Three-body Interaction Term Research Articles

Investigating the impact of non-spherical bodies and three-body interactions on equilibrium dynamics in the circular restricted three-body problem

In this paper, we study a modified version of the classical restricted 3-body problem, which introduces an additional mutual interaction force. Moreover, we extend our analysis to include non-spherical shapes, specifically prolate or oblate shapes, for the primary bodies within the system. Our main objective is to investigate how the additional interaction and non-sphericity of the primaries influence the locations and dynamical characteristics of the equilibrium points in the system. To accomplish this, we employ standard numerical methods and techniques. Through a meticulous examination of the system’s parameter space, we have identified a range of 1 to 13 libration points. We have observed that the total number of equilibrium points is directly related to the sign and intensity of the three-body interaction term. Consequently, our findings reveal a substantial difference when compared to scenarios where only three-body interactions or the non-sphericity of the primaries are considered independently.

Structural phases of classical 2D clusters with competing two-body and three-body interactions

In modeling systems of interacting particles, many-body terms beyond pairwise interactions are often overlooked. Nevertheless, in certain scenarios, even small contributions from three-body or higher-order terms can disrupt significant changes in their collective behavior. Here we investigate the effects of three-body interactions on the structure and stability of 2D, harmonically confined clusters. We consider clusters with three distinct pairwise interactions: , , and , thus covering a wide range of condensed and soft matter systems, such as vortices in mesoscopic superconductors, charged colloids, and dusty plasma. In each case, we evaluate the energetics and normal mode spectra of equilibrium and metastable configurations as the intensity of an attractive, Gaussian three-body potential is varied. We demonstrate that, above a threshold value of the three-body energy strength, the cluster shrinks and eventually becomes self-sustained, that is, it remains cohesive after the confinement potential is shut down. Depending on the strengths of the two-body and three-body interaction terms, this compaction can be continuous or abrupt. The latter case is characterized by a discontinuous jump in the particle density and coexsitence of the compact and non-compact phases as metastable states, as in a first-order phase transition. For some values of the particle number, the compaction is preceded by one or more structural changes, resulting in configurations not usually seen in purely pairwise-additive clusters.

Fast and accurate prediction of material properties with three-body tight-binding model for the periodic table.

Parametrized tight-binding models fit to first-principles calculations can provide an efficient and accurate quantum mechanical method for predicting properties of molecules and solids. However, well-tested parameter sets are generally only available for a limited number of atom combinations, making routine use of this method difficult. Furthermore, many previous models consider only simple two-body interactions, which limits accuracy. To tackle these challenges, we develop a density functional theory database of nearly 1 000 000 materials, which we use to fit a universal set of tight-binding parameters for 65 elements and their binary combinations. We include both two-body and three-body effective interaction terms in our model, plus self-consistent charge transfer, enabling our model to work for metallic, covalent, and ionic bonds with the same parameter set. To ensure predictive power, we adopt a learning framework where we repeatedly test the model on new low-energy crystal structures and then add them to the fitting data set, iterating until predictions improve. We distribute the materials database and tools developed in this paper publicly.

Development of a fully analytical equation of state using ab initio interaction potentials. Application to pure simple fluids: Noble gases Ne, Ar, Kr, and Xe

In this work, we have extended the first-order mean spherical approximation (FMSA) equation of state (EOS) of Tang and Lu [J. Chem. Phys., 99, 9828 (1993)] in order to predict accurately fluid phase diagrams using ab initio potentials. At this level of development, we restricted to simple spherical compounds.The original equation based on hard-core two-Yukawa (HC2Y) was improved by the following:•Adding a new approximate simple correction to include higher orders in the development of Tang and Lu to get an analytical model closer to the full MSA.•Including a term to a better account for the long-range behavior of two-body potentials.•Adding a three-body interaction term (1st order perturbation) based on Axilrod-Teller potential.A general recommendation for setting the hard-sphere diameter value was also given.The predictive capability of the EOS was tested in a systematic manner. First, we checked that various simple theoretical potential (Mie n-6 and Exp n-6) phase diagrams are well reproduced. Second, the EOS was used for predicting fluid phase diagrams of the pure noble gases fluid series Ne, Ar, Kr, and Xe using realistic (i.e. derived from ab initio) two-body and three-body interaction potentials. The model is in good agreement with the experimental phase diagrams.As a conclusion, the simple statistical-mechanics-based fully analytical EOS developed in this work predicts accurately fluid phase diagrams of simple spherical compounds using ab initio potentials. No adjustable parameter was used. This EOS constitutes a strong basis for future development of a predictive model based on ab initio potentials and applicable to more complex compounds.

Fragmentation-Based Decomposition of a Metalloenzyme-Substrate Interaction: A Case Study for a Lytic Polysaccharide Monooxygenase.

We present a novel decomposition scheme for electronic interaction energies based on the flexible formulation of fragmentation schemes through fragment combination ranges (FCRs; J. Chem. Phys., 2021, 155, 164105). We devise a clear additive decomposition with contribution of nondisjoint fragments and correction terms for overlapping fragments and apply this scheme to the metalloenzyme-substrate complex of a lytic polysaccharide monooxygenase (LPMO) with an oligosaccharide. By this, we further illustrate the straightforward adaptability of the FCR-based schemes to novel systems. Our calculations suggest that the description of the electronic structure is a larger error source than the fragmentation scheme. In particular, we find a large impact of the basis set size on the interaction energies. Still, the introduction of three-body interaction terms in the fragmentation setup improves the agreement to the supermolecular reference. Yet, the qualitative results for the decomposition scheme with two-body terms only largely agree within the investigated electronic-structure approaches and basis sets, which are B97-3c, DFT (TPSS and B3LYP), and MP2 methods. The overlap contributions are found to be small, allowing analysis of the interaction energy into individual amino acid residues: We find a particularly strong interaction between the substrate and the LPMO copper active site.

Controlling the anisotropic self-assembly of polybutadiene-grafted silica nanoparticles by tuning three-body interaction forces.

Recently, the significant improvements in polymer composites properties have been mainly attributed to the ability of filler nanoparticles (NPs) to self-assemble into highly anisotropic self-assembled structures. In this work, we investigate the self-assembly of core-shell NPs composed of a silica core grafted with polybutadiene (PB) chains, generating the so-called "hairy" NPs (HNPs), immersed in tetrahydrofuran solvent. While uncoated silica beads aggregate forming uniform compact structures, the presence of a PB shell affects the silica NPs organization to the point that by increasing the polymer density at the corona, they tend to self-assemble into linear chain-like structures. To reproduce the experimental observations, we propose a theoretical model for the two-body that considers the van der Waals attractive energy together with the polymer-induced repulsive steric contribution and includes an additional three-body interaction term. This term arises due to the anisotropic distribution of PB, which increases their concentration near the NPs contact region. The resulting steric repulsion experienced by a third NP approaching the dimer prevents its binding close to the dimer bond and favors the growth of chain-like structures. We find good agreement between the simulated and experimental self-assembled superstructures, confirming that this three-body steric repulsion plays a key role in determining the cluster morphology of these core-shell NPs. The model also shows that further increasing the grafting density leads to low-density gel-like open structures.

Slow dynamics of the Fredkin spin chain

The dynamical behavior of a quantum many-particle system is characterized by the lifetime of its excitations. When the system is perturbed, observables of any non-conserved quantity decay exponentially, but those of a conserved quantity relax to equilibrium with a power law. Such processes are associated with a dynamical exponent $z$ that relates the spread of correlations in space and time. We present numerical results for the Fredkin model, a quantum spin chain with a three-body interaction term, which exhibits an unusually large dynamical exponent. We discuss our efforts to produce a reliable estimate $z$=3.16(1) through direct simulation of the quantum evolution and to explain the slow dynamics in terms of an excited bond that executes a constrained random walk in Monte Carlo time.

Field-theoretical aspects of one-dimensional Bose and Fermi gases with contact interactions

We investigate local quantum field theories for one-dimensional (1D) Bose and Fermi gases with contact interactions, which are closely connected with each other by Girardeau's Bose-Fermi mapping. While the Lagrangian for bosons includes only a two-body interaction, a marginally relevant three-body interaction term is found to be necessary for fermions. Because of this three-body coupling, the three-body contact characterizing a local triad correlation appears in the energy relation for fermions, which is one of the sum rules for a momentum distribution. In addition, we apply in both systems the operator product expansion to derive large-energy and momentum asymptotics of a dynamic structure factor and a single-particle spectral density. These behaviors are universal in the sense that they hold for any 1D scattering length at any temperature. The asymptotics for the Tonks-Girardeau gas, which is a Bose gas with a hardcore repulsion, as well as the Bose-Fermi correspondence in the presence of three-body attractions are also discussed.

Introducing SU(3) color charge in undergraduate quantum mechanics

We present a framework for investigating effective dynamics of SU(3) color charge. Two- and three-body effective interaction terms inspired by the Heisenberg spin model are considered. In particular, a toy model for a three-source “baryon” is constructed and investigated analytically and numerically for various choices of interactions. vpython is used to visualize the nontrivial color charge dynamics. The treatment should be accessible to undergraduate students who have taken a first course in quantum mechanics, and suggestions for independent student projects are proposed.

Liquid state anomalies and the relationship to the crystalline phase diagram.

A relationship between the observation of a density anomaly and the underlying crystalline phase diagram is demonstrated. The crystal phase diagram and temperature of maximum density (TMD) lines are calculated over a range of parameter space using a Stillinger-Weber potential. Relationships between the loci of density maxima in the PT plane for the liquid state and the underlying crystalline phase diagram are investigated. Two key potential parameters are systematically varied in order to control the balance between the model two- and three-body interaction terms, and the relative effects of varying the potential parameters analyzed. The respective TMD lines diverge at extreme values with one set of lines showing a reentrant behavior. For each parameter set the TMD lines are extrapolated to T=0K. The corresponding pressures are related to the crystalline phase diagram and are found to lie on or near specific crystal-crystal coexistence lines for a wide range of potential parameters. The density anomaly is observed to vanish corresponding to regions in the crystal phase diagram which lack crystal-crystal coexistence lines potentially offering a new interpretation for the emergence of anomalous behavior.

Chain-like ground states in three dimensions

Abstract We investigate the minimization of configurational energies of Brenner type. These include two- and three-body interaction terms, which favor the alignment of first neighbors. In particular, such configurational energies arise in connection with the molecular-mechanical modeling of covalent$sp$-bonding in carbon. Ground states in three dimensions are characterized and the stability of chains and rings is discussed. The interaction energy is then augmented with terms corresponding to weaker interactions favoring the stratification of configurations. This gives rise to stratified structures, which are reminiscent of nanoscrolls and multi-wall nanotubes. Optimal stratified configurations are identified and their geometry is discussed.

Effective three-body interactions for bosons in a double-well confinement

When describing the low-energy physics of bosons in a double-well potential with a high barrier between the wells and sufficiently weak atom-atom interactions, one can to a good approximation ignore the high energy states and thereby obtain an effective two-mode model. Here, we show that the regime in which the two-mode model is valid can be extended by adding an on-site three-body interaction term and a three-body interaction-induced tunneling term to the two-mode Hamiltonian. These terms effectively account for virtual transitions to the higher energy states. We determine appropriate strengths of the three-body terms by an optimization of the minimal value of the wave function overlap within a certain time window. Considering different initial states with three or four atoms, we find that the resulting model accurately captures the dynamics of the system for parameters where the two-mode model without the three-body terms is poor. We also investigate the dependence of the strengths of the three-body terms on the barrier height and the atom-atom interaction strength. The optimal three-body interaction strengths depend on the initial state of the system.

ChIMES: A Force Matched Potential with Explicit Three-Body Interactions for Molten Carbon.

We present a new force field and development scheme for atomistic simulations of materials under extreme conditions. These models, which explicitly include two- and three-body interactions, are generated by fitting linear combinations of Chebyshev polynomials through force matching to trajectories from Kohn-Sham density functional theory (DFT). We apply our method to liquid carbon near the diamond/graphite/liquid triple point and at higher densities and temperatures, where metallization and many-body effects may be substantial. We show that explicit inclusion of three-body interaction terms allows our model to yield improved descriptions of both dynamic and structural properties over previous empirical potential efforts, while exhibiting transferability to nearby state points. The simplicity of our functional form and subsequent efficiency of parameter determination allow for extension of DFT to experimental time and length scales while retaining most of its accuracy.

Jastrow-like ground states for quantum many-body potentials with near-neighbors interactions

We completely solve the problem of classifying all one-dimensional quantum potentials with nearest- and next-to-nearest-neighbors interactions whose ground state is Jastrow-like, i.e., of Jastrow type but depending only on differences of consecutive particles. In particular, we show that these models must necessarily contain a three-body interaction term, as was the case with all previously known examples. We discuss several particular instances of the general solution, including a new hyperbolic potential and a model with elliptic interactions which reduces to the known rational and trigonometric ones in appropriate limits.

Three-body interactions improve contact prediction within direct-coupling analysis.

The prediction of residue contacts in a protein solely from sequence information is a promising approach to computational structure prediction. Recent developments use statistical or information theoretic methods to extract contact information from a multiple sequence alignment. Despite good results, accuracy is limited due to usage of two-body interactions within a Potts model. In this paper we generalize this approach and propose a Hamiltonian with an additional three-body interaction term. We derive a mean-field approximation for inference of three-body couplings within a Potts model which is fast enough on modern computers. Finally, we show that our model has a higher accuracy in predicting residue contacts in comparison with the plain two-body-interactionmodel.

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.

Parent Hamiltonians for lattice Halperin states from free-boson conformal field theories

We introduce a family of many-body quantum states that describe interacting spin one-half hard-core particles with bosonic or fermionic statistics on arbitrary one- and two-dimensional lattices. The wave functions at lattice filling fraction ν=2/(2m+1) are derived from deformations of the Wess–Zumino–Witten model su(3)1 and are related to the (m+1,m+1,m) Halperin fractional quantum Hall states. We derive long-range SU(2) invariant parent Hamiltonians for these states which in two dimensions are chiral t–J–V models with additional three-body interaction terms. In one dimension we obtain a generalisation to open chains of a periodic inverse-square t–J–V model proposed in [25]. We observe that the gapless low-energy spectrum of this model and its open-boundary generalisation can be described by rapidity sets with the same generalised Pauli exclusion principle. A two-component compactified free boson conformal field theory is identified as the low-energy effective theory for the periodic inverse-square t–J–V model.

Consistent description of C12 and O16 using a finite-range three-body interaction

Consistent description of 12C and 16O has been a long standing problem of microscopic alpha cluster models, where the wave function is fully antisymmetrized and the effective interaction is applied not between alpha clusters but between nucleons. When the effective interaction is designed to reproduce the binding energy of 16O (four alpha), the binding energy of 12C (three alpha) becomes underbound by about 10 MeV. In the present study, by taking into account the coupling with the jj-coupling shell model components and utilizing Tohsaki interaction, which is phenomenological but has finite-range three-body interaction terms, we show that consistent understanding of these nuclei can be achieved. The original Tohsaki interaction gives small overbound of about 3 MeV for 16O, and this is improved by slightly modifying three-body Majorana exchange parameter. Also, the coupling with the jj-coupling shell model wave function strongly contributes to the increase of the binding energy of 12C. So far the application of Tohsaki interaction has been limited to 4N nuclei, and here, we add Bartlet and Heisenberg exchange terms in the two-body interaction for the purpose of applying it to neutron-rich systems, and it is applied to 6He.

Deconvoluting chain heterogeneity from driven translocation through a nanopore

We study translocation dynamics of a driven compressible semi-flexible chain consisting of alternate blocks of stiff and flexible segments of size m and n, respectively, for different chain length N in two dimensions (2D). The free parameters in the model are the bending rigidity which controls the three-body interaction term, the elastic constant kF in the FENE (bond) potential between successive monomers, as well as the segmental lengths m and n and the repeat unit and the solvent viscosity γ. We demonstrate that due to the change in entropic barrier and the inhomogeneous viscous drag on the chain backbone a variety of scenarios are possible, amply manifested in the waiting time distribution of the translocating chain. This information can be deconvoluted to extract the mechanical properties of the chain at various length scales and thus can be used to nanopore based methods to probe bio-molecules, such as DNA, RNA and proteins.

Ultrafast pump-probe and 2DIR anisotropy and temperature-dependent dynamics of liquid water within the E3B model.

Recently, Tainter et al. [J. Chem. Phys. 134, 184501 (2011)] reparameterized a new rigid water model (E3B) that explicitly includes three-body interactions in its Hamiltonian. Compared to commonly used water models such as SPC/E and TIP4P, the new model shows better agreement with experiment for many physical properties including liquid density, melting temperature, virial coefficients, etc. However, the dynamics of the E3B model, especially as a function of temperature, has not been systematically evaluated. Experimental nonlinear vibrational spectroscopy is an ideal tool to study the dynamics of matter in condensed phases. In the present study, we calculate linear and nonlinear vibrational spectroscopy observables for liquid water using the E3B model at five temperatures: 10, 30, 50, 70 and 90°C. Specifically, we calculate absorption and Raman spectra and pump-probe anisotropy for HOD in H2O at all temperatures, frequency-resolved pump-probe anisotropy for HOD in both H2O and D2O at 30°C, and 2DIR anisotropy for HOD in D2O at 30°C. In all cases, we find reasonable agreement with experiment, and for the ultrafast spectroscopy our results are a significant improvement over those of the SPC/E model. A likely reason for this improvement is that the three-body interaction terms in the E3B model are able to model cooperative hydrogen bonding. We also calculate rotational and frequency relaxation times at all temperatures, and fit the results to the Arrhenius equation. We find that the activation energy for hydrogen-bond switching in liquid water is 3.8 kcal/mol, which agrees well with the experimental value of 3.7 kcal/mol obtained from anisotropy decay experiments.