Short-range Interatomic Potentials Research Articles

A simple algorithm to accelerate the computation of non‐bonded interactions in cell‐based molecular dynamics simulations

Cell lists are ubiquitous in molecular dynamics simulations--be it for the direct computation of short-range inter-atomic potentials, the short-range direct part of a long-range interaction or for the periodic construction of Verlet lists. The conventional approach to computing pairwise interactions using cell lists leads to a large number of unnecessary interparticle distance calculations. In this paper, an algorithm is presented which reduces the number of spurious distance calculations by first sorting the particles along the cell pair axis and then only interacting two particles if their distance along the axis is smaller than the cutoff distance of the interaction. This approach is shown to be more efficient than the conventional approach and similar approaches using smaller cells.

Use of a variable-charge interatomic potential for atomistic simulations of bulk, oxygen vacancies, and surfaces of rutileTiO2

In this paper, interatomic potential models used for atomistic simulations of insulating oxides are revisited through the example of ${\mathrm{TiO}}_{2}$ rutile. The cohesive energy of oxides comprises an electrostatic part and a short-range part whose relative importance differs with the models. The electrostatic part can be evaluated by considering either point fixed atomic charges or, alternatively, charges that are allowed to vary in response to the local atomic environment, with a shielding correction to coulombic interactions at short range. We deeply analyzed this latter approach in the framework of the Rapp\'e and Goddard QEq charge equilibration scheme. We conclude that it is an efficient model to describe heterogeneous situations due to point defects or surfaces. Moreover, whatever the description of the electrostatic part of the energy is, several short-range interatomic potentials are found to describe in an acceptable way the crystal bulk properties (cohesive energy, elastic constants, etc). To compare the efficiency of various short-range potentials, we selected the ${\mathrm{TiO}}_{2}$ rutile whose experimental formation energy of the oxygen vacancy is available. By combining it with the cohesive energy, we have been able to accurately analyze the energetics of ${\mathrm{TiO}}_{2}$ as a function of those potentials. In this paper we show first that Morse potential is not adapted to oxygen-oxygen interactions and that pair-wise potentials between $\mathrm{Ti}\text{\ensuremath{-}}\mathrm{O}$ pairs are not suitable to describe defects. As a result, we propose a model that combines the QEq description for electrostatic energy, a Buckingham potential for $\mathrm{O}\text{\ensuremath{-}}\mathrm{O}$ interactions and a $N$-body potential for the covalent part of the $\mathrm{Ti}\text{\ensuremath{-}}\mathrm{O}$ interactions. This model efficiency has been tested on bulk, oxygen vacancy, and surfaces of rutile and turned out to provide results which fit very satisfactorily the experimental data.

Calculations of the atomic structure of the KNbO 3 (110) surface

The O-terminated KNbO 3 (110) surface is modeled using a semi-empirical shell model and two different short-range interatomic potentials. We find this surface to be unstable with respect to a strong reconstruction and K-termination. This conclusion is confirmed by preliminary calculations using the ab initio linear combination of atomic orbitals (LCAO) formalism.

Collision cross sections for argon atoms with argon atomsfor energies from 0.01 eV to 10 keV

Differential and angular integrated cross sections for elasticcollisions of Ar atoms with Ar atoms are calculated fromrepresentative potential energy curves for collision energiesfrom 0.01 eV to 10 keV. The scattering phase shifts arecalculated using the WKB approximation. The cross sections arecompared with data obtained from beam scattering experiments andtransport coefficient measurements. On the basis of assessmentsof experimental reliability and of theoretical potentials, wemake a selection from the available short-range interatomicpotentials. Consideration of experimental elastic and inelasticcross section data leads to the suggestion that our theoreticalresults should be interpreted as the sum of the elastic andinelastic differential cross sections. The theoreticaldifferential, total and viscosity cross sections are fittedwith empirical functions covering the energy range from 1 eV to10 keV to facilitate their use in models of discharge plasmas,etc. Procedures for use of these cross sections are summarizedbriefly.

Molecular-dynamics simulation of shock-stress-induced amorphization ofα-quartz

The molecular-dynamics technique is used to investigate the shock propagation in $\ensuremath{\alpha}$-quartz using a very long periodic macrocell, and semiempirical long-range Coulomb and short-range interatomic potentials. The equation of state and the phase transformation pressure are in good agreement with published experimental data. The transformed phase is identified to be amorphous, and not as stishovite, and is retained on release of the shock pressure. The Raman ${A}_{1}$ phonon frequency is also simulated successfully which is known to show a significantly different variation with static and shock pressures.

Simulations of the Effects of Tip Apex Geometries on Atomic Force Microscopy Images

Simulation works on the effects of tip apex geometries on atomic force microscopy (AFM) images were examined. Tips and samples employed in those simulations were mostly made of a single component. Short-range interatomic potentials such as Lennard-Jones and Morse were used. With these potentials, it was found that a single atom tip (a tip with an atom protruding at its apex) is necessary for obtaining true atomic resolution. In many cases flat tip geometries (tips with multiple atoms at their apexes) produce various images that do not correspond to the surface atom arrangements, which may lead to various faulty AFM image interpretations.

Computer modelling of phosphate biominerals. Transfer of parameters for interatomic potentials for different polymorphs of divalent metal diphosphates

Manganese, zinc and calcium diphosphates have been modelled using atomistic simulation techniques. The ionic model was used for the cation–anion interactions. Parameters for the short-range interatomic potentials previously calculated using the electron gas methods for the diphosphate anion of α-magnesium diphosphate, were used together with specific metal oxygen parameters. The structural data for each compound were reproduced well, indicating that the anion parameters were transferable. These studies present new opportunities for modelling important aspects of biominerals which are not readily accessible to experimental studies.

An interatomic pontential for fullerences from their vibrational spectrum

The vibrational analysis ofsp 2-bonded carbon clusters with different nearest-neighbour interatomic distances (2 in C60, 8 in C70), performed in the framework of the bond-charge model, leads to the determination of an exponential form for the short-range interatomic potential which is inclusive of charge transfer effects. The potential, besides leading to excellent agreement with the existing spectroscopic data andab initio Car-Parrinello calculations, ensures a good transferability of the model to other clusters and possibly an empirical basis for molecular dynamics simulations.

Lattice dynamics of FCC transition metals: A pseudopotential approach

Simple pseudopotential model for the binding energy of transition metals is proposed. The contribution of thes-like electrons is calculated in the second-order perturbation theory for the local model pseudopotential while that of thed-like electrons is taken into account by introduction of repulsive short-range interatomic potential. Model parameters were determined for ten fcc transitions metals (Cu, Ni, Fe, Co, Ag, Pd, Rh, Au, Pt, and Ir). This model was used for the calculation of the phonon dispersion and the density of states, as well as for the elastic constants and their pressure derivatives. Good agreement with experimental data was achieved for the overall shape of phonon spectra and even for the position of the Kohn anomalies in Pd and Pt. Existence of such anomalies is also stated for predicted phonon spectra of rhodium and iridium.

Interatomic Potentials for Micas

Abstract We investigate the transferability of short range interatomic potentials and the applicability of the fully ionic model to the simulation of the layer structured mica, muscovite, using energy minimisation and free energy minimisation techniques.

Attractive short-range interatomic potential in the lattice dynamics of niobium and tantalum

It is shown in the framework of the pseudopotential approach that there is a sizable attractive short-range component of the interatomic potential due to thes-d interaction which has the same functional form in real space as the Born-Mayer repulsion due to the overlap of core electron wave functions centred on neighbouring ions. The magnitude of this attractive component is such as to completely cancel the conventional Born-Mayer repulsion, making the resultant short-range interatomic potential attractive rather than repulsive. Numerical calculations show that the attractive interatomic potential, which represents the local-field correction, leads to a better understanding of the occurrence of the soft modes in the phonon dispersion curves of niobium and tantalum.

Local-field correction in the lattice dynamics of b.b.c. transition metals

It is shown that the off-diagonal components of the inverse dielectric matrix which determine the local-field correction associated with s-d interactions, make contributions to the dynamical matrix for phonon dispersion in the body-centred cubic transition metals V, Nb and Ta which tend to cancel the Born-Mayer contribution, just as the diagonal components of the inverse dielectric matrix tend to cancel or screen the long-range (Coulombic) contribution. Numerical calculations show that the can-cellation of the Born-Mayer contribution to the dynamical matrix by the local-field correction is such that the effective short-range interatomic potential turns out to be attractive rather than repulsive in these metals and accounts for some peculiar shapes of the major soft modes observed in these metals.

Attractive short-range interatomic potential in transition metals

A generalization of the pseudopotential method is used to calculate the contribution to interatomic potential in d-band (transition) metals due to s-d interaction. The contribution is found to contain an attractive component of the Born-Mayer type which is an order of magnitude larger than the conventional Born-Mayer repulsion. The implications of such an attractive short-range interatomic potential in the occurence of soft modes in the phonon spectra of the b.c.c. transition metals - V, Nb and Ta - are discussed.

On the mechanical stability of bcc transition elements and alloys

A volume independent and a volume dependent lattice energy function involving short-range interatomic potentials were able to be fitted to the elastic constants, cohesive energy, lattice parameter and for the latter function to the vacancy formation energy and bcc-fcc lattice stability energy, as well, for fcc metals and bcc alkali metals, but not to the cohesive energy and C' elastic constant of bcc transition metals. The assumption that directional, but partial, covalent bonds exist between nearest-neighbors in the bcc transition elements provides an explanation for the latter results and in addition explains the identical dependence of C' and the bcc-fcc lattice stability upon N d , where N d is the average number of d electrons, for the bcc transition metals and alloys. Both the mechanical and thermodynamic stability of the bcc structure for transition metals and all transition metal alloys disappears for 5 − N d > 2 and <−1.

Surface relaxation and thermal expansion for the (001) face of α-Fe and Cu

The surface relaxation and the near-surface enhancement of thermal expansion have been calculated for the (001) face of a bcc crystal, α-Fe, and an fcc crystal, Cu. The calculations make use of the anharmonic perturbation formalism of Dobrzynski and Maradudin; the results for certain equal-time vibrational correlation functions which arise in this formalism are also presented. The crystal potential is described in terms of several kinds of short-range empirical interatomic potentials, such as have been used in studies of defects in bulk; in the near-surface region, the effects of surface redistribution of the electron distribution are modelled by the addition of a simple surface Madelung (SSM) force. The effect of the SSM force is to limit severely the usual outward relaxation driven by short-range interatomic potentials. For Fe(001), the five and one-half percent outward static relaxation driven by the short-range potentials acting alone is changed to a one percent inward static relaxation when the SSM force is incorporated; for Cu(001), the comparable change is from a one percent outward relaxation to a one-half percent outward relaxation. On the other hand, the SSM force makes only a small effect on the surface-enhanced thermal expansion coefficients (STEC) for interplanar spacings. The STEC for the outermost spacing is between 2.5. and 3.0 times of that for the bulk at the Debye temperature for both Fe(001) and Cu(001); for the second interplanar spacing, the STEC is smaller than 1.5 times of that of the bulk at the Debye temperature. The ratios of the near-surface mean-square amplitudes (MSA) to those of the bulk at high temperatures are, for Fe(001), about 1.75 for z-components (normal to surface) and 1.55 for x-components (parallel to surface) in the surface layer; for Cu(001), about 1.95 for z-components and 1.30 for x-components. The interplanar correlation functions, while smaller than the MSA on an absolute scale, do show considerable surface-enhancement, particularly for the zz-compoments. For example, the zz-correlation between an atom in the outermost layer and its nearest neighbor in the next layer is nearly twice the comparable bulk correlation above the Debye temperature for both Fe(001) and Cu(001).

Calculation of the Temperature Dependence of the Second-Order Elastic Constants of fcc Ar, Kr, and Xe Using a Two-Body Short-Range Interatomic Potential

The temperature dependence of the second-order elastic constants of fcc Ar, Kr, and Xe have been studied using phenomenological ($m\ensuremath{-}6$) Lennard-Jones potentials acting between nearest neighbors and fitted to the zero-temperature zero-pressure lattice constant and the sublimation energy. The theory of the second-order elastic constants is briefly reviewed, and the second-order strain dependence of the quasiharmonic free-energy density is derived using perturbation theory. The resulting expressions for the temperature dependence of the elastic constants involve both third- and fourth-order force constants, and require a single scan of the Brillouin zone, which is carried out to give an accuracy of about 1%. We find that the contribution of the third-order force constants is comparable to that of the fourth-order ones and in some cases predominates. Adiabatic and isothermal results are presented both for constant volume (0\ifmmode^\circ\else\textdegree\fi{}K $M$ volume) and for the experimentally observed equilibrium $M$ volume. We did not solve the equation of state. Wave velocities derived from our elastic constants are compared with recent experiments on crystals of Ar and Kr. Our results show that there are large anharmonic contributions to the temperature dependence of the elastic constants. Consequently, our Ne results are quantitatively unrealiable (except at $T=0$) and we omit them. For $T&gt;\ensuremath{\sim}\frac{{\ensuremath{\Theta}}_{\ensuremath{\infty}}}{2}$ there are indications of the breakdown of perturbation theory. The way our results may be affected by including higher-order anharmonic terms is illustrated by considering the temperature dependence of the zero-pressure bulk modulus of Ar.