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.     

Toward a robust and general molecular simulation method for computing solid-liquid coexistence

A rigorous and generally applicable method for computing solid-liquid coexistence is presented. The method overcomes some of the technical difficulties associated with other solid-liquid simulation procedures and can be implemented within either a molecular dynamics or Monte Carlo framework. The method consists of three steps: First, relative Gibbs free energy curves are created for the solid and liquid phases using histogram reweighting. Next, the free energy difference between the solid and liquid phases is evaluated at a single state point by integrating along a pseudosupercritical transformation path that connects the two phases. Using this result, the solid and liquid free energy curves are referenced to a common point, allowing a single coexistence point to be determined. Finally, Gibbs-Duhem integration is used to determine the full coexistence curve. To evaluate its utility, this method is applied to the Lennard-Jones and NaCl systems. Results for solid-liquid coexistence agree with previous calculations for these systems. In addition, it is shown that the NaCl model does not correctly describe solid-liquid coexistence at high pressures. An analysis of the accuracy of the method indicates that the results are most sensitive to the transformation free energy calculation.     

Drops sitting on a tilted plate: receding and advancing pinning

The wetting behavior of a liquid drop sitting on an inclined plane is investigated experimentally and theoretically. Using Surface Evolver, the numerical simulations are performed based on the liquid-induced defect model, in which only two thermodynamic parameters (solid-liquid interfacial tensions before and after wetting) are required. A drop with contact angle (CA) equal to θ is first placed on a horizontal plate, and then the plate is tilted. Two cases are studied: (i) θ is adjusted to the advancing CA (θ(a)) before tilting, and (ii) θ is adjusted to the receding CA (θ(r)) before tilting. In the first case, the uphill CA declines and the downhill CA remains unchanged upon inclination. When the tilted drop stays at rest, the pinning of the receding part of the contact line (receding pinning) and the depinning of the advancing part of the contact line (advancing depinning) are observed. The free energy analysis reveals that upon inclination, the reduction of the solid-liquid free energy dominates over the increment of the liquid-gas free energy associated with shape deformation. In the second case, the downhill CA grows and the uphill CA remains the same upon inclination. Advancing pinning and receding depinning are noted for the tilted drop at rest. The free energy analysis indicates that upon inclination, the decrease of the liquid-gas free energy compensates the increment of the solid-liquid free energy. The experimental results are in good agreement with those of simulations.     

Cavitation and crystallization in a metastable Lennard-Jones liquid at negative pressures and low temperatures

Molecular dynamics simulations have been used to investigate the kinetics of spontaneous cavitation and crystallization in a Lennard-Jones liquid at negative pressures in the temperature range where these processes compete with each other. The nucleation rate has been calculated in NVE and NpT ensembles by the method of mean lifetime and the transition interface sampling method with parallel path swapping. The data obtained have been used to determine in the framework of classical nucleation theory the value of the ratio of the solid-liquid and the liquid-void interfacial free energy for critical crystals and cavities and the values of their volumes at points where the cavitation rate of the liquid is equal to the rate of its crystallization.     

Test of classical nucleation theory via molecular-dynamics simulation

A direct test of classical nucleation theory (CNT) is made using molecular-dynamics simulations. The relation between critical nucleus size and undercooling temperature is extracted and the result yields the solid-liquid interfacial energy. It is shown that the CNT, within the assumptions made for spherical nucleus in supercooled liquid, is valid in the critical regime of nucleation for a large range of undercooling and nucleus size.     

Rationalization of the behavior of solid-liquid surface free energy of water in Cassie and Wenzel wetting states on rugged solid surfaces at the nanometer scale

The present work aims to contribute to the understanding at a molecular level of the origin of the hydrophobic nature of surfaces exhibiting roughness at the nanometer scale. Graphite-based smooth and model surfaces whose roughness dimension stretches from a few angstroms to a few nanometers were used in order to generate Cassie and Wenzel wetting states of water. The corresponding solid-liquid surface free energies were computed by means of molecular dynamics simulations. The solid-liquid surface free energy of water-smooth graphite was found to be -12.7 ± 3.3 mJ/m(2), which is in reasonable agreement with a value estimated from experiments and fully consistent with the features of the employed model. All the rugged surfaces yielded higher surface free energy. In both Cassie and Wenzel states, the maximum variation of the surface free energy with respect to the smooth surface was observed to represent up to 50% of the water model surface tension. The solid-liquid surface free energy of Cassie states could be well predicted from the Cassie-Baxter equation where the surface free energies replace contact angles. The origin of the hydrophobic nature of surfaces yielding Cassie states was therefore found to be the reduction of the number of interactions between water and the solid surface where atomic defects were implemented. Wenzel's theory was found to fail to predict even qualitatively the variation of the solid-liquid surface free energy with respect to the roughness pattern. While graphite was found to be slightly hydrophilic, Wenzel states were found to be dominated by an unfavorable effect that overcame the favorable enthalpic effect induced by the implementation of roughness. From the quantitative point of view, the solid-liquid surface free energy of Wenzel states was found to vary linearly with the roughness contour length.     

Determination of the solid-fluid coexistence of the n - 6 Lennard-Jones system from free energy calculations

The solid-fluid coexistence properties of the n - 6 Lennard-Jones system, n from 7 to 12, are reported. The procedure relies on determining Helmholtz free energy curves as a function of volume for each phase independently, from several NVT simulations, and then connecting it to points of known absolute free energy. For n = 12 this requires connecting the simulated points to states of very low densities on the liquid phase, and to a harmonic crystal for the solid phase, which involves many extra simulations for each temperature. For the reference points of the remaining systems, however, the free energy at a given density and temperature can be calculated relative to the n = 12 system. The method presented here involves a generalization of the multiple histogram method to combine simulations performed with different potentials, provided they visit overlapping regions of the phase space, and allows for a precise calculation of relative free energies. The densities, free energies, average potential energies, pressure, and chemical potential at coexistence are presented for up to T? = 5.0 and new estimations of the triple points are given for the n - 6 Lennard-Jones system.     

Characterization of soil particle surfaces using adsorption excess isotherms

Measurement of adsorption excess isotherms of methanol-benzene mixtures was applied to the characterization of soil particle surfaces. The sorption capacity and Gibbs energy of sorption of the solid-liquid interface were determined for montmorillonite, three types of soil, and their humin fractions. The soils were found to be less polar or less hydrophilic than the clay, and the humin fraction of soils was found to be less hydrophilic than the whole soils. The soil and humin samples have heterogeneous surfaces which can be divided in two regions on the basis of their relative polarity. The x-axis intersection of the straight section of isotherm assigns the relative proportions of the hydrophilic and hydrophobic regions of the surface.     

氟化钾团簇的相变、成核和重结晶的分子动力学模拟

我们利用Born-Mayer-Huggins相互作用势函数对(KF)_N(N=108，256，500和864)团簇进行了分子动力学(MD)模拟。为了避免周期性边界条件对相变、成核和重结晶的干扰作用，对体系采用了自由边界。基于MD模拟结果，对团簇的熔化温度、熔化焓、扩散系数、成核速率、固液界面自由能、临界核大小等进行了计算和讨论。在对(KF)₈₆₄双晶团簇的热退火模拟中，观察到了固态的重结晶和晶粒的生长。经典的成核理论成功地解释了(KF)₈₆₄双晶团簇的重结晶MD模拟结果。     

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.     

Finite element interpolation for combined classical/quantum mechanical molecular dynamics simulations

A method is presented to interpolate the potential energy function for a part of a system consisting of a few degrees of freedom, such as a molecule in solution. The method is based on a modified finite element (FE) interpolation scheme. The aim is to save computer time when expensive methods such as quantum-chemical calculations are used to determine the potential energy function. The expensive calculations are only carried out if the molecule explores new unknown regions of the conformation space. If the molecule resides in regions previously explored, a cheap interpolation is performed instead of an expensive calculation, using known neighboring points. We report the interpolation techniques for the energies and the forces of the molecule, the handling of the FE mesh, and an application to a simple test example in molecular dynamics (MD) simulations. Good performance of the method was obtained (especially for MD simulations with a preceding Monte Carlo mesh generation) without losing accuracy. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1484–1495, 1997     

Simple fitting of energy-resolved reactive cross sections in threshold collision-induced dissociation (T-CID) experiments

An operationally much simpler method for the extraction of thermochemical data from energy-resolved collision-induced dissociation cross sections, which is specifically designed for ligand binding energy determinations by tandem mass spectrometry, is presented. Compared to previous methods available in the literature, the present method has three advantages: (i) A more realistic treatment of the electrostatic potential for the approach of the ion to the collision partner leads to a better, nonempirical threshold function, allowing fitting of the cross section over the entire energy range rather than just the onset. (ii) Treatment of the kinetic shift with a new model for the density-of-states function eliminates the need for explicit entry of frequencies for the starting ion or the transition state without loss of accuracy relative to direct state counts. (iii) Data fitting using Monte Carlo simulation and a genetic algorithm instead of the usual Marquardt-Levenburg least-squares routines not only produces an equivalent fit but also produces statistically relevant error bounds on the derived fit parameters. Although the method is conceived for medium-to-large organometallic complexes, the theory is general enough to be appropriate for a wide range of binding phenomena of a small molecule to a larger one observed in mass spectrometry.     

Homogeneous nucleation and growth of melt in copper

Molecular dynamics simulations are conducted to investigate homogeneous nucleation and growth of melt in copper described by an embedded-atom method (EAM) potential. The accuracy of this EAM potential for melting is validated by the equilibrium melting point obtained with the solid-liquid coexistence method and the superheating-supercooling hysteresis method. We characterize the atomistic melting process by following the temperature and time evolution of liquid atoms. The nucleation behavior at the extreme superheating is analyzed with the mean-first-passage-time (MFPT) method, which yields the critical size, steady-state nucleation rate, and the Zeldovich factor. The value of the steady-state nucleation rate obtained from the MFPT method is consistent with the result from direct simulations. The size distribution of subcritical nuclei appears to follow a power law similar to three-dimensional percolation. The diffuse solid-liquid interface has a sigmoidal profile with a 10%-90% width of about 12 A near the critical nucleation. The critical size obtained from our simulations is in reasonable agreement with the prediction of classical nucleation theory if the finite interface width is considered. The growth of melt is coupled with nucleation and can be described qualitatively with the Johnson-Meh-Avrami law. System sizes of 10(3)-10(6) atoms are explored, and negligible size dependence is found for bulk properties and for the critical nucleation.     

Potential of mean force between two nanometer-scale particles in a polymer solution

Expanded ensemble density-of-states simulations and a connectivity altering algorithm are used to investigate the effective interactions that arise between nanoparticles suspended in polymer solutions. Our calculations with systems of long polymeric chains reveal oscillations in the effective polymer-induced interactions between the particles, even at low concentrations. The range of these interactions is considerably longer than originally anticipated, and their origin is traced back to the chain-end effects and density fluctuations that were absent in previous treatments of these systems.     

A comparative study of vibrational dynamics of α- and β-forms of poly(β-hydroxybutyrate)

Normal modes and their dispersion are obtained for planar zig-zag form of poly(β-hydroxybutyrate) using Urey-Bradley force field. A comparison is made with the spectra of its helical form. Apart from detailed assignment of modes, various characteristic features of dispersion curves have been explained as arising due to internal symmetry in energy momentum space. The density-of-states have been used to calculate heat capacity in the temperature range 10-450 K using Debye's formalism.     

Dispersion of normal modes in cis 1,4 polybutadiene

Among the synthetic polymers of commercial potential, poly-butadiene is an important rubbery material and it encompasses the bulk elastomers in use. To the best of our knowledge, a complete normal coordinate analysis with full phonon dispersion curves for cis 1,4 polybutadiene (CPBD) have not been reported so far. In the present communication, we report a complete normal coordinate analysis with full dispersion curves, density-of-states and calculation of heat capacity. The normal coordinate analysis has been carried out using the Urey-Bradley force field and the Wilson's GF matrix method as modified by Higgs. A comparison has been made with trans 1,4 polybutadiene (TPBD). The prominent features of the dispersion curves like crossing over and regions of zero-slope away from the zone centre are discussed. To check the validity of the force field used and the assignments, normal mode calculations are also performed for unsaturated C-deuterated and fully deuterated CPBD.     

Using the local elevation method to construct optimized umbrella sampling potentials: Calculation of the relative free energies and interconversion barriers of glucopyranose ring conformers in water

A method is proposed to combine the local elevation (LE) conformational searching and the umbrella sampling (US) conformational sampling approaches into a single local elevation umbrella sampling (LEUS) scheme for (explicit‐solvent) molecular dynamics (MD) simulations. In this approach, an initial (relatively short) LE build‐up (searching) phase is used to construct an optimized biasing potential within a subspace of conformationally relevant degrees of freedom, that is then used in a (comparatively longer) US sampling phase. This scheme dramatically enhances (in comparison with plain MD) the sampling power of MD simulations, taking advantage of the fact that the preoptimized biasing potential represents a reasonable approximation to the negative of the free energy surface in the considered conformational subspace. The method is applied to the calculation of the relative free energies of β‐D ‐glucopyranose ring conformers in water (within the GROMOS 45A4 force field). Different schemes to assign sampled conformational regions to distinct states are also compared. This approach, which bears some analogies with adaptive umbrella sampling and metadynamics (but within a very distinct implementation), is shown to be: (i) efficient (nearly all the computational effort is invested in the actual sampling phase rather than in searching and equilibration); (ii) robust (the method is only weakly sensitive to the details of the build‐up protocol, even for relatively short build‐up times); (iii) versatile (a LEUS biasing potential database could easily be preoptimized for small molecules and assembled on a fragment basis for larger ones). © 2009 Wiley Periodicals, Inc. J Comput Chem 2010     

Ab initio molecular dynamics simulation of liquid Al88Si12 alloys

First-principles molecular dynamics simulations are carried out to study the structures, dynamics, and electronic properties of liquid Al88Si12 in the temperature ranging from 898 to 1298 K. The temperature dependence of static structure factors, pair correlation functions, and electronic density-of-states are investigated. The structural properties obtained from the simulations are in good agreement with the x-ray diffraction experimental results.     

Absolute binding free energy calculations of CBClip host–guest systems in the SAMPL5 blind challenge

Herein, we report the absolute binding free energy calculations of CBClip complexes in the SAMPL5 blind challenge. Initial conformations of CBClip complexes were obtained using docking and molecular dynamics simulations. Free energy calculations were performed using thermodynamic integration (TI) with soft-core potentials and Bennett’s acceptance ratio (BAR) method based on a serial insertion scheme. We compared the results obtained with TI simulations with soft-core potentials and Hamiltonian replica exchange simulations with the serial insertion method combined with the BAR method. The results show that the difference between the two methods can be mainly attributed to the van der Waals free energies, suggesting that either the simulations used for TI or the simulations used for BAR, or both are not fully converged and the two sets of simulations may have sampled difference phase space regions. The penalty scores of force field parameters of the 10 guest molecules provided by CHARMM Generalized Force Field can be an indicator of the accuracy of binding free energy calculations. Among our submissions, the combination of docking and TI performed best, which yielded the root mean square deviation of 2.94 kcal/mol and an average unsigned error of 3.41 kcal/mol for the ten guest molecules. These values were best overall among all participants. However, our submissions had little correlation with experiments.