Three-body Potential Research Articles

From two-dimensional (super-integrable) quantum dynamics to (super-integrable) three-body dynamics

It is shown that planar quantum dynamics can be related to three-body quantum dynamics in the space of relative motion with a special class of potentials. As an important special case the O(d) symmetry reduction from d degrees of freedom to one degree is presented. A link between two-dimensional (super-integrable) systems and three-body (super-integrable) systems is revealed. As illustration we present number of examples. We demonstrate that the celebrated Calogero–Wolfes three-body potential has a unique property: two-dimensional quantum dynamics coincides with three-body quantum dynamics on the line at d = 1; it is governed by the Tremblay–Turbiner–Winternitz potential for parameter k = 3.

Statistical correlations in quantum systems with explicit three-body interactions

Higher-order and pairwise statistical correlations are quantified via mutual information, in quantum systems consisting of three pairwise interacting oscillators, that are subjected to a three-body Gaussian type potential. Variational wave functions are used for these calculations. The correlation measures are calculated in both position and momentum space, to examine their dependence on the coupling strength and width of the three-body potential. Results are presented for both positive and negative three-body potentials, and attractive and repulsive two-body ones. Extremal points are observed when the pair and higher-order measures are examined as a function of the coupling strength for positive three-body potentials. This illustrates that the magnitudes of these statistical correlations can be adjusted with the strength of the three-body potential. Higher-order mutual information is positive-valued in momentum space and negative-valued in position space, in systems with attractive pair and positive three-body potentials. The interpretation is that synergistic interactions among the three particles are dominant in momentum space while the redundant (pairwise) ones prevail in position space. These behaviours are reversed in systems with repulsive pair potentials and negative three-body ones. The demeanour of the correlation measures with respect to the width of the Gaussian potential is also examined. The extremal points that are present as a function of the coupling strength, are more pronounced for broader potentials, while they disappear for narrower potentials. The positions of these extremal points move to smaller coupling strengths, as the potential narrows. Trends in the one-, two-, and three-variable Shannon entropies in these systems are also discussed.

A Possibility of a Long Range Three-Body Force in the Hadron System

The existence of a kinematic long range component in the one particle transfer three-body potential or so-called “general particle transfer (GPT) potential” was proposed several years ago. In this investigation the mass dependence of the exchanged particle and the index number of the long range property are clarified. On the basis of the GPT potential, a new long range three-body force is proposed in the hadron system, which will be compared with the Efimov potential.

Three-neutron bound and continuum states

The three-neutron ($3n$) system is studied by numerical calculations with the Faddeev three-body formalism for a realistic nucleon-nucleon (NN) potential. A response function for the transition from $^{3}\mathrm{H}$ to $3n$ continuum states by an isospin excitation operator is calculated, from which no evidence of $3n$ resonance state is found. Different methods to extrapolate the $3n$ energy from bound state energies with an extra attractive effect to the NN potential are examined. While extrapolations with attractive effects by enhanced NN potentials or three-body potentials result in the nonexistence of $3n$ resonance states, one by external trapping potentials leads to a positive $3n$ energy, which may be considered as a resonance state. It is found that this contradiction is due to a general defect of the trapping method.

UEP: an open-source and fast classifier for predicting the impact of mutations in protein-protein complexes.

Single protein residue mutations may reshape the binding affinity of protein-protein interactions. Therefore, predicting its effects is of great interest in biotechnology and biomedicine. Unfortunately, the availability of experimental data on binding affinity changes upon mutation is limited, which hampers the development of new and more precise algorithms. Here, we propose UEP, a classifier for predicting beneficial and detrimental mutations in protein-protein complexes trained on interactome data. Regardless of the simplicity of the UEP algorithm, which is based on a simple three-body contact potential derived from interactome data, we report competitive results with the gold standard methods in this field with the advantage of being faster in terms of computational time. Moreover, we propose a consensus selection procedure by involving the combination of three predictors that showed higher classification accuracy in our benchmark: UEP, pyDock and EvoEF1/FoldX. Overall, we demonstrate that the analysis of interactome data allows predicting the impact of protein-protein mutations using UEP, a fast and reliable open-source code. UEP algorithm can be found at: https://github.com/pepamengual/UEP. Supplementary data are available at Bioinformatics online.

Empirical interatomic potential for Fe-C system using original Finnis-Sinclair potential function

The Finnis-Sinclair (FS) potential is one of the three-body potentials and the potential function is the simplest in them. We developed the FS potential for an Fe-C binary system without changing the original form of the function. The potential parameters for the Fe-C and C-C interactions were determined to fit the physical properties (structural parameters, bulk modulus and cohesive energy) of five iron carbides (γ′-Fe4C, θ-Fe3C, χ-Fe5C2ο-Fe7C3 and NaCl type-FeC). The developed potential reproduced fourteen iron carbides and migration energy barriers of interstitial carbon atoms in body-centered cubic (bcc) and face-centered cubic (fcc) irons. Moreover, the reproducibility of the phonon densities of states for the iron atoms of cementite (θ-Fe3C) and hexagonal-Fe7C3 (h-Fe7C3) was confirmed and the diffusion coefficient of carbon atoms in bcc iron was good agreement with the experimental value.

Li-Ion Conduction Behaviors of Glass-Ceramic Lithium Thiophosphates: Empirical Force Fields and Molecular Dynamics Simulations

The all-solid-state batteries (ASSBs) have drawn increasing interests and demands as the next-generation rechargeable Li-ion batteries (LIBs) for electric vehicles and energy storage devices since they have much more potentials than conventional LIBs [1,2]. However, all we know any further advances in ASSBs are not possible without solving the current raising issues of ASSBs, such as low Li-ion conductivity (σ ion), structural instability, and high resistance of electrode/electrolyte interface [1,2]. Recently, sulfide-based ASSBs are exhibiting the best performance approaching to the commercialization stage with various material advantages (e.g., excellent σ ion, room-temperature formability, and so on) [3,4]. Despite various recent studies on the development of advanced ASSBs, fundamental understanding of fast Li-ion conductors are still lacking. Here, we present an analysis of the Li-ion migration behavior of glass-ceramic (Li2S)0.75(P2S5)0.25 (LPS) structure, a topic that has not yet been investigated, by employing molecular dynamics (MD) simulations.First, we identified unique PS4 3− anion clusters in the short-range region of the glassy structure and newly developed the empirical pair potential (EPP) of the Li-[PS4 3−] bonds. To reasonably represent the ionic and covalent bonds that constitute Li-[PS4 3−] in γ-Li3PS4, EPP was composed of the long-range Coulombic, short-range Morse, and three-body harmonic potentials [5]. The two-body-interaction E I of the Coulombic and Morse potential was expressed as E I = (qiqj / εr) e 2 + D[e -α(r - r0 ) - 2e-2α(r - r0 )], where qi and qj are the ionic charges of the ion i and j, e is the elementary charge, ε is the dielectric constant, r is the distance between the ion i and j, r0 is the equilibrium distance, D is the well-depth, and α is the stiffness parameter, respectively. The three-body harmonic potential E II was expressed as E II = K(θ - θ0)2 , where K is the prefactor and θ0 is the equilibrium angle, respectively. The final converged fitting values are summarized in Table 1, and well reproduce the experimentally observed thermomechanical properties of γ-Li3PS4 [5]. Employing EPP, we constructed the glass−ceramic structure including the crystalline γ-Li3PS4, interfacial, and glassy LPS regions. The density obtained from each part of the glass−ceramic LPS structure agree well with the reported experimental results, and we concluded that our constructed glass−ceramic structure is reasonable. Based on the equilibrated glass-ceramic LPS structure, MD calculation was performed to evaluate the σ ion of each region. The glassy LPS has a σ ion of 4.08 × 10− 1 mS cm− 1, an improvement of ∼100 times relative to that of the γ-phase, which is in agreement with the experiments. By introducing the local S-sublattice analysis, we also found that 40% of the glassy and interfacial region comprised cubic S-sublattice, unlike the crystalline γ-phase, which consisted of only hexagonally closed-packed S-sublattice. These S-sublattice evolutions in the interfacial and glassy domains led to a notable improvement of σ ion.In summary, we determined the EPP of the Li-[PS4 3-] building blocks in (Li2S)0.75(P2S5)0.25 and predicted the σ ion of its glass-ceramic structure. The Li-ion conduction characteristics in the crystalline/interfacial/glassy structure were decomposed by considering the structural ordering differences, The superior σ ion of the glassy structure could be attributed to the fact that ~40% of its structure consists of the short-ranged cubic S-sublattice instead of hexagonally close-packed γ-phase. These results provide new directions for understanding glass−ceramic sulfides with the view of achieving superior Li-ion conducting materials as a solid electrolyte for ASSBs.

Studying the Validity of the Quasi-Classical Approach to Three-Body Decays

The hyperspherical harmonics approach is especially suited to studies of true three-body decays. Reducing the hyperspherical equations set to a single-channel approximation provides the basis for using the standard quasi-classical expression for calculating resonance widths. It is shown that the quasi-classical approach is itself quite precise when applied to the three-body single-channel effective potentials. However, reduction to the single-channel formalism seems to be unacceptable, as it leads to considerable overestimation of decay widths.

Few-body structures in the mirror nuclei O11 and Li11

We investigate the dripline mirror nuclei, $^{11}$Li and $^{11}$O, located on the neutron and proton dripline, respectively. We calculate the lowest four states, $3/2^-$, $1/2^+$, $3/2^+$ and $5/2^+$, built on double occupancy in the nuclear $s_{1/2}$ and $p_{1/2}$ valence single-particle states. We use the hyperspherical adiabatic expansion method to solve the three-body problem for a frozen nuclear core surrounded by two identical nucleons. The four analogue states in $^{11}$O are obtained with precisely the same interactions as used for the four states in $^{11}$Li, except for addition of the Coulomb interaction from the charge of the substituted valence protons. Surprisingly the four energies deviate from each other only by less than a few hundred keV. Any of them could then turn out to be the ground state, due to the uncertainty related to the angular momentum and parity dependence of the three-body potential. Still, our calculations marginally favor the $1/2^+$ state. The structures of these four states in $^{11}$O deviate substantially from the analogue states in the mirror, $^{11}$Li.

A Non-Ordinary State-Based Peridynamic Constitutive Model Based on Three-Body Interaction Potential and Its Implementation on Algorithm

In the framework of peridynamics (PD), bond-based constitutive model is more intuitional but less universal than that of state-based one. In order to demonstrate the advantages of these two models, a non-ordinary state-based peridynamic constitutive model is developed based on three-body interaction potential. An explicit general relation between PD material parameters and elastic constants (Young’s modulus and Poisson’s ratio) is rigorously derived, without the need for any particular assumptions about the modes of deformation. Two numerical examples, namely, the uniaxial tension of a bar and the penetration of a plate impacted by a rigid ball, respectively, are presented. Results show that the proposed constitutive model can be used to correctly and effectively characterize the Poisson’s effect of solid deformation and fragmentation caused by impact.

A Computational Model of Cd2+ Doped Fluorapatite Ca10(PO4)6F2 Biomaterial by Molecular Dynamics Simulations

We have presented a computational model studied with the Cd2+ ions doped hexagonal fluorapatite (FAP), Ca10(PO4)F2 by classic molecular dynamics (MD) simulations using the general utility lattice program (GULP). The potential model has included long-range Coulomb interactions, general three-body, Buckingham and spring (core-shell) interatomic potentials. The Cd2+ ions have substituted into the Ca2+ sublattice of FAP. The structure optimization calculations are carried out for each composition of CdxCa10-x(PO4)F2 (x=1-9) by minimizing the energy of the system. We have predicted lattice parameters, density, bulk modulus and elastic constants of new stoichiometric apatites. The computed results are compared with available experimental data and those obtained by other methods [1]. We have concluded that those interatomic potentials can be applied to Cd2+ ions doped mineral apatites. The developed computing model may provide a useful method in understanding and design of new biomaterials.

Embryonic Iridium nanoclusters (n=3–13): A molecular dynamics computer simulation

The determination of the physical and chemical properties of small nanoparticles plays a fundamental role in homogeneous and heterogeneous catalysis since a large number of the surface atoms of these nanoparticles can be exposed to chemical reactions, as well as in chemisorption, solid state physics, laser physics, crystal growth, epitaxy and surface science in general as most recent experimental and theoretical investigations have been disclosed. An empirical many-body Potential Energy Function (PEF) incorporating two-plus three-body atomistic potential derived by fitting experimental data pertaining to bulk Iridium has been applied to study the structural stability and energetics of Iridium nanoparticles of Irn([Formula: see text]–13). A constant temperature Molecular Dynamics (MD) technique is employed in the simulations. It is found that the energetically most stable structures of Iridium nanoparticles are in three-dimensional distorted compact forms close to symmetric geometries with the MD technique. The theoretical predictions are compared to the available theoretical and experimental literature data for binding energies, bond lengths and the most stable nanocluster geometry.

General energy-strain scheme for accurate evaluation of the Born elasticity term for solid and liquid systems under finite temperature and pressure conditions

The stress fluctuation approach is well known for evaluation of elastic constants due to its remarkable advantages of rapid convergence and the use of unstrained systems. The major contribution to the elastic constants comes from the Born term of the formula. However, the demand of the second energy derivative sets challenges for systems with many-body potentials. In this study, a general energy-strain scheme is proposed to evaluate the Born term of the elastic constants of solids under finite temperature and pressure conditions. It is shown theoretically how the Born term can be extracted from the system’s potential energy variation under a small strain. Then this prediction is further verified by using a pairwise potential and a three-body potential, the Lennard-Jones (LJ) model and crystalline silicon with a Stillinger–Weber potential. The results show that the Born term from the energy-strain scheme agrees very well with the one obtained by analytical formula. Incorporating this term in the stress fluctuation formalism, we investigate the elastic constants of LJ system under various pressures and temperatures. It is found that this scheme is also valid for liquid state.

Contribution of chiral three-body forces to the monopole component of the effective shell-model Hamiltonian

We present a study of the role played by realistic three-body forces in providing a reliable monopole component of the effective shell-model Hamiltonian. To this end, starting from a nuclear potential built up within the chiral perturbation theory, we derive effective shell-model Hamiltonians with and without the contribution of the three-body potential and compare the results of shell-model calculations with a set of observables that evidence shell-evolution properties. The testing ground of our investigation are nuclei belonging to fp shell, since the shell evolution towards shell closures in 48Ca and 56Ni provides a paradigm for shell-model Hamiltonians. Our analysis shows that only by including contributions of the three-body force the monopole component of the effective shell-model Hamiltonian is then able to reproduce the experimental shell evolution towards and beyond the closure at N=28.

Molecular Calculation of the Critical Parameters of Classical Helium

We compute the vapor-liquid critical coordinates of a model of helium in which nuclear quantum effects are absent. We employ highly accurate ab initio pair and three-body potentials and calculate the critical parameters rigorously in two ways. First, we calculate the virial coefficients up to the seventh and find the point where an isotherm satisfies the critical conditions. Second, we use Gibbs Ensemble Monte Carlo (GEMC) to calculate the vapor-liquid equilibrium, and extrapolate the phase envelope to the critical point. Both methods yield results that are consistent within their uncertainties. The critical temperature of "classical helium" is 13.0 K (compared to 5.2 K for real helium), the critical pressure is 0.93 MPa, and the critical density is 28.4 mol·L-1, with expanded uncertainties (corresponding to a 95% confidence interval) on the order of 0.1 K, 0.02 MPa, and 0.5 mol·L-1, respectively. The effect of three-body interactions on the location of the critical point is small (lowering the critical temperature by roughly 0.1 K), suggesting that we are justified in ignoring four-body and higher interactions in our calculations. This work is motivated by the use of corresponding-states models for mixtures containing helium (such as some natural gases) at higher temperatures where quantum effects are expected to be negligible; in these situations, the distortion of the critical properties by quantum effects causes problems for the corresponding-states treatment.

Effects of an attractive three-body interaction on a spin-1 Bose Hubbard model

We study the effects of an attractive three-body interaction potential on a spin-1 ultracold Bose gas using the mean field approach (MFA). For an antiferromagnetic interaction, the third Mott insulator (MI) lobe is predominantly affected, where it completely engulfs the second and the fourth MI lobes at large values of interaction strength. However, no significant change is observed beyond the fourth MI lobe. The formation of the spin singlet (nematic) MI phase and the different order of phase transitions to the superfluid phase have been carefully scrutinized with the help of spin eigenvalues and the spin nematic order parameter. In the ferromagnetic case, the phase diagram shows similar features to that of a scalar Bose gas. We have compared our results on the MFA phase diagrams for both types of interaction potential via a perturbation expansion in both cases.

Molecular simulation of orthobaric isochoric heat capacities near the critical point.

A molecular simulation strategy is investigated for detecting the divergence of the isochoric heat capacity (C_{V}) on the vapor and liquid coexistence branches of a fluid near the critical point. The procedure is applied to the empirical Lennard-Jones potential and accurate state-of-the-art ab initio two-body and two-body + three-body potentials for argon. Simulations with the Lennard-Jones potential predict the divergence of C_{V}, and the phenomenon is also observed for both two-body and two-body + three body potentials. The potentials also correctly predict the crossover between vapor and liquid C_{V} values and the subcritical liquid C_{V} minimum, which marks the commencement C_{V} divergence. The effect of three-body interactions is to delay the onset of divergence to higher subcritical temperatures.

Structure and dynamics of B2O3 melts and glasses: From ab initio to classical molecular dynamics simulations

Boron oxide (B2O3) is investigated by a combination of ab initio (DFT-based) molecular dynamics (MD) simulations and classical MD simulations. From the trajectories of the ab initio MD simulation, we derive a three-body interaction potential which is used in classical MD simulations to study various structural and dynamic properties on larger time and length scales than possible in the ab initio simulations. Differences and similarities to the structure and dynamics of other network glass formers such as SiO2 and GeO2 are discussed. Moreover, various properties as obtained from the simulations are compared to those from experiments of B2O3.

Thermodynamic Properties of Vapor-Liquid Equilibria from Monte-Carlo Simulation using ab initio Intermolecular Potentials of Systems H2-H2 and F2-F2

Abstract In this work, we have been carried out GEMC-NVT simulations in the temperature range 18 K–32 K for fluid hydrogen and in range 60 K–140 K for fluid fluorine using four our developed ab initio 5-site intermolecular potentials for dimers H2-H2 and F2-F2, respectively. The thermodynamic properties of vapor-liquid equilibria and the critical points of fluids hydrogen and fluorine were calculated with the obtained densities of coexisting phases and vapor pressures. The simulation results drived from ab initio pair potentials were compared with those from ab initio potential plus three-body Axilrod-Teller potential and experimental data as well as those from Monte Carlo simulation using Lennard-Jones potentials, Deiters equation of state (D1-EOS) and Benedict-Webb-Rubin equation of state (EOS) reported in the literature.

Realistic shell-model calculations for p -shell nuclei including contributions of a chiral three-body force

In this paper we present an evolution of our derivation of the shell-model effective Hamiltonian, namely introducing effects of three-body contributions. More precisely, we consider a three-body potential at next-to-next-to-leading order in chiral perturbation theory, and the induced three-body forces that arise from many-body correlations among valence nucleons. The first one is included, in the derivation of the effective Hamiltonian for one- and two-valence nucleon-systems, at first order in the many-body perturbation theory. Namely, we include only the three-body interaction between one or two valence nucleons and those belonging to the core. For nuclei with more than two valence particles, both induced - turned on by the two-body potential - and genuine three-body forces come into play. Since it is difficult to perform shell-model calculations with three-body forces, these contributions are estimated for the ground-state energy only. In order to establish the reliability of our approximations, we focus attention on nuclei belonging to the p shell, aiming to benchmark our calculations against those performed with the ab initio no-core shell-model. The obtained results are satisfactory, and pave the way to the application of our approach to nuclear systems with heavier masses.