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.     

Monte Carlo simulations of thermodynamic and structural properties of Mie(14,7) fluids

The vapor-liquid phase envelope of Mie(14,7) fluids is determined by the Gibbs ensemble Monte Carlo (MC) simulation technique. The NVT-MC simulation method is then utilized to compute the equation of state and the pair correlation function over a wide range of densities and temperatures. The effective diameters are calculated via the virial minimization method and the results are applied as the repulsion-attraction splitting distance within the generic van der Waals (GvdW) theory to compute the mean free volume. The density and temperature dependence of these parameters are studied and discussed. The results for the effective diameter, and the GvdW parameters are fitted to analytical functions of density and temperature. An examination of the results for the fluid phase equilibria of argon shows excellent agreement with empirical data for the densities of the coexisting phases, the vapor pressure, and the critical point. The computed free volumes are used to compute the diffusion coefficient of argon and the results are compared with experimental data.     

Molecular theory of thermal conductivity of the Lennard-Jones fluid

In this paper the thermal conductivity of the Lennard-Jones fluid is calculated by applying the combination of the density-fluctuation theory, the modified free volume theory of diffusion, and the generic van der Waals equation of state. A Monte Carlo simulation method is used to compute the equilibrium pair-correlation function necessary for computing the mean free volume and the coefficient in the potential-energy and virial contributions to the thermal conductivity. The theoretical results are compared with our own molecular dynamics simulation results and with those reported in the literature. They agree in good accuracy over wide ranges of density and temperature examined in molecular dynamics simulations. Thus the combined theory represents a molecular theory of thermal conductivity of the Lennard-Jones fluid and by extension simple fluids, which enables us to compute the nonequilibrium quantity by means of the Monte Carlo simulations for the equilibrium pair-correlation function.     

Modified free volume theory of self-diffusion and molecular theory of shear viscosity of liquid carbon dioxide

In previous work on the density fluctuation theory of transport coefficients of liquids, it was necessary to use empirical self-diffusion coefficients to calculate the transport coefficients (e.g., shear viscosity of carbon dioxide). In this work, the necessity of empirical input of the self-diffusion coefficients in the calculation of shear viscosity is removed, and the theory is thus made a self-contained molecular theory of transport coefficients of liquids, albeit it contains an empirical parameter in the subcritical regime. The required self-diffusion coefficients of liquid carbon dioxide are calculated by using the modified free volume theory for which the generic van der Waals equation of state and Monte Carlo simulations are combined to accurately compute the mean free volume by means of statistical mechanics. They have been computed as a function of density along four different isotherms and isobars. A Lennard-Jones site-site interaction potential was used to model the molecular carbon dioxide interaction. The density and temperature dependence of the theoretical self-diffusion coefficients are shown to be in excellent agreement with experimental data when the minimum critical free volume is identified with the molecular volume. The self-diffusion coefficients thus computed are then used to compute the density and temperature dependence of the shear viscosity of liquid carbon dioxide by employing the density fluctuation theory formula for shear viscosity as reported in an earlier paper (J. Chem. Phys. 2000, 112, 7118). The theoretical shear viscosity is shown to be robust and yields excellent density and temperature dependence for carbon dioxide. The pair correlation function appearing in the theory has been computed by Monte Carlo simulations.     

Liquid methanol Monte Carlo simulations with a refined potential which includes polarizability, nonadditivity, and intramolecular relaxation

Monte Carlo simulations of liquid methanol were performed using a refined ab initio derived potential which includes polarizability, nonadditivity, and intramolecular relaxation. The results present good agreement between the energetic and structural properties predicted by the model and those predicted by ab initio calculations of methanol clusters and experimental values of gas and condensed phases. The molecular level picture of methanol shows the existence of both rings and linear polymers in the methanol liquid phase.     

Prediction of the thermophysical properties of pure neon, pure argon, and the binary mixtures neon-argon and argon-krypton by Monte Carlo simulation using ab initio potentials

Gibbs ensemble Monte Carlo simulations were used to test the ability of intermolecular pair potentials derived ab initio from quantum mechanical principles, enhanced by Axilrod-Teller triple-dipole interactions, to predict the vapor-liquid phase equilibria of pure neon, pure argon, and the binary mixtures neon-argon and argon-krypton. The interaction potentials for Ne-Ne, Ar-Ar, Kr-Kr, and Ne-Ar were taken from literature; for Ar-Kr a different potential has been developed. In all cases the quantum mechanical calculations had been carried out with the coupled-cluster approach [CCSD(T) level of theory] and with correlation consistent basis sets; furthermore an extrapolation scheme had been applied to obtain the basis set limit of the interaction energies. The ab initio pair potentials as well as the thermodynamic data based on them are found to be in excellent agreement with experimental data; the only exception is neon. It is shown, however, that in this case the deviations can be quantitatively explained by quantum effects. The interaction potentials that have been developed permit quantitative predictions of high-pressure phase equilibria of noble-gas mixtures.     

Finite temperature path integral Monte Carlo simulations of structural and dynamical properties of Ar(N)-CO(2) clusters

We report finite temperature quantum mechanical simulations of structural and dynamical properties of Ar(N)-CO(2) clusters using a path integral Monte Carlo algorithm. The simulations are based on a newly developed analytical Ar-CO(2) interaction potential obtained by fitting ab initio results to an anisotropic two-dimensional Morse∕Long-range function. The calculated distributions of argon atoms around the CO(2) molecule in Ar(N)-CO(2) clusters with different sizes are consistent to the previous studies of the configurations of the clusters. A first-order perturbation theory is used to quantitatively predict the CO(2) vibrational frequency shift in different clusters. The first-solvation shell is completed at N = 17. Interestingly, our simulations for larger Ar(N)-CO(2) clusters showed several different structures of the argon shell around the doped CO(2) molecule. The observed two distinct peaks (2338.8 and 2344.5 cm(-1)) in the υ(3) band of CO(2) may be due to the different arrangements of argon atoms around the dopant molecule.     

Voids, generic van der Waals equation of state, and transport coefficients of liquids

In this Perspective, we discuss the role of voids in transport processes in liquids and the manner in which the concept of voids enters the generic van der Waals equation of state and the modified free volume theory. The density fluctuation theory is then discussed and we show how the density fluctuation theory can be made a molecular theory with the help of the modified free volume theory and the generic van der Waals equation of state. The confluence of the aforementioned three theories makes it possible to calculate the transport coefficients of liquids by using the information on the equilibrium pair correlation function, which can be calculated either by an integral equation theory or Monte Carlo simulations. A number of relations between transport coefficients are also presented, which are derived on the basis of the density fluctuation theory. Since they can be used to obtain one transport coefficient from another they can be very useful in handling experimental and theoretical data. An application of the modified free volume theory to polymer melts is discussed as an example for a theory of transport properties of complex liquids.     

Implementation of dynamical nucleation theory effective fragment potentials method for modeling aerosol chemistry

In this work, the dynamical nucleation theory (DNT) model using the ab initio based effective fragment potential (EFP) is implemented for evaluating the evaporation rate constant and molecular properties of molecular clusters. Predicting the nucleation rates of aerosol particles in different chemical environments is a key step toward understanding the dynamics of complex aerosol chemistry. Therefore, molecular scale models of nanoclusters are required to understand the macroscopic nucleation process. On the basis of variational transition state theory, DNT provides an efficient approach to predict nucleation kinetics. While most DNT Monte Carlo simulations use analytic potentials to model critical sized clusters, or use ab initio potentials to model very small clusters, the DNTEFP Monte Carlo method presented here can treat up to critical sized clusters using the effective fragment potential (EFP), a rigorous nonempirical intermolecular model potential based on ab initio electronic structure theory calculations, improvable in a systematic manner. The DNTEFP method is applied to study the evaporation rates, energetics, and structure factors of multicomponent clusters containing water and isoprene. The most probable topology of the transition state characterizing the evaporation of one water molecule from a water hexamer at 243 K is predicted to be a conformer that contains six hydrogen bonds, with a topology that corresponds to two water molecules stacked on top of a quadrangular (H(2)O)(4) cluster. For the water hexamer in the presence of isoprene, an increase in the cluster size and a 3-fold increase in the evaporation rate are predicted relative to the reaction in which one water molecule evaporates from a water hexamer cluster.     

基于密度泛函理论研究二元排斥Yukawa流体的表面结构性质

基于自由能密度泛函理论(DFT)考察了二元排斥Yukawa (HCRY)流体在不同外场下的密度分布. 基于微扰理论, 体系的Helmholtz自由能泛函采用硬球排斥部分和长程色散部分贡献之和, 其中Kierlik和Rosinberg的加权密度近似(WDA)被用来计算硬球排斥部分, 而色散部分采用平均场理论(MFT)进行描述. 为了验证DFT计算结果的合理性, 研究中采用巨正则Monte Carlo(GCMC)模拟计算了在不同主体相密度、硬核直径和位能参数比的条件下二元HCRY混合流体的密度分布. 结果表明, 该DFT计算结果与GCMC模拟值吻合良好.     

Assessing group-based cutoffs and the Ewald method for electrostatic interactions in clusters and in saturated,superheated, and supersaturated vapor phases of dipolar molecules

Monte Carlo simulations in the canonical, isobaric-isothermal, grand canonical, and Gibbs ensembles were used to assess whether the computationally expensive Ewald summation method for the computation of the first-order electrostatic energy can be replaced with a simpler truncation approach for accurate simulations of the saturated, superheated, and supersaturated vapor phases of dipolar and hydrogen-bonding molecules. Rotationally averaged hydrogen fluoride dimer and trimer energies, thermophysical properties and aggregation in the superheated vapor phase of hydrogen fluoride, nucleation free energy barriers for water, and the vapor–liquid coexistence properties of hydrogen fluoride and water were investigated over a wide range of state points. We find that for densities not too close to the critical density, results obtained from simulations using a spherical potential truncation based on neutral groups (molecules or fragments) for the Coulomb interactions are statistically identical to those obtained using the Ewald summation method. Use of the simpler spherical truncation results in a significant reduction of the computational effort for simulations employing molecular mechanics force fields and also allows for straightforward implementation of many-body expansion methods to compute the potential energy from electronic structure calculations of subsystems of the entire vapor-phase system.     

Hydrogen bonding and solvent effects on the lowest 1(n, pi*) excitations of triazines in water

Our method for estimating solvent effects on electronic spectra in media with strong solute-solvent interactions is applied here to calculate the absorption and fluorescence solvatochromatic shifts of dilute triazines in water. First, the ab initio CASSCF method is used to estimate the gas-phase electronic excitation properties and state charge distributions; second, Monte Carlo simulations are performed to elucidate liquid structures around the ground and excited state solute; finally, the solvent shift is evaluated based on the gas-phase charge distributions and the explicit solvent structures. For the dilute triazine solutions, simulations predict one linear (different) hydrogen bond attached to each nitrogen atom. Upon the first (1)(n, pi*)electronic excitation one hydrogen bond is completely broken. For the absorption and fluorescence spectra, our calculations demonstrated that the specific solvent-solute interaction, in any electronic state, plays a critical role in the determination of solvent shifts.     

Statistical-mechanical theory of rheology: Lennard-Jones fluids

The generalized Boltzmann equation for simple dense fluids gives rise to the stress tensor evolution equation as a constitutive equation of generalized hydrodynamics for fluids far removed from equilibrium. It is possible to derive a formula for the non-Newtonian shear viscosity of the simple fluid from the stress tensor evolution equation in a suitable flow configuration. The non-Newtonian viscosity formula derived is applied to calculate the non-Newtonian viscosity as a function of the shear rate by means of statistical mechanics in the case of the Lennard-Jones fluid. For that purpose we have used the density-fluctuation theory for the Newtonian viscosity, the modified free volume theory for the self-diffusion coefficient, and the generic van der Waals equation of state to compute the mean free volume appearing in the modified free volume theory. Monte Carlo simulations are used to calculate the pair-correlation function appearing in the generic van der Waals equation of state and shear viscosity formula. To validate the Newtonian viscosity formula obtained we first have examined the density and temperature dependences of the shear viscosity in both subcritical and supercritical regions and compared them with molecular-dynamic simulation results. With the Newtonian shear viscosity and thermodynamic quantities so computed we then have calculated the shear rate dependence of the non-Newtonian shear viscosity and compared it with molecular-dynamics simulation results. The non-Newtonian viscosity formula is a universal function of the product of reduced shear rate (gamma*) times reduced relaxation time (taue*) that is independent of the material parameters, suggesting a possibility of the existence of rheological corresponding states of reduced density, temperature, and shear rate. When the simulation data are reduced appropriately and plotted against taue*gamma* they are found clustered around the reduced (universal) non-Newtonian viscosity formula. Thus we now have a molecular theory of non-Newtonian shear viscosity for the Lennard-Jones fluid, which can be implemented with a Monte Carlo simulation method for the pair-correlation function.     

Thermodynamic properties of model solids with short-ranged potentials from Monte Carlo simulations and perturbation theory

Monte Carlo simulations have been performed to determine the excess energy and the equation of state of fcc solids with Sutherland potentials for wide ranges of temperatures, densities, and effective potential ranges. The same quantities have been determined within a perturbative scheme by means of two procedures: (i) Monte Carlo simulations performed on the reference hard-sphere system and (ii) second-order Barker-Henderson perturbation theory. The aim was twofold: on the one hand, to test the capability of the "exact" MC-perturbation theory of reproducing the direct MC simulations and, on the other hand, the reliability of the Barker-Henderson perturbation theory, as compared with direct MC simulations and MC-perturbation theory, to determine the thermodynamic properties of these solids depending on temperature, density, and potential range. We have found that the simulation data for the excess energy obtained from the two procedures are in close agreement with each other. For the equation of state, the results from the MC-perturbation procedure also agree well with the direct MC simulations except for very low temperatures and extremely short-ranged potentials. Regarding the Barker-Henderson perturbation theory, we have found that in general the second-order approximation does not provide significant improvement over the first-order one.     

Critical and phase-equilibrium properties of an ab initio based potential model of methanol and 1-propanol using two-phase molecular dynamics simulations

Two-phase molecular dynamics simulations employing a Monte Carlo volume sampling method were performed using an ab initio based force field model parameterized to reproduce quantum-mechanical dimer energies for methanol and 1-propanol at temperatures approaching the critical temperature. The intermolecular potential models were used to obtain the binodal vapor-liquid phase dome at temperatures to within about 10 K of the critical temperature. The efficacy of two all-atom, site-site pair potential models, developed solely from the energy landscape obtained from high-level ab initio pair interactions, was tested for the first time. The first model was regressed from the ab initio landscape without point charges using a modified Morse potential to model the complete interactions; the second model included point charges to separate Coulombic and dispersion interactions. Both models produced equivalent phase domes and critical loci. The model results for the critical temperature, density, and pressure, in addition to the sub-critical equilibrium vapor and liquid densities and vapor pressures, are compared to experimental data. The model's critical temperature for methanol is 77 K too high while that for 1-propanol is 80 K too low, but the critical densities are in good agreement. These differences are likely attributable to the lack of multi-body interactions in the true pair potential models used here.     

Monte Carlo study of four dimensional binary hard hypersphere mixtures

A multithreaded Monte Carlo code was used to study the properties of binary mixtures of hard hyperspheres in four dimensions. The ratios of the diameters of the hyperspheres examined were 0.4, 0.5, 0.6, and 0.8. Many total densities of the binary mixtures were investigated. The pair correlation functions and the equations of state were determined and compared with other simulation results and theoretical predictions. At lower diameter ratios the pair correlation functions of the mixture agree with the pair correlation function of a one component fluid at an appropriately scaled density. The theoretical results for the equation of state compare well to the Monte Carlo calculations for all but the highest densities studied.     

Effective interaction between charged nanoparticles and DNA

We investigate the effective interaction mediated by salt ions between charged nanoparticles (NPs) and DNA. DNA is modeled as an infinite cylinder with a constant surface charge in an implicit solvent. Monte Carlo simulations are used to compute the free energy of the system described in the framework of the primitive model of electrolytes, which accounts for excluded volumes of salt ions. A mean-field Poisson-Boltzmann theory also allows us to compute the free energy and provides us with explicit formulae for its main characteristics (position and depth of the minimum). We intend here to identify the physical parameters that have a major impact on the NP-DNA interaction, in an attempt to evaluate physico-chemical properties which could play a role in genotoxicity or, which could be exploited for therapeutic use. Thus, we investigate the influence on the effective interaction of: the shape of the nanoparticle, the magnitude of the nanoparticle charge and its distribution, the value of the pH of the solution, the magnitude of Van der Waals interactions depending on the nature of the constitutive material of the NP (metal vs. dielectric). We show that for positively charged concave NPs the effective interaction is repulsive at short distance, so that it presents a minimum at distance from the DNA. This short-range repulsion is specific to indented particles and is a robust property that holds for a large range of materials and charge densities.     

Orientational ordering in hard rectangles: The role of three-body correlations

We investigate the effect of three-body correlations on the phase behavior of hard rectangle two-dimensional fluids. The third virial coefficient B3 is incorporated via an equation of state that recovers scaled particle theory for parallel hard rectangles. This coefficient, a functional of the orientational distribution function, is calculated by Monte Carlo integration, using an accurate parametrized distribution function, for various particle aspect ratios in the range of 1-25. A bifurcation analysis of the free energy calculated from the obtained equation of state is applied to find the isotropic (I)-uniaxial nematic (N(u)) and isotropic-tetratic nematic (N(t)) spinodals and to study the order of these phase transitions. We find that the relative stability of the N(t) phase with respect to the isotropic phase is enhanced by the introduction of B3. Finally, we have calculated the complete phase diagram using a variational procedure and compared the results with those obtained from scaled particle theory and with Monte Carlo simulations carried out for hard rectangles with various aspect ratios. The predictions of our proposed equation of state as regards the transition densities between the isotropic and orientationally ordered phases for small aspect ratios are in fair agreement with simulations. Also, the critical aspect ratio below which the N(t) phase becomes stable is predicted to increase due to three-body correlations, although the corresponding value is underestimated with respect to simulation.     

Generic van der Waals equation of state, modified free volume theory of diffusion, and viscosity of simple liquids

The shear viscosity formula derived by the density fluctuation theory in previous papers is computed for argon, krypton, and methane by using the self-diffusion coefficients derived in the modified free volume theory with the help of the generic van der Waals equation of state. In the temperature regime near or above the critical temperature, the density dependence of the shear viscosity can be accounted for by ab initio calculations with the self-diffusion coefficients provided by the modified free volume theory if the minimum (critical) free volume is set equal to the molecular volume and the volume overlap parameter (alpha) is taken about unity in the expression for the self-diffusion coefficient. In the subcritical temperature regime, if the density fluctuation range parameter is chosen appropriately at a temperature, then the resulting expression for the shear viscosity can well account for its density and temperature dependence over the ranges of density and temperature experimentally studied. In the sense that once the density fluctuation range is fixed at a temperature, the theory can account for the experimental data at other subcritical temperatures on the basis of the intermolecular force only; the theory is predictive even in the subcritical regime of temperature. Theory is successfully tested in comparison with experimental data for self-diffusion coefficients and shear viscosity for argon, krypton, and methane.     

Water liquid-vapor equilibria predicted by refined ab initio derived potentials

Coexistence properties for water near the critical point using several ab initio models were calculated using grand canonical Monte Carlo simulations with multiple histogram reweighting techniques. These models, that have proved to yield a good reproduction of the water properties at ambient conditions, perform rather well, improving the performance of a previous ab initio model. It is also shown that bulk geometry and dipole values, predicted by the simulation, can be used and a good approximation obtained with a polarizable rigid water model but not when polarization is excluded.