Two-body Interatomic Potential Research Articles

New alternatives to the Lennard-Jones potential

We present a new method for approximating two-body interatomic potentials from existing ab initio data based on representing the unknown function as an analytic continued fraction. In this study, our method was first inspired by a representation of the unknown potential as a Dirichlet polynomial, i.e., the partial sum of some terms of a Dirichlet series. Our method allows for a close and computationally efficient approximation of the ab initio data for the noble gases Xenon (Xe), Krypton (Kr), Argon (Ar), and Neon (Ne), which are proportional to r-6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r^{-6}$$\\end{document} and to a very simple depth=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$depth=1$$\\end{document} truncated continued fraction with integer coefficients and depending on n-r\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n^{-r}$$\\end{document} only, where n is a natural number (with n=13\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n=13$$\\end{document} for Xe, n=16\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n=16$$\\end{document} for Kr, n=17\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n=17$$\\end{document} for Ar, and n=27\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n=27$$\\end{document} for Neon). For Helium (He), the data is well approximated with a function having only one variable n-r\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n^{-r}$$\\end{document} with n=31\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n=31$$\\end{document} and a truncated continued fraction with depth=2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$depth=2$$\\end{document} (i.e., the third convergent of the expansion). Also, for He, we have found an interesting depth=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$depth=0$$\\end{document} result, a Dirichlet polynomial of the form k16-r+k248-r+k372-r\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k_1 \\, 6^{-r} + k_2 \\, 48^{-r} + k_3 \\, 72^{-r}$$\\end{document} (with k1,k2,k3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k_1, k_2, k_3$$\\end{document} all integers), which provides a surprisingly good fit, not only in the attractive but also in the repulsive region. We also discuss lessons learned while facing the surprisingly challenging non-linear optimisation tasks in fitting these approximations and opportunities for parallelisation.

The race between relaxation and nucleation in supercooled liquid and glassy BaS – A molecular dynamics study

Details of the microscopic mechanisms and dynamics of most processes in supercooled liquids (SCL) and glasses remain blurred due to their complexity and the extraordinarily long or inaccessibly short timescales, depending on the supercooling degree. In this paper, we determined the structural relaxation times in an intermediate supercooling window (0.67–0.78 Tm, Tm = melting point) of barium sulfide liquid, used as a model material, through molecular dynamics (MD) simulations based on a reliable two-body interatomic potential. We also inferred these dynamics in the glassy state using extrapolated data and well-accepted models. The average structural α-relaxation times, <tα>, were determined via the intermediate scattering function. Relaxation kinetics were also estimated by the Maxwell relation via the equilibrium shear viscosity and shear modulus, obtained by MD. We found that the viscosity derived (Maxwell) relaxation times are significantly shorter than the intrinsic α -relaxation times, corroborating two recent experimental studies of other substances. For the simulated system, with 36,000 particles and average volume of 1.4x103 nm3, the structural relaxation and nucleus birth time curves cross at the kinetic spinodal temperature, TKS (=0.33 Tm), which is significantly below the glass transition temperature, Tg (=0.44 Tm). However, for larger sample sizes, the TKS occurs at higher temperatures. As for temperatures above TKS, crystal nucleation starts after structural relaxation, and vice-versa, to understand and describe crystal nucleation one must necessarily take the relaxation process into account, however, this is not included in nucleation theories. These discoveries shed light on some obscure aspects of supercooled liquids, i.e., they challenge a critical assumption of nucleation theories (that crystal nucleation always occurs in a fully relaxed SCL), and show that crystallization is BaS ultimate fate, corroborating studies with other substances.

Fully a priori prediction of the vapor-liquid equilibria of Ar, Kr, and Xe from ab initio two-body plus three-body interatomic potentials.

Fully a priori predictions are reported for the vapor-liquid equilibria (VLE) properties of Ar, Kr, and Xe using molecular simulation techniques and recently developed ab initio two-body interatomic potentials. Simulation data are reported at temperatures from near the triple point to close to the critical point. The two-body ab initio potentials exaggerate the size of the experimental VLE temperature-density envelope, overestimating the critical temperature and underestimating the vapor pressure. These deficiencies can be partially rectified by the addition of a density-dependent three-body term. At many temperatures, the ab initio + three-body simulations for Kr and Xe predict the vapor pressure to an accuracy that is close to experimental uncertainty. The predicted VLE coexisting densities for Xe almost match experimental data. The improvement with experiment is also reflected in more accurate enthalpies of vaporization. The fully a priori predictions for all of the VLE properties of either Kr or Xe are noticeably superior to simulations using the Lennard-Jones potential.

Two-body interatomic potentials for He, Ne, Ar, Kr, and Xe from ab initio data.

A new method is reported for developing accurate two-body interatomic potentials from existing ab initio data. The method avoids the computational complexity of alternative methods without sacrificing accuracy. Two-body potentials are developed for He, Ne, Ar, Kr, and Xe, which accurately reproduce the potential energy at all inter-atomic separations. Monte Carlo simulations of the pressure, radial distribution function, and isochoric heat capacity using the simplified potential indicate that the results are in very close, and sometimes almost indistinguishable, agreement with more complicated current state-of-the-art two-body potentials.

Successful test of the classical nucleation theory by molecular dynamic simulations of BaS

We used a recently developed two-body interatomic potential for barium sulfide (BaS), and performed molecular dynamics (MD) simulations with 36,000 particles to determine the kinetics of spontaneous, homogeneous nucleation and growth of BaS crystals in the supercooled liquid. Isothermal-isobaric MD simulations were accomplished at three temperatures. The calculated pair correlation function, along with several snapshots, allowed us to quantify the nucleation times, their crystal growth rates, and the time evolution of overall crystallization. Nucleation was spontaneously achieved in the supercooled liquid state; therefore, we computed the average birth times of the critical nuclei (also known as average onset time of the first nucleus) from 15 samples at each temperature, from which we computed the steady-state nucleation rates, MD Jss(T). Then, we independently obtained by MD the diffusion coefficients, D(T), the melting point, Tm, and the enthalpy of melting, ΔHm. Thus, the MD Jss could be compared with the predictions of the Classical Nucleation Theory (CNT) for homogeneous nucleation using only one fitting parameter, the nucleus/liquid interfacial free energy, σ. The calculated critical nucleus is made of only 2 to 3-unit cells, which is consistent with the critical size observed in the simulations, approximately 10–15 atoms. Using a constant (fitted value of) σ, and the D(T) and thermodynamic parameters from the simulations, we found that the MD pre-exponential factor has the same order of magnitude as the theoretical value predicted by the CNT. To the best of our knowledge, this agreement of the predictions of CNT and MD simulations has seldom been reported. Therefore, our results corroborate the validity of the CNT for simple supercooled liquids.

Ab initio interatomic potentials and the thermodynamic properties of fluids

Monte Carlo simulations with accurate ab initio interatomic potentials are used to investigate the key thermodynamic properties of argon and krypton in both vapor and liquid phases. Data are reported for the isochoric and isobaric heat capacities, the Joule-Thomson coefficient, and the speed of sound calculated using various two-body interatomic potentials and different combinations of two-body plus three-body terms. The results are compared to either experimental or reference data at state points between the triple and critical points. Using accurate two-body ab initio potentials, combined with three-body interaction terms such as the Axilrod-Teller-Muto and Marcelli-Wang-Sadus potentials, yields systematic improvements to the accuracy of thermodynamic predictions. The effect of three-body interactions is to lower the isochoric and isobaric heat capacities and increase both the Joule-Thomson coefficient and speed of sound. The Marcelli-Wang-Sadus potential is a computationally inexpensive way to utilize accurate two-body ab initio potentials for the prediction of thermodynamic properties. In particular, it provides a very effective way of extending two-body ab initio potentials to liquid phase properties.

Theoretical prediction of the structural, elastic, mechanical and phonon properties of bismuth telluride under pressure

Bismuth telluride (Bi2Te3) is one of the most intricate materials with its semiconducting, insulating and pressure-induced superconducting properties. Although different theoretical works have been carried out to understand the confusing properties of Bi2Te3, information about the high pressure structural, elastic, mechanical and phonon properties of this significant material is still rare. Unlike earlier theoretical approaches, two-body interatomic potentials in the Morse potential form have been employed for the first time to predict the density, phase transition pressure, elastic constants, bulk, shear and Young moduli and elastic wave velocities of Bi2Te3under pressures up to 12 GPa. [Formula: see text] phase transition pressure of Bi2Te3was found to be 10 GPa. The results of above elastic quantities agree well with experiments and are better than some of the published theoretical data. In addition, the effect of pressure on the phonon dispersion and density of states (DOS) were also evaluated with the same potential and their results are satisfactory, especially for the low-frequency acoustic portions of phonons.

Molecular Dynamics Simulations of Perovskites: The Effect of Potential Function Representation on Equilibrium Structural Properties

The perovskites with general formula ABX3 have been widely used as for materials with their unique properties (ferroelectric, piezoelectric, dielectric, catalytic and so on). Hybrid organolead halide perovskites are a class of semiconductors with ABX3 (X = Cl, Br, and I) structures consisting of lead cations in 6-fold coordination (B site), surrounded by an octahedron of halide anions (X site, face centered) together with the organic components in 12-fold cub octahedral coordination. These hybrid perovskites have a direct band gap, a large absorption coefficient as well as high charge carrier mobility that represent a very attractive characteristic of cost-effective solar cells. Basically, these crystals are inorganic solids of CaTiO3 type held together by bonds that are either ionic or partially ionic and partially covalent. In spite of the partially covalent character of the Ti-O bond, the system is modeled by a two-body central force interatomic potential (the form of the Vashishta and Rahman interatomic potential), which has been used successfully for many materials with a perovskite structure. In the present work using molecular dynamics (MD) simulation method we investigate the dynamical and structural behavior of CaTiO3 perovskite at normal pressure and temperature conditions. The MD calculations were performed on a system of 16,000 particles (3200Ca + 3200Ti + 96,00O), initially in an orthorhombic-Pbnm structure. The orthorhombic MD box had edges Lx = 53.4 A, Ly = 53.4 A and Lz = 61.12 A, which provided a density matching the experimental value of ρ = 4 g/cm3. Starting with this structure and using proposed interatomic potentials the MD system stabilizes at room temperature in its initial configuration. The aim of the present study to explore the effect of potential function representations on structural equilibrium properties for the perovskite models including hybrid halide ones outlined above. Concerning the perovskite equilibrium state we elucidate the role of potential function modification on the atomic pair correlation and structural re-organization. The details of the interatomic potential representation have to be crucially important for obtaining of correct analysis data in crystallic, liquid and amorphous phases including perovskite systems.

An interaction potential for barium sulfide: A molecular dynamics study

Structural, dynamical and thermodynamic properties of barium sulfide, as well as the structural transformation induced by pressure, are investigated in a molecular dynamics simulation based on an effective two-body interatomic potential. The two-body interatomic potential proposed for BaS is made up of steric repulsions, Coulomb interactions due to charge transfer, charge-induced dipole attractions due to the electronic polarizability and van der Waals attraction. The stability of the most stable phases of this compound, the vibrational density of states, heat capacity as a function of temperature, melting and recrystallization, as well as the structural phase transformation induced by pressure, are correctly described. It is shown that this phase transformation depends strongly on the temperature and crystallinity of the material. The simulated results are compared with experimental observations and other calculations reported in the literature.

Molecular dynamics simulations of lattice thermal conductivity of bismuth telluride using two-body interatomic potentials

Two-body interatomic potentials in the Morse potential form have been developed for bismuth telluride, and the potentials are used in molecular dynamics simulations to predict the thermal conductivity. The density-functional theory with local-density approximations is first used to calculate the total energies for many artificially distorted ${\text{Bi}}_{2}{\text{Te}}_{3}$ configurations to produce the energy surface. Then by fitting to this energy surface and other experimental data, the Morse potential form is parameterized. The fitted empirical interatomic potentials are shown to reproduce the elastic and phonon data well. Molecular dynamics simulations are then performed to predict the thermal conductivity of bulk ${\text{Bi}}_{2}{\text{Te}}_{3}$ at different temperatures, and the results agree with experimental data well.

Interatomic Potentials for Metal/Metal Wetting Systems

Considering the uniqueness of wetting systems consisting of three components, namely, the surface, liquid and liquid/solid interface, it is desirable to construct interatomic potentials following a consistent policy. To investigate the physical meaning of the behavior in terms of the interatomic potentials, the wetting systems are modeled by simple two-body interatomic potentials derived using ab initio molecular orbital calculations for hypothetical clusters representing the above three components. For In and Sn liquid atoms, spreading occurs on a Cu (111) surface, while in contrast, liquid atoms penetrate the substrate and form a surface alloy in the case of a Pd (111) surface.

Magnesium Diffusion at Dislocation in Wurtzite-Type GaN Crystal

The behavior of interstitial Mg atoms at an edge dislocation is studied in the wurtzite-type GaN crystal by molecular dynamics (MD) simulation. Parameters for a two-body interatomic potential are determined by the Hartree–Fock ab initio method. First, an edge dislocation extending to the [0001] direction is generated in an MD basic cell composed of about 11,000 atoms. Second, Mg atoms are placed at substitutional and interstitial positions in the MD basic cell, and the Mg atoms are traced. It is found that the diffusivity of Mg atoms at a dislocation is enhanced along the dislocation. At 1000 K, the diffusivity of interstitial Mg atoms inside the dislocation core is approximately three orders of magnitude larger than that of interstitial Mg atoms located outside the dislocation. The enhanced diffusion along the dislocation originates from unbalanced atomic forces between the Mg atom and surrounding atoms.

Conservation laws for multibody interatomic potentials

We consider here a formulation given by Hardy (1982 J. Chem. Phys. 76 622–8) that relates the interatomic potential to the conservation equations for linear momentum and energy. Hardy's formulation was restricted to two-body interatomic potentials. We show that it can be extended to general multibody potentials. Of particular interest is a resulting general expression for the local Cauchy stress that results from the equation for conservation of linear momentum.

A comparative numerical analysis of liquid silica and germania

A two-body interatomic potential is used to describe the structural properties of liquid germania and silica by Molecular Dynamics simulation. The results show that the short-range order is identical in the liquid and the glass phase, made of a tetrahedrally connected network while longer range order displays differences with temperature. The most striking difference in thermodynamical behaviour appears to be driven by pressure as illustrated from the simulation of the pressurized amorphous systems.

Molecular dynamics simulation of dislocations in wurtzite-type GaN crystal

Microscopic dislocation structures in wurtzite-type GaN crystal have been studied by the use of molecular dynamics simulation. Parameters for a two-body interatomic potential are determined by the Hartree-Fock ab initio method. A dislocation is generated by the coalescence of the facing planes of a semi-infinite trench structure in the crystal. Six types of trench structures with different depth-directions and extension-directions are examined. Temperatures of 1000 and 1500K are considered. A core structure with an eightfold ring has been confirmed for edge dislocations along the c axis, though there appear a few atoms that are shifted from the ring core structure. The ring core structure is consistent with reported theoretical expectations and experimental observations. A tenfold ring core structure is also observed for edge dislocations along the c axis. A screw dislocation is generated by an attracting force between gallium and nitrogen atoms across the trench space when the attracting force has a large component parallel to the trench extension direction.

Molecular Dynamics of Magnesium Diffusion in Wurtzite-type GaN Crystal

The behaviors of Ga and N vacancies (Schottky defects, Frenkel defects), lattice-site and interstitial Mg atoms, and interstitial H atoms are studied in the wurtzite-type GaN crystal by molecular dynamic simulation. Parameters for a two-body interatomic potential are determined by the Hartree–Fock ab initio method. When there are Schottky defects, Ga and N vacancies are often paired, and the paired vacancies repeatedly form and disappear during the simulation. When there are Frenkel defects, interstitial Ga or N atoms become lattice-site ones by the substitutional-interstitial mechanism. The lattice-site Mg atom shows a very stable state, stays there for a long period and undergoes thermal vibration. The interstitial Mg atom is in a semistable state at the cage center of a hexagonal crystal structure. The Mg atom undergoes thermal vibration there, then hops from one cage center to an adjacent one. The diffusivity of interstitial Mg atoms on the (0001) plane is predominant compared with the diffusivity along the [0001] direction.

Relative stability of hcp and fcc crystalline structures of4He

The relative stability of the hcp and fcc crystalline structures of ${}^{4}\mathrm{He}$ is investigated using the Monte Carlo method. The calculations are made for a recent ab initio two-body interatomic potential and a given solid helium model. The results favor the experimentally observed hcp structure. Based on the reweighting technique, the correlated sampling methodology introduced is described. It is quite general and can be applied to other interatomic potentials, models of the solid phase, and quantum many-body systems.

Statisticalphysics of structural glasses

This paper gives an introduction to and brief overview of some of ourrecent work on the equilibrium thermodynamics of glasses. We havefocused on first-principles computations for simple fragile glasses,starting from the two-body interatomic potential. A replicaformulation translates this problem into that of a gas ofinteracting molecules, each molecule being built of m atoms, andhaving a gyration radius (related to the cage size) which vanishesat zero temperature. We use a small-cage expansion, valid at lowtemperatures, which allows us to compute the cage size, the specificheat (which follows the Dulong and Petit law), and theconfigurational entropy. The no-replica interpretation of thecomputations is also briefly described. The results, particularlythose concerning the Kauzmann temperature and the configurationalentropy, are compared to recent numerical simulations.

Molecular Dynamics Simulations of Atomic Scale Indentation and Cutting Process with Atomic Force Microscope.

This paper describes the effect of the material used for a tool on atomic scale indentation and cutting mechanisms of metal workpieces, by means of molecular dynamics simulations. The interatomic force between the tool and workpiece is assumed to be a two-body interatomic potential using parameters based on the ab-initio molecular orbital calculation for a(Cr, Ni)-(C, Si)6H9 atom cluster. Molecular dynamics simulated the atomic scale indentation and cutting process of the chromium and nickel workpieces using the diamond, silicon and diamond-like carbon(DLC) tools. The diamond and DLC tools formed the indentation mark. Young's modulus of the chromium and nickel in indentation simulations was larger than that in experiments. This was qualitatively explained by the effect of the surface energy for the workpiece on the elastic modulus. The machinability of the chromium and nickel with the diamond tool was better than that of the silicon tool in atomic scale cutting simulations. The depth of the cut for the workpieces in nano scale cutting experiments with AFM, was similar to that in atomic scale cutting by molecular dynamics simulations.

Thermodynamics of glasses: a first principles computation

We propose a first principles computation of the thermodynamics of simple fragile glasses starting from the two-body interatomic potential. A replica formulation translates this problem into that of a gas of interacting molecules, each molecule being build of m atoms, and having a gyration radius (related to the cage size) which vanishes at zero temperature. We use a small cage expansion, valid at low temperatures, which allows us to compute the cage size, the specific heat (which follows the Dulong-Petit law) and the configurational entropy.