Three-body Terms Research Articles

On Parallel Nonequilibrium Molecular Dynamics Simulations of Heat Conduction in Heterogeneous Materials with Three-Body Potentials: Si/Ge Superlattice

Parallelization strategies for nonequilibrium molecular dynamics (NEMD) simulations of heat conduction in heterogeneous materials are presented. In particular, a previously published algorithm involving the pair decomposition of three-body potentials is extended for heterogeneous materials. In addition, a novel and linear scaling scheme, also based on pair decomposition of three-body terms, is introduced for the calculation of the heat flux. The distributed-computing-based implementation of this algorithm is outlined and its speed-up characteristics are demonstrated to be close to ideal. Example NEMD simulations using the new algorithm are performed for the Si/Ge superlattice based on the three-body Stillinger-Weber potential.

Dissociative Water Potential for Molecular Dynamics Simulations

A new interatomic potential for dissociative water was developed for use in molecular dynamics simulations. The simulations use a multibody potential, with both pair and three-body terms, and the Wolf summation method for the long-range Coulomb interactions. A major feature in the potential is the change in the short-range O-H repulsive interaction as a function of temperature and/or pressure in order to reproduce the density-temperature curve between 273 K and 373 at 1 atm, as well as high-pressure data at various temperatures. Using only the change in this one parameter, the simulations also reproduce room-temperature properties of water, such as the structure, cohesive energy, diffusion constant, and vibrational spectrum, as well as the liquid-vapor coexistence curve. Although the water molecules could dissociate, no dissociation is observed at room temperature. However, behavior of the hydronium ion was studied by introduction of an extra H+ into a cluster of water molecules. Both Eigen and Zundel configurations, as well as more complex configurations, are observed in the migration of the hydronium.

Elastic charge density representation of the interaction via the nematic director field

The interaction between particle-like sources of the nematic director distortions (e.g., colloids, point defects, macromolecules in nematic emulsions) allows for a useful analogy with the electrostatic multipole interaction between charged bodies. In this paper we develop this analogy to the level corresponding to the charge density and consider the general status of the pairwise approach to the nematic emulsions with finite-size colloids. It is shown that the elastic analog of the surface electric charge density is represented by the two transverse director components on the surface imposing the director distortions. The elastic multipoles of a particle are expressed as integrals over the charge density distribution on this surface. Because of the difference between the scalar electrostatics and vector nematostatics, the number of elastic multipoles of each order is doubled compared to that in the electrostatics: there are two elastic charges, two vectors of dipole moments, two quadrupolar tensors, and so on. The two-component elastic charge is expressed via the vector of external mechanical torque applied on the particle. As a result, the elastic Coulomb-like coupling between two particles is found to be proportional to the scalar product of the two external torques and does not directly depend on the particles' form and anchoring. The real-space Green function method is used to develop the pairwise approach to nematic emulsions and determine its form and restrictions. The pairwise potentials are obtained in the familiar form, but, in contrast to the electrostatics, they describe the interaction between pairs (dyads) of the elastic multipole moments. The multipole moments are shown to be uniquely determined by the single-particle director field, unperturbed by other particles. The pairwise approximation is applicable only in the leading order in the small ratio particle size-to-interparticle distance as the next order contains irreducible three-body terms.

Structure and energetics of weakly bound water–sulfur dioxide complexes

Optimal structures, interaction energies and harmonic vibrational frequencies of the H 2O⋯SO 2 dimers, 1:2 and 2:1 trimers have been determined from the MP2 calculations with the aug-cc-pVDZ and aug-cc-pVTZ basis sets. Some properties of the complexes have been calculated at the CCSD(T) levels. The nature of the intermolecular interactions in the dimers have been investigated by symmetry-adapted perturbation theory (SAPT). We have located two stable configurations as well as two transition states on the potential energy surface for the dimer. Six low-energy configurations on the potential energy surface for 1:2 and 2:1 trimers have been found. The contribution of the three-body term represents as much as 19% for the (H 2O) 2⋯SO 2. The calculated frequency shifts are presented for trimers to facilitate the frequency assignments of the experimental spectra.

IBM-1 description of the fission products 108,110,112Ru

IBM-1 calculations for the fission products 108,110,112Ru have been carried out. The even–even isotopes of Ru can be described as transitional nuclei situated between the U(5) (spherical vibrator) and SO(6) ( γ-unstable rotor) symmetries of the interacting Boson Model. At first, a Hamiltonian with only one- and two-body terms has been used. Excitation energies and B(E2) ratios of gamma transitions have been calculated. A satisfactory agreement has been obtained, with the exception of the odd–even staggering in the quasi- γ bands of 110,112Ru. The observed pattern is rather similar to the one for a rigid triaxial rotor. A calculation based on a Hamiltonian with three-body terms was able to remove this discrepancy. The relation between the IBM and the triaxial rotor model was also examined.

Development of a Fe–He interatomic potential based on electronic structure calculations

A new empirical Fe–He potential has been developed by fitting results obtained from first-principles calculations. Both the formation and relaxation energies of single He defects and small He clusters were accounted for in the fitting process. The new potential consists of a repulsive pair-potential term and a three-body interaction term, and was applied in combination with three commonly used iron interatomic potentials, and a potential describing the behavior of helium in vacuum. As an application of the new potential, the stability of He–vacancy clusters at zero temperature was evaluated. The calculated results were similar for all three Fe potentials, and the new potentials provide results that are more consistent with ab initio calculations than those obtained from previous Fe–He potentials.

Three-body interactions in the condensed phases of helium atom systems

In this work we investigate how the description of several properties of helium atoms in thecondensed phases are affected by the three-body terms of a very accurate inter-atomicpotential. We introduce two phenomenological parameters in the three-body part of theinter-atomic potential in order to describe properly the equations of state of the solid andliquid phases. The calculations were performed using the multi-weight extension to thediffusion Monte Carlo method which allows accurate calculations of small energy differencesin a significant way. The results show how the equations of state for both theliquid and solid phases and properties like the isothermal compressibility, theequilibrium, melting and freezing densities are affected by three-body interactions.

Accurate ab initio based multisheeted double many-body expansion potential energy surface for the three lowest electronic singlet states of H3+

The authors present diabatic and adiabatic potential energy surfaces for the three lowest electronic singlet states of H3+. The modeling of the surfaces is based on the multi-sheeted double many-body expansion method which consists of dressing the various matrix elements of the diatomics-in-molecules potential matrix with three-body terms. The avoided crossing between the two lowest states and the conical intersection between the second and the third state are accurately represented by construction.

Nuclear collective excitations using correlated realistic interactions: The role of explicit random-phase approximation correlations

We examine to what extent correlated realistic nucleon-nucleon interactions, derived within the unitary correlation operator method (UCOM), can describe nuclear collective motion in the framework of first-order random-phase approximation (RPA). To this end we employ the correlated Argonne V18 interaction in calculations within the so-called ''Extended'' RPA (ERPA) and investigate the response of closed-shell nuclei. The ERPA is a renormalized RPA version which considers explicitly the depletion of the Fermi sea due to long-range correlations and thus allows us to examine how these affect the excitation spectra. It is found that the effect on the properties of giant resonances is rather small. Compared to the standard RPA, where excitations are built on top of the uncorrelated Hartree-Fock (HF) ground state, their centroid energies decrease by up to 1 MeV, approximately, in the isovector channel. The isoscalar response is less affected in general. Thus, the disagreement between our previous UCOM-based RPA calculations and the experimental data are to be attributed to other effects, namely to residual three-body terms in the Hamiltonian and to higher-order configurations. Single-particle energies and occupation probabilities obtained within the ERPA are compared with corresponding HF and perturbation-theory results and are discussed as well. The ERPA formalism ismore » presented in detail.« less

Light absorption during alkali atom-noble gas atom interactions at thermal energies: A quantum dynamics treatment

The absorption of light during atomic collisions is treated by coupling electronic excitations, treated quantum mechanically, to the motion of the nuclei described within a short de Broglie wavelength approximation, using a density matrix approach. The time-dependent electric dipole of the system provides the intensity of light absorption in a treatment valid for transient phenomena, and the Fourier transform of time-dependent intensities gives absorption spectra that are very sensitive to details of the interaction potentials of excited diatomic states. We consider several sets of atomic expansion functions and atomic pseudopotentials, and introduce new parametrizations to provide light absorption spectra in good agreement with experimentally measured and ab initio calculated spectra. To this end, we describe the electronic excitation of the valence electron of excited alkali atoms in collisions with noble gas atoms with a procedure that combines l-dependent atomic pseudopotentials, including two- and three-body polarization terms, and a treatment of the dynamics based on the eikonal approximation of atomic motions and time-dependent molecular orbitals. We present results for the collision induced absorption spectra in the Li-He system at 720 K, which display both atomic and molecular transition intensities.

Classical Molecular Dynamics Simulation of Structural and Dynamical Properties of II-VI and III-V Semiconductors

An effective inter-atomic potential is proposed in order to describe structural and dynamical properties of II-VI and III-V semiconductors. The interaction potential consists of twoand three-body interactions. The two-body term takes into account steric repulsion, charge-induce dipole interaction due to the electronic polarizability of ions, Coulomb interaction due to charge transfer between ions, and dipole-dipole (van der Waals) interactions. The three-body term, which has a modified Stillinger-Weber form, describes bond-bending as well as bond-stretching effects. Here we report the fitting and the application of this interaction potential for InP in the crystalline phase and for CdTe in the crystalline and liquid phases. The structural correlations are discussed through pair distribution, coordination number and bond-angle functions. Vibrational density of states for InP and CdTe as well as the static structure factor for liquid CdTe are in very good agreement with experimental data.

Study of the C(3P) + OH(X2Π) → CO(XΣg+) + H(2S) Reaction: A Fully Global ab Initio Potential Energy Surface of the XA‘ State

The C((3)P) + OH(X (2)Pi) --> CO(X (1)Sigma(g)(+)) + H((2)S) reaction has been investigated by ab initio electronic structure calculations of the X(2)A' state based on the multireference (MR) internally contracted single and double configuration interaction (SDCI) method plus Davidson correction (+Q) using Dunning aug-cc-pVQZ basis sets. In particular, the multireference space is taken to be a complete active space (CAS). Improvement over previously proposed potential energy surfaces for HCO/COH is obtained in the sense that present surface describes also the potential part where the CO interatomic distance is large. A large number of geometries (around 2000) have been calculated and analytically fitted using the reproducing kernel Hilbert space (RKHS) method of Ho and Rabitz both for the two-body and three-body terms following the many-body decomposition of the total electronic energies. Results show that the global reaction is highly exothermic ( approximately 6.4 eV) and barrierless (relative to the reactant channel), while five potential barriers are located on this surface. The three minima and five saddle points observed are characterized and found to be in good agreement with previous work. The three minima correspond to the formation of HCO and COH complexes and to the CO + H products, with the COH complex being a metastable minimum relative to the product channel. The five saddle points correspond to potential barriers for both the dissociation/formation of HCO and COH into/from CO + H, to barriers for the isomerization of HCO into COH and to barriers for the inversion of HCO and COH through their respective linear configuration.

Analysis of the mixing rules for the Stillinger–Weber potential: a case-study of Ge–Si interactions in the liquid phase

A liquid Ge0.25Si0.75 alloy was simulated by means of the molecular dynamics method, using the Stillinger–Weber potential. The influence of precise parametrization of the three-body term in the unlike-species interactions on the alloy structure was studied and found to be significant. Differences in the parameters of only a few percent have led to marked changes in the pair correlation functions, angular distribution functions and diffusion coefficients. A separation of the system into Ge- and Si-rich regions was observed for two parametrizations, while it was absent for the other three.

Lattice structure of mercury: Influence of electronic correlation

Mercury condenses at $233\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ into the rhombohedral structure with an angle of 70.53\ifmmode^\circ\else\textdegree\fi{}. Theoretical predictions of this structure are difficult. While a Hartree-Fock treatment yields no binding at all, density-functional theory (DFT) approaches with gradient-corrected functionals predict a structure with a significantly too large lattice constant and an orthorhombic angle of about 60\ifmmode^\circ\else\textdegree\fi{}, which corresponds to an fcc structure. Surprisingly, the use of the simple local density approximation (LDA) functional yields the correct structure and lattice constants in very good agreement with experiment; relativistic effects are shown to be essential for reaching this agreement. In addition to DFT results, we present a wave-function-based correlation treatment of mercury and discuss in detail the effects of electron correlation on the lattice parameters of mercury including $d$-shell correlation and the influence of three-body terms in the many-body decomposition of the interatomic correlation energy. The lattice parameters obtained with this scheme at the coupled cluster level of theory agree within 1.5% with the experimental values. We further present the bulk modulus calculated within the wave-function approach, and compare to LDA and experimental values.

Properties of cyclo-β-tetrapeptide assemblies investigated by means of DFT calculations

We present a theoretical study of structural, energetic, and electronic properties of hollow tubular structures of cyclo-β-tetrapeptides using density functional theory methods. Our calculations consider first a cyclic subunit made of four β-peptide residues, which is fully optimized with gradient-corrected exchange-correlation functionals. Second, we completely optimize the structures of dimer and trimer composed of these ring-shaped subunits. It is found that these tubular structures form strongly hydrogen-bonded systems with interaction energy of −0.86 and −1.68 eV, respectively, after correcting for basis set superposition error. Also, we evaluate the cooperative effects in the trimer formation. This is obtained as ∼19% of the total interaction energy. Considering a decomposition energy scheme, the calculated three-body term corresponds to ∼13% of the total binding energy.

Effect of incorporating three-body interaction in the low-density energy expansion of Bose–Einstein condensate of 87Rb atoms trapped in a harmonic potential

It is shown that if one incorporates all terms related to three-body interaction, except the recombination term, in a dilute homogeneous Bose assembly of 87Rb gas, the lower bound is not violated even when n a 3 ⩾ 10 −3 (where n = | ψ ( r → ) | 2 is the number density and ‘ a’ is the s-wave triplet spin scattering length), in contrast to the earlier result when only terms up to logarithm term in three-body interaction were taken into account. Making use of all the terms in Ginzburg, Pitaevskii and Gross (GPG) equation the effect of including terms beyond logarithmic have been computed. It turns out that there is substantial change in physical quantities like effective interaction potential energy per particle, three-body interaction term, hard-core interaction term contribution and condensate wave function, ψ ( r → ) , also referred to as order parameter, in comparison with the corresponding quantities when only terms up to logarithmic are considered.

On the Uniqueness of the Solution to the Three-Body Problem with Zero-Range Interactions

We consider the uniqueness of the solution to a three-body problem with zero-range Skyrme interactions in configuration space. With the lowest, k0, two-body term alone the problem is known to have no unique solution as the system collapses – the variational estimate of the energy tends towards negative infinity, the size of the system towards zero. We argue that the next, k2, two-body term removes the collapse and the three-body system acquires finite ground-state energy and size. The three-body interaction term is thus not necessary to provide a unique solution to the problem.

EFFECT OF HIGHER ORDER ENERGY CORRECTIONS INCLUDING THREE-BODY INTERACTION ON THE BOSE-EINSTEIN CONDENSATE WITH THE VARIATION OF REPULSIVE SELF INTERACTION ENERGY

Various ground state properties such as chemical potential, differential and total energy per particle etc. of Bose-Einstein condensate of 10000 85 Rb atoms with varying repulsive self-interaction energy have been reported considering not only two-body interaction but also including the higher order terms of the low-density energy expansion of homogeneous Bose gas in the Ginzburg, Pitaevskii and Gross (GPG) equation. These include hard-core approximation of the bosons neglected earlier and the three-body interaction terms. The study is more general as it includes the terms beyond logarithm in energy density expansion. It is also shown that such a consideration does not violate the lower bound predicted earlier in which the 'constant' beyond logarithm term in the three-body interaction was neglected.

<b>STRUCTURE OF Co(III) AND Fe(III) TRANSITION METAL IONS IN AQUEOUS SOLUTION</b>

The hydration structures of Co(III) and Fe(III) ions have been investigated by Metropolis Monte Carlo (MC) simulations using only ion-water pair interaction potentials and by including up to three body correction terms. The hydration structures were evaluated in terms of radial distribution functions, coordination numbers and angular distributions. The structural parameters obtained by including three-body correction terms are in good agreement with experimental values proving that many-body effects play a crucial role in the description of the hydration structure of these highly charged ions. KEY WORDS: Metropolis Monte Carlo simulation, Hydration structure, Fe(III) and Co(III) ions, Three-body corrections Bull. Chem. Soc. Ethiop. 2006, 20(1), 121-131.

Importance of anisotropic three-body forces in solid hydrogen

We take into account three-body anisotropic forces between molecules to calculate the energy of the ${S}_{0}(0)$ triplet in solid hexagonal close packed hydrogen under pressure. Three-body contributions result in one term depending on the orientation of only one molecule (crystal field term) and two others that couple rotations of different molecules (roton terms). Three-body interactions contribute, to a large extent, to the roton frequencies. Their inclusion in the calculation increases the calculated average frequency of the triplet, even at relatively low density, changing substantially the estimate of the internuclear distance. By contrast, the triplet splitting is substantially unaffected by three-body terms, resulting therefore a good candidate to test anisotropic two-body potential models against experiment.