Roles of Repulsive and Attractive Forces in Liquids : The Equilibrium Theory of Classical Fluids

Algebraic second virial coefficient of the Mie m - 6 intermolecular potential based on perturbation theory

We propose several simple algebraic approximations for the second virial coefficient of fluids whose molecules interact by a generic Mie m - 6 intermolecular pair potential. In line with a perturbation theory, the parametric equations are formulated as the sum of a contribution due to a reference part of the intermolecular potential and a perturbation. Thereby, the equations provide a convenient (low-density) starting point for developing equation-of-state models of fluids or for developing similar approximations for the virial coefficient of (polymeric-)chain fluids. The choice of Barker and Henderson [J. Chem. Phys. 47, 4714 (1967)] and Weeks, Chandler, and Andersen [Phys. Rev. Lett. 25, 149 (1970); J. Chem. Phys. 54, 5237 (1971); and Phys. Rev. A 4, 1597 (1971)] for the reference part of the potential is considered. Our analytic approximations correctly recover the virial coefficient of the inverse-power potential of exponent m in the high-temperature limit and provide accurate estimates of the temperatures for which the virial coefficient equals zero or takes on its maximum value. Our description of the reference contribution to the second virial coefficient follows from an exact mapping onto the second virial coefficient of hard spheres; we propose a simple algebraic equation for the corresponding effective diameter of the hard spheres, which correctly recovers the low- and high-temperature scaling and limits of the reference fluid's second virial coefficient.

Deconstructing the Local Intermolecular Ordering and Dynamics of Liquid Chloroform and Bromoform

Local intermolecular structure and dynamics of the polar molecular liquids chloroform and bromoform are studied by molecular dynamics simulation. Structural distribution functions, including 1- and 2-D pair correlations and dipole contour plots allow direct comparison and show agreement with recent analyses of diffraction experiments. Studies of the haloforms' reorientational dynamics and longevity of structural features resulting from intermolecular interaction extend previous work toward deeper understanding of the factors controlling these features. Analyses of ensemble average structures and dynamical properties isolate mass, electrostatics, and steric packing as driving forces or contributing factors for the observed ordering and dynamics.

Accurate first-order perturbation theory for fluids: uf-theory

We propose a new first-order perturbation theory that provides a near-quantitative description of the thermodynamics of simple fluids. The theory is based on the ansatz that the Helmholtz free energy is bounded below by a first-order Mayer-f expansion. Together with the rigorous upper bound provided by a first-order u-expansion, this brackets the actual free energy between an upper and (effective) lower bound that can both be calculated based on first-order perturbation theory. This is of great practical use. Here, the two bounds are combined into an interpolation scheme for the free energy. The scheme exploits the fact that a first-order Mayer-f perturbation theory is exact in the low-density limit, whereas the accuracy of a first-order u-expansion grows when density increases. This allows an interpolation between the lower "f"-bound at low densities and the upper "u" bound at higher liquid-like densities. The resulting theory is particularly well behaved. Using a density-dependent interpolating function of only two adjustable parameters, we obtain a very accurate representation of the full fluid-phase behavior of a Lennard-Jones fluid. The interpolating function is transferable to other intermolecular potential types, which is here shown for the Mie m-6 family of fluids. The extension to mixtures is simple and accurate without requiring any dependence of the interpolating function on the composition of the mixture.

Phase behavior of hard C_{2h}-symmetric particle systems

Using Monte Carlo numerical simulation, this work sketches the phase diagram of systems of certain hard C_{2h}-symmetric particles, formed by gluing two aligned and displaced hard spherocylinders with a cylindrical-length-to-diameter ratio realistically, if viewed not only from the lyotropic colloidal liquid-crystal side but also from the thermotropic low-molecular-mass liquid-crystal side, equal to 5, as a function of the displacement. Several distinctive phases are observed, such as a nonperiodic smectic-B-like phase, a nonperiodic smectic-H-like phase, a smectic-C phase, and a short-layer-spacing uniaxial smectic-A phase but no biaxial nematic phase.

Rotational diffusion of shape switching particles in nematic liquid crystals

The theory of rotational diffusion of particles of various symmetry embedded in a liquid crystal host, essential to interpret a variety of spectroscopic observables, has been available for some time, but only for the case of rigid molecules. Here we generalize the treatment and present a theory to describe the rotational diffusion of shape-changing particles dispersed in nematic liquid crystals. The interaction of the particles with the environment is modeled by an effective field potential, while the particles are allowed to assume an arbitrary discrete number of shapes. The transition between shapes is modeled by a Markovian process which is combined with rotational diffusion. Our model is applied to the simple case of a particle that can exchange between three shapes: a rod, a disk, and a sphere. We consider in detail the effect of shape transitions in some selected correlation functions which are relevant for experiments.

Van der Waals Perspective on Coarse-Graining: Progress toward Solving Representability and Transferability Problems

Low-resolution coarse-grained (CG) models provide the necessary efficiency for simulating phenomena that are inaccessible to more detailed models. However, in order to realize their considerable promise, CG models must accurately describe the relevant physical forces and provide useful predictions. By formally integrating out the unnecessary details from an all-atom (AA) model, "bottom-up" approaches can, at least in principle, quantitatively reproduce the structural and thermodynamic properties of the AA model that are observable at the CG resolution. In practice, though, bottom-up approaches only approximate this "exact coarse-graining" procedure. The resulting models typically reproduce the intermolecular structure of AA models at a single thermodynamic state point but often describe other state points less accurately and, moreover, tend to provide a poor description of thermodynamic properties. These two limitations have been coined the "transferability" and "representability" problems, respectively. Perhaps, the simplest and most commonly discussed manifestation of the representability problem regards the tendency of structure-based CG models to dramatically overestimate the pressure. Furthermore, when these models are adjusted to reproduce the pressure, they provide a poor description of the compressibility. More generally, it is sometimes suggested that CG models are fundamentally incapable of reproducing both structural and thermodynamic properties. After all, there is no such thing as a "free lunch"; any significant gain in computational efficiency should come at the cost of significant model limitations. At least in the case of structural and thermodynamic properties, though, we optimistically propose that this may be a false dichotomy. Accordingly, we have recently re-examined the "exact coarse-graining" procedure and investigated the intrinsic consequences of representing an AA model in reduced resolution. These studies clarify the origin and inter-relationship of representability and transferability problems. Both arise as consequences of transferring thermodynamic information from the high resolution configuration space and encoding this information into the many-body potential of mean force (PMF), that is, the potential that emerges from an exact coarse-graining procedure. At least in principle, both representability and transferability problems can be resolved by properly addressing this thermodynamic information. In particular, we have demonstrated that "pressure-matching" provides a practical and rigorous means for addressing the density dependence of the PMF. The resulting bottom-up models accurately reproduce the structure, equilibrium density, compressibility, and pressure equation of state for AA models of molecular liquids. Additionally, we have extended this approach to develop transferable potentials that provide similar accuracy for heptane-toluene mixtures. Moreover, these potentials provide predictive accuracy for modeling concentrations that were not considered in their parametrization. More generally, this work suggests a "van der Waals" perspective on coarse-graining, in which conventional structure-based methods accurately describe the configuration dependence of the PMF, while independent variational principles infer the thermodynamic information that is necessary to resolve representability and transferability problems.

Short-Range Electron Correlation Stabilizes Noncavity Solvation of the Hydrated Electron

The hydrated electron, e^-_(aq), has often served as a model system to understand the influence of condensed-phase environments on electronic structure and dynamics. Despite over 50 years of study, however, the basic structure of e^-_(aq) is still the subject of controversy. In particular, the structure of e^-_(aq) was long assumed to be an electron localized within a solvent cavity, in a manner similar to halide solvation. Recently, however, we suggested that e^-_(aq) occupies a region of enhanced water density with little or no discernible cavity. The potential we developed was only subtly different from those that give rise to a cavity solvation motif, which suggests that the driving forces for noncavity solvation involve subtle electron-water attractive interactions at close distances. This leads to the question of how dispersion interactions are treated in simulations of the hydrated electron. Most dispersion potentials are ad hoc or are not designed to account for the type of close-contact electron-water overlap that might occur in the condensed phase, and where short-range dynamic electron correlation is important. To address this, in this paper we develop a procedure to calculate the potential energy surface between a single water molecule and an excess electron with high-level CCSD(T) electronic structure theory. By decomposing the electron-water potential into its constituent energetic contributions, we find that short-range electron correlation provides an attraction of comparable magnitude to the mean-field interactions between the electron and water. Furthermore, we find that by reoptimizing a popular cavity-forming one-electron model potential to better capture these attractive short-range interactions, the enhanced description of correlation predicts a noncavity e^-_(aq) with calculated properties in better agreement with experiment. Although much attention has been placed on the importance of long-range dispersion interactions in water cluster anions, our study reveals that largely unexplored short-range correlation effects are crucial in dictating the solvation structure of the condensed-phase hydrated electron.

Perturbation theory for multicomponent fluids based on structural properties of hard-sphere chain mixtures

An analytical expression for the Laplace transform of the radial distribution function of a mixture of hard-sphere chains of arbitrary segment size and chain length is used to rigorously formulate the first-order Barker-Henderson perturbation theory for the contribution of the segment-segment dispersive interactions into thermodynamics of the Lennard-Jones chain mixtures. Based on this approximation, a simple variant of the statistical associating fluid theory is proposed and used to predict properties of several mixtures of chains of different lengths and segment sizes. The theory treats the dispersive interactions more rigorously than the conventional theories and provides means for more accurate description of dispersive interactions in the mixtures of highly asymmetric components.

Exponential approximation for one-component Yukawa plasma

A theory based on the exponential approximation of the liquid-state theory is applied to study properties of several models of one-component Yukawa plasma characterized by different values of the screening parameter z. The results of the new theory are compared to the results of a conventional theory, which is based on the first-order mean spherical approximation, and to the results of a Monte Carlo simulation. The new theory shows improvements in the predictions for the thermodynamic and structural properties of Yukawa plasmas with high and intermediate values of the screening parameter, z, and coupling parameter, Γ. For low values of z and Γ, the new theory is comparable in accuracy to the conventional theory, which in turn agrees well with the results of the Monte Carlo simulation.

Perspective: Coarse-grained models for biomolecular systems

By focusing on essential features, while averaging over less important details, coarse-grained (CG) models provide significant computational and conceptual advantages with respect to more detailed models. Consequently, despite dramatic advances in computational methodologies and resources, CG models enjoy surging popularity and are becoming increasingly equal partners to atomically detailed models. This perspective surveys the rapidly developing landscape of CG models for biomolecular systems. In particular, this review seeks to provide a balanced, coherent, and unified presentation of several distinct approaches for developing CG models, including top-down, network-based, native-centric, knowledge-based, and bottom-up modeling strategies. The review summarizes their basic philosophies, theoretical foundations, typical applications, and recent developments. Additionally, the review identifies fundamental inter-relationships among the diverse approaches and discusses outstanding challenges in the field. When carefully applied and assessed, current CG models provide highly efficient means for investigating the biological consequences of basic physicochemical principles. Moreover, rigorous bottom-up approaches hold great promise for further improving the accuracy and scope of CG models for biomolecular systems.

Properties of the Lennard-Jones dimeric fluid in two dimensions: an integral equation study

The thermodynamic and structural properties of the planar soft-sites dumbbell fluid are examined by Monte Carlo simulations and integral equation theory. The dimers are built of two Lennard-Jones segments. Site-site integral equation theory in two dimensions is used to calculate the site-site radial distribution functions for a range of elongations and densities and the results are compared with Monte Carlo simulations. The critical parameters for selected types of dimers were also estimated. We analyze the influence of the bond length on critical point as well as tested correctness of site-site integral equation theory with different closures. The integral equations can be used to predict the phase diagram of dimers whose molecular parameters are known.

An improved first-order mean spherical approximation theory for the square-shoulder fluid

The theory, which utilizes an exponential enhancement of the first-order mean spherical approximation (FMSA) for the radial distribution functions of the hard-core plus square-well fluid, is adopted to study the properties of the simplest model of the core-softened fluids, i.e., the hard spheres with a square-shoulder interaction. The results for structure and thermodynamic properties are reported and compared against both the Monte Carlo simulation data as well as with those obtained within the conventional FMSA theory. We found that in the region of low densities and low temperatures, where the conventional FMSA theory fails, the exponential-based FMSA theory besides being qualitatively correct also provides with a notable quantitative improvement of the theoretical description.

Systematic methods for structurally consistent coarse-grained models

This chapter provides a primer on theories for coarse-grained (CG) modeling and, in particular, reviews several systematic methods for determining effective potentials for CG models. The chapter first reviews a statistical mechanics framework for relating atomistic and CG models. This framework naturally leads to a quantitative criterion for CG models that are "consistent" with a particular atomistic model for the same system. This consistency criterion is equivalent to minimizing the relative entropy between the two models. This criterion implies that a many-body PMF is the appropriate potential for a CG model that is consistent with a particular atomistic model. This chapter then presents a unified exposition of the theory and numerical methods for several approaches for approximating this many-body PMF. Finally, this chapter closes with a brief discussion of a few of the outstanding challenges facing the field of systematic coarse-graining.

Reference state for the generalized Yvon-Born-Green theory: application for coarse-grained model of hydrophobic hydration

Coarse-grained (CG) models provide a computationally efficient means for investigating phenomena that remain beyond the scope of atomically detailed models. Although CG models are often parametrized to reproduce the results of atomistic simulations, it is highly desirable to determine accurate CG models from experimental data. Recently, we have introduced a generalized Yvon-Born-Green (g-YBG) theory for directly (i.e., noniteratively) determining variationally optimized CG potentials from structural correlation functions. In principle, these correlation functions can be determined from experiment. In the present work, we introduce a reference state potential into the g-YBG framework. The reference state defines a fixed contribution to the CG potential. The remaining terms in the potential are then determined, such that the combined potential provides an optimal approximation to the many-body potential of mean force. By specifying a fixed contribution to the potential, the reference state significantly reduces the computational complexity and structural information necessary for determining the remaining potentials. We also validate the quantitative accuracy of the proposed method and numerically demonstrate that the reference state provides a convenient framework for transferring CG potentials from neat liquids to more complex systems. The resulting CG model provides a surprisingly accurate description of the two- and three-particle solvation structures of a hydrophobic solute in methanol. This work represents a significant step in developing the g-YBG theory as a useful computational framework for determining accurate CG models from limited experimental data.

Soret effect in molecular mixtures

A theoretical approach to the description of the Soret effect in binary nonpolar liquids is proposed. The temperature gradient of the partial pressure is determined as the driving force of thermal diffusion. The hard-sphere fluid is chosen as a reference system and an explicit relation for the Soret coefficient is found. Two additive contributions owing to steric repulsions and attractive interactions form the so-called chemical contribution to S_{T} [C. Debuschewitz and W. Köhler, Phys. Rev. Lett. 87, 055901 (2001)]. The parameters of interparticle interactions are defined with the help of the solvation theory. In particular, the van der Waals constant of cross interactions is expressed via the excess volume of mixture. The proposed theory is applied to the benzene-cyclohexane system. A reasonable agreement of theoretical and experimental results is revealed for the Soret coefficient and its temperature dependence.

Model energy landscapes of low-temperature fluids: Dipolar hard spheres

An analytical model of non-Gaussian energy landscape of low-temperature fluids is developed based on the thermodynamics of the fluid of dipolar hard spheres. The entire excitation profile of the liquid, from the high-temperature liquid to the point of ideal-glass transition, has been obtained from Monte Carlo simulations. The fluid of dipolar hard spheres loses stability close to the point of ideal-glass transition transforming via a first-order transition into a columnar liquid phase of dipolar chains locally arranged in a body-centered-tetragonal order. Significant non-Gaussianity of the energy landscape is responsible for narrowing of the distribution of potential energies and energies of inherent structures with decreasing temperature. We suggest that the proposed functionality of the enumeration function is widely applicable to both polar and nonpolar low-temperature liquids.

Orientational relaxation in a discotic liquid crystal

We investigate orientational relaxation of a model discotic liquid crystal, consisting of disclike molecules, by molecular dynamics simulations along two isobars starting from the high temperature isotropic phase. The two isobars have been so chosen that (a) the phase sequence isotropic- (I-) nematic- (N-) columnar (C) appears upon cooling along one of them and (b) the sequence isotropic- (I-) columnar- (C) along the other. While the orientational relaxation in the isotropic phase near the I-N phase transition in system (a) shows a power law decay at short to intermediate times, such power law relaxation is not observed in the isotropic phase near the I-C phase boundary in system (b). In order to understand this difference (the existence or the absence of the power law decay), we calculated the growth of the orientational pair distribution functions (OPDFs) near the I-N phase boundary and also near the I-C phase boundary. We find that the OPDF shows a marked growth in long range correlation as the I-N phase boundary is approached in the I-N-C system (a), but such a growth is absent in the I-C system, which appears to be consistent with the result that I-N phase transition in the former is weakly first order while the I-C phase transition in the latter is not weak. As the system settles into the nematic phase, the decay of the single-particle second-rank orientational time correlation function follows a pattern that is similar to what is observed with calamitic liquid crystals and supercooled molecular liquids.

The dielectric virial expansion and the models of dipolar hard-sphere fluid

The virial expansion technique to determine the dielectric constant epsilon of dipolar hard-sphere fluid is developed. It is shown that the formalism allows to bring into agreement the results of Debye's, Onsager's, and Langevin's to the problem. The third virial coefficient of epsilon is considered as a series over dipolar parameter lambda=m(2)d(3)kT. The terms up to O(lambda(11)) are calculated analytically providing a correct description of the third virial coefficient for small and intermediate values of lambda (0<or=lambda<or=4). The results of the dielectric virial series are compared with the Monte Carlo data for epsilon found by Matyushov and Ladanyi [J. Chem. Phys. 110, 994 (1999)]. The theory is in agreement with simulations only at small values of lambda<or=2. At higher polarities, the virial series diverges. Realization of the renormalization procedure permits to enlarge the range of applicability of the virial series. In this way, the new expression for the dielectric constant as a function of two dipolar parameters, lambda and y=4 pi nm(2)9kT, has been found explicitly. The expression gives a perfect upper bound of the dielectric constant and is more reliable for determination of epsilon than the previously known ones.

Hydration properties and potentials of mean force of nonpolar amino acid residues in water: A pertubation theoretic approach

We use a perturbation approach to calculate the solute-solvent and solute-solute pair correlations for infinitely dilute solutions of nonpolar amino acid side chains in water. In particular, from the solute-solute correlations we derive potentials of mean force for all the distances between different residues of amino acids. Comparison with molecular dynamics simulations performed using GROMOS package shows that the goodness of the approximation varies with the amino acid considered. We discuss in terms of hydrophobicity the different effect that the inclusion of the attractions causes on the solute-water and solute-solute correlations.

Dynamic regimes of fluids simulated by multiparticle-collision dynamics

We investigate the hydrodynamic properties of a fluid simulated with a mesoscopic solvent model. Two distinct regimes are identified, the "particle regime" in which the dynamics is gaslike and the "collective regime" where the dynamics is fluidlike. This behavior can be characterized by the Schmidt number, which measures the ratio between viscous and diffusive transport. Analytical expressions for the tracer diffusion coefficient, which have been derived on the basis of a molecular-chaos assumption, are found to describe the simulation data very well in the particle regime, but important deviations are found in the collective regime. These deviations are due to hydrodynamic correlations. The model is then extended in order to investigate self-diffusion in colloidal dispersions. We study first the transport properties of heavy pointlike particles in the mesoscopic solvent, as a function of their mass and number density. Second, we introduce excluded-volume interactions among the colloidal particles and determine the dependence of the diffusion coefficient on the colloidal volume fraction for different solvent mean-free paths. In the collective regime, the results are found to be in good agreement with previous theoretical predictions based on Stokes hydrodynamics and the Smoluchowski equation.

Hard sphere perturbation theory for fluids with soft-repulsive-core potentials

The thermodynamic properties of fluids with very soft repulsive-core potentials, resembling those of some liquid metals, are predicted with unprecedented accuracy using a new first-order thermodynamic perturbation theory. This theory is an extension of Mansoori-Canfield/Rasaiah-Stell (MCRS) perturbation theory, obtained by including a configuration integral correction recently identified by Mon, who evaluated it by computer simulation. In this work we derive an analytic expression for Mon's correction in terms of the radial distribution function of the soft-core fluid, g(0)(r), approximated using Lado's self-consistent extension of Weeks-Chandler-Andersen (WCA) theory. Comparisons with WCA and MCRS predictions show that our new extended-MCRS theory outperforms other first-order theories when applied to fluids with very soft inverse-power potentials (n< or =6), and predicts free energies that are within 0.3 kT of simulation results up to the fluid freezing point.