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This paper investigates effects of using monodisperse inverse analyses to extract particle-particle and particle-surface potentials from simulated interfacial colloidal fluids of polydisperse attractive particles. Effects of polydispersity are investigated as functions of particle concentration and attractive well depth and range for van der Waals and depletion potentials. Forward Monte Carlo simulations are used to generate particle distribution functions for polydisperse interfacial colloidal fluids from which inverted potentials are obtained using an inverse Ornstein-Zernike analysis and an inverse Monte Carlo simulation method. Attractive potentials are successfully recovered for monodisperse colloidal fluids, but polydispersity that is unaccounted for in inverse analyses produces (1) apparent softening of strong forces, (2) anomalous repulsive and attractive interactions, and (3) aphysical particle overlaps. This investigation provides insights into the role of polydispersity in altering the equilibrium structure and corresponding inverted potentials of attractive colloidal fluids near surfaces. These findings should assist the design and interpretation of optical microscopy experiments involving interfacial colloidal fluids similar to the simulated experiments reported here. [ABSTRACT FROM AUTHOR]

Hypothetical scanning Monte Carlo (HSMC) is a method for calculating the absolute entropy S and free energy F from a given MC trajectory developed recently and applied to liquid argon, TIP3P water, and peptides. In this paper HSMC is extended to random coil polymers by applying it to self-avoiding walks on a square lattice—a simple but difficult model due to strong excluded volume interactions. With HSMC the probability of a given chain is obtained as a product of transition probabilities calculated for each bond by MC simulations and a counting formula. This probability is exact in the sense that it is based on all the interactions of the system and the only approximation is due to finite sampling. The method provides rigorous upper and lower bounds for F, which can be obtained from a very small sample and even from a single chain conformation. HSMC is independent of existing techniques and thus constitutes an independent research tool. The HSMC results are compared to those obtained by other methods, and its application to complex lattice chain models is discussed; we emphasize its ability to treat any type of boundary conditions for which a reference state (with known free energy) might be difficult to define for a thermodynamic integration process. Finally, we stress that the capability of HSMC to extract the absolute entropy from a given sample is important for studying relaxation processes, such as protein folding. [ABSTRACT FROM AUTHOR]

Kinetic Monte Carlo (KMC) simulations are carried out to directly study diffusion of benzene through thin (37–100 nm) NaX zeolite membranes under a gradient in chemical potential. Nonlinearities in adsorbate loading near the membrane boundaries are shown to arise from the difference in adsorbate density between the zeolite and adjacent fluid phase. Direct extraction of the transport diffusivity from gradient KMC simulations enables testing of the Darken approximation. This rigorous approach reveals limitations of the Darken approximation and, for the first time, the potentially complex nonunique functionality and multiplicity of the transport diffusivity for strongly interacting adsorbates. In the companion paper we explore these nonlinear interfacial effects in the context of permeation through both single-crystal and polycrystalline membranes. [ABSTRACT FROM AUTHOR]

In this second paper of a two part series, we investigate the implications of the interfacial phenomenon, caused by adsorbate-adsorbate interactions coupled with the difference in adsorbate density between the zeolite and the gas phase, upon benzene permeation through single-crystal and polycrystalline microporous NaX membranes. The high flux predicted for thin single-crystal membranes reveals that substantially enhanced flux should be expected in submicron films. Simulations also indicate that the standard local equilibrium assumption made for larger scale membranes is inapplicable at the submicron scale associated with nanometer size grains of thin and/or polycrystalline membranes. Apparent activation energies predicted for benzene permeation through NaX membranes via kinetic Monte Carlo (KMC) simulations are in good agreement with laboratory experiments. The simulations also uncover temperature-dependent flux pathways leading to non-Arrhenius behavior observed experimentally. The failure of the Darken approximation, especially in the presence of the interfacial phenomenon, leads to a substantial overprediction of the flux. Simulations of polycrystalline membranes suggest that this same interfacial phenomenon leads to resistance that can reduce flux by an order of a magnitude with only moderate polycrystallinity. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the effects of using inverse analyses developed for monodisperse particles to extract particle-particle and particle-surface potentials from simulated interfacial colloidal configurations having finite-size polydispersity. Forward Monte Carlo simulations are used to generate three-dimensional equilibrium configurations of log normal-distributed polydisperse particles confined by gravity near an underlying surface. Particles remain levitated above the substrate and stabilized against aggregation by repulsive electrostatic Derjaguin-Landau-Verwey-Overbeck pair potentials. An inverse Ornstein-Zernike analysis and an inverse Monte Carlo simulation method are used to obtain interactions from simulated distribution functions as a function of polydispersity (σ), relative range of repulsion (κ...), and projected interfacial concentration (ρ). Both inverse analyses successfully recover input potentials for all monodisperse cases, but fail for polydispersities often encountered in experiments. For different conditions (σ, κ..., and ρ, our results indicate softened short-range repulsion, anomalous long-range attraction, and apparent particle overlaps, which are similar to commonly reported observations in optical microscopy measurements of quasi-two-dimensional interfacial colloidal ensembles. By demonstrating signatures of, and limitations due to, polydispersity when extracting pair potentials from measured distribution functions, our specific goal is to provide a basis to objectively interpret and resolve the effects of polydispersity in optical microscopy experiments. [ABSTRACT FROM AUTHOR]

The rheological behaviors of polymer brush under oscillatory shear flow were investigated by nonequilibrium Monte Carlo simulation. The grafted chain under oscillatory shear flow exhibited a waggling behavior like a flower, and the segments were found to have different oscillatory phases along the chain contour. Stress tensor was further obtained based on the statistics of sampled configuration distribution functions. The simulation reproduced the abrupt increase of the first normal stress difference N1 with the flow velocity over a critical value, as observed in the experiment of Klein et al. [Nature (London) 352, 143 (1991)]. However, our simulation did not reproduce the brush thickening with shear velocity increased, which was suggested to be responsible for the abrupt increase of N1 in the above-mentioned paper. This simulation demonstrates that the increase of normal stress might be an inherent behavior of polymer brush due to chain deformation under flow. [ABSTRACT FROM AUTHOR]

In this paper the problem of stiffness in stochastic simulation of singularly perturbed systems is discussed. Such stiffness arises often from partial equilibrium or quasi-steady-state type of conditions. A multiscale Monte Carlo method is discussed that first assesses whether partial equilibrium is established using a simple criterion. The exact stochastic simulation algorithm (SSA) is next employed to sample among fast reactions over short time intervals (microscopic time steps) in order to compute numerically the proper probability distribution function for sampling the slow reactions. Subsequently, the SSA is used to sample among slow reactions and advance the time by large (macroscopic) time steps. Numerical examples indicate that not only long times can be simulated but also fluctuations are properly captured and substantial computational savings result. [ABSTRACT FROM AUTHOR]

In this paper we consider the adsorption of argon on the surface of graphitized thermal carbon black and in slit pores at temperatures ranging from subcritical to supercritical conditions by the method of grand canonical Monte Carlo simulation. Attention is paid to the variation of the adsorbed density when the temperature crosses the critical point. The behavior of the adsorbed density versus pressure (bulk density) shows interesting behavior at temperatures in the vicinity of and those above the critical point and also at extremely high pressures. Isotherms at temperatures greater than the critical temperature exhibit a clear maximum, and near the critical temperature this maximum is a very sharp spike. Under the supercritical conditions and very high pressure the excess of adsorbed density decreases towards zero value for a graphite surface, while for slit pores negative excess density is possible at extremely high pressures. For imperfect pores (defined as pores that cannot accommodate an integral number of parallel layers under moderate conditions) the pressure at which the excess pore density becomes negative is less than that for perfect pores, and this is due to the packing effect in those imperfect pores. However, at extremely high pressure molecules can be packed in parallel layers once chemical potential is great enough to overcome the repulsions among adsorbed molecules. [ABSTRACT FROM AUTHOR]

Despite intensive work there are still controversial issues about desorption and adsorption of hydrogen on Si(100)-(2×1). In particular, the relative importance of the various interdimer- and intradimer-desorption paths is not clear. Nanosecond-pulse-laser desorption data have been used to argue that the 4H interdimer path is important, while data from thermal-desorption time-of-flight measurements suggest a large translationally hot contribution which cannot arise from the 4H interdimer path. The observation of a translationally hot desorption fraction at low to medium coverage can be accounted for by including the 2H interdimer path in quantum dynamical calculations. In this paper we investigate this issue further and present evidence that supports the inclusion of the intradimer path. Specifically, our results show that the intradimer and 3H interdimer paths provide the major contributions to the translationally hot fraction in the desorbate. Our conclusions are based on density-functional calculations of hydrogen translational excitation, mean-field analysis of thermal-desorption experiments over a range of ramp rate, and Monte Carlo simulations of nanosecond-pulse-laser experiments. [ABSTRACT FROM AUTHOR]

This paper formulates a hybrid Monte Carlo implementation of the Fourier path integral (FPI-HMC) approach with partial averaging. Such a hybrid Monte Carlo approach allows one to generate collective moves through configuration space using molecular dynamics while retaining the computational advantages associated with the Fourier path integral Monte Carlo method. In comparison with the earlier Metropolis Monte Carlo implementations of the FPI algorithm, the present HMC method is shown to be significantly more efficient for quantum Lennard-Jones solids and suggests that such algorithms may prove useful for efficient simulations of a range of atomic and molecular systems. [ABSTRACT FROM AUTHOR]

We suggest a practical solution to dealing with the three-body interactions in the transcorrelated variational Monte Carlo method (TC-VMC). In the TC-VMC method, which was suggested in our previous paper [N. Umezawa and S. Tsuneyuki, J. Chem. Phys. 119, 10015 (2003)], the Jastrow–Slater-type wave function is efficiently optimized through a self-consistent procedure by minimizing the variance of the local energy. The three-body terms in the transcorrelated self-consistent-field equation, which have been simply ignored in our previous works, are efficiently calculated by the Monte Carlo numerical integration. We found that our treatment for the three-body interactions is successful for atoms from Li to Ne. [ABSTRACT FROM AUTHOR]

An optimized molecular potential model for carbon dioxide is presented in this paper. Utilizing the established techniques of molecular-dynamics and histogram reweighting grand canonical Monte Carlo simulations, this model is demonstrated to show excellent predictability for thermodynamic, transport, and liquid structural properties in a wide temperature-pressure range with remarkable accuracies. The average deviations of this new model from experimental data for the saturated liquid densities, vapor densities, vapor pressures, and heats of vaporization are around 0.1%, 2.3%, 0.7%, and 1.9%, respectively. The calculated critical point is almost pinpointed by the new model. The experimental radial distribution functions ranging from 240.0 to 473.0 K are well reproduced as compared to neutron-diffraction measurements. The predicted self-diffusion coefficients are in good agreement with the nuclear-magnetic-resonance measurements. The previously published potential models for CO2 are also systematically evaluated, and our proposed new model is found to be superior to the previous models in general. [ABSTRACT FROM AUTHOR]

This paper describes a new Monte Carlo method based on a novel stochastic potential switching algorithm. This algorithm enables the equilibrium properties of a system with potential V to be computed using a Monte Carlo simulation for a system with a possibly less complex stochastically altered potential V. By proper choices of the stochastic switching and transition probabilities, it is shown that detailed balance can be strictly maintained with respect to the original potential V. The validity of the method is illustrated with a simple one-dimensional example. The method is then generalized to multidimensional systems with any additive potential, providing a framework for the design of more efficient algorithms to simulate complex systems. A near-critical Lennard-Jones fluid with more than 20 000 particles is used to illustrate the method. The new algorithm produced a much smaller dynamic scaling exponent compared to the Metropolis method and improved sampling efficiency by over an order of magnitude. [ABSTRACT FROM AUTHOR]

Lattice Monte Carlo simulation is used to study micellization of both pure and surfactant-polymer mixture, with an emphasis on cluster size distribution. The amphiphile molecule is of the type H4T4 where the H (head) monomers like the solvent molecules and the T (tail) monomers are solvophobic. To compare polymer- and surfactant-centered theories, copolymers with the structure of (H4T4)5 are used instead of homopolymers. Since above copolymer molecules have the structural unit like the structure of surfactant molecules, it is possible to study the competition between the binding of surfactant molecules to the copolymer and the micellization in a copolymer-free solution. Results show that, first, surfactant molecules bind to the copolymer molecules, and not until copolymers are saturated do micelles form. Furthermore, it is shown that for the model used in this paper, the polymer-centered theory is more appropriate than the surfactant-centered theory, and finally the cooperative nature of cluster formation on copolymers is also discussed. [ABSTRACT FROM AUTHOR]

Previously we developed a general method for calculating the free energy of any surface constrained to a distinct surface excess number/density. In this paper we show how to combine a range of such surfaces, whose free energies have been calculated, to produce an ad hoc semigrand canonical ensemble of surfaces from which ensemble surface properties can be calculated, including the ensemble surface free energy. We construct such an ensemble for the disordered Au(100) semihexagonal reconstructed surface using a Glue model potential at 1000 K and calculate the ensemble surface free energy to be 0.088 18 eV/Å2. The ensemble average surface lateral density was found to be 1.375 (with respect to the bulk), which is in agreement with previous grand canonical Monte Carlo studies. [ABSTRACT FROM AUTHOR]

This paper has extended nonequilibrium Monte Carlo (MC) approach to simulate oscillatory shear flow in a lattice block copolymer system. Phase transition and associated rheological behaviors of multiple self-avoiding chains have been investigated. Stress tensor has been obtained based upon sampled configuration distribution functions. At low temperatures, micellar structures have been observed and the underlying frequency-dependent rheological properties exhibit different initial slopes. The simulation outputs are consistent with the experimental observations in literature. Chain deformation during oscillatory shear flow has also been revealed. Although MC simulation cannot account for hydrodynamic interaction, the highlight of our simulation approach is that it can, at small computing cost, investigate polymer chains simultaneously at different spatial scales, i.e., macroscopic rheological behaviors, mesoscopic self-assembled structures, and microscopic chain configurations. [ABSTRACT FROM AUTHOR]

This paper describes a systematic study on the clathrate structure of H+(H2O)21 using tandem mass spectrometry, vibrational predissociation spectroscopy, Monte Carlo simulations, and density functional theory calculations. We produced H+(H2O)n from a continuous corona-discharged supersonic expansion and observed three anomalies simultaneously at the cluster temperature near 150 K, including (1) the peak at n=21 is more intense than its neighboring ions in the mass spectrum, (2) the size-dependent dissociation fractions show a distinct drop for the 21-mer, and (3) the infrared spectrum of H+(H2O)21 exhibits only a single feature at 3699 cm-1, corresponding to the free-OH stretching of three-coordinated water molecules. Interestingly, the anomalies appear or disappear together with cluster temperature, indicating close correlation of these three observations. The observations, together with Monte Carlo simulations and density functional theory calculations, corroborate the notion for the formation of a distorted pentagonal dodecahedral (512) cage with a H2O molecule in the cage and a H3O+ ion on the surface for this “magic number” water cluster ion. The dodecahedral cage melts at higher temperatures, as evidenced by the emergence of a free-OH stretching feature at 3717 cm-1 for the two-coordinated water in H+(H2O)21 produced in a warmer molecular beam. Extension of this study to larger clusters strongly suggests that the experimentally observed isomer of H+(H2O)28 is most likely to consist of a distorted protonated pentakaidecahedral (51263) cage enclosing two neutral water molecules. [ABSTRACT FROM AUTHOR]

While lattice kinetic Monte Carlo (KMC) methods provide insight into numerous complex physical systems governed by interatomic interactions, they are limited to relatively short length and time scales. Recently introduced coarse-grained Monte Carlo (CGMC) simulations can reach much larger length and time scales at considerably lower computational cost. In this paper we extend the CGMC methods to spatially adaptive meshes for the case of surface diffusion (canonical ensemble). We introduce a systematic methodology to derive the transition probabilities for the coarse-grained diffusion process that ensure the correct dynamics and noise, give the correct continuum mesoscopic equations, and satisfy detailed balance. Substantial savings in CPU time are demonstrated compared to microscopic KMC while retaining high accuracy. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In this paper we investigate the phase behavior of a “simple” fluid confined to a chemically heterogeneous slit pore of nanoscopic width sz by means of Monte Carlo simulations in the grand canonical ensemble. The fluid-substrate interaction is purely repulsive except for elliptic regions of semiaxes A and B attracting fluid molecules. On account of the interplay between confinement (i.e., sz) and chemical decoration, three fluid phases are thermodynamically permissible, namely, gaslike and liquidlike phases and a “bridge phase” where the molecules are preferentially adsorbed by the attractive elliptic patterns and span the gap between the opposite substrate surfaces. Because of their lack of cylindrical symmetry, bridge phases can be exposed to a torsional strain 0≤θ≤π/2 by rotating the upper substrate while holding the lower one in position. Depending on the thermodynamic state of the confined fluid, torsion-induced first-order phase transitions are feasible during which a bridge phase may be transformed into either a gaslike (evaporation) or a liquidlike phase (condensation). Since the chemical patterns decorating the substrates are finite in size, system properties are not translationally invariant in any spatial direction. Therefore, in order to study these phase transitions, we resorted to the thermodynamic integration scheme developed earlier to calculate the grand potential Ω in a system of low symmetry. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We perform a Monte Carlo simulation of irreversible template copolymerization near a chemically heterogeneous surface with a regular distribution of discrete adsorption sites that selectively adsorb from solution one of the two polymerizing monomers and the corresponding chain segments. In the polymerization model, the chain propagation process is simulated by adding individual monomers to the end of growing macroradical. We focus in this paper on the influence of polymerization rate, adsorption energy, and the distance between adsorption sites on the chain conformation and the primary sequence of the resulting two-letter (AB) copolymers and, specifically, on the coupling between polymerization and adsorption. The conditions for the realization of conformation-dependent copolymerization are formulated. For this regime, we observe the formation of a quasiregular copolymer with two types of alternating sections. One of them contains randomly distributed A and B segments. The second one consists mainly of strongly adsorbed A segments. It is found that the average length of the random sections is proportional to the distance between the nearest neighbor adsorption sites. The average length of the A-rich sections is determined by the “adsorption capacity” of adsorption site. By varying the strength of the effective monomer-substrate interaction and the distribution of adsorption sites on the substrate, the copolymers with different surface-induced primary sequences can be designed and synthesized in a controlled fashion. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Recently, we have proposed an efficient scheme for Monte Carlo simulations, the multiple “time step” Monte Carlo (MTS-MC) [J. Chem. Phys. 117, 8203 (2002)] based on the separation of the potential interactions into two additive parts. In this paper, the structural and thermodynamic properties of the simple point charge water model combined with the Ewald sum are compared for the MTS-MC real-/reciprocal-space split of the Ewald summation and the common Metropolis Monte Carlo method. We report a number of observables as a function of CPU time calculated using MC and MTS-MC. The correlation functions indicate that speedups on the order of 4.5–7.5 can be obtained for systems of 108–500 waters for n=10 splitting parameter. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In this paper, we propose a path integral influence functional from a solvent to determine a self-correlation function of a quantum particle in classical simple fluid. It is shown that the influence functional is related to a grand potential functional of the pure solvent under a three-dimensional external field arising from a classical isomorphic polymer, on which the quantum particle is mapped. The influence functional can be calculated from the self-correlation function, the solute–solvent and the solvent–solvent pair correlation function. The obtained equation of the self-correlation function is applied to an excess electron problem in fluid helium. The Fourier path-integral Monte Carlo method is employed to perform the path integral of the electron. The solute–solvent pair correlation function is estimated from a reference interaction site model integral equation. These results obtained form our proposed influence functional and from that proposed by Chandler, Singh, and Richardson are compared with those provided by a path integral Monte Carlo simulation with the explicit helium solvent. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The configurational-bias Monte Carlo method, which is used for efficient generation of molecular models of n–alkane chains, is combined for the first time with the dual control-volume grand-canonical molecular-dynamics simulation, which has been developed for studying transport of molecules in pores under an external potential gradient, to investigate transport and separation of binary mixtures of n–alkanes, as well as mixtures of CO2 and n–alkanes, in carbon nanopores. The effect of various factors, such as the temperature of the system, the composition of the mixture, and the pore size, on the separation of the mixtures is investigated. We also report the preliminary results of an experimental study of transport and separation of some of the same mixtures in a carbon molecular-sieve membrane with comparable pore sizes. The results indicate that, for the mixtures considered in this paper, even in very small carbon nanopores the energetic effects still play a dominant role in the transport and separation properties of the mixtures, whereas in a real membrane they are dominated by the membrane’s morphological characteristics. As a result, for the mixtures considered, a single pore may be a grossly inadequate model of a real membrane, and hence one must resort to three-dimensional molecular pore network models of the membrane. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Previous heat capacity estimators used in path integral simulations either have large variances that grow to infinity with the number of path variables or require the evaluation of first- and second-order derivatives of the potential. In the present paper, we show that the evaluation of the total energy by the T-method estimator and of the heat capacity by the TT-method estimator can be implemented by a finite difference scheme in a stable fashion. As such, the variances of the resulting estimators are finite and the evaluation of the estimators requires the potential function only. By comparison with the task of computing the partition function, the evaluation of the estimators requires k+1 times more calls to the potential, where k is the order of the difference scheme employed. Quantum Monte Carlo simulations for the Ne[sub 13] cluster demonstrate that a second order central-difference scheme should suffice for most applications. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The hypothetical scanning (HS) method provides the absolute entropy and free energy from a Boltzmann sample generated by Monte Carlo, molecular dynamics or any other exact simulation procedure. Thus far HS has been applied successfully to magnetic and polymer chain models; in this paper and the following one it is extended to fluid systems by treating a Lennard-Jones model of argon. With HS a probability P[sub i] approximating the Boltzmann probability of system configuration i is calculated with a stepwise reconstruction procedure, based on adding atoms gradually layer-by-layer to an initially empty volume, where they are replaced in their positions at i. At each step a transition probability (TP) is obtained from local grand canonical partition functions calculated over a limited space of the still unvisited (future) volume, the larger this space the better the approximation. P[sub i] is the product of the step TPs, where ln P[sub i] is an upper bound of the absolute entropy, which leads to upper and lower bounds for the free energy. We demonstrate that very good results for the entropy and the free energy can be obtained for a wide range of densities of the argon system by calculating TPs that are based on only a very limited future volume. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

HArF and HKrF are chemically bound rare-gas compounds that have been produced by photolysis of HF and subsequent thermal annealing in the respective rare-gas matrices. In this paper we present a computational study of the delayed, thermally induced formation of these molecules in the matrix. Using realistic potentials for the molecular and guest–host interactions, the potential energy along the minimum energy paths for formation is evaluated, and thermal transition rates are computed using a Monte Carlo transition state method. A closely packed, dissociated configuration of the molecular fragments is found to play an important role, both as the possible trapping site of the photolyzed fragments, and as an intermediate structure for diffusion-controlled formation. The computed threshold temperatures of formation for the HArF and HKrF molecules at different matrix sites are in good agreement with experimental findings and with previous site assignments for these molecules. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Recent Monte Carlo simulation studies of a model superheated liquid [Punnathanam and Corti, Ind. Eng. Chem. Res. 41, 1113 (2002)] suggest that cavity formation plays an important role in the process of homogeneous bubble nucleation. These simulations revealed that when spherical cavities beyond some certain size, i.e., the so-called critical cavity, were placed inside the superheated Lennard-Jones liquid, an instability was generated that led to phase separation towards the stable vapor phase. In this paper, we explore further the relevance of cavities, and the critical cavity in particular, to the molecular mechanism of homogeneous bubble nucleation. Density-functional theory (DFT) calculations are used to verify the existence of the critical cavity within the superheated Lennard-Jones liquid. In addition, DFT reveals that the critical cavity represents a limit of thermodynamic stability, further strengthening the connection between cavities and bubble nucleation. The DFT calculations also show that the size of the critical cavity is a lower bound to the size of the critical bubble and the work of formation of the critical cavity is a tight upper bound to the work of formation of the critical bubble. These results suggest that the free energy surface of bubble nucleation is influenced by the properties of the critical cavity, thereby possibly leading to a new picture of the molecular mechanism of bubble formation in superheated liquids. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Forward–backward semiclassical dynamics (FBSD) methods are emerging as a practical way of simulating dynamical processes in large quantum systems. In this paper we develop a pair-product approximation to the coherent state density. This form is accurate at low temperatures, enhancing significantly the convergence of Monte Carlo methods and thus allowing the simulation of quantum fluids. The scheme is applied to the calculation of velocity autocorrelation function of liquid para-hydrogen at several thermodynamic state points (between T=14 K and T=25 K). The results of the forward–backward semiclassical method with the pair-product approximation to the coherent state density exhibit good agreement with experimental measurements and other theoretical calculations. These calculations demonstrate that the FBSD method, in conjunction with an accurate representation of the coherent state density, allows an accurate description of dynamical processes in condensed phase systems at low temperatures where quantum mechanical effects play a significant role. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Grand canonical Monte Carlo simulations are used to investigate the effect of surfactant on binary Lennard-Jones mixtures confined between planar, chemically patterned surfaces. Near bulk demixing coexistence, confined binary mixtures form liquid “bridges” joining specifically patterned surface areas. The length of these bridges is restricted by the unfavorable liquid–liquid interfacial tension, and in the present paper we show that this constraint can be significantly reduced by adding surfactant to the system. This leads to very extended liquid bridges and to other structures not found in the simple two-component case. We give a qualitative discussion of the surface-surfactant -induced liquid structures and examine in detail the associated forces acting between the plates. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Various versions of quantum transition state theory (QTST) for the calculation of chemical reaction rate coefficients have been developed. The Hansen-Andersen formulation of QTST approximates the reactive flux autocorrelation function of Miller, Schwartz, and Tromp for the problem of interest by the correlation function for a one-dimensional system with a suitably chosen parabolic reference potential. In this paper, we present a systematic method for correcting this approximation in order to obtain more accurate rate constants at low temperatures. Values of the correlation function for real or imaginary times, such as might be obtained from path integral Monte Carlo calculations, are used to construct an improved approximation for the flux autocorrelation function. Our method uses a Bayesian analysis that incorporates a modified form of the maximum entropy method. In contrast to other applications of the maximum entropy method to this problem, the improved approximation is consistent with the known analyticity properties of the correlation function. The method is applied to several test problems, including one based on the H[SUB2] + Cl reaction. Our method yields significant corrections using a remarkably small amount of information. [ABSTRACT FROM AUTHOR]

In this paper, calculation of nine first-row diatomic dissociation energies (D[SUBe]) and six first-row heterodiatomic equilibrium dipole moments (μ[SUBe]) highlights the strength of Ornstein -- Uhlenbeck diffusion quantum Monte Carlo with the fixed-node approximation. By combining explicitly correlated wave functions based on spherical Gaussian-type orbitals and geminals obtained by an optimization of energy functional, it was possible to achieve satisfied agreement with experiment in most cases. Calculations on the molecules LiH, Li[SUB2], BH, BF, HF, LiF, CO, N[SUB2], and F[SUB2] are presented. This work gives an accuracy that is comparable to or better than previous theoretical estimates. We also compare the performance of three different approximations in estimating dipole moments of molecules. [ABSTRACT FROM AUTHOR]

The replica-exchange multicanonical algorithm and the multicanonical replica-exchange method for molecular dynamics simulations have recently been developed. In the former method the multicanonical weight factor is determined from a short replica-exchange simulation with the multiple-histogram reweighting techniques. A long multicanonical production run with high statistics is then performed with this weight factor. In this method, the process of determining the multicanonical weight factor is faster and simpler than that in the usual iterative determination. The multicanonical replica-exchange method is a further extension of the first in which a replica-exchange multicanonical simulation is performed with a small number of replicas. In this paper, we give the formulations of these two methods for Monte Carlo simulations and demonstrate the effectiveness of these algorithms for a penta peptide in the gas phase. [ABSTRACT FROM AUTHOR]

In Paper I of this series the formulations of the replica-exchange multicanonical algorithm and the multicanonical replica-exchange method for Monte Carlo versions have been presented. The effectiveness of these algorithms were then tested with the system of a penta peptide, Met-enkephalin, in the gas phase. In this article the detailed comparisons of performances of these algorithms together with the regular replica-exchange method are made, taking a more complex system of a 17-residue helical peptide. It is shown that these two new algorithms are more efficient than the regular replica-exchange method. [ABSTRACT FROM AUTHOR]

A new ab initio three-body potential [E. M. Mas et al., J. Chem. Phys. 118, 4386 (2003), preceding paper] has been employed, together with an accurate ab initio pair potential SAPT-5s, in Monte Carlo simulations of liquid water in the canonical ensemble at ambient conditions. Analysis of radial distribution functions from these simulations illustrates the profound effect nonadditive forces have on the hydrogen-bonded structure of the liquid. Simulations using only the two-body potential give one hydrogen bond per molecule less than observed experimentally, radial distribution functions far from measured ones, and the internal energy underestimated relative to the experimental value. When three-body effects are introduced, all these quantities become significantly closer to experimental ones. In particular, we show that three-body effects result in a reorientation of water molecules leading to significantly increased number of hydrogen bonds. Our simulations indicate that three-body effects contribute 14.5% to the internal energy of water, whereas four- and higher-body effects contribute 1.4%. Since the ab initio three-body terms which are relevant for simulations are well reproduced by the nonadditive portion of classical induction interaction, our work confirms to some extent the validity of polarization models of water. [ABSTRACT FROM AUTHOR]

The structure and energetics of the Ar[sub n]O[sup -] clusters for n=1, …,13 have been modeled in the framework of Diffusion Monte Carlo (DMC), using two- and three-body ab initio determined potentials derived previously by Buchachenko et al. [J. Chem. Phys. 112, 5852 (2000)], and Jakowski et al. [preceding paper, J. Chem. Phys. 118, 2731 (2003)], respectively. The anion cluster structures are largely determined by the two-body potential since the dominant contribution to the stabilization energy is due to pair interactions. However, the three-body effects are important since their role grows with n, from a few percent for n = 2 to ca. 30% for n = 12. The three-body effects are well approximated by the induction component only. The exchange and dispersion three-body and the induction many-body effects were found to be much less important. The effect of the spin-orbit coupling on the stabilization energies is small and almost independent of the size of a cluster. Specifically, it amounts to about 5% for ArO[sup -], and to 0.1% for Ar[sub 12]O[sup -]. The ab initio cluster stabilization energies are compared with those derived from the experimental measurements of electron detachment energies. The agreement is qualitatively good, and the origins of quantitative discrepancies are discussed. [ABSTRACT FROM AUTHOR]

Makarov, Keller, Plaxco, and Metiu (MKPM) (to be published) have proposed a model that assumes that the kinetics of protein folding is controlled by the formation of the native contacts. An approximate solution of this model leads to a connection between the rate constant and the number of contacts in the folded state, which agrees with the measurements. In the present article, we perform Kinetic Monte Carlo simulations to test the assumptions and the results of MKPM theory. These simulations require us to know the rate constant for contact formation and dissociation. We show that these can be calculated for the case of a Gaussian chain and then used, in a Kinetic Monte Carlo program, to simulate folding kinetics. It is likely that a Gaussian chain is not a realistic model for the folding of a specific protein. However, it is reasonable to use it to test the assumptions made by MKPM, or by other kinetic models, or to derive generic features of folding rate, such as the dependence on the number of contacts. Another valuable feature of the simulation is that it provides information about the stochastic kinetics of a single chain, which is not yet available experimentally. The simulations find that the probability that a single chain folds at a time t has a maximum, at a time t[sub m], and decays exponentially for longer times. We show that t[sub m] is shorter than the time resolution of the experiments and therefore the measurements will conclude that folding is a first-order rate process. This is what is observed experimentally. The folding rate constant produced by simulations agrees with the one obtained by the simplified MKPM theory. Moreover, the simulations were used to test directly some of the assumptions made by MKPM. For example, we show that the free energy of a chain that has made a fair number of contacts can be approximated by a linear function of the number of contacts. The paper also contains two simplified models, which do not assume that the... [ABSTRACT FROM AUTHOR]

The dynamics of expulsion of the last liquidlike monolayer of molecules confined between two surfaces (measured recently for the first time [J. Chem. Phys. 114, 1831 (2001)]) has been analyzed by solving the two-dimensional Navier-Stokes equation combined with kinetic Monte Carlo simulations. Instabilities in the boundary line of the expelled film produce a rough boundary for all length scales above a critical value. The squeeze-out of liquid is shown to result from the 2D-pressure gradient in the lubrication film in the contact area. The Monte Carlo simulations agrees well with experiments, reproducing most qualitative and quantitative features. In particular it shows the formation of small islands, which (in the absence of pinning mechanism) drift slowly to the periphery of the contact area. We calculate the drift velocity analytically as a function of the distance of the island to the periphery of the contact area. Experiments indicate that some kind of pinning mechanism prevails, trapping fluid pockets for very long times. When including such pinning areas in the simulations, three distinct squeeze phases and time scales were observed: (1) initial fast squeeze of most of the fluid; (2) slower squeeze of unpinned fluid pockets; (3) long term pinning of fluid pockets. We also show that a distribution of small pinning areas may produce a synergistic effect, slowing down the second phase of the squeeze, compared to a small number of big pinning areas. The paper presents a new stochastic numerical approach to problems of moving boundaries which naturally accounts for thermal fluctuations and their effect in unstable dynamics. © 2001 American Institute of Physics. [DOI: 10.1063/1.1421105]. [ABSTRACT FROM AUTHOR]

In this paper, we propose some physical quantities for characterizing gels. Polymer networks (gels) were investigated by Monte Carlo method using a model of free-radical cross-linked polymerization in a continuous system. The distributions of the degree of polymerization for clusters in this simulation are in good qualitative agreement with experimental results. Linkers can be classified into two types according to their role in the network: One forms a simple closed loop within a polymer, and another forms polymer clusters. Their respective amounts and ratios are examined with regard to changes in the distribution of the degree of polymerization. © 2001 American Institute of Physics. [DOI: 10.1063/1.1421363]. [ABSTRACT FROM AUTHOR]

In this paper a simple lattice gas model for the catalytic CO+NO→CO2+1/2N2 surface reaction is studied by means of Monte Carlo simulations. In the simulations we take into consideration the diffusion of all particles and the desorption of CO. The square and triangular lattices are used to model the surface of an ideal catalyst, whereas percolation clusters, diffusion limited aggregates (DLA), the Sierpinski carpet, and the Sierpinski gasket are introduced as better models for supported catalysts. In many simulations an interval of the gas phase concentration yCO∈[y1,y2] exists, where the simulation remains in a reactive state. The kinetic phase transitions of second (y1) and first-order (y2) which appear in this reaction system are studied as a function of the system parameters. The above interval is broadened with increasing diffusion of the adsorbed particles. Desorption of CO results in a shift of y2 to yCO=1. On the Sierpinski lattices only very small reactive intervals appear, whereas on DLA and percolation clusters no reaction occurs. Estimates for the order parameter β of the second order phase transition from an active into one (out of infinitely many) absorbing states show that the model belongs to the universality class of directed percolation. The very strong influence of the lattice structure on the reaction system is dicussed in detail. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We present in this paper a computer simulation study of the phase behavior of the Gay–Berne liquid crystal model. The effect of the anisotropic attractive interactions on stabilizing orientationally ordered phases is analyzed by varying the anisotropy parameter κ′ at fixed values of the molecular elongation parameter κ. Molecular dynamics simulations have been performed at constant density and temperature along several isotherms and approximate transition densities are reported. It is found that, for a given value of the molecular elongation κ=3, smectic order is favored at lower densities as κ′ increases. When κ′ is lowered, the smectic phase is preempted by the nematic phase. As a result, the nematic phase becomes increasingly stable at lower temperatures as κ′ is decreased. Additionally, we have studied the liquid–vapor coexistence region for different values of κ′ by using Gibbs ensemble and Gibbs–Duhem Monte Carlo techniques. We have found evidence of a vapor–isotropic–nematic triple point for κ′=1 and κ′=1.25. For temperatures below this triple point, we have observed nematic–vapor coexistence as is found for many liquid crystals in experiments. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The majority of molecules which form liquid crystals are elongated in shape. However, disk shaped molecules have also been shown to exhibit liquid crystalline phases. In this paper we report a series of constant pressure Monte Carlo simulations of model discotic molecules. We have used the Gay–Berne potential, which is in essence an anisotropic version of a shifted Lennard-Jones potential, to model the interactions between the disks. Initially we studied a system of 512 molecules over a range of pressures to determine the mesophases formed and to construct the phase diagram. The system was found to exhibit isotropic, nematic, and columnar phases. We have also studied a larger system of 2000 molecules at a single pressure to calculate more accurately the distribution functions used to describe the translational and orientational order within the various phases. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A two-dimensional lattice model, originally introduced by Granek et al. [J. Chem. Phys. 101, 4331 (1994)], is used to demonstrate the intricate coupling between the intramicellar interactions that determine the optimal aggregation geometry of surfactant molecules in dilute solution, and the intermicellar interactions that govern the phase behavior at higher concentrations. Three very different scenarios of self-assembly and phase evolution are analyzed in detail, based on Monte Carlo studies and theoretical interpretations involving mean-field, Landau–Ginzburg, Bethe–Peierls, and virial expansion schemes. The basic particles in the model are ‘‘unit micelles’’ which, due to spontaneous self-assembly or because of excluded area interactions, can fuse to form larger aggregates. These aggregates are envisaged as flat micelles composed of a bilayerlike body surrounded by a curved semitoroidal rim. The system’s Hamiltonian involves one- through four-body potentials between the unit micelles, which account for their tendency to form aggregates of different shapes, e.g., elongated vs disklike micelles.Equivalently, the configurational energy of the system is a sum of micellar self-energies involving the packing free energies of the constituent molecules in the bilayer body and in rim segments of different local curvature. The rim energy is a sum of a line tension term and a 1D curvature energy which depends on the rim spontaneous curvature and bending rigidity. Different combinations of these molecular parameters imply different optimal packing geometries and hence different self-assembly and phase behaviors. The emphasis in this paper is on systems of ‘‘curvature loving’’ amphiphiles which, in our model, are characterized by negative line tension. The three systems studied are: (i) A dilute solution of stable disklike micelles which, upon increasing the concentration, undergoes a first-order... [ABSTRACT FROM AUTHOR]

In earlier work [J. Chem. Phys. 100, 2154 (1994)] we presented a new method of determining the chemical potential in Monte Carlo or molecular dynamics simulations which makes use of a detailed balance method (DBM). In the present paper we present results of a careful study of this method applied to liquid palladium down to and below the zero-pressure melting temperature. A new surface detailed balance method (SDBM) is introduced, which is much more efficient near and below the melting temperature where the original method becomes too inefficient to determine an accurate value of the chemical potential. We also present results where the new surface detailed balance method is used to determine the chemical potential of the solid phase at a number of different temperatures. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

This paper reports a Monte Carlo (MC) study of the ordering in a semiflexible liquid crystal model designed to give a crude representation of 4-n-octyl-4′-cyanobiphenyl (PCB). A mechanically stable nematic phase is obtained and the question of its thermodynamic stability is addressed by comparing the free energy to that of the isotropic phase. The free energies are calculated by thermodynamic integration using an efficient configuration biased MC scheme. Pair distribution functions, orientational correlation functions, and conformational properties of the nematic and isotropic phases are contrasted. In the isotropic phase the equation of state is compared with theoretical predictions for systems of convex molecules and chains made up of tangent hard spheres. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In this paper we study CO oxidation on a catalyst consisting of a Pt/Sn alloy. On this catalyst the reaction can take place at room temperature. We use for the description two basically different methods: Monte Carlo simulations and a theoretical stochastic ansatz. The stochastic ansatz introduced recently [Mai, Kuzovkov, and von Niessen, Physica A 203, 298 (1994)] is a general method for the description of surface reaction systems including mono- and bimolecular steps. Using the Markovian behavior of these systems we formulate this ansatz in terms of master equations. It turns out that the stochastic ansatz can be used as an interesting and advantageous alternative to the standard Monte Carlo simulations. The particles involved in the reaction system have different tendencies toward building structures on the surface. The coverages show a strong dependency, not only on the composition of the gas phase but also on the initial concentration of the reaction promotor OH and the concentration of Pt sites in the catalyst material. The reaction probability does not influence the qualitative trends of the coverages versus the gas phase concentration of CO. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We examine the nonideal behavior of real vapor in the context of the theory of noninteracting molecular clusters. The vapor is treated as a perfect mixture of clusters, which in equilibrium attain a distribution in size determined by formation energies ΔGi, where ΔGi is the energy required to form a cluster of i molecules from i molecules in bulk saturated liquid. A theory for the ΔGi gives an equation of state that captures the nonideal behavior of the vapor; conversely, equation of state data provide a validation of the theory. In this paper, we compare the predictions of this equation of state to experimental data. Utilizing the ΔGi proposed by Dillmann and Meier and based on Fisher’s droplet model, we compute the vapor compressibility along the saturation curve for several nonpolar substances and obtain excellent agreement with experiment. We also compute the third virial coefficient for these substances and observe correct qualitative behavior; in the case of benzene and n-octane, for which some data are available, we find rough agreement with experiment. The conventional kinetic theory of homogeneous nucleation, which is based on the assumption of noninteracting clusters, demonstrates that the cluster series equation of state can be continued past the saturation point to describe metastable vapor, a claim that no nonvirial equation of state can make a priori. Furthermore, the noninteracting cluster theory readily accommodates results of more detailed calculations of molecular clusters (e.g., results of Monte Carlo or molecular dynamics studies). These considerations and the success of the simple Fisher–Dillmann–Meier model in predicting the behavior of nonideal vapor suggest possible avenues of investigation in equation of state research. [ABSTRACT FROM AUTHOR]

Gibbs ensemble Monte Carlo simulations are undertaken in order to determine the vapor–liquid and liquid–liquid phase equilibria for mixtures containing square-well particles. Two types of binary systems are examined, namely, a mixture of hard spheres and square wells, and a symmetrical mixture of square wells in which the unlike interaction is purely repulsive, i.e., hard sphere like. The latter system exhibits liquid–liquid immiscibility as well as the usual vapor–liquid coexistence. Intermolecular potential ranges which are intermediate (λ=1.5) and moderately long (λ=2) are examined in order to determine the effect of range on the phase behavior. The coexistence data are also analyzed using a Wegner expansion; the differences in densities and compositions of the two coexisting phases can both be used as the order parameter. This approach enables a description of the phase equilibria over the entire fluid range. In the case of the vapor–liquid coexistence exhibited by the mixture of hard spheres and square-wells, the leading amplitude term and a universal critical exponent are sufficient to describe the coexistence curve. The same was found for pure square-well systems in an earlier paper. However, extended scaling has to be used in order to describe the liquid–liquid coexistence curves exhibited by the symmetrical square-well mixture; the first and second Wegner correction to scaling terms are used together with a universal value of the critical exponent. In contrast to what is found for the pure component systems, an increase in the range of the potential has little effect on the shapes of the coexistence curves of the mixtures, although the phase equilibria are, of course, shifted to higher temperatures. Other authors have reported a substantial system size dependence for the liquid–liquid phase equilibria of the symmetrical square-well mixture. We do not find a significant size dependence for this... [ABSTRACT FROM AUTHOR]

A new closure to the Ornstein–Zernike (OZ) equation is proposed for ionic liquids and is investigated for primitive models of high valency (2:2) aqueous electrolyte solutions and molten salts. The new closure, which is related to an earlier closure for the soft-sphere case proposed by Ichiye and Haymet, may be viewed as a prescription for the so-called ‘‘bridge functions.’’ These functions are approximated by zero in the hypernetted-chain (HNC) closure which is generally used for ionic systems. In both the new closure and the soft-sphere closure, the recognition that the unlike bridge function is opposite in sign from the like bridge function leads to an approximation for these missing graphs by adding (for the unlike case) or subtracting (for the like case) a set of graphs similar to those used in Percus–Yevick theory to the HNC equation. Compared to the HNC closure, the pair correlation functions predicted for primitive models by the new closure are generally in much better agreement with Monte Carlo (MC) simulations of molten salts and aqueous 2:2 electrolytes. The fundamental improvement of this paper over the Ichiye–Haymet work is that the separation of long- and short-range part of c(r) for the hard-sphere case is clearly defined, whereas it was done numerically for the soft-sphere case. Moreover, the present theory is in better agreement with MC simulations both in the molten salt as well as in the dilute solution regimes than the soft-sphere case. Finally, a study was made of the transition of the like charge pair correlation functions from monotonic behavior at low densities to a nonmonotonic behavior at high densities. The new closure clearly predicts such a transition region at concentrations near 0.02 M and temperatures near 314 K. There is also a region below 0.02 M and 314 K where the new closure fails to converge. Compared to MC simulations, the critical region predicted by the new closure appears... [ABSTRACT FROM AUTHOR]

In this paper we present the results of a Monte Carlo (MC) simulation study of the structural properties of concentrated aqueous solutions of various alkali halides at 25 °C using a simple civilized model (SCM). A simplified version of the rigid nonpolarizable SPC model of liquid water, in which the Lennard-Jones interaction between intermolecular oxygen sites is changed into a hard-core repulsion, is combined in our SCM with a treatment of the ions as charged hard spheres. Changes in the structure of the solvent, and the behavior of ionic solvation and ion pairing upon varying the concentration and size of the ions, are determined by computing the corresponding ten radial distribution functions from sufficiently long MC simulation runs for various aqueous alkali halide solutions at concentrations above 1 M. Hydration numbers are reported for the first time for NaBr and KBr, and the first simulation-based estimates for LiBr, NaI, and KI are also obtained. Whenever possible, results for the hydration numbers are compared with available experimental data and also with other simulation studies. The excellent predictive capability and simplicity of the SCM proposed here, should lead to the development of tractable theoretical approaches to aqueous 1:1 electrolyte solutions in the near future. [ABSTRACT FROM AUTHOR]

This paper elaborates on the method introduced by Reinhardt and Hunter [J. Chem. Phys. 97, 1599 (1992)] for determining upper and lower bounds on free energy changes and systematically improving these bounds by variational optimization of the Hamiltonian switching path connecting the two states of interest. The advantages, conditions of applicability, and potential pitfalls of this finite-time variational method are illustrated in detail in a Monte Carlo calculation of the free energy change accompanying the reversal of magnetic field in a two-dimensional Ising model. The power of its flexibility in an inhomogeneous system is demonstrated by computing the boundary tension between domains of positive and negative magnetization in the Ising model. Its success in a problem involving molecular dynamics and continuous potentials is illustrated by computing the free energy difference between a Lennard-Jones fluid and a soft-sphere fluid. Finally, its connection with the method of dynamically modified slow growth is discussed. [ABSTRACT FROM AUTHOR]