Melting line of the Lennard-Jones system, infinite size, and full potential

Literature estimates of the melting curve of the Lennard-Jones system vary by as much as 10%. The origin of such discrepancies remains unclear. We present precise values for the Lennard-Jones melting temperature, and we examine possible sources of systematic errors in the prediction of melting points, including finite-size and interaction-cutoff effects. A hypothetical thermodynamic integration path is used to find the relative free energies of the solid and liquid phases, for various system sizes, at constant cutoff radius. The solid-liquid relative free energy and melting temperature scale linearly as the inverse of the number of particles, and it is shown that finite-size effects can account for deviations in the melting temperature (from the infinite-size limit) of up to 5%. An extended-ensemble density-of-states method is used to determine free energy changes for each phase as a continuous function of the cutoff radius. The resulting melting temperature predictions exhibit an oscillatory behavior as the cutoff radius is increased. Deviations in the melting temperature (from the full potential limit) arising from a finite cutoff radius are shown to be of comparable magnitude as those resulting from finite-size effects. This method is used to identify melting temperatures at five different pressures, for the infinite-size and full potential Lennard-Jones system. We use our simulation results as references to connect the Lennard-Jones solid equation of state of van der Hoef with the Lennard-Jones fluid equation of state of Johnson. Once the references are applied the two equations of state are used to identify a melting curve. An empirical equation that fits this melting curve is provided. We also report a reduced triple point temperature T(tr)=0.694.     

Free energy calculations for a flexible water model

In this work, we consider the problem of calculating the classical free energies of liquids and solids for molecular models with intramolecular flexibility. We show that thermodynamic integration from the fully-interacting solid of interest to a Debye crystal reference state, with anisotropic harmonic interactions derived from the Hessian of the original crystal, provides a straightforward route to calculating the Gibbs free energy of the solid. To calculate the molecular liquid free energy, it is essential to correctly account for contributions from both intermolecular and intramolecular motion; we employ thermodynamic integration to a Lennard-Jones reference fluid, coupled with direct evaluation of the molecular ro-vibrational partition function. These approaches are used to study the low-pressure classical phase diagram of the flexible q-TIP4P/F water model. We find that, while the experimental ice-I/liquid and ice-III/liquid coexistence lines are described reasonably well by this model, the ice-II phase is predicted to be metastable. In light of this finding, we go on to examine how the coupling between intramolecular flexibility and intermolecular interactions influences the computed phase diagram by comparing our results with those of the underlying rigid-body water model.     

Energy landscapes of quantum Lennard-Jones solids

To generalize inherent structure analysis to understand structural changes in quantum liquids and solids, differences between classical (V(x)) and quantum-corrected (U(qeff)(x)) energy landscapes are estimated as a function of the de Boer parameter (Λ). Path integral simulations of quantum Lennard-Jones solids are performed at zero pressure and a dimensionless reduced temperature of 0.123, corresponding to an absolute temperature of 4.2K. At constant temperature and pressure, Λ is increased from the classical limit of zero to Λ = 0.28, corresponding to para-H(2). Increasing quantum delocalization effects result in a continuous decrease in density and local order but without a transition to a disordered, liquid state. The inherent structure landscape of bulk systems is strongly dependent on density with the energy and stability of crystalline minima decreasing relative to that of amorphous packing minima as the system is stretched. For Λ ≈ 0.23, the volume fluctuations in quantum solids are sufficient to result in sampling of disordered minima while for Λ = 0.28, the underlying classical inherent structures are completely disordered, indicating that the topography of U(qeff)(x) and V(x) are qualitatively different for such values of Λ. To assess the nature of the quantum-corrected energy landscape, effective pair potentials are defined by u(qeff)(r) = -kT ln g(r) using the pair correlation function (g(r)) of the quantum system in the neighborhood of the first peak. Our results show that as Λ increases, the pair potentials become increasingly softer, shallower, and of increasing range with a shifting of the potential minimum to larger distances. For example, the reduction of the entropy of fusion and melting temperatures of quantum solids with increasing Λ are analogous to the changes in thermodynamics of melting seen in classical solids with increasing range and softness of interactions. The energy landscapes associated with such coarse-grained potentials should be useful as predictors of structural transformations in quantum systems, analogous to their use in understanding phase diagrams of complex fluids.     

Quantum path integral simulation of isotope effects in the melting temperature of ice Ih

The isotope effect in the melting temperature of ice Ih has been studied by free energy calculations within the path integral formulation of statistical mechanics. Free energy differences between isotopes are related to the dependence of their kinetic energy on the isotope mass. The water simulations were performed by using the q-TIP4P/F model, a point charge empirical potential that includes molecular flexibility and anharmonicity in the OH stretch of the water molecule. The reported melting temperature at ambient pressure of this model (T=251?K) increases by 6.5±0.5 and 8.2±0.5?K upon isotopic substitution of hydrogen by deuterium and tritium, respectively. These temperature shifts are larger than the experimental ones (3.8 and 4.5 K, respectively). In the classical limit, the melting temperature is nearly the same as that for tritiated ice. This unexpected behavior is rationalized by the coupling between intermolecular interactions and molecular flexibility. This coupling makes the kinetic energy of the OH stretching modes larger in the liquid than in the solid phase. However, the opposite behavior is found for intramolecular modes, which display larger kinetic energy in ice than in liquid water.     

Atomistic simulation of solid-liquid coexistence for molecular systems: application to triazole and benzene

A method recently developed to rigorously determine solid-liquid equilibrium using a free-energy-based analysis has been extended to analyze multiatom molecular systems. This method is based on using a pseudosupercritical transformation path to reversibly transform between solid and liquid phases. Integration along this path yields the free energy difference at a single state point, which can then be used to determine the free energy difference as a function of temperature and therefore locate the coexistence temperature at a fixed pressure. The primary extension reported here is the introduction of an external potential field capable of inducing center of mass order along with secondary orientational order for molecules. The method is used to calculate the melting point of 1-H-1,2,4-triazole and benzene. Despite the fact that the triazole model gives accurate bulk densities for the liquid and crystal phases, it is found to do a poor job of reproducing the experimental crystal structure and heat of fusion. Consequently, it yields a melting point that is 100 K lower than the experimental value. On the other hand, the benzene model has been parametrized extensively to match a wide range of properties and yields a melting point that is only 20 K lower than the experimental value. Previous work in which a simple "direct heating" method was used actually found that the melting point of the benzene model was 50 K higher than the experimental value. This demonstrates the importance of using proper free energy methods to compute phase behavior. It also shows that the melting point is a very sensitive measure of force field quality that should be considered in parametrization efforts. The method described here provides a relatively simple approach for computing melting points of molecular systems.     

Constrained fluid lambda-integration: constructing a reversible thermodynamic path between the solid and liquid state

A novel lambda-integration path is proposed for calculating the Gibbs free energy difference between any arbitrary solid and liquid state needed for the location of melting lines. This technique involves reversibly forcing a liquid state to a solid state across the phase transition along a nonphysical path, thermodynamically coupling the two states directly. The process eliminates the need for coupling to idealized reference states as is presently performed and hence simplifies the location of phase transitions for computer simulation systems. More specifically the path involves a three stage process, whereby, initially a liquid state is transformed to a weakly attractive fluid using linear lambda-integration scaling of the intermolecular potential. In the second stage, the resulting fluid is then constrained to the required solid configurational phase space via the insertion of a periodic lattice of 3D Gaussian wells. The final stage involves reversing to full strength the main intermolecular potential while gradually turning off the constraining 3D Gaussian lattice finally resulting in a stable (or metastable) solid state. Each stage was found to be completely reversible and the resulting change in free energy was thermodynamically integrable. The methodology is demonstrated and validated by calculating solid-liquid coexistence points using the new technique and comparing to those in present literature for the truncated and shifted Lennard-Jones system. The results are found to be in good agreement. The new method is not limited to melting phase transitions and is readily applicable to any simulation methodology, simulation cell size and/or intermolecular potential including ab initio methods.     

System-size dependence of the free energy of crystalline solids

We investigate the system-size dependence of the Helmholtz free energy of crystalline solids from computer simulation. We employ a standard thermodynamic integration technique along a reversible path that links the crystalline solid with a noninteracting Einstein crystal with the same structure. The key contribution to the free energy is computed by using the so-called expanded-ensemble technique and the results are compared with those obtained from conventional integration of the derivative of the free energy along the path using Gaussian-Legendre quadrature. We find that both methods yield fully consistent results. The free energy is found to exhibit a strong dependence with system size, in agreement with the behavior found by Polson et al. [J. Chem. Phys. 112, 5339 (2000)] but at variance with the dependence reported more recently by Chang and Sandler [J. Chem. Phys. 118, 8390 (2003)]. This has been tested for the face-centered cubic (fcc) and hexagonal close-packed phases of a crystal of hard spheres at a density close to the melting point. We also investigate any possible dependence of the free energy of the solid phase with the shape of the simulation box. We find that this contribution may not be as important as previous investigations suggest. The present results seem to indicate that there is a non-negligible contribution to the free energy arising from the orientation of the closed-packed crystal layers with respect to the simulation cell. This contribution is particularly noticeable for small system sizes and is believed to be an effect of the periodic boundary conditions used in the simulations. The results presented here corroborate the stability of the fcc phase of the hard-sphere solid close to melting.     

Phase diagram of Gaussian-core nematics

The authors study a simple model of a nematic liquid crystal made of parallel ellipsoidal particles interacting via a repulsive Gaussian law. After identifying the relevant solid phases of the system through a careful zero-temperature scrutiny of as many as eleven candidate crystal structures, they determine the melting temperature for various pressure values, also with the help of exact free energy calculations. Among the prominent features of this model are pressure-driven reentrant melting and the stabilization of a columnar phase for intermediate temperatures.     

Efficient calculation of temperature dependence of solid-phase free energies by overlap sampling coupled with harmonically targeted perturbation

We examine a method for computing the change in free energy with temperature of a crystalline solid. In the method, the free-energy difference between nearby temperatures is calculated via overlap-sampling free-energy perturbation with Bennett's optimization. Coupled to this is a harmonically targeted perturbation that displaces the atoms in a manner consistent with the temperature change, such that for a harmonic system, the free-energy difference would be recovered with no error. A series of such perturbations can be assembled to bridge larger gaps in temperature. We test this harmonically targeted temperature perturbation (HTTP) method through the application to the inverse-power soft potential, u(r)=ε(σ/r)(n), over a range of temperatures up to the melting condition. Three exponent values (n=12, 9, and 6) for the potential are studied with different crystal structures, specifically face-centered cubic (fcc), body-centered cubic (bcc), and hexagonal close packing. Absolute free energies (classical only) for each system are obtained by implementing the series to near-zero temperature, where the harmonic model becomes very accurate. The HTTP method is shown to provide very precise results, with errors in the free energy smaller than two parts in 10(5). An analysis of the thermodynamic stability of the various structures in the infinite-system limit confirms previous findings. In particular, for n=12 and 9, the fcc structure is stable for all temperatures up to melting, and for n=6, the bcc crystal becomes stable relative to fcc for temperatures above kT/ε=0.802±0.001. The effects of vacancies and other defects are not considered in the analysis.     

Quantum effects in ice Ih

Quantum and classical simulations are carried out on ice Ih over a range of temperatures utilizing the TIP4P water model. The rigid-body centroid molecular dynamics method employed allows for the investigation of equilibrium and dynamical properties of the quantum system. The impact of quantization on the local structure, as measured by the radial and spatial distribution functions, as well as the energy is presented. The effects of quantization on the lattice vibrations, associated with the molecular translations and librations, are also reported. Comparison of quantum and classical simulation results indicates that shifts in the average potential energy are equivalent to rising the temperature about 80 K and are therefore non-negligible. The energy shifts due to quantization and the quantum mechanical uncertainties observed in ice are smaller than the values previously reported for liquid water. Additionally, we carry out a comparative study of melting in our classical and quantum simulations and show that there are significant differences between classical and quantum ice.     

Nonequilibrium melting and crystallization of a model Lennard-Jones system

Nonequilibrium melting and crystallization of a model Lennard-Jones system were investigated with molecular dynamics simulations to quantify the maximum superheating/supercooling at fixed pressure, and over-pressurization/over-depressurization at fixed temperature. The temperature and pressure hystereses were found to be equivalent with regard to the Gibbs free energy barrier for nucleation of liquid or solid. These results place upper bounds on hysteretic effects of solidification and melting in high heating- and strain-rate experiments such as shock wave loading and release. The authors also demonstrate that the equilibrium melting temperature at a given pressure can be obtained directly from temperatures at the maximum superheating and supercooling on the temperature hysteresis; this approach, called the hysteresis method, is a conceptually simple and computationally inexpensive alternative to solid-liquid coexistence simulation and thermodynamic integration methods, and should be regarded as a general method. We also found that the extent of maximum superheating/supercooling is weakly pressure dependent, and the solid-liquid interfacial energy increases with pressure. The Lindemann fractional root-mean-squared displacement of solid and liquid at equilibrium and extreme metastable states is quantified, and is predicted to remain constant (0.14) at high pressures for solid at the equilibrium melting temperature.     

The significant structure theory applied to halobenzenes

Abstract

Just as molecular structure, as revealed by X-ray diffraction, can be interpreted in terms of intuitive models, so liquid structure can be interpreted in terms of a model which leads to a partition function giving the Helmholtz free energy in terms of volume, temperature, and composition. From this explicit expression for the Helmholtz free energy all thermodynamic properties are calculable and can be compared with experiment. Absolute Rate Theory permits the prediction of transport properties from this same model, providing still further insight into liquid structure. Here, Significant Liquid Structure Theory has been applied to twelve substituted benzenes and the results compared with experiment. A single equation is derived for the twelve substances differing in ten of the cases only in three parameters having to do with the solid-like part of the liquid. For simple liquids these properties are those of the solid at the melting point. These properties are the energy of sublimation, molar volume of the solid, and the Einstein characteristic temperature, θ. Hindered rotation is explained in terms of a barrier to rotation of one tenth the energy of sublimation     

Computational study of the melting-freezing transition in the quantum hard-sphere system for intermediate densities. I. Thermodynamic results

The points where the fluid-solid (face-centered-cubic) transition takes place in the quantum hard-sphere system, for reduced densities 0.85>rhoN*>0.5 (reduced de Broglie wavelengths lambdaB*相似文献   

Quantum versus classical electron transfer energy as reaction coordinate for the aqueous Ru2+/Ru3+ redox reaction

Applying density functional theory (DFT)-based molecular dynamics simulation methods we investigate the effect of explicit treatment of electronic structure on the solvation free energy of aqueous Ru²⁺ and Ru³⁺.Our approach is based on the Marcus theory of redox half reactions, focussing on the vertical energy gap for reduction or oxidation of a single aqua ion. We compare the fluctuations of the quantum and classical energy gap along the same equilibrium ab initio molecular dynamics trajectory for each oxidation state. The classical gap is evaluated using a standard point charge model for the charge distribution of the solvent molecules (water). The quantum gap is computed from the full DFT electronic ground state energies of reduced and oxidized species, thereby accounting for the delocalization of the electron in the donor orbital and reorganization of the electron cloud after electron transfer (ET). The fluctuations of the quantum ET energy are well approximated by gaussian statistics giving rise to parabolic free energy profiles. The curvature is found to be independent of the oxidation state in agreement with the linear response assumption underlying Marcus theory. By contrast, the diabatic free energy curves evaluated using the classical gap as order parameter, while also quadratic, are asymmetric reflecting the difference in oxidation state. The response of these two order parameters is further analysed by a comparison of the spectral density of the fluctuations and the corresponding reorganization free energies.     

A method for computing the solubility limit of solids: application to sodium chloride in water and alcohols

We present an adaptable method to compute the solubility limit of solids by molecular simulation, which avoids the difficulty of reference state calculations. In this way, the method is highly adaptable to molecules of complex topology. Results are shown for solubility calculations of sodium chloride in water and light alcohols at atmospheric conditions. The pseudosupercritical path integration method is used to calculate the free energy of the solid and gives results that are in good agreement with previous studies that reference the Einstein crystal. For the solution phase calculations, the self-adaptive Wang-Landau transition-matrix Monte Carlo method is used within the context of an expanded isothermal-isobaric ensemble. The method shows rapid convergence properties and the uncertainty in the calculated chemical potential was 1% or less for all cases. The present study underpredicts the solubility limit of sodium chloride in water, suggesting a shortcoming of the molecular models. Importantly, the proper trend for the chemical potential in various solvents was captured, suggesting that relative solubilities can be computed by the method.     

Liquid-solid transition in fully ionized hydrogen at ultra-high pressures

We study the phase diagram of an effective ion model of fully ionized hydrogen at ultra-high pressure. We assume that the protons interact with a screened Coulomb potential derived from a static linear response theory. This model accurately reproduces the physical properties of hydrogen for densities greater than g/ρ(m)=10 cm(3) corresponding to the range of the coupling parameter r(s) ? 0.6. The pressure range, P ? 20 TPa, is well beyond present experimental limitations. Assuming classical protons, we find that the zero temperature enthalpy of the perfect bcc crystal is slightly lower than for other structures at g/ρ(m)=12.47 cm(3) while the fcc structure gains stability at higher density. Using Monte Carlo calculations, we compute the free energy of various phases and locate the melting transition versus density. We find that on melting, bcc is energetically favored with respect to fcc over the entire range investigated. In the solid phase the system undergoes a structural transition from bcc at higher temperature to fcc at lower temperature. The free energy difference between these two structures is very small so that obtaining a quantitative estimate of this second transition line requires accuracy beyond that provided by our method. We estimate the effect of proton zero point motion on the bcc melting line for hydrogen, deuterium, and tritium by a path integral Monte Carlo method. Although zero point effects on hydrogen are large, since the two competing phases (bcc and liquid) have locally similar environments, the effect on the melting line is small; the melting temperature for hydrogen is lowered by about 10% with respect to the classical value.     

Effect of the structural nonequilibrium of solid samples on the low temperature limit of the photochemical reaction rate

The results from two cryogenic experiments at helium temperatures are compared. Widely separated and adjacent aggregations formed by vapor deposition are considered. It is shown that upon the photochlorination of methane in a solid structural nonequilibrium mixture prepared from the gas phase at liquid helium temperatures, the quantum yield of chlorine consumption at the low temperature limit falls to zero while the effective activation energy in the Arrhenius region rises due to achieving a state of supersaturation with vacancies and a vibrational mode of sintering. It is demonstrated that upon the photobromination of ethylene under conditions of disequilibrium decay, accompanied by halogen-olefin self-organization of the condensate structure (complexation), the quantum yield of bromine consumption in the athermal region rises while the activation energy in the Arrhenius region falls.     

Nanosolids, slushes, and nanoliquids: characterization of nanophases in metal clusters and nanoparticles

One of the keys to understanding the emergent behavior of complex materials and nanoparticles is understanding their phases. Understanding the phases of nanomaterials involves new concepts not present in bulk materials; for example, the phases of nanoparticles are quantum mechanical even when no hydrogen or helium is present. To understand these phases better, molecular dynamics (MD) simulations on size-selected particles employing a realistic analytic many-body potential based on quantum mechanical nanoparticle calculations have been performed to study the temperature-dependent properties and melting transitions of free Al n clusters and nanoparticles with n = 10-300 from 200 to 1700 K. By analyzing properties of the particles such as specific heat capacity (c), radius of gyration, volume, coefficient of thermal expansion (beta), and isothermal compressibility (kappa), we developed operational definitions of the solid, slush, and liquid states of metal clusters and nanoparticles. Applying the definitions, which are based on the temperature dependences of c, beta, and ln kappa, we determined the temperature domains of the solid, slush, and liquid states of the Al n particles. The results show that Al n clusters ( n or= 19, diameter of more than 1 nm) do have a melting transition and are in the liquid state above 900-1000 K. However, all aluminum nanoparticles have a wide temperature interval corresponding to the slush state in which the solid and liquid states coexist in equilibrium, unlike a bulk material where coexistence occurs only at a single temperature (for a given pressure). The commonly accepted operational marker of the melting temperature, namely, the peak position of c, is not unambiguous and not appropriate for characterizing the melting transition for aluminum particles with the exception of a few particle sizes that have a single sharp peak (as a function of temperature) in each of the three properties, c, beta, and ln kappa.     

Quantum instanton evaluation of the thermal rate constants and kinetic isotope effects for SiH4+H-->SiH3+H2 reaction in full Cartesian space

The quantum instanton calculations of thermal rate constants for the gas-phase reaction SiH4+H-->SiH3+H2 and its deuterated analogs are presented, using an analytical potential energy surface. The quantum instanton approximation is manipulated by full dimensionality in Cartesian coordinate path integral Monte Carlo approach, thereby taking explicitly into account the effects of the whole rotation, the vibrotational coupling, and anharmonicity of the reaction system. The rates and kinetic isotope effects obtained for the temperature range of 200-1000 K show good agreements with available experimental data, which give support to the accuracy of the underlying potential surface used. In order to investigate the sole quantum effect to the rates, the authors also derive the classical limit of the quantum instanton and find that it can be exactly expressed as the classical variation transition state theory. Comparing the quantum quantities with their classical analogs in the quantum instanton formula, the authors demonstrate that the quantum correction of the prefactor is more important than that of the activation energy at the transition state.     

Quasi-harmonic approximation of thermodynamic properties of ice Ih, II, and III

Several thermodynamic properties of ice Ih, II, and III are studied by a quasi-harmonic approximation and compared to results of quantum path integral and classical simulations. This approximation allows to obtain thermodynamic information at a fraction of the computational cost of standard simulation methods, and at the same time permits studying quantum effects related to zero-point vibrations of the atoms. Specifically, we have studied the crystal volume, bulk modulus, kinetic energy, enthalpy, and heat capacity of the three ice phases as a function of temperature and pressure. The flexible q-TIP4P/F model of water was employed for this study, although the results concerning the capability of the quasi-harmonic approximation are expected to be valid independently of the employed water model. The quasi-harmonic approximation reproduces with reasonable accuracy the results of quantum and classical simulations showing an improved agreement at low temperatures (T< 100 K). This agreement does not deteriorate as a function of pressure as long as it is not too close to the limit of mechanical stability of the ice phases.