The study of freezing using perturbative classical density-functional theory is revisited, using a bridge functional approach to resum all terms beyond second order in the free energy expansion. More precisely, the first-order direct correlation function of the solid phase is written as a functional expansion about the homogeneous liquid phase, and the sum of all higher-order terms is represented as a functional of the second-order term. Information about the shape and uniqueness of this bridge functional for the case of hard spheres is obtained via an inversion procedure that employs Monte Carlo fluid-solid coexistence data from the literature. The parametric plots obtained from the inversion procedure show very little scatter in certain regions, suggesting a unique functional dependence, but large scatter in other regions. The scatter is related to the anisotropy of the solid lattice at the particle scale. Interestingly, the thermodynamic properties of the phase transition are quite insensitive to the regions where the scatter is large, and several simple closures (i.e., analytical forms of the bridge function) reproduce exactly the liquid-solid coexistence densities and Lindemann parameter from simulation. The form of these closures is significantly different from the usual closures employed in liquid-state integral equation theory.

Structure and stability of isotropic states of hard platelet fluids

We study the thermodynamics and the pair structure of hard, infinitely thin, circular platelets in the isotropic phase. Monte Carlo simulation results indicate a rich spatial structure of the spherical expansion components of the direct correlation function, including nonmonotonical variation of some of the components with density. Integral equation theory is shown to reproduce the main features observed in simulations. The hypernetted chain closure, as well as its extended versions that include the bridge function up to second and third order in density, perform better than both the Percus-Yevick closure and Verlet bridge function approximation. Using a recent fundamental measure density functional theory, an analytic expression for the direct correlation function is obtained as the sum of the Mayer bond and a term proportional to the density and the intersection length of two platelets. This is shown to give a reasonable estimate of the structure found in simulations, but to fail to capture the nonmonotonic variation with density. We also carry out a density functional stability analysis of the isotropic phase with respect to nematic ordering and show that the limiting density is consistent with that where the Kerr coefficient vanishes. As a reference system, we compare to simulation results for hard oblate spheroids with small, but nonzero elongations, demonstrating that the case of vanishingly thin platelets is approached smoothly.

Structure of molecular liquids: hard rod-disk mixtures

The structure of hard rod-disk mixtures is studied using Monte Carlo simulations and integral equation theory, for a range of densities in the isotropic phase. By extension of methods used in single component fluids, the pair correlation functions of the molecules are calculated and comparisons between simulation and integral equation theory, using a number of different closure relations, are made. Comparison is also made for thermodynamic data and phase behavior.

Structure of molecular liquids: closure relations for hard spheroids

We present the results of Monte Carlo simulations of hard spheroids of revolution of different elongations. Both prolate and oblate shapes are examined. A systematic study of the bridge function b(1,2), and direct comparison with the indirect correlation function gamma(1,2)=h(1,2)-c(1,2) at densities spanning the isotropic fluid range, allow us to evaluate the accuracy of various proposed closure relations for integral equations.

Chemical potentials and phase equilibria of Lennard-Jones mixtures: a self-consistent integral equation approach

We explore the vapor-liquid phase behavior of binary mixtures of Lennard-Jones-type molecules where one component is supercritical, given the system temperature. We apply the self-consistency approach to the Ornstein-Zernike integral equations to obtain the correlation functions. The consistency checks include not only thermodynamic consistencies (pressure consistency and Gibbs-Duhem consistency), but also pointwise consistencies, such as the zero-separation theorems on the cavity functions. The consistencies are enforced via the bridge functions in the closure which contain adjustable parameters. The full solution requires the values of not only the monomer chemical potentials, but also the dimer chemical potentials present in the zero-separation theorems. These are evaluated by the direct chemical-potential formula [L. L. Lee, J. Chem. Phys. 97, 8606 (1992)] that does not require temperature nor density integration. In order to assess the integral equation accuracy, molecular-dynamics simulations are carried out alongside the states studied. The integral equation results compare well with simulation data. In phase calculations, it is important to have pressure consistency and valid chemical potentials, since the matching of phase boundaries requires the equality of the pressures and chemical potentials of both the liquid and vapor phases. The mixtures studied are methane-type and pentane-type molecules, both characterized by effective Lennard-Jones potentials. Calculations on one isotherm show that the integral equation approach yields valid answers as compared with the experimental data of Sage and Lacey. To study vapor-liquid phase behavior, it is necessary to use consistent theories; any inconsistencies, especially in pressure, will vitiate the phase boundary calculations.

A Coupled Reference Interaction Site Model/Molecular Dynamics Study of the Potential of Mean Force Curve of the SN2 Cl- + CH3Cl Reaction in Water

An application of the coupled reference interaction site model (RISM)/simulation methodology to the calculation of the potential of mean force (PMF) curve in aqueous solution for the identity nucleophilic substitution reaction Cl(-) + CH(3)Cl is performed. The free energy of activation is calculated to be 27.1 kcal/mol which compares very well with the experimentally determined barrier height of 26.6 kcal/mol. Furthermore, the calculated PMF is almost superimposed with that previously calculated using the computationally rigorous Monte Carlo with importance sampling method (Chandrasekhar, J.; Smith, S. F.; Jorgensen, W. L. J. Am. Chem. Soc. 1985, 107, 154). Using the calculated PMF, a crude estimate of the solvated kinetic transmission coefficient also compares well with that of previous more accurate simulations. These results indicate that the coupled RISM/simulation method provides a cost-effective methodology for studying reactions in solution.

Coupled reference interaction site model/simulation approach for thermochemistry of solvation: Theory and prospects

We present a new methodology for computing solvation free energy, which is based upon the reference interaction site model (RISM)/hypernetted chain (HNC) solvation free energy expression, but which substitutes radial distribution functions taken from simulations for those calculated by simultaneous solution of the RISM and HNC equations. Consequently, solvation free energy can be obtained from a single molecular dynamics or Monte Carlo simulation. Here we describe in detail the coupled RISM/simulation approach, and offer some error analysis. Finally we give the results of its application to a set of small test molecules in aqueous solution. The success shown in some of our results demonstrates that the coupled RISM/simulation approach is worth considering further as a potentially useful tool in studies of solvated systems, such as aqueous molecular biosystems.

Computer simulation study of the closure relations in hard sphere fluids

We study, using Monte Carlo simulations, the cavity and the bridge functions of various hard sphere fluids: one component system, equimolar additive, and nonadditive binary mixtures. In particular, we numerically check the assumption of local dependency of the bridge functions from the indirect correlation functions, on which most of the existing integral equation theories hinge. We find that this condition can be violated either in the region around the first and second neighbors shell, or inside the hard core, for the systems here considered. The violations manifest themselves clearly in the so-called Duh-Haymet plots of the bridge functions versus the indirect correlation functions and become amplified as the coupling of the system increases.

An application of coupled reference interaction site model/molecular dynamics to the conformational analysis of the alanine dipeptide

We present an application of our recently proposed coupled reference interaction site model (RISM) molecular dynamics (MD) solvation free energy methodology [Freedman and Truong, Chem. Phys. Lett. 381, 362 (2003); J. Chem. Phys. 121, 2187 (2004)] to study the conformational stability of alanine dipeptide in aqueous solution. In this methodology, radial distribution functions obtained from a single MD simulation are substituted into a RISM expression for solvation free energy. Consequently, iterative solution of the RISM equation is not needed. The relative solvation free energies of seven different conformations of the alanine dipeptide in aqueous solution are calculated. Results from the coupled RISM/MD methodology are in good agreement with those from earlier simulations using the accurate free energy perturbation approach, showing that the alphaR conformation is most stabilized by solution. This study establishes a framework for applying this coupled RISM/MD method to larger biological systems.