Cutoff radius effect of isotropic periodic sum method for transport coefficients of Lennard-Jones liquid

Molecular dynamics simulations of a Lennard-Jones (LJ) liquid were applied to compare the isotropic periodic sum (IPS) method [X. Wu and B. R. Brooks, J. Chem. Phys. 122, 044107 (2005)], which can reduce the calculation cost of long-range interactions, such as the Lennard-Jones and Coulombic ones, with the cutoff method for the transport coefficients which includes the self-diffusion coefficient, bulk viscosity, and thermal conductivity. The self-diffusion coefficient, bulk viscosity, and thermal conductivity were estimated with reasonable accuracy if the cutoff distance of the LJ potential for the IPS method was greater than 3sigma. The IPS method is an effective technique for estimating the transport coefficients of the Lennard-Jones liquid in a homogeneous system.     

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.     

Communication: Shifted forces in molecular dynamics

Simulations involving the Lennard-Jones potential usually employ a cutoff at r = 2.5σ. This communication investigates the possibility of reducing the cutoff. Two different cutoff implementations are compared, the standard shifted potential cutoff and the less commonly used shifted forces cutoff. The first has correct forces below the cutoff, whereas the shifted forces cutoff modifies Newton's equations at all distances. The latter is nevertheless superior; we find that for most purposes realistic simulations may be obtained using a shifted forces cutoff at r = 1.5σ, even though the pair force is here 30 times larger than at r = 2.5σ.     

Application of Ewald summations to long-range dispersion forces

Results illustrating the effects of using explicit summation terms for the r(-6) dispersion term on the interfacial properties of a Lennard-Jones fluid and SPC/E water are presented. For the Lennard-Jones fluid, we find that the use of long-range summations, even with a short "crossover radius," yields results that are consistent with simulations using large cutoff radii. Simulations of SPC/E water demonstrate that the long-range dispersion forces are of secondary importance to the Coulombic forces. In both cases, we find that the ratio of the box size L( parallel) to the crossover radius r(c) (k) plays an important role in determining the magnitude of the long-range dispersion correction, although its effect is secondary when Coulombic interactions are also present.     

Effect of long-range interactions on the surface tension

The effect of long-range interactions on the surface tension at a liquid-gas interface was considered. An analytical expression for the correction to the surface tension for the cutoff of the particle interaction potential at the distance r _c was derived based on a step density profile. For the Lennard-Jones fluid, this correction was calculated numerically from the results of computer simulations of the density profiles. It was established that, in the vicinity of the triple point, the correction is as great as ～6% at the potential cutoff radius r _c=6.78 molecular diameters, a quantity insensitive to the form of the density profile in the interfacial layer.     

Further application of the constrained fluid lambda-integration method

Previously we proposed a three stage, and recently a single stage nonphysical lambda-integration path for thermodynamically coupling bulk solid and liquid states directly. In this work we further apply these paths, specifically the newer single stage path, to the calculation of the complete truncated and shifted Lennard-Jones (R(cutoff)=2.5sigma) and aluminum glue potential melting lines, and the zero pressure melting point for a commonly used gold glue potential. The results showed accurate agreement with presently available literature. We found the single stage constrained fluid lambda-integration methodology to be robust in terms of reversibility over this extended range of temperatures, pressures, and intermolecular potentials.     

Molecular dynamics simulation in the grand canonical ensemble

An extended system Hamiltonian is proposed to perform molecular dynamics (MD) simulation in the grand canonical ensemble. The Hamiltonian is similar to the one proposed by Lynch and Pettitt (Lynch and Pettitt, J Chem Phys 1997, 107, 8594), which consists of the kinetic and potential energies for real and fractional particles as well as the kinetic and potential energy terms for material and heat reservoirs interacting with the system. We perform a nonlinear scaling of the potential energy parameters of the fractional particle, as well as its mass to vary the number of particles dynamically. On the basis of the equations of motion derived from this Hamiltonian, an algorithm has been proposed for MD simulation at constant chemical potential. The algorithm has been tested for the ideal gas, for the Lennard-Jones fluid over a wide range of temperatures and densities, and for water. The results for the low-density Lennard-Jones fluid are compared with the predictions from a truncated virial equation of state. In the case of the dense Lennard-Jones fluid and water our predicted results are compared with the results reported using other available methods for the calculation of the chemical potential. The method is also applied to the case of vapor-liquid coexistence point predictions.     

Exact Non-Linear Relationship Between Exponential-6 and Lennard-Jones (12-6) Potential Functions

The relationship between two of the most frequently adopted van der Waals potential functions – Exponential-6 and Lennard-Jones (12-6) – is shown to be faulty upon comparison of the repulsive terms. By using the Maclaurin's series expansions, an exact relationship between both the potential functions is obtained by means of a non-linear correction factor. A purely Exponential-6 form is recovered when the correction factor is taken at zeroth order, while a purely Lennard-Jones (12-6) form is attained as the order of the correction factor tends to infinity. For real van der Waals systems that are bounded by the Exponential-6 and Lennard-Jones (12-6) potential functions, a positive integer order of the correction factor may possibly provide good curve-fitting to experimental data.     

NVU dynamics. I. Geodesic motion on the constant-potential-energy hypersurface

An algorithm is derived for computer simulation of geodesics on the constant-potential-energy hypersurface of a system of N classical particles. First, a basic time-reversible geodesic algorithm is derived by discretizing the geodesic stationarity condition and implementing the constant-potential-energy constraint via standard Lagrangian multipliers. The basic NVU algorithm is tested by single-precision computer simulations of the Lennard-Jones liquid. Excellent numerical stability is obtained if the force cutoff is smoothed and the two initial configurations have identical potential energy within machine precision. Nevertheless, just as for NVE algorithms, stabilizers are needed for very long runs in order to compensate for the accumulation of numerical errors that eventually lead to "entropic drift" of the potential energy towards higher values. A modification of the basic NVU algorithm is introduced that ensures potential-energy and step-length conservation; center-of-mass drift is also eliminated. Analytical arguments confirmed by simulations demonstrate that the modified NVU algorithm is absolutely stable. Finally, we present simulations showing that the NVU algorithm and the standard leap-frog NVE algorithm have identical radial distribution functions for the Lennard-Jones liquid.     

Simple physics-based analytical formulas for the potentials of mean force for the interaction of amino acid side chains in water. 2. Tests with simple spherical systems

Simple analytical functions consisting of electrostatic, polarization, Lennard-Jones or modified Lennard-Jones, and cavity terms are proposed to express the potentials of mean force analytically for spherical particles interacting in water. The cavity term was expressed either through the molecular-surface area of the solute or by using the Gaussian-overlap model of hydrophobic hydration developed in paper 1 of this series. The analytical expressions were fitted to the potentials of mean force of a methane homodimer, heterodimers composed of a methane molecule, and an ammonium cation or a chloride anion, respectively, and dimers consisting of two chloride anions, two ammonium cations, or a chloride ion and an ammonium cation. The potentials of mean force for these dimers were determined by umbrella-sampling molecular dynamics simulations with the AMBER 7.0 force field with TIP3P water either in our earlier work or in this work. For all systems, the analytical formulas fitted the potentials of mean force very well. However, using the molecular-surface area to express the cavity term provided a good fit only when the nonbonded interactions were expressed by an all-repulsive modified Lennard-Jones potential but also resulted in non-physical values of some of the parameters. Conversely, the use of our new Gaussian-overlap-based expression for the cavity term provided a good fit to the potentials of mean force (PMFs) with Lennard-Jones nonbonded potential, and the values of all parameters were physically reasonable.     

Analysis and prediction of hydrogen bonding in protein-DNA complexes using parallel processors

A number of essential biological functions are controlled by proteins that bind to specific sequences in genomic DNA. In this article we present a simplified model for analyzing DNA-protein interactions mediated exclusively by hydrogen bonds. Based on this model, an optimized algorithm for geometric pattern recognition was developed. The large number of local energy minima are efficiently screened by using a geometric approach to pattern matching based on a square-well potential. The second part of the algorithm represents a closed form solution for minimization based on a quadratic potential. A Monte Carlo method applied to a modified Lennard-Jones potential is used as a third step to rank DNA sequences in terms of pattern matching. Using protein structures derived from four DNA-protein complexes with three-dimensional coordinates established by X-ray diffraction analysis, all possible DNA sequences to which these proteins could bind were ranked in terms of binding energies. The algorithm predicts the correct DNA sequence when at least two hydrogen bonds per base pair are involved in binding to the protein, providing a partial solution to the three-dimensional docking problem. This study lays a framework for future refinements of the algorithm in which the number of assumptions made in the present analysis are reduced. © 1996 by John Wiley & Sons, Inc.     

用密度泛函理论研究Lennard-Jones 流体在狭缝中的相平衡

用改进的基础度量理论(modified fundamental measure theory, MFMT)和密度Taylor展开分别表达过剩自由能中的短程作用和色散作用. 流体分子与狭缝壁之间的相互作用以10-4-3势能函数表达. 由巨势最小原理确定Lennard-Jones (LJ)流体在狭缝中的密度分布和过剩吸附量, 所得结果与分子模拟数据吻合良好. 根据平衡时两相温度, 化学势及巨势相等, 计算了LJ流体在狭缝中的相平衡.     

Molecular Dynamisc Simulation of Polyelectrolites

We carried out simulations of a polymer chain using molecular dynamics algorythm. As a model we used a three-dimensional set monomers (electrically charged material points) connected with its nearest neighbours by harmonic potential. Additionally all pairs of segments interacts by the Lennard-Jones (LJ) and Coulomb forces. The aim of the simulation was to determine chain conformation and other basic properties like radius of gyration and moment of inertia for various polymer length and electric charge distribution.Presented model could be alternative tool for structure prediction to typically used ones based on AMBER 99 [1] or another advanced force field.     

On the Applicability of Mathematical Constants and Sequences in Intermolecular Potential Energy Functions

Six intermolecular potential energy functions incorporating mathematical functions such as the Golden ratio, Euler number and Pi, and three consecutive numbers in the Half Square, Lucas and Fibonacci sequences are proposed herein. It is shown that the Lucas potential function exhibits reasonable agreement with the Lennard-Jones(12-10) function, whilst the Golden ratio potential function describes the argon gas potential energy and the Lennard-Jones(14-7) function excellently. Both the Euler and Pi potential functions agree well with the Lennard-Jones(12-6) function, whilst the Fibonacci potential function exhibits very good correlation with the Lennard-Jones(9-6) function. The relatedness of the mathematical constants and sequences examined in this paper with application to intermolecular potential functions suggests their additional significance in the field of chemistry.     

A parameter-free, solid-angle based, nearest-neighbor algorithm

We propose a parameter-free algorithm for the identification of nearest neighbors. The algorithm is very easy to use and has a number of advantages over existing algorithms to identify nearest-neighbors. This solid-angle based nearest-neighbor algorithm (SANN) attributes to each possible neighbor a solid angle and determines the cutoff radius by the requirement that the sum of the solid angles is 4π. The algorithm can be used to analyze 3D images, both from experiments as well as theory, and as the algorithm has a low computational cost, it can also be used "on the fly" in simulations. In this paper, we describe the SANN algorithm, discuss its properties, and compare it to both a fixed-distance cutoff algorithm and to a Voronoi construction by analyzing its behavior in bulk phases of systems of carbon atoms, Lennard-Jones particles and hard spheres as well as in Lennard-Jones systems with liquid-crystal and liquid-vapor interfaces.     

Liquid-vapor density profiles from equilibrium limit of diffusion equation for interacting particles

Liquid-vapor density profiles are derived from the equilibrium limit of diffusion equation for interacting particles. These profiles are in good agreement with classical hyperbolic tangent relation. For simple Lennard-Jones fluids, predicted density distributions agree with computer simulation data, but have a slightly sharper transition zone. For alkali metals with Lennard-Jones-like potentials, the new equations predict a very good average distribution with quite satisfactory agreement with Monte Carlo simulation results. For liquid metals and water surfaces, accurate interfacial profile predictions also can be achieved by using effective two-body potential data instead of Lennard-Jones parameters.     

氢在沸石上的吸附行为

应用基于Ono-Kondo格子理论得到的通用吸附等温方程, 通过分析氢在不同温度下, 在沸石NaX、CaA、NaA和ZSM-5上的吸附数据, 确定了氢的最大单层吸附容量. 并引入维里吸附方程, 由第二维里吸附系数和圆柱孔的Lennard-Jones(12-6)势模型计算了氢与沸石微孔壁面的作用势. 结果表明, 通用吸附等温方程可较好地描述氢在沸石上的超临界吸附行为, 拟合所得的氢在沸石上的最大单层吸附容量与吸附剂相关, 而与吸附温度无关. 圆柱孔作用势模型计算所得的氢分子在沸石上的吸附作用势与吸附热相近. 氢分子间的作用力表现为吸引力.     

Monte Carlo versus molecular dynamics simulations in heterogeneous systems: an application to the n-pentane liquid-vapor interface

The Monte Carlo (MC) and molecular dynamics (MD) methodologies are now well established for computing equilibrium properties in homogeneous fluids. This is not yet the case for the direct simulation of two-phase systems, which exhibit nonuniformity of the density distribution across the interface. We have performed direct MC and MD simulations of the liquid-gas interface of n-pentane using a standard force-field model. We obtained density and pressure components profiles along the direction normal to the interface that can be very different, depending on the truncation and long range correction strategies. We discuss the influence on predicted properties of different potential truncation schemes implemented in both MC and MD simulations. We show that the MD and MC profiles can be made in agreement by using a Lennard-Jones potential truncated via a polynomial function that makes the first and second derivatives of the potential continuous at the cutoff distance. In this case however, the predicted thermodynamic properties (phase envelope, surface tension) deviate from experiments, because of the changes made in the potential. A further readjustment of the potential parameters is needed if one wants to use this method. We conclude that a straightforward use of bulk phase force fields in MD simulations may lead to some physical inconsistencies when computing interfacial properties.     

Study of structural and thermodynamic characteristics of adsorption layers by the density functional method: Local density in adsorption layer on planar solid surface and adsorption isotherms

The local density profiles in Lennard-Jones adsorption layers, as well as the excess (Gibbs) and absolute adsorption values, are calculated by the density functional method (weighting factor approximations). The substrate is described using the single-particle potential corresponding to the Lennard-Jones potential integrated over the half space occupied by the substrate. The Steele potential is used as a single-particle potential to consider methane adsorption on the surface of nonporous graphite as a specific system. The calculations are performed for both sub- and supercritical temperature regions. It is established that the density profiles are characterized by the existence of one to three maxima, which reflect the positional order of molecules in adsorption layers, i.e., the layered structure of an adsorbate.