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Hybrid methods that combine molecular dynamics methods capable of analyzing dynamics with Monte Carlo (MC) methods that can efficiently treat thermodynamically stable states are valuable for understanding complex chemical processes in which an equilibrium state is reached through many elementary processes. The hybrid MC (HMC) method is one such promising method; however, it often fails to sample configurations properly from the canonical multimodal distribution due to the rugged potential energy surfaces. In this paper, we extend the HMC method to overcome this difficulty. The new method, which is termed potential scaling HMC (PS-HMC), makes use of an artificially modulated trajectory to propose a new configuration. The trajectory is generated from Hamilton's equations, but the potential energy surface is scaled to be gradually flattened and then recovered to the original surface, which facilitates barrier-crossing processes. We apply the PS-HMC method to three kinds of molecular processes: the thermal motion of argon particles, butane isomerization, and an atom transfer chemical reaction. These applications demonstrate that the PS-HMC method is capable of correctly constructing the canonical ensemble with a multimodal distribution. The sampling efficiency and accepted trajectories are examined to clarify the features of the PS-HMC method. Despite the potential scaling, many reactive atom transfer trajectories (elementary processes) pass through the vicinity of the minimum energy path. Furthermore, we demonstrate that the method can properly imitate the relaxation process owing to the inherent configurational continuity. By comparing the PS-HMC method with other relevant methods, we can conclude that the new method is a unique approach for studying both the dynamic and thermodynamic aspects of chemical processes. [ABSTRACT FROM AUTHOR]

Inelastic collisions of OH with an inert liquid perfluoropolyether (PFPE) surface have been studied experimentally. A pulsed molecular beam of OH with a kinetic energy distribution peaking at 35 kJ mol−1 was directed at a continually refreshed PFPE surface. OH molecules were detected state-selectively with spatial and temporal resolution by pulsed, planar laser-induced fluorescence. The scattered speed distributions were confirmed to be strongly superthermal, regardless of the incidence angle (0° or 45°). Angular scattering distributions were measured for the first time; their reliability was confirmed through extensive Monte Carlo simulations of experimental averaging effects, described in Paper II [A. G. Knight et al., J. Chem. Phys. 158, 244705 (2023)]. The distributions depend markedly on the incidence angle and are correlated with scattered OH speed, consistent with predominantly impulsive scattering. For 45° incidence, the angular distributions are distinctly asymmetric to the specular side but peak at sub-specular angles. This, along with the breadth of the distributions, is incompatible with scattering from a surface that is flat on a molecular scale. New molecular dynamics simulations corroborate the roughness of the PFPE surface. A subtle but unexpected systematic dependence of the angular distribution on the OH rotational state was found, which may be dynamical in origin. The OH angular distributions are similar to those for kinematically similar Ne scattering from PFPE and hence not strongly perturbed by OH being a linear rotor. The results here are broadly compatible with prior predictions from independent quasiclassical trajectory simulations of OH scattering from a model-fluorinated self-assembled monolayer surface. [ABSTRACT FROM AUTHOR]

Molecular dynamics simulations require barostats to be performed at a constant pressure. The usual recipe is to employ the Berendsen barostat first, which displays a first-order volume relaxation efficient in equilibration but results in incorrect volume fluctuations, followed by a second-order or a Monte Carlo barostat for production runs. In this paper, we introduce stochastic cell rescaling, a first-order barostat that samples the correct volume fluctuations by including a suitable noise term. The algorithm is shown to report volume fluctuations compatible with the isobaric ensemble and its anisotropic variant is tested on a membrane simulation. Stochastic cell rescaling can be straightforwardly implemented in the existing codes and can be used effectively in both equilibration and production phases. [ABSTRACT FROM AUTHOR]

The Gibbs ensemble molecular dynamics algorithm introduced in the preceding paper (paper I) [C. Bratschi and H. Huber, J. Chem. Phys. v126, 164104 (2007)] is applied to two recently published CO2 ab initio pair potentials, the Bock-Bich-Vogel and symmetry-adapted perturbation theory site-site potentials. The critical properties of these potentials are calculated for the first time. Critical values and points in the single and two-phase zones are compared with Monte Carlo results to demonstrate the accuracy of the molecular dynamics algorithm, and are compared with experiment to test the accuracy of the potentials. Pressure calculations in the liquid, gas, and supercritical states are carried out and are used to explain potential-related effects and systematic discrepancies. The best ab initio potential yields results in good agreement with experiment. [ABSTRACT FROM AUTHOR]

In this paper (paper I) and the following paper (paper II) [C. Bratschi, H. Huber, and D. J. Searles, J. Chem. Phys. 126, 164105 (2007)], a new molecular dynamics algorithm implementing the Gibbs ensemble will be presented and then on applied to the liquid-vapor coexistence curve for two ab initio CO2 potentials. In paper I, the Gibbs ensemble molecular dynamics algorithm using non-Hamiltonian molecular dynamics techniques is introduced. It is shown that states of the correct probability density function are sampled and the correct exchange probability is generated. The extended system Nosé-Hoover formalism is used to generate a constant temperature ensemble with equal pressures in the subsystems, combined with single particle transfers between the subsystems, over several time steps, to get equal chemical potentials. [ABSTRACT FROM AUTHOR]

We report on tests of the shifted potential (SP), gradient shifted force (GSF), and Taylor shifted force (TSF) real-space methods for multipole interactions developed in Paper I of this series, using the multipolar Ewald sum as a reference method. The tests were carried out in a variety of condensed-phase environments designed to test up to quadrupole-quadrupole interactions. Comparisons of the energy differences between configurations, molecular forces, and torques were used to analyze how well the real-space models perform relative to the more computationally expensive Ewald treatment. We have also investigated the energy conservation, structural, and dynamical properties of the new methods in molecular dynamics simulations. The SP method shows excellent agreement with configurational energy differences, forces, and torques, and would be suitable for use in Monte Carlo calculations. Of the two new shifted-force methods, the GSF approach shows the best agreement with Ewald-derived energies, forces, and torques and also exhibits energy conservation properties that make it an excellent choice for efficient computation of electrostatic interactions in molecular dynamics simulations. Both SP and GSF are able to reproduce structural and dynamical properties in the liquid models with excellent fidelity. [ABSTRACT FROM AUTHOR]

In this paper, we present a Monte Carlo simulation study on the structure of the electrical double layer around a spherical colloid surrounded by a binary electrolyte composed of spherical and non-spherical ions. Results are provided for the radial distribution functions between the colloid and ions, the orientation correlations between the colloid and non-spherical particles, and the integrated charge. Work is reported mainly for non-spherical particles modeled as spherocylinders, although a particular comparison is made between spherocylindrical particles and dimers. For the conditions investigated here, spherocylinders and dimers produce essentially the same structural information. Additionally, it is shown that spherocylinders mostly orient tangentially to the colloid at its surface; this preferred orientation disappears for larger distances. We also evidence that, near the colloid, the integrated charge attenuates monotonically when the macroparticle is highly charged, whereas for intermediate and low charged states of the colloid, the integrated charge can display charge reversal, overcharging, or both, with magnitudes that are sensitive to the salt concentration and to the localization of charge inside the spherocylinders. [ABSTRACT FROM AUTHOR]

Molecular dynamics (MD) simulations give access to equilibrium structures and dynamic properties given an ergodic sampling and an accurate force-field. The force-field parameters are calibrated to reproduce properties measured by experiments or simulations. The main contribution of this paper is an approximate Bayesian framework for the calibration and uncertainty quantification of the force-field parameters, without assuming parameter uncertainty to be Gaussian. To this aim, since the likelihood function of the MD simulation models is intractable in the absence of Gaussianity assumption, we use a likelihood-free inference scheme known as approximate Bayesian computation (ABC) and propose an adaptive population Monte Carlo ABC algorithm, which is illustrated to converge faster and scales better than the previously used ABCsubsim algorithm for the calibration of the force-field of a helium system. The second contribution is the adaptation of ABC algorithms for High Performance Computing to MD simulations within the Python ecosystem ABCpy. This adaptation includes a novel use of a dynamic allocation scheme for Message Passing Interface (MPI). We illustrate the performance of the developed methodology to learn posterior distribution and Bayesian estimates of Lennard-Jones force-field parameters of helium and the TIP4P system of water implemented for both simulated and experimental datasets collected using neutron and X-ray diffraction. For simulated data, the Bayesian estimate is in close agreement with the true parameter value used to generate the dataset. For experimental as well as for simulated data, the Bayesian posterior distribution shows a strong correlation pattern between the force-field parameters. Providing an estimate of the entire posterior distribution, our methodology also allows us to perform the uncertainty quantification of model prediction. This research opens up the possibility to rigorously calibrate force-fields from available experimental datasets of any structural and dynamic property. [ABSTRACT FROM AUTHOR]

In the present paper, a generalized hybrid Monte Carlo method to generate the multicanonical ensemble has been developed, which is a generalization of the multicanonical hybrid Monte Carlo (HMC) method by Hansmann and co-workers [Chem. Phys. Lett. 259, 321 (1996)]. The generalized hybrid Monte Carlo (GHMC) method is an equations-of-motion guided Monte Carlo combined with partial momentum refreshment. We successfully applied our multicanonical GHMC to dense Lennard-Jones fluids and a coarse grained protein model. It is found that good computational efficiency can be gained in the case of the acceptance ratio around 60% for the models examined. While a large number of molecular dynamics (MD) steps in a single GHMC cycle is needed to yield good computational efficiency at a large mixing ratio of momenta with thermal noise vectors, corresponding to the original multicanonical HMC method, a small number of MD steps are enough to achieve good efficiency at a small mixing ratio. This property is useful to develop a composite algorithm combining the present GHMC method with other Monte Carlo moves. [ABSTRACT FROM AUTHOR]

This paper deals with molecular simulation of the chemical potentials in aqueous electrolyte solutions for the water solvent and its relationship to chemical potential simulation results for the electrolyte solute. We use the Gibbs-Duhem equation linking the concentration dependence of these quantities to test the thermodynamic consistency of separate calculations of each quantity. We consider aqueous NaCl solutions at ambient conditions, using the standard SPC/E force field for water and the Joung-Cheatham force field for the electrolyte. We calculate the water chemical potential using the osmotic ensemble Monte Carlo algorithm by varying the number of water molecules at a constant amount of solute. We demonstrate numerical consistency of these results in terms of the Gibbs-Duhem equation in conjunction with our previous calculations of the electrolyte chemical potential. We present the chemical potential vs molality curves for both solvent and solute in the form of appropriately chosen analytical equations fitted to the simulation data. As a byproduct, in the context of the force fields considered, we also obtain values for the Henry convention standard molar chemical potential for aqueous NaCl using molality as the concentration variable and for the chemical potential of pure SPC/E water. These values are in reasonable agreement with the experimental values. [ABSTRACT FROM AUTHOR]

We present a short overview of pressure calculation in molecular dynamics or Monte Carlo simulations. The emphasis is given to polarizable models in order to resolve the controversy caused by the paper of M. J. Louwerse and E. J. Baerends [Chem. Phys. Lett. 421, 138 (2006)] about pressure calculation in systems with periodic boundaries. We systematically derive expressions for the pressure and show that despite the lack of explicit pairwise additivity, the pressure formula for polarizable models is identical with that of nonpolarizable ones. However, a strict condition for using this formula is that the induced dipole should be in perfect mechanical equilibrium prior to pressure calculation. The perfect convergence of induced dipoles ensures conservation of energy as well. We demonstrate using more cumbersome but exact methods that the derived expressions for the polarizable model of water provide correct numerical results. We also show that the inaccuracy caused by imperfect convergence of the induced dipoles correlates with the inaccuracy of the calculated pressure. [ABSTRACT FROM AUTHOR]

A numerical solution for the quantum dynamics of the spin boson problem is obtained using the semiclassical initial value series representation approach to the quantum dynamics. The zeroth order term of the series is computed using the new forward-backward representation for correlation functions presented in the preceding adjacent paper. This leads to a rapid convergence of the Monte Carlo sampling, as compared to previous attempts. The zeroth order results are already quite accurate. The first order term of the series is small, demonstrating the rapid convergence of the semiclassical initial value representation series. This is the first time that the first order term in the semiclassical initial value representation series has been converged for systems with the order of 50 degrees of freedom. [ABSTRACT FROM AUTHOR]

In this paper, we present a path integral hybrid Monte Carlo (PIHMC) method for rotating molecules in quantum fluids. This is an extension of our PIHMC for correlated Bose fluids [S. Miura and J. Tanaka, J. Chem. Phys. 120, 2160 (2004)] to handle the molecular rotation quantum mechanically. A novel technique referred to be an effective potential of quantum rotation is introduced to incorporate the rotational degree of freedom in the path integral molecular dynamics or hybrid Monte Carlo algorithm. For a permutation move to satisfy Bose statistics, we devise a multilevel Metropolis method combined with a configurational-bias technique for efficiently sampling the permutation and the associated atomic coordinates. Then, we have applied the PIHMC to a helium-4 cluster doped with a carbonyl sulfide molecule. The effects of the quantum rotation on the solvation structure and energetics were examined. Translational and rotational fluctuations of the dopant in the superfluid cluster were also analyzed. [ABSTRACT FROM AUTHOR]

This paper investigates the conformational and scaling properties of long linear polymer chains. These investigations are done with the aid of Monte Carlo (MC) and molecular dynamics (MD) simulations. Chain lengths that comprise several orders of magnitude to reduce errors of finite size scaling, including the effect of solvent quality, ranging from the athermal limit over the θ-transition to the collapsed state of chains are investigated. Also the effect of polydispersity on linear chains is included which is an important issue in the real fabrication of polymers. A detailed account of the hybrid MD and MC simulation model and the exploited numerical methods is given. Many results of chain properties in the extrapolated limit of infinite chain lengths are documented and universal properties of the chains within their universality class are given. An example of the difference between scaling exponents observed in actual solvents and those observed in the extremes of “good solvents” and “θ-solvents” in simulations is provided by comparing simulation results with experimental data on low density polyethylene. This paper is concluded with an outlook on the extension of this study to branched chain systems of many different branching types. [ABSTRACT FROM AUTHOR]

The paper aims at a comparison of techniques based on the kinetic Monte Carlo (kMC) and the conventional Metropolis Monte Carlo (MC) methods as applied to the hard-sphere (HS) fluid and solid. In the case of the kMC, an alternative representation of the chemical potential is explored [E. A. Ustinov and D. D. Do, J. Colloid Interface Sci. 366, 216 (2012)], which does not require any external procedure like the Widom test particle insertion method. A direct evaluation of the chemical potential of the fluid and solid without thermodynamic integration is achieved by molecular simulation in an elongated box with an external potential imposed on the system in order to reduce the particle density in the vicinity of the box ends. The existence of rarefied zones allows one to determine the chemical potential of the crystalline phase and substantially increases its accuracy for the disordered dense phase in the central zone of the simulation box. This method is applicable to both the Metropolis MC and the kMC, but in the latter case, the chemical potential is determined with higher accuracy at the same conditions and the number of MC steps. Thermodynamic functions of the disordered fluid and crystalline face-centered cubic (FCC) phase for the hard-sphere system have been evaluated with the kinetic MC and the standard MC coupled with the Widom procedure over a wide range of density. The melting transition parameters have been determined by the point of intersection of the pressure-chemical potential curves for the disordered HS fluid and FCC crystal using the Gibbs-Duhem equation as a constraint. A detailed thermodynamic analysis of the hardsphere fluid has provided a rigorous verification of the approach, which can be extended to more complex systems. [ABSTRACT FROM AUTHOR]

In the present study, variational path integral molecular dynamics and associated hybrid Monte Carlo (HMC) methods have been developed on the basis of a fourth order approximation of a density operator. To reveal various parameter dependence of physical quantities, we analytically solve one dimensional harmonic oscillators by the variational path integral; as a byproduct, we obtain the analytical expression of the discretized density matrix using the fourth order approximation for the oscillators. Then, we apply our methods to realistic systems like a water molecule and a para-hydrogen cluster. In the HMC, we adopt two level description to avoid the time consuming Hessian evaluation. For the systems examined in this paper, the HMC method is found to be about three times more efficient than the molecular dynamics method if appropriate HMC parameters are adopted; the advantage of the HMC method is suggested to be more evident for systems described by many body interaction. [ABSTRACT FROM AUTHOR]

Phospholipid bilayers supported on hydrophilic solids like silica and mica play a substantial role in fundamental studies and technological applications of phospholipid membranes. In both cases the molecular mechanism of adhesion between the bilayer and the support is of primary interest. Since the possibilities of experimental methods in this specific area are rather limited, the methods of computer simulation acquire great importance. In this paper we use the grand canonical Monte Carlo technique and an atomistic force field to simulate the behavior of a mica supported phospholipid bilayer in pure water as a function of the distance between the bilayer and the support. The simulation reveals a possible adhesion mechanism, where the adhesion is due to individual lipid molecules that protrude from the bilayer and form widely spaced links with the support. Simultaneously, the bilayer remains separated from the bilayer by a thin water interlayer which maintains the bilayer fluidity. [ABSTRACT FROM AUTHOR]

Both experiments and theory have evidenced that multivalent cations can mediate the interaction between negatively charged polyelectrolytes and like-charged objects, such as anionic lipoplexes (DNA-cation-anionic liposome complexes). In this paper, we use Monte Carlo simulations to study the electrostatic interaction responsible for the trivalent-counterion-mediated adsorption of polyelectrolytes onto a like-charged planar surface. The evaluation of the Helmholtz free energy allows us to characterize both the magnitude and the range of the interaction as a function of the polyelectrolyte charge, surface charge density, [3:1] electrolyte concentration, and cation size. Both polyelectrolyte and surface charge favor the adsorption. It should be stressed, however, that the adsorption will be negligible if the surface charge density does not exceed a threshold value. The effect of the [3:1] electrolyte concentration has also been analyzed. In certain range of concentrations, the counterion-mediated attraction seems to be independent of this parameter, whereas very high concentrations of salt weaken the adsorption. If the trivalent cation diameter is doubled the adsorption moderates due to the excluded volume effects. The analysis of the integrated charge density and ionic distributions suggests that a delicate balance between charge inversion and screening effects governs the polyelectrolyte adsorption onto like-charged surfaces mediated by trivalent cations. [ABSTRACT FROM AUTHOR]

Finding informative low-dimensional descriptions of high-dimensional simulation data (like the ones arising in molecular dynamics or kinetic Monte Carlo simulations of physical and chemical processes) is crucial to understanding physical phenomena, and can also dramatically assist in accelerating the simulations themselves. In this paper, we discuss and illustrate the use of nonlinear intrinsic variables (NIV) in the mining of high-dimensional multiscale simulation data. In particular, we focus on the way NIV allows us to functionally merge different simulation ensembles, and different partial observations of these ensembles, as well as to infer variables not explicitly measured. The approach relies on certain simple features of the underlying process variability to filter out measurement noise and systematically recover a unique reference coordinate frame. We illustrate the approach through two distinct sets of atomistic simulations: a stochastic simulation of an enzyme reaction network exhibiting both fast and slow time scales, and a molecular dynamics simulation of alanine dipeptide in explicit water. [ABSTRACT FROM AUTHOR]

We provide a systematic comparative analysis of various simulation methods for studying steady-state diffusive transport of molecular systems. The methods differ in two respects: (1) the actual method with which the dynamics of the system is handled can be a direct simulation technique [molecular dynamics (MD) and dynamic Monte Carlo (DMC)] or can be an indirect transport equation [the Nernst-Planck (NP) equation], while (2) the driving force of the steady-state transport can be maintained with control cells on the two sides of the transport region [dual control volume (DCV) technique] or it can be maintained in the whole simulation domain with the local equilibrium Monte Carlo (LEMC) technique, where the space is divided into small subvolumes, different chemical potentials are assigned to each, and grand canonical Monte Carlo simulations are performed for them separately. The various combinations of the transport-methods with the driving-force methods have advantages and disadvantages. The MD+DCV and DMC+DCV methods are widely used to study membrane transport. The LEMC method has been introduced with the NP+LEMC technique, which was proved to be a fast, but somewhat empirical method to study diffusion [D. Boda and D. Gillespie, J. Chem. Theor. Comput. 8, 824 (2012)]. In this paper, we introduce the DMC+LEMC method and show that the resulting DMC+LEMC technique has the advantage over the DMC+DCV method that it provides better sampling for the flux, while it has the advantage over the NP+LEMC method that it simulates dynamics directly instead of hiding it in an external adjustable parameter, the diffusion coefficient. The information gained from the DMC+LEMC simulation can be used to construct diffusion coefficient profiles for the NP+LEMC calculations, so a simultaneous application of the two methods is advantageous. [ABSTRACT FROM AUTHOR]

Signal proteins are able to adapt their response to a change in the environment, governing in this way a broad variety of important cellular processes in living systems. While conventional molecular-dynamics (MD) techniques can be used to explore the early signaling pathway of these protein systems at atomistic resolution, the high computational costs limit their usefulness for the elucidation of the multiscale transduction dynamics of most signaling processes, occurring on experimental timescales. To cope with the problem, we present in this paper a novel multiscale-modeling method, based on a combination of the kinetic Monte-Carlo- and MD-technique, and demonstrate its suitability for investigating the signaling behavior of the photoswitch light-oxygen-voltage-2-Jα domain from Avena Sativa (AsLOV2-Jα) and an AsLOV2-Jα-regulated photoactivable Rac1-GTPase (PA-Rac1), recently employed to control the motility of cancer cells through light stimulus. More specifically, we show that their signaling pathways begin with a residual re-arrangement and subsequent H-bond formation of amino acids near to the flavin-mononucleotide chromophore, causing a coupling between β-strands and subsequent detachment of a peripheral α-helix from the AsLOV2-domain. In the case of the PA-Rac1 system we find that this latter process induces the release of the AsLOV2-inhibitor from the switchII-activation site of the GTPase, enabling signal activation through effector-protein binding. These applications demonstrate that our approach reliably reproduces the signaling pathways of complex signal proteins, ranging from nanoseconds up to seconds at affordable computational costs. [ABSTRACT FROM AUTHOR]

Functionalizing nanoparticles with organic ligands, such as oligomers, polymers, DNA, and proteins, is an attractive way to manipulate the interfacial interactions between the nanoparticles and the medium the particles are placed in, and thus control the nanoparticle assembly. In this paper we have conducted a Monte Carlo simulation study on copolymer grafted spherical nanoparticles to show the tremendous potential of using monomer sequence on the copolymers to tune the grafted chain conformation, and thus the effective interactions between copolymer grafted nanoparticles. We have studied AB copolymers with alternating, multiblock, or diblock sequences, where either A monomers or B monomers have monomer-monomer attractive interactions. Our focus has been to show the nontrivial effect of monomer sequence on the conformations of the grafted copolymers at various particle diameters, grafting densities, copolymer chain lengths, and monomer-monomer interactions in an implicit small molecule solvent. We observe that the monomer sequence, particle diameter, and grafting density dictate whether (a) the grafted chains aggregate to bring attractive monomers from multiple grafted chains together (interchain and intrachain monomer aggregation) if the enthalpy gained by doing so offsets the entropic loss caused by stretching of chains, or (b) each grafted chain folds onto itself to bring its attractive monomers together (only intrachain monomer aggregation) if the entropic loss from interchain aggregation cannot be overcome by the enthalpic gain. For six copolymers of chain length N=24 grafted on a spherical particle of diameter D=4, interchain and intrachain monomer aggregation occurs, and the radius of gyration varies nonmonotonically with increasing blockiness of the monomer sequence. At larger particle diameters the grafted chains transition to purely intrachain monomer aggregation. The radius of gyration varies monotonically with monomer sequence for intrachain monomer aggregation because as the sequence becomes blockier (like monomers are grouped together), the copolymer chain has to fold less compactly to maximize the enthalpically favorable contacts while maintaining high conformational entropy. The radius of gyration of alternating and diblock copolymers scales with chain length N through a power law g2>1/2=αNν with the prefactor α and scaling exponent ν, varying with monomer sequence and monomer-monomer attraction strength. [ABSTRACT FROM AUTHOR]

The Inhomogeneous Stochastic Simulation Algorithm (ISSA) is a variant of the stochastic simulation algorithm in which the spatially inhomogeneous volume of the system is divided into homogeneous subvolumes, and the chemical reactions in those subvolumes are augmented by diffusive transfers of molecules between adjacent subvolumes. The ISSA can be prohibitively slow when the system is such that diffusive transfers occur much more frequently than chemical reactions. In this paper we present the Multinomial Simulation Algorithm (MSA), which is designed to, on the one hand, outperform the ISSA when diffusive transfer events outnumber reaction events, and on the other, to handle small reactant populations with greater accuracy than deterministic-stochastic hybrid algorithms. The MSA treats reactions in the usual ISSA fashion, but uses appropriately conditioned binomial random variables for representing the net numbers of molecules diffusing from any given subvolume to a neighbor within a prescribed distance. Simulation results illustrate the benefits of the algorithm. [ABSTRACT FROM AUTHOR]

In view of the wide success of molecular quasichemical theory of liquids, this paper develops the soft-cutoff version of that theory. This development allows molecular dynamics simulations to be used for the calculation of solvation free energy, whereas the hard-cutoff version of the theory needs Monte Carlo simulations. This development also shows how fluids composed of molecules with smooth repulsive interactions can be treated analogously to the molecular-field theory of the hard-sphere fluid. In the treatment of liquid water, quasichemical theory with soft-cutoff conditioning does not change the fundamental convergence characteristics of the theory using hard-cutoff conditioning. In fact, hard cutoffs are found here to work better than softer ones in that case. [ABSTRACT FROM AUTHOR]

In this paper, we construct an effective model for the dynamics of an excluded-volume chain under confinement by extending the formalism of Rouse modes. We make specific predictions about the behavior of the modes for a single polymer confined to a tube. The results are tested against Monte Carlo simulations using the bond-fluctuation algorithm which uses a lattice representation of the polymer chain with excluded-volume effects. [ABSTRACT FROM AUTHOR]

This paper describes the application of a relatively simple, but computationally tractable, “particle-on-a-sphere” (POS) model for quantum-mechanical calculation of large-amplitude, H atom dynamics in polyatomic hydrides (XHn), based on radially relaxed, two-dimensional angular motion of H atoms on the surface of a sphere. This work focuses on systems with many degrees of freedom, i.e., XH4 (eight dimensional) and XH5 (ten dimensional), with corresponding molecular analogs of CH4 and CH5+ and is applicable to rovibrationally excited states with J>=0. A pairwise-additive potential fit for CH5+, which yields remarkable agreement with geometries, energies, and barrier heights on the full-dimensional surface of Brown et al. [J. Chem. Phys. 121, 4105 (2004)] is presented. Comparisons with experimental data and diffusion quantum Monte Carlo (DMC) methods test convergence for the POS model and provide insight into multidimensional quantum rovibrational dynamics. In particular, POS energy-level patterns for a series of scaled CH5+ potentials indicate an absence of strong tunneling behavior, consistent with the highly delocalized wave functions, large zero-point energies, and small interconversion barriers noted in previous DMC studies of Brown et al. [ABSTRACT FROM AUTHOR]

Large scale molecular dynamics and grand canonical Monte Carlo simulation techniques are used to study the behavior of the interdiffusion of a solvent into an entangled polymer matrix as the state of the polymer changes from a melt to a glass. The weight gain by the polymer increases with time t as t1/2 in agreement with Fickian diffusion for all cases studied, although the diffusivity is found to be strongly concentration dependent especially as one approaches the glass transition temperature of the polymer. The diffusivity as a function of solvent concentration determined using the one-dimensional Fick’s model of the diffusion equation is compared to the diffusivity calculated using the Darken equation from simulations of equilibrated solvent-polymer solutions. The diffusivity calculated using these two different approaches are in good agreement. The behavior of the diffusivity strongly depends on the state of the polymer and is related to the shape of the solvent concentration profile.© 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]

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]

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]

This paper describes novel numerical methods for constructing reaction paths and evaluating transition state theory (TST) rate constants for multidimensional, multistate systems. The reaction path is represented as a tethered, freely jointed chain of states with configuration specified by minimization of a function that is derived from the differential description of the path. The method is general and applicable to systems of arbitrary dimension and does not require a priori knowledge of the first-order saddle point, or the topology of the states. Also presented is a novel procedure for numerical determination of the TST rate constant. The procedure is based on Monte Carlo importance sampling using a tethered chain with links modeled as harmonic springs. The beads of the chain and the points at which links pierce the dividing surface separating states serve as biased sampling points for Monte Carlo numerical integration. The methods presented here are tested using the Muller potential surface. The application to problems involving transitions between clusters of states, i.e., macrostates, is discussed. [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]

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]

Variational autoencoders (VAEs) are rapidly gaining popularity within molecular simulation for discovering low-dimensional, or latent, representations, which are critical for both analyzing and accelerating simulations. However, it remains unclear how the information a VAE learns is connected to its probabilistic structure and, in turn, its loss function. Previous studies have focused on feature engineering, ad hoc modifications to loss functions, or adjustment of the prior to enforce desirable latent space properties. By applying effectively arbitrarily flexible priors via normalizing flows, we focus instead on how adjusting the structure of the decoding model impacts the learned latent coordinate. We systematically adjust the power and flexibility of the decoding distribution, observing that this has a significant impact on the structure of the latent space as measured by a suite of metrics developed in this work. By also varying weights on separate terms within each VAE loss function, we show that the level of detail encoded can be further tuned. This provides practical guidance for utilizing VAEs to extract varying resolutions of low-dimensional information from molecular dynamics and Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

Molecular dynamics computer simulations of a polydisperse soft-sphere model under shear are presented. The starting point for these simulations are deeply supercooled samples far below the critical temperature, Tc, of mode coupling theory. These samples are fully equilibrated with the aid of the swap Monte Carlo technique. For states below Tc, we identify a lifetime τlt that measures the time scale on which the system can be considered as an amorphous solid. The temperature dependence of τlt can be well described by an Arrhenius law. The existence of transient amorphous solid states below Tc is associated with the possibility of brittle yielding, as manifested by a sharp stress drop in the stress–strain relation and shear banding. We show that brittle yielding requires, on the one hand, low shear rates and, on the other hand, the time scale corresponding to the inverse shear rate has to be smaller or of the order of τlt. Both conditions can only be met for a large lifetime τlt, i.e., for states far below Tc. [ABSTRACT FROM AUTHOR]

In spite of the increasing interest in and application of ultrathin film oxides in commercial devices, the understanding of the mechanisms that control the growth of these films at the atomic scale remains limited and scarce. This limited understanding prevents the rational design of novel solutions based on precise control of the structure and properties of ultrathin films. Such a limited understanding stems in no minor part from the fact that most of the available modeling methods are unable to access and robustly sample the nanosecond to second timescales required to simulate both atomic deposition and surface reorganization at ultrathin films. To contribute to this knowledge gap, here we have combined molecular dynamics and adaptive kinetic Monte Carlo simulations to study the deposition and growth of oxide materials over an extended timescale of up to ∼0.5 ms. In our pilot studies, we have examined the growth of binary oxide thin films on oxide substrates. We have investigated three scenarios: (i) the lattice parameter of both the substrate and thin film are identical, (ii) the lattice parameter of the thin film is smaller than the substrate, and (iii) the lattice parameter is greater than the substrate. Our calculations allow for the diffusion of ions between deposition events and the identification of growth mechanisms in oxide thin films. We make a detailed comparison with previous calculations. Our results are in good agreement with the available experimental results and demonstrate important limitations in former calculations, which fail to sample phase space correctly at the temperatures of interest (typically 300–1000 K) with self-evident limitations for the representative modeling of thin films growth. We believe that the present pilot study and proposed combined methodology open up for extended computational support in the understanding and design of ultrathin film growth conditions tailored to specific applications. [ABSTRACT FROM AUTHOR]

Moreover, they illustrate the wide range of available tools, including crystal structure prediction (CSP) methods,[[11]] high-throughput calculations,[[13]] and machine learning (ML),[[15], [17]] and the role that databases, such as AFLOW,[19] Materials Project,[20] the Open Quantum Materials Database,[21] the Computational Materials Repository,[22] and the International Crystallographic Structure Database,[23] among many others, play in materials discovery. Tremendous advances in first-principles program packages, spectacular speed-ups in computer hardware coupled with significant algorithmic developments in crystal structure prediction, high-throughput screenings, data-mining, machine learning (ML), and artificial intelligence have made the dream of computational materials discovery a reality.[1] Recent success stories of materials that were first predicted and later verified experimentally include high-temperature superconductors,[[2], [4]] high-entropy high-hardness materials,[5] Heusler intermetallics for thermoelectrics and spintronics,[6] organic light-emitting diodes,[7] Li battery cathode materials,[8] porous materials for gas storage,[9] and carbon-boron clathrates.[10] The broad range of materials-by-design success stories with applications, including energy, quantum, structural, 2D materials, molecular crystals, molecular organic frameworks, and so on, have inspired us to devote this issue of JCP toward recent advances in this field. Parsaeifard I et al. i present a method to calculate fingerprint vectors from fingerprint distances, which measure the similarity of two structures.[27] This method is shown to automatically detect grain boundaries and the edges of carbon flakes without human input. [Extracted from the article]

We present a new and improved method for simultaneous control of temperature and pressure in molecular dynamics simulations with periodic boundary conditions. The thermostat-barostat equations are built on our previously developed stochastic thermostat, which has been shown to provide correct statistical configurational sampling for any time step that yields stable trajectories. Here, we extend the method and develop a set of discrete-time equations of motion for both particle dynamics and system volume in order to seek pressure control that is insensitive to the choice of the numerical time step. The resulting method is simple, practical, and efficient. The method is demonstrated through direct numerical simulations of two characteristic model systems--a one-dimensional particle chain for which exact statistical results can be obtained and used as benchmarks, and a three-dimensional system of Lennard-Jones interacting particles simulated in both solid and liquid phases. The results, which are compared against the method of Kolb and Dünweg [J. Chem. Phys. 111, 4453 (1999)], show that the new method behaves according to the objective, namely that acquired statistical averages and fluctuations of configurational measures are accurate and robust against the chosen time step applied to the simulation. [ABSTRACT FROM AUTHOR]

Semicrystalline polymers are ubiquitous, yet despite their fundamental and industrial importance, the theory of homogeneous nucleation from a melt remains a subject of debate. A key component of the controversy is that polymer crystallization is a non-equilibrium process, making it difficult to distinguish between effects that are purely kinetic and those that arise from the underlying thermodynamics. Due to computational cost constraints, simulations of polymer crystallization typically employ non-equilibrium molecular dynamics techniques with large degrees of undercooling that further exacerbate the coupling between thermodynamics and kinetics. In a departure from this approach, in this study, we isolate the near-equilibrium nucleation behavior of a simple model of a melt of short, semiflexible oligomers. We employ several Monte Carlo methods and compute a phase diagram in the temperature–density plane along with two-dimensional free energy landscapes (FELs) that characterize the nucleation behavior. The phase diagram shows the existence of ordered nematic and crystalline phases in addition to the disordered melt phase. The minimum free energy path in the FEL for the melt–crystal transition shows a cooperative transition, where nematic order and monomer positional order move in tandem as the system crystallizes. This near-equilibrium phase transition mechanism broadly agrees with recent evidence that polymer stiffness plays an important role in crystallization but differs in the specifics of the mechanism from several recent theories. We conclude that the computation of multidimensional FELs for models that are larger and more fine-grained will be important for evaluating and refining theories of homogeneous nucleation for polymer crystallization. [ABSTRACT FROM AUTHOR]

This paper presents a general coarse-grained molecular mechanics model based on electric point multipole expansion and Gay-Berne [J. Chem. Phys. 74, 3316 (1981)] potential. Coarse graining of van der Waals potential is achieved by treating molecules as soft uniaxial ellipsoids interacting via a generalized anisotropic Gay-Berne function. The charge distribution is represented by point multipole expansion, including point charge, dipole, and quadrupole moments placed at the center of mass. The Gay-Berne and point multipole potentials are combined in the local reference frame defined by the inertial frame of the all-atom counterpart. The coarse-grained model has been applied to rigid-body molecular dynamics simulations of molecular liquids including benzene and methanol. The computational efficiency is improved by several orders of magnitude, while the results are in reasonable agreement with all-atom models and experimental data. We also discuss the implications of using point multipole for polar molecules capable of hydrogen bonding and the applicability of this model to a broad range of molecular systems including highly charged biopolymers. [ABSTRACT FROM AUTHOR]

Hypothetical scanning (HS) is a method for calculating the absolute entropy S and free energy F from a sample generated by any simulation technique. With this approach each sample configuration is reconstructed with the help of transition probabilities (TPs) and their product leads to the configuration’s probability, hence to the entropy. Recently a new way for calculating the TPs by Monte Carlo (MC) simulations has been suggested, where all system interactions are taken into account. Therefore, this method—called HSMC—is in principle exact where the only approximation is due to insufficient sampling. HSMC has been applied very successfully to liquid argon, TIP3P water, self-avoiding walks on a lattice, and peptides. Because molecular dynamics (MD) is considered to be significantly more efficient than MC for a compact polymer chain, in this paper HSMC is extended to MD simulations as applied to peptides. Like before, we study decaglycine in vacuum but for the first time also a peptide with side chains, (Val)2(Gly)6(Val)2. The transition from MC to MD requires implementing essential changes in the reconstruction process of HSMD. Results are calculated for three microstates, helix, extended, and hairpin. HSMD leads to very stable differences in entropy TΔS between these microstates with small errors of 0.1–0.2 kcal/mol (T=100 K) for a wide range of calculation parameters with extremely high efficiency. Various aspects of HSMD and plans for future work are discussed. [ABSTRACT FROM AUTHOR]

The hypothetical scanning (HS) method is a general approach for calculating the absolute entropy, S, and free energy, F, by analyzing Boltzmann samples obtained by Monte Carlo (MC) or molecular dynamics (MD) techniques. With HS applied to a fluid, each configuration i of the sample is reconstructed by gradually placing the molecules in their positions at i using transition probabilities (TPs). With our recent version of HS, called HSMC-EV, each TP is calculated from MC simulations, where the simulated particles are excluded from the volume reconstructed in previous steps. In this paper we remove the excluded volume (EV) restriction, replacing it by a “free volume” (FV) approach. For liquid argon, HSMC-FV leads to an improvement in efficiency over HSMC-EV by a factor of 2–3. Importantly, the FV treatment greatly simplifies the HS implementation for liquids, allowing a much more natural application of the method for MD simulations. Given the success and popularity of MD, the present development of the HSMD method for liquids is an important advancement for HS methodology. Results for the HSMD-FV approach presented here agree well with our HSMC and thermodynamic integration results. The efficiency of HSMD-FV is equivalent to HSMC-EV. The potential use of HSMC(MD)-FV in protein systems with explicit water is discussed. [ABSTRACT FROM AUTHOR]

The calculation of thermodynamic state variables, particularly derivatives of the pressure with respect to density and temperature, in conventional molecular-dynamics simulations is considered in the frame of the comprehensive treatment of the molecular-dynamics ensemble by Lustig [J. Chem. Phys. 100, 3048 (1994)]. This paper improves the work of Lustig in two aspects. In the first place, a general expression for the basic phase-space functions in the molecular-dynamics ensemble is derived, which takes into account that a mechanical quantity G is, in addition to the number of particles, the volume, the energy, and the total momentum of the system, a constant of motion. G is related to the initial position of the center of mass of the system. Secondly, the correct general expression for volume derivatives of the potential energy is derived. This latter result solves a problem reported by Lustig [J. Chem. Phys. 109, 8816 (1998)] and Meier [Computer Simulation and Interpretation of the Transport Coefficients of the Lennard-Jones Model Fluid (Shaker, Aachen, 2002)] and enables the correct calculation of the isentropic and isothermal compressibilities, the speed of sound, and, in principle, all higher pressure derivatives. The derived equations are verified by calculations of several state variables and pressure derivatives up to second order by molecular-dynamics simulations with 256 particles at two state points of the Lennard-Jones fluid in the gas and liquid regions. It is also found that it is impossible for systems of this size to calculate third- and higher-order pressure derivatives due to the limited accuracy of the algorithm employed to integrate the equations of motion. [ABSTRACT FROM AUTHOR]

Two microscopic transition theorems are given for the probability of nonequilibrium work performed on a subsystem of a thermal reservoir along the trajectory in phase space of the subsystem. The resultant transition probability is applied to the case of heat flow down an applied temperature gradient. A combined molecular dynamics and Monte Carlo algorithm is given for such a nonequilibrium steady state. Results obtained for the thermal conductivity are in good agreement with previous Green-Kubo and nonequilibrium molecular dynamics results. [ABSTRACT FROM AUTHOR]

Numerical algorithms are developed for the centroid molecular dynamics (centroid MD) method to calculate dynamical time correlation functions for general many-body quantum systems. Approaches based on the normal mode path integral molecular dynamics and staging path integral Monte Carlo methods are described to carry out a direct calculation of the force on the centroid variables in the centroid MD algorithm. A more efficient, but approximate, scheme to compute the centroid force is devised which is based on the locally optimized harmonic approximation for the centroid potential. The centroid MD equations in the latter method can be solved with the help of an iterative procedure or through extended Lagrangian dynamics. A third algorithm introduces an effective centroid pseudopotential to approximate the full many-body centroid mean force potential by effective pairwise centroid interactions. Numerical simulations for both prototype models and more realistic many-body systems are performed to explore the feasibility and limitations of each algorithm. [ABSTRACT FROM AUTHOR]

The quantizer problem is a tessellation optimization problem where point configurations are identified such that the Voronoi cells minimize the second moment of the volume distribution. While the ground state (optimal state) in 3D is almost certainly the body-centered cubic lattice, disordered and effectively hyperuniform states with energies very close to the ground state exist that result as stable states in an evolution through the geometric Lloyd's algorithm [M. A. Klatt et al. Nat. Commun. 10, 811 (2019)]. When considered as a statistical mechanics problem at finite temperature, the same system has been termed the "Voronoi liquid" by Ruscher, Baschnagel, and Farago [Europhys. Lett. 112, 66003 (2015)]. Here, we investigate the cooling behavior of the Voronoi liquid with a particular view to the stability of the effectively hyperuniform disordered state. As a confirmation of the results by Ruscher et al., we observe, by both molecular dynamics and Monte Carlo simulations, that upon slow quasi-static equilibrium cooling, the Voronoi liquid crystallizes from a disordered configuration into the body-centered cubic configuration. By contrast, upon sufficiently fast non-equilibrium cooling (and not just in the limit of a maximally fast quench), the Voronoi liquid adopts similar states as the effectively hyperuniform inherent structures identified by Klatt et al. and prevents the ordering transition into a body-centered cubic ordered structure. This result is in line with the geometric intuition that the geometric Lloyd's algorithm corresponds to a type of fast quench. [ABSTRACT FROM AUTHOR]

We present in detail and validate an effective Monte Carlo approach for the calculation of the nuclear vibrational densities via integration of molecular eigenfunctions that we have preliminary employed to calculate the densities of the ground and the excited OH stretch vibrational states in the protonated glycine molecule [Aieta et al., Nat Commun 11, 4348 (2020)]. Here, we first validate and discuss in detail the features of the method on a benchmark water molecule. Then, we apply it to calculate on-the-fly the ab initio anharmonic nuclear densities in the correspondence of the fundamental transitions of NH and CH stretches in protonated glycine. We show how we can gain both qualitative and quantitative physical insight by inspection of different one-nucleus densities and assign a character to spectroscopic absorption peaks using the expansion of vibrational states in terms of harmonic basis functions. The visualization of the nuclear vibrations in a purely quantum picture allows us to observe and quantify the effects of anharmonicity on the molecular structure, also to exploit the effect of IR excitations on specific bonds or functional groups, beyond the harmonic approximation. We also calculate the quantum probability distribution of bond lengths, angles, and dihedrals of the molecule. Notably, we observe how in the case of one type of fundamental NH stretching, the typical harmonic nodal pattern is absent in the anharmonic distribution. [ABSTRACT FROM AUTHOR]

We study nonideal mixing effects in the regime of warm dense matter (WDM) by computing the shock Hugoniot curves of BN, MgO, and MgSiO3. First, we derive these curves from the equations of state (EOS) of the fully interacting systems, which were obtained using a combination of path integral Monte Carlo calculations at high temperature and density functional molecular dynamics simulations at lower temperatures. We then use the ideal mixing approximation at constant pressure and temperature to rederive these Hugoniot curves from the EOS tables of the individual elements. We find that the linear mixing approximation works remarkably well at temperatures above ∼2 × 105 K, where the shock compression ratio exceeds ∼3.2. The shape of the Hugoniot curve of each compound is well reproduced. Regions of increased shock compression, which emerge because of the ionization of L and K shell electrons, are well represented, and the maximum compression ratio of the Hugoniot curves is reproduced with high precision. Some deviations are seen near the onset of the L shell ionization regime, where ionization equilibrium in the fully interacting system cannot be well reproduced by the ideal mixing approximation. This approximation also breaks down at lower temperatures, where chemical bonds play an increasingly important role. However, the results imply that the equilibrium properties of binary and ternary mixtures in the regime of WDM can be derived from the EOS tables of the individual elements. This significantly simplifies the characterization of binary and ternary mixtures in the WDM and plasma phases, which otherwise requires large numbers of more computationally expensive first-principles computer simulations. [ABSTRACT FROM AUTHOR]

The seventh and eighth virial coefficients for hard hyperspheres are calculated by Monte Carlo techniques. It is found that B7/B26=0.001 43±0.000 13 and 0.000 44±0.000 12 in four and five dimensions, respectively, and that B8/B27=0.000 414±0.000 20 in four dimensions. These values are used to investigate various proposed equations of state. Comparisons against the molecular dynamics calculations of Luban and Michels [M. Luban and J. P. J. Michels, Phys. Rev. A 41, 6796 (1990)] show that their proposed semiempirical form is excellent at higher densities. Moreover, we confirm Santos [A. Santos, J. Chem. Phys. 112, 10680 (2000)] observation in five dimensions that a suitable linear combination of the Percus–Yevick compressibility and virial equations of state fits the molecular dynamics data nearly as well as any other proposed form. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We introduce a mean-field theoretical framework for generalizing isotropic pair potentials to anisotropic shapes. This method is suitable for generating pair potentials that can be used in both Monte Carlo and molecular dynamics simulations. We demonstrate the application of this theory by deriving a Lennard-Jones (LJ)-like potential for arbitrary geometries along with a Weeks–Chandler–Anderson-like repulsive variant, showing that the resulting potentials behave very similarly to standard LJ potentials while also providing a nearly conformal mapping of the underlying shape. We then describe an implementation of this potential in the simulation engine HOOMD-blue and discuss the challenges that must be overcome to achieve a sufficiently robust and performant implementation. The resulting potential can be applied to smooth geometries like ellipsoids and to convex polytopes. We contextualize these applications with reference to the existing methods for simulating such particles. The pair potential is validated using standard criteria, and its performance is compared to existing methods for comparable simulations. Finally, we show the results of self-assembly simulations, demonstrating that this method can be used to study the assembly of anisotropic particles into crystal structures. [ABSTRACT FROM AUTHOR]