Two-body Potential Research Articles

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 potential of Vainshtein screened theories

Adding a light scalar degree of freedom to General Relativity often induces a fifth force whose magnitude is strongly constrained by laboratory experiments and solar system tests. The Vainshtein screening mechanism ensures that the effects of this supplementary force are suppressed in dense environments. However, the field solution of theories exhibiting Vainshtein screening is only known in spherically symmetric situations. In this article we examine in different configurations the two-body potential energy of pointlike particles in a specific $P(X)$ theory with Vainshtein screening. We use ideas borrowed from the Effective One-Body approach of Buonanno and Damour in order to restrict the form of the solution. Our results indicate that, even if Vainshtein screening is also fully active in the equal-mass case, the nonlinear dependance of the two-body energy on the mass ratio implies a violation of the Equivalence Principle. We compute the contribution of this effect to the Moon orbit for generic theories equipped with Vainshtein screening.

Many-body effects on Equation of state of solid Ar4

Based on the first-principles, using many-body expansion method and the double cluster with full single and double excitations plus perturbative treatment of triples (CCSD(T)) calculation method and augmented correlation consistent quadruple zeta (aug-cc-pVQZ) basis set, many-body contributions to the equation of state (EOS) of solid argon are accurately calculated with the atomic distance R from 2.0Å to 3.6Å at the room temperature (T=300K) in the experimentally studied range of pressures (0∼80GPa). In addition, we obtain the two- and three-body potential energies of fcc solid Ar. The results showed that, only taking into account the two-body potential, our calculated results were in good agreement with the experimental values, the results of GGA and LDA at the low-pressure regions (<15GPa). Further adding three-body term up to 80GPa, and it may be helpful to accurately explain the phenomenon of the experiment above 80GPa when the effect of four-body and higher-body potential pressures are considered.

A microscopic study of spin-polarized 6Li atoms in highly elongated traps using the static fluctuation approximation (SFA)

The thermodynamic properties of spin-polarized 6Li atoms in highly elongated traps are studied within the Static Fluctuation Approximation. The chemical potential μ, energy per particle U/N, specific heat capacity CV/N, and the effective magnetic field h are determined as a function of temperature and potential strength (magnetic field B). We used the contact potential as the two-body interaction potential. For a repulsive interaction μ and U increase parabolically with B, while for an attractive interaction both increase monotonically with B until saturation at B larger than the resonance field. The effect of the two-body interaction on CV appears at temperatures comparable with the Fermi temperature. μ and U/N of the system were studied of different channels; It is found that these quantities are channel dependent, and the behavior of h at low temperature depends on the potential strength. Our results are consistent with that obtained by the mean-field Bogoliubov–de Gennes method.

Like-Charge Attraction between Metal Nanoparticles in a 1∶1 Electrolyte Solution.

We calculate the force between two spherical metal nanoparticles of charge Q_{1} and Q_{2} in a dilute 1∶1 electrolyte solution. Numerically solving the nonlinear Poisson-Boltzmann equation, we find that metal nanoparticles with the same sign of charge can attract one another. This is fundamentally different from what is found for like-charged, nonpolarizable, colloidal particles, the two-body interaction potential for which is always repulsive inside a dilute 1∶1 electrolyte. Furthermore, the existence of like-charge attraction between spherical metal nanoparticles is even more surprising in view of the result that such attraction is impossible between parallel metal slabs, showing the fundamental importance of curvature. To overcome a slow convergence of the numerical solution of the full nonlinear Poisson-Boltzmann equation, we developed a modified Derjaguin approximation which allows us to accurately and rapidly calculate the interaction potential between two metal nanoparticles or between a metal nanoparticle and a phospholipid membrane.

Static Two-Body Potential at Fifth Post-Newtonian Order.

We determine the gravitational interaction between two compact bodies up to the sixth power in Newton's constant, G_{N}, in the static limit. This result is achieved within the effective field theory approach to general relativity, and exploits a manifest factorization property of static diagrams which allows us to derive static post Newtonian (PN) contributions of (2n+1) order in terms of lower order ones. We recompute in this fashion the 1PN and 3PN static potential, and present the novel 5PN contribution.

Effects of an induced three-body force in the incident channel of ( d,p ) reactions

A widely accepted practice for treating deuteron breakup in $A(d,p)B$ reactions relies on solving a three-body $A+n+p$ Schr\"odinger equation with pairwise $A$-$n$, $A$-$p$ and $n$-$p$ interactions. However, it was shown in [Phys. Rev. C \textbf{89}, 024605 (2014)] that projection of the many-body $A+2$ wave function into the three-body $A+n+p$ channel results in a complicated three-body operator that cannot be reduced to a sum of pairwise potentials. It contains explicit contributions from terms that include interactions between the neutron and proton via excitation of the target $A$. Such terms are normally neglected. We estimate the first order contribution of these induced three-body terms and show that applying the adiabatic approximation to solving the $A+n+p$ model results in a simple modification of the two-body nucleon optical potentials. We illustrate the role of these terms for the case of $^{40}$Ca($d,p$)$^{41}$Ca transfer reactions at incident deuteron energies of 11.8, 20 and 56 MeV, using several parameterisations of nonlocal optical potentials.

Heavy-quark spin and flavor symmetry partners of the X(3872) revisited: What can we learn from the one boson exchange model?

Heavy-quark symmetry as applied to heavy hadron systems implies that their interactions are independent of their heavy-quark spin (heavy-quark spin symmetry) and heavy flavour contents (heavy flavour symmetry). In the molecular hypothesis the $X(3872)$ resonance is a $1^{++}$ $D^*\bar{D}$ bound state. If this is the case, the application of heavy-quark symmetry to a molecular $X(3872)$ suggests the existence of a series of partner states, the most obvious of which is a possible $2^{++}$ $D^*\bar{D}^*$ bound state for which the two-body potential is identical to that of the $1^{++}$ $D^*\bar{D}$ system, the reason being that these two heavy hadron-antihadron states have identical light-spin content. As already discussed in the literature this leads to the prediction of a partner state at $4012\,{\rm MeV}$, at least in the absence of other dynamical effects which might affect the location of this molecule. However the prediction of further heavy-quark symmetry partners cannot be done solely on the basis of symmetry and requires additional information. We propose to use the one boson exchange model to fill this gap, in which case we will be able to predict or discard the existence of other partner states. Besides the isoscalar $2^{++}$ $D^*\bar{D}^*$ bound state, we correctly reproduce the location and quantum numbers of the isovector hidden-bottom $Z_b(10610)$ and $Z_b(10650)$ molecular candidates. We also predict the hidden-bottom $1^{++}$ $B^*\bar{B}^*$ and $2^{++}$ $B^*\bar{B}^*$ partners of the $X(3872)$, in agreement with previous theoretical speculations, plus a series of other states. The isoscalar, doubly charmed $1^+$ $D D^*$ and $D^* D^*$ molecules and their doubly bottomed counterparts are likely to bind, providing a few instances of explicitly exotic systems.

Series expansions of the deflection angle in the scattering problem for power-law potentials

We present a rigorous study of the classical scattering for any two-body interparticle potential of the form v(r) = g/rγ, with γ &amp;gt; 0, for repulsive (g &amp;gt; 0) and attractive (g &amp;lt; 0) interactions. We first derive an explicit series expansion of the deflection angle in the impact factor b. Then, we study carefully the modifications of the results when a regularization (softening) is introduced in the potential at small scales. We check and illustrate all the results with the exact integration of the equations of motion.

Effects of finite size of constituent quarks on nucleon–nucleon interaction

We have investigated the effect of the finite size of the constituent quarks on singlet and triplet nucleon–nucleon potentials, obtained in the framework of the SU(2) nonrelativistic quark model using the resonating group method in the Born–Oppenheimer approximation. The full Hamiltonian used in the investigation includes the kinetic energy, two-body confinement potential, one gluon exchange potential, and instanton induced interaction. The effects of the smearing of the contact interactions and the variation of the constituent mass of the quarks are discussed.

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.

Chemical Dynamics Simulation of Energy Transfer: Propylbenzene Cation and N2 Collisions.

Collisional energy transfer of highly vibrationally excited propylbenzene cation in a N2 bath has been studied with chemical dynamics simulations. In this work, an intermolecular potential of propylbenzene cation interacting with N2 was developed from SCS-MP2/6-311++G** ab initio calculations. Using a particle swarm optimization algorithm, the ab initio results were simultaneously fit to a sum of three two-body potentials, consisting of C a-N, C b-N, and H-N, where C a is carbon on the benzene ring and C b is carbon on the propyl side chain. Using the developed intermolecular potential, classical trajectory calculations were performed with a 100.1 kcal/mol excitation energy at 473 K to compare with experiment. Varying the density of the N2 bath, the single collision limit of propylbenzene cation with the N2 bath was obtained at a density of 20 kg/m3 (28 atm). For the experimental excitation energy and in the single collision limit, the average energy transferred per collision, ⟨Δ Ec⟩, is 1.04 ± 0.04 kcal/mol and in good agreement with the experimental value of 0.82 kcal/mol.

Erratum: "Two-body intermolecular potentials from second virial coefficient properties" [J. Chem. Phys. 150, 024503 (2019)

Erratum: "Two-body intermolecular potentials from second virial coefficient properties" [J. Chem. Phys. 150, 024503 (2019)

Role of relativistic effects and three-body forces in nuclear matter properties

The role of three-body force (TBF) and the relativistic corrections (RC) on the equations of state of nuclear matter and $\ensuremath{\beta}$-stable matter (BSM) within the relativistic lowest-order constrained variation (RLOCV) approach are studied. The AV14 potential and its relativistic version $({\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{v}}_{14})$ as well as the AV18 potential are considered as the bare two-body potentials by employing the nuclear many-body Hamiltonian. It is shown that by using ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{v}}_{14}$, all properties of cold nuclear matter can be correctly reproduced if TBF is used in RLOCV framework. The energy and proton abundance of BSM are calculated for a wide range of baryon number densities, which are of interest in astrophysics. It is also shown that by adding RC or TBF to our calculations, the maximum proton abundance is pushed toward lower densities. Furthermore, the particle number densities decrease by including RC and increase when TBF is added to the interactions. The opposite behaviors for the role TBF and RC on saturation properties of nuclear matter as well as proton number densities of nuclear $\ensuremath{\beta}$-stable matter are found. It is also shown that the effects of three-body forces are much larger than those of relativistic corrections.

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.

Molecular interaction between asymmetric ligand-capped gold nanocrystals.

Atomistic molecular dynamics simulations are performed to study the potential of mean force (PMF) between two asymmetric gold nanocrystals (NCs) capped by alkylthiols in a vacuum. We systematically investigate the dependence of the PMF on the sizes and capping ligand lengths of two NCs. The results show that the potential well depth scales linearly with increasing total length of two capping ligands on asymmetric dimers, but it hardly depends on the NC size. The predicted equilibrium distance between two asymmetric NCs grows significantly and linearly with the total size of two NCs and exhibits only a slight increase with increasing total ligand length. These findings are explained in terms of the amount of ligand interdigitation between NC surfaces as well as its alterations caused by the change in ligand length and NC size. Furthermore, we introduce a simple formula to estimate the equilibrium distance of two asymmetric NCs. On the basis of the computed PMFs, we propose an empirical two-body potential between asymmetric capped gold NCs.

Two-body intermolecular potentials from second virial coefficient properties.

A method is reported that enables second virial coefficient properties to be used to obtain relatively simple two-body intermolecular potentials. Generic n-m Lennard-Jones/Mie potentials are transformed into two-body potentials for neon, argon, krypton, and xenon. Comparison with results from highly accurate ab initio potentials indicates good agreement. A complete potential for real fluids is obtained by combining the two-body potentials with a density-dependent term for three-body interactions. Vapor-liquid equilibria molecular simulation data for the new potentials are compared with the experiment, which demonstrates the effectiveness of the two- and three-body contributions. The combination of the two-body 10-8 Lennard-Jones/Mie potential and three-body term is a good overall choice for the noble gases.

Strong Substrate Mediation of Attractive Lateral Interactions of CO on Cu(110).

The mechanism of chemical reactions between adsorbed species is defined by the combined effects of the adsorbate-substrate potential landscape and lateral interactions. Such lateral interactions are therefore integral to catalytic processes, but their study is often complicated by "substrate mediation", the regulation of a two-body potential between adsorbed particles by the surface itself. Substrate mediation can influence the sign and magnitude of lateral interactions. There are notable exceptions of ordered structures forming at low coverage, indicative of short-range attractive forces where repulsive forces are expected to dominate, suggesting a strong substrate-mediated contribution. To explore further the origins of such interactions, we have investigated the adsorption of CO on Cu(110) using a combination of low-temperature microscopy and first-principles calculations. Our studies reveal that lateral adsorbate interactions, which are constrained by the metal surface, regulate the bonding between the adsorbate and substrate. Anisotropic CO-CO coupling is seen to arise from a perfect balance between the intermolecular accumulation of charge that acts as a glue (chemical coupling) at sufficiently large distances to avoid repulsive effects (dipole-dipole coupling and Pauli's repulsion between electron clouds).

Large-N properties of a non-ideal Bose gas

We rigorously discuss the large- thermodynamics of a Bose gas with a short-range two-body potential. Considering the system as a mixture of identical components with a symmetric interaction we calculate numerically the temperature dependence of the leading-order corrections to the depletion of the Bose–Einstein condensate and to the isothermal compressibility.

Renormalisation group analysis of electromagnetic couplings in the pionless effective field theory

.The Wilsonian renormalisation group is applied to a system of two nonrelativistic particles interacting via short-range forces and coupled to an external EM field. By demanding that a fully off-shell one-particle-irreducible 5-point amplitude is independent of the cutoff, a renormalisation group equation is derived for the interaction current density. This is solved to obtain the fixed point corresponding to the unitary limit. The scaling behaviour of perturbations around this point is analysed. Some of these terms are related by gauge invariance to terms in the effective-range expansion; others describe short-range physics that is not included in the two-body potential. We construct observables including the bound-state form factor and show how the scaling of the terms in the interaction current is reflected in the power counting for their contributions to observables.