Three-body Terms Research Articles

Approximate Energy Expression for Spin-Polarized Fermi Liquids

An approximate energy expression is proposed for arbitrarily spin-polarized Fermi liquids with central two-body forces. It is explicitly expressed as a functional of spin-dependent radial distribution functions and can be used conveniently in the variational method. It includes the potential energies completely and the kinetic energies up to main parts of the three-body cluster terms. This approximation is similar to that used previously for spinunpolarized and fully polarized matter. A notable feature of this expression is that it guarantees the necessary conditions on arbitrarily spin-polarized structure functions automatically. The Euler-Lagrange equations are derived from this energy expression and are numerically solved for arbitrarily spin-polarized liquid 3 He. The results for liquid 3 He with the HFDHE2 potential are consistent with the nearly ferromagnetic property.

Three-body monopole corrections to realistic interactions.

It is shown that a very simple three-body monopole term can solve practically all the spectroscopic problems-in the p, sd, and pf shells-that were hitherto assumed to need drastic revisions of the realistic potentials.

LOCV calculation for the uniform electron fluid at finite temperature

The free energy of the homogeneous electron fluid at finite temperature is obtained using the lowest order constrained variational (LOCV) method. In order to test the convergence of cluster expansion series the three-body cluster terms are calculated with the LOCV correlation functions. The results agree reasonably with those of Monte Carlo, coupled-cluster, perturbational expansion etc, techniques at zero temperature. The flashing and critical temperatures as well as the critical exponent are found to be about 0.6, 1.3 eV and 0.384 respectively. A similar liquid-gas phase transition to that of nuclear matter and liquid He3 is observed.

Prediction of the Interface Response Functions for Amorphous and Crystalline Phases of Silicon and Germanium

AbstractInterface response functions that govern the solidification kinetics of amorphous and crystalline phases of Si and Ge have been determined for reparameterized versions of the Stillinger-Weber (SW) potential. The strength of the three-body term in the SW potential and the energy scaling parameter were modified to obtain agreement with the experimental melting temperatures of both the amorphous and crystalline phases. These modified models were used to produce predictions of the interface response function for both Si and Ge that adequately fit the few known experimental data.

The nonadditive effects in the mixed trimers composed of the water dimer and diatomics H 2, HF, HCl, HBr, and ClF

Optimal structures, interaction energies and harmonic vibrational frequencies of the (H 2O) 2⋯HX, HX=H 2, HF, HCl, HBr, and (H 2O) 2⋯CIF ternary complexes have been determined from the supermolecular MP4 and CCSD(T) calculations with the aug-cc-pVDZ and the aug-cc-pVTZ basis sets. We located three low-energy configurations on the potential energy surface corresponding to H-bonded cyclic complexes and one linear structure in the case of (H 2O) 2⋯CIF and (H 2O) 2⋯H 2. The tunneling motion of the water molecule across the plane of the heavy atom ring was studied. The contribution of the three-body term represents as much as 24% for (H 2O) 2⋯HBr and the smallest value of 5% for (H 2O) 2⋯H 2 of the total CCSD(T) interaction energy. The nonadditivity originates mainly from the induction effect.

MD and MC simulations of hydrated manganous ion including three-body effects

An ab initio three-body analytical potential function was constructed for the Mn(II)–water system. Classical molecular dynamics (MD) and Monte Carlo (MC) simulations including the three-body correction terms were carried out to study the hydration structure of Mn(II). Structural data in form of radial distribution functions, coordination numbers, angular distributions and bond length distributions were obtained. The inclusion of the three-body correction was found to be crucial for the description of the system, and results thus obtained are in good agreement with experimental values.

Development of first-principles interaction model potentials. An application to the study of the bromide hydration

This work presents the development of first-principles bromide ion–water interaction potentials using the mobile charge density in harmonic oscillators-type model. This model allows for a flexible and polarizable character of the interacting molecules and has already been parametrized for water–water interactions. The prospected potential energy surfaces of the bromide ion-water system were computed quantum-mechanically at Hartree–Fock and Møller–Plesset second-order perturbation levels. In addition to the ion–solvent molecule pair, structures formed by the anion and two or three water molecules were considered in order to include many body effects. Minimizations of hydrated bromide clusters in gas phase [Br(H2O)n]− (n=1–6,10,15,20) and Monte Carlo computations of bromide aqueous solutions were performed to test the new potentials. Both structural and thermodynamic properties have been studied in detail and compared to the available experimental and theoretical values. From these comparisons, it was concluded the importance of including basis set superposition error corrections for the two-body interactions, and the small role of both electron correlation on the three-body terms and the four-body terms. Monte Carlo simulation results have also been used to investigate if the presence of the anion significantly affects the intramolecular geometry of the water molecules and the degree of disruption of the water solvent structure in its vicinity.

Energetic and Topological Analyses of Cooperative σH- and πH-Bonding Interactions

A recent high-level ab initio study (J. Phys. Chem. A 2002, 106, 567) analyzed the formation of cooperative πH- and σH-bonding motifs in MP2/6-311++G(2d,2p)-optimized complexes of either one or two water molecules with ethene, propene, or allyl alcohol. The present study explores energetics and electron density redistributions associated with hydrogen bonding interactions in these clusters. Despite a substantial correlation component in the binding energy, the nonadditive three-body term, a descriptor of cooperative effects, is completely accounted for at the Hartree−Fock level. Natural bond orbital analysis attributes this cooperativity to the nonadditive character of charge-transfer interactions among local bond orbitals. Topological analysis of the electron density performed using Bader's theory of atoms in molecules confirms the closed shell, hydrogen-bonding nature of OH···π interactions and indicates their additional floppiness compared to conventional hydrogen bonds. The extension of these calculations to larger molecular systems validates the formation of a cooperative network of πH and σH bonds between the interfacial region of ceramide and water molecules. The OH···π bond serves to tether a water molecule to the trans double bond of the sphingolipid, extending the hydrophilicity of the interfacial region. This may contribute to the differences in biological activity between ceramide and its saturated counterpart, dihydroceramide.

Molecular Dynamics Simulations of the Hydrated Trivalent Transition Metal Ions Ti3+, Cr3+, and Co3+

Molecular dynamics (MD) simulations based on ab initio evaluated two- and three-body potentials were performed for Ti3+, Cr3+, and Co3+ ions in water. The ions' hydration structure was evaluated in terms of radial distribution functions, coordination numbers, and angular distributions. The first solvation shell shows an exact coordination number of 6 for all ions and average M3+−O distances of 2.08, 2.05, and 2.03 A for Ti3+, Cr3+, and Co3+, respectively. The structural parameters obtained after inclusion of three-body correction terms are in good agreement with experimental values. The energies of hydration obtained from three-body corrected molecular dynamics simulations are also in good agreement with experiment, except for Ti3+ where the classical simulations are failing to reproduce the Jahn−Teller effect.

Tracer-diffusion in binary colloidal hard-sphere suspensions

We calculate the short-time translational and rotational self-diffusion coefficients of mixtures of colloidal hard spheres. The influence of hydrodynamic interactions is accounted for by a series expansion of the two-body mobility tensors, and by considering the leading hydrodynamic three-body term. Explicit results are presented for the rotational–translational diffusion coefficients, Ds,Tr and Ds,Tt, of a dilute tracer component in a concentrated host dispersion of hard spheres. These coefficients are shown to depend strongly on the host volume fraction, φ, and on the size ratio, λ, of tracer and host particles. For large λ, the tracer diffusion coefficients are related to the viscosity of the host dispersion by effective Stokes–Einstein relations.

First principles dynamics of Li–He collisional excitation using atomic core potentials

A first principles description of electronic excitation in Li–He colliding pairs is developed introducing l-dependent pseudopotentials and including two- and three-body polarization terms. The treatment combines an eikonal approximation and time-dependent molecular orbitals to provide interatomic potentials, their non-adiabatic couplings, and state populations during interactions. We discuss the effects of the basis set size on the calculations, and compare our results with experiment and other calculations. Our integral cross-sections obtained with a large basis set are in excellent agreement with experiment.

Detailed analysis of the three-quark potential in SU(3) lattice QCD

The static three-quark (3Q) potential is studied in detail using SU(3) lattice QCD with $12^3 \times 24$ at $\beta=5.7$ and $16^3 \times 32$ at $\beta=5.8$, 6.0 at the quenched level. For more than 300 different patterns of the 3Q systems, we perform the accurate measurement of the 3Q Wilson loop with the smearing method, which reduces excited-state contaminations, and present the lattice QCD data of the 3Q ground-state potential $V_{\rm 3Q}$. We perform the detailed fit analysis on $V_{\rm 3Q}$ in terms of the Y-ansatz both with the continuum Coulomb potential and with the lattice Coulomb potential, and find that the lattice QCD data of the 3Q potential $V_{\rm 3Q}$ are well reproduced within a few % deviation by the sum of a constant, the two-body Coulomb term and the three-body linear confinement term $\sigma_{\rm 3Q} L_{\rm min}$, with $L_{\rm min}$ the minimal value of the total length of color flux tubes linking the three quarks. From the comparison with the Q-$\bar {\rm Q}$ potential, we find a universality of the string tension as $\sigma_{\rm 3Q} \simeq \sigma_{\rm Q \bar Q}$ and the one-gluon-exchange result for the Coulomb coefficients as $A_{\rm 3Q} \simeq \frac12 A_{\rm Q \bar Q}$. We investigate also the several fit analyses with the various ans\"atze: the Y-ansatz with the Yukawa potential, the $\Delta$-ansatz and a more general ansatz including the Y and the $\Delta$ ans\"atze in some limits. All these fit analyses support the Y-ansatz on the confinement part in the 3Q potential $V_{\rm 3Q}$, although $V_{\rm 3Q}$ seems to be approximated by the $\Delta$-ansatz with $\sigma_\Delta \simeq 0.53 \sigma$.

Ab initio calculations of nonadditive effects in the trimers [formula omitted], BF, CS

Optimal structures, interaction energies and harmonic vibrational frequencies of the (H 2O) 2⋯XY, XY= N 2 , BF, CS ternary complex have been determined from the supermolecular (SM) calculations with the aug-cc-pVDZ and the aug-cc-pVTZ basis sets. Energetic properties of the complex have been calculated at the MP4 level. We located three low-energy configurations corresponding to two isomeric H-bonded cyclic complexes and one linear structure. Nonadditive interactions play an important role for the (H 2O) 2⋯BF and (H 2O) 2⋯CS trimers. The contribution of the three-body term represents as much as 17% and 13% of the total MP4 interaction energy. Partitioning of the three-body energy was performed in terms of the intermolecular perturbation theory. The nonadditivity originates mainly from the induction effect. The calculations of the vibrational frequencies and infrared intensities for these complexes are presented to facilitate the frequency assignments of future experimental spectra.

Effects of three-body interactions on the structure and thermodynamics of liquid krypton

Large-scale molecular dynamics simulations are performed to predict the structural and thermodynamic properties of liquid krypton using a potential energy function based on the two-body potential of Aziz and Slaman plus the triple-dipole Axilrod–Teller (AT) potential. By varying the strength of the AT potential we study the influence of three-body contribution beyond the triple-dipole dispersion. It is seen that the AT potential gives an overall good description of liquid Kr, though other contributions such as higher order three-body dispersion and exchange terms cannot be ignored.

Chaotic oscillation in an attractive Bose-Einstein condensate under an impulsive force

For an attractive trapped Bose-Einstein condensate an imaginary three-body recombination loss term and an imaginary linear source term are usually included in the Gross-Pitaevskii (GP) equation for a proper account of dynamics. Under the action of an impulsive force, generated by suddenly changing the atomic interaction or the trapping potential, the solution of this complex GP equation for attractive interaction is found to lead to a very long term chaotic oscillation.

Theoretical calculations on the structure and photoabsorption of Xe n+ cations ( n=3,4,19)

The extended diatomics-in-molecules method, involving spin–orbit coupling and leading three-body terms, and the most recent ab initio potential energy curves for Xe 2 + due to Paidarová and Gadéa [Chem. Phys. 274 (2001) 1] are employed to calculate structures and photoabsorption spectra of singly charged xenon cluster cations, Xe n +, n=3,4,19. The extended diatomics-in-molecules models reproduce available experimental data with sufficient accuracy.

Molecular dynamics investigation of lithium borate glasses: Local structure and ion dynamics

The effect of alkali content and temperature on the microstructure of lithium borate glasses, $x{\mathrm{Li}}_{2}\mathrm{O}\ensuremath{-}(1\ensuremath{-}x){\mathrm{B}}_{2}{\mathrm{O}}_{3},$ has been investigated for glass compositions $x=0.2--0.5$ and temperatures up to 1250 K. The molecular dynamics technique has been applied, with Ewald summation and periodic boundary conditions, to a collection of ca. 256 particles confined in a primitive cubic cell and interacting through a Born-Mayer-Huggins-type potential augmented with three-body angular terms. The short-range order (SRO) structure was found to consist of boron-oxygen tetrahedral, ${\mathrm{B}\mathrm{\O{}}}_{4}^{\ensuremath{-}}$ $[\mathrm{\O{}}=\mathrm{bridging}$ oxygen atom (BO)], and triangular units with variable number of nonbridging oxygen (NBO) atoms, ${\mathrm{B}\mathrm{\O{}}}_{3},$ ${\mathrm{B}\mathrm{\O{}}}_{2}{\mathrm{O}}^{\ensuremath{-}},$ and ${\mathrm{B}\mathrm{\O{}}\mathrm{O}}_{2}^{2\ensuremath{-}}$ $({\mathrm{O}}^{\ensuremath{-}}=\mathrm{NBO}).$ The relative abundance of SRO units was determined and found to depend on both glass composition and temperature. Increasing ${\mathrm{Li}}_{2}\mathrm{O}$ content at constant temperature or increasing temperature at a fixed composition was shown to cause rearrangements of the SRO structure and to lead towards ${\mathrm{B}\mathrm{\O{}}\mathrm{O}}_{2}^{2\ensuremath{-}}$ units in the range of compositions and temperatures investigated. Such changes were expressed in terms of chemical equilibria involving the SRO units. The local environments hosting the Li ions were investigated and distinguished in two main types: the first type of site is formed by BO's, while the second type involves the participation of NBO's. The vibrational response of Li ions in the two types of site was computed and found to correlate very well with the experimental far-infrared profiles. Calculation of diffusion coefficients of Li ions showed that diffusion is carried out predominantly through NBO sites. In addition, glass regions rich in Li/NBO were found to develop with increasing lithium oxide content and to percolate eventually into microchannels suitable for ion migration.

Comment on “Anti-cooperativity in hydrophobic interactions: A simulation study of spatial dependence of three-body effects and beyond” [J. Chem. Phys. 115, 1414 (2001)

We address the criticism of our methodology for determination of the three-body cooperative terms in the potential of mean force (PMF) of the hydrophobic interaction of methane molecules in water [Czaplewski et al., Prot. Sci. 9, 1235 (2000)] expressed in the title paper of Shimizu and Chan, as well as their conclusion that hydrophobic association is predominantly anti-cooperative. We demonstrate that their reference two-methane PMF curve is subject to a systematic error, which invalidates their conclusions about the sign of the cooperative PMF.

Electrostatic and Association Phenomena in Aggregates of Polymers and Micelles

An automatic, continuous-mixing technique is introduced to measure light scattering and viscosity simultaneously over a wide range of solute concentrations in multicomponent systems. Behavior along arbitrary curves in component coordinates can be monitored. This technique is used to investigate the association and electrostatically based excluded-volume interactions that arise in solutions of interacting neutral polymers and charged micelles. In this study, the ionic surfactant sodium dodecyl sulfate (SDS) and a neutral polymer poly(vinylpyrrolidone) (PVP) were chosen. The SDS confers pseudopolyelectrolyte properties on the polymer/micelle aggregates (PSA), such as electrostatically enhanced second and third virial coefficients A2 and A3, respectively. The presence of a large A3 is directly observed as a well-defined maximum in scattering intensity versus [PVP] under saturating SDS conditions. The electrostatically enhanced three-body effects represented by A3 in light scattering are nearly 3 orders of magnitude greater than the corresponding three-body terms in viscosity. A viscosity effect reminiscent of the electroviscous effect seen for linear polyelectrolytes is observed, but it occurs under very different PSA concentration and solution ionic strength conditions.

Analytical three-body interaction potentials and hydrogen bond dynamics of hydrogen fluoride aggregates, (HF)n, n≥3

Oligomeric aggregates of hydrogen fluoride are important prototype molecules for a detailed understanding of the structure, energetics, spectroscopy and dynamics of hydrogen bonding. The pairwise additive description of these oligomers is known to be inadequate. We have sampled the three-body potential for HF at 3000 (HF)3 configurations selected by various classical and quantum sampling techniques, including dynamic sampling based on Voronoi step representation. The counterpoise-corrected Møller-Plesset second-order three-body energies using a double zeta Gaussian basis set with polarization functions (DZP+MP2) at these configurations are fitted by analytical 12-dimensional potentials. Cooperative effects are found to be sizeable and predominantly stabilizing in hydrogen fluoride ring aggregates. Test calculations with larger basis sets and for larger HF aggregates show that in combination with available high quality pair potentials, the analytical three-body terms give an excellent description of the (HF)3 surface in the hydrogen bonding region and a good approximation for clusters up to at least the hexamer. Multidimensional vibrational quantum Monte Carlo calculations indicate that degenerate HF stretch excitation in (HF)3 (3712cm−1) is in close coincidence with (HF)3→3HF dissociation channels at low HF angular momentum, whereas degenerate DF stretch excitation in (DF)3 (2725cm−1) falls slightly below any (DF)3→(DF)2+DF dissociation channels. The (HF)3 potential surface, its stationary points, possible interconversion tunneling pathways, zero point energies, adiabatic channels, unusual isotope effects, fully centrifugal rotational states and the harmonic infrared spectrum are discussed in detail and compared to ab initio calculations and experiment. The applicability of the (1+2+3)-body approach for larger oligomers (3<n<8) is investigated with special emphasis on structure, energetics, infrared and microwave spectra, and predissociation. Neglect of four- and higher-body contributions and hydrogen exchange symmetry is found to affect some properties significantly, but the preference for simple ring structures remains pronounced.