Three-body Terms Research Articles

New density-independent interactions for nuclear structure calculations

We present a new two-body finite-range and momentum-dependent but density-independent effective interaction, which can be interpreted as a regularized zero-range force. We show that no three-body or density-dependent terms are needed for a correct description of saturation properties in infinite matter, that is, on the level of low-energy density functional, the physical three-body effects can be efficiently absorbed in effective two-body terms. The new interaction gives a very satisfying equation of state of nuclear matter and opens up extremely interesting perspectives for the mean-field and beyond-mean-field descriptions of atomic nuclei.

Many-Body Convergence of the Electrostatic Properties of Water.

The many-body convergence of the dipole moment and the dipole-dipole polarizability of water is investigated. It is found that, for systems of low symmetry like the water clusters examined here, simple measures such as dipole magnitudes and average polarizabilities may lead to an incomplete interpretation of the underlying physics. Alternative metrics are introduced that allow for an unambiguous characterization of both properties. The convergence of the many-body decomposition of the total dipole and the polarizability is studied for (H2O)N, with N = 4-6 being minimum energy water clusters and N = 14 being clusters that were extracted from condensed phase simulations. For these clusters, it is demonstrated that both the total dipole and polarizability are almost entirely pairwise additive, with three-body terms contributing less than 4% and all higher-order terms being essentially negligible.

Quantum phases of one-dimensional Hubbard models with three- and four-body couplings

The experimental advances in cold atomic and molecular gases stimulate the investigation of lattice correlated systems beyond the conventional on-site Hubbard approximation, by possibly including multiparticle processes. We study fermionic extended Hubbard models in a one-dimensional lattice with different types of particle couplings, including also three- and four-body interactions up to nearest neighboring sites. By using the bosonization technique, we investigate the low-energy regime and determine the conditions for the appearance of ordered phases, for arbitrary particle filling. We find that three- and four-body couplings may significantly modify the phase diagram. In particular, diagonal three-body terms that directly couple the local particle densities have qualitatively different effects from off-diagonal three-body couplings originating from correlated hopping, and favor the appearance of a Luther-Emery phase even when two-body terms are repulsive. Furthermore, the four-body coupling gives rise to a rich phase diagram and may lead to the realization of the Haldane insulator phase at half-filling.

Single-particle momentum distributions of Efimov states in mixed-species systems

We solve the three-body bound state problem in three dimensions for mass imbalanced systems of two identical bosons and a third particle in the universal limit where the interactions are assumed to be of zero-range. The system displays the Efimov effect and we use the momentum-space wave equation to derive formulas for the scaling factor of the Efimov spectrum for any mass ratio assuming either that two or three of the two-body subsystems have a bound state at zero energy. We consider the single-particle momentum distribution analytically and numerically and analyse the tail of the momentum distribution to obtain the three-body contact parameter. Our finding demonstrate that the functional form of the three-body contact term depends on the mass ratio and we obtain an analytic expression for this behavior. To exemplify our results, we consider mixtures of Lithium with either two Caesium or Rubium atoms which are systems of current experimental interest.

Pnicogen-Bonded Cyclic Trimers (PH2X)3with X = F, Cl, OH, NC, CN, CH3, H, and BH2

Ab initio MP2/aug'-cc-pVTZ calculations have been carried out to determine the structures and binding energies of cyclic trimers (PH2X)3 with X = F, Cl, OH, NC, CN, CH3, H, and BH2. Except for [PH2(CH3)]3, these complexes have C3h symmetry and binding energies between -17 and -63 kJ mol(-1). Many-body interaction energy analyses indicate that the two-body terms are dominant, accounting for 97-103% of the total binding energy. Except for the trimer [PH2(OH)]3, the three-body terms are stabilizing. Charge transfer from the lone pair on one P atom to an antibonding σ* orbital of the P atom adjacent to the lone pair plays a very significant role in stabilization. The charge-transfer energies correlate linearly with the trimer binding energies. NBO, AIM, and ELF analyses have been used to characterize bonds, lone pairs, and the degree of covalency of the P···P pnicogen bonds. The NMR properties of chemical shielding and (31)P-(31)P coupling constants have also been evaluated. Although the (31)P chemical shieldings in the five most strongly bound trimers increase relative to the corresponding isolated monomers, there is no correlation between the chemical shieldings and the charges on the P atoms. EOM-CCSD (31)P-(31)P spin-spin coupling constants computed for four (PH2X)3 trimers fit nicely onto a plot of (1p)J(P-P) versus the P-P distance for (PH2X)2 dimers. A coupling constant versus distance plot for the four trimers has a second-order trendline which has been used to predict the values of (1p)J(P-P) for the remaining trimers.

Water 16-mers and Hexamers: Assessment of the Three-Body and Electrostatically Embedded Many-Body Approximations of the Correlation Energy or the Nonlocal Energy As Ways to Include Cooperative Effects

This work presents a new fragment method, the electrostatically embedded many-body expansion of the nonlocal energy (EE-MB-NE), and shows that it, along with the previously proposed electrostatically embedded many-body expansion of the correlation energy (EE-MB-CE), produces accurate results for large systems at the level of CCSD(T) coupled cluster theory. We primarily study water 16-mers, but we also test the EE-MB-CE method on water hexamers. We analyze the distributions of two-body and three-body terms to show why the many-body expansion of the electrostatically embedded correlation energy converges faster than the many-body expansion of the entire electrostatically embedded interaction potential. The average magnitude of the dimer contributions to the pairwise additive (PA) term of the correlation energy (which neglects cooperative effects) is only one-half of that of the average dimer contribution to the PA term of the expansion of the total energy; this explains why the mean unsigned error (MUE) of the EE-PA-CE approximation is only one-half of that of the EE-PA approximation. Similarly, the average magnitude of the trimer contributions to the three-body (3B) term of the EE-3B-CE approximation is only one-fourth of that of the EE-3B approximation, and the MUE of the EE-3B-CE approximation is one-fourth that of the EE-3B approximation. Finally, we test the efficacy of two- and three-body density functional corrections. One such density functional correction method, the new EE-PA-NE method, with the OLYP or the OHLYP density functional (where the OHLYP functional is the OptX exchange functional combined with the LYP correlation functional multiplied by 0.5), has the best performance-to-price ratio of any method whose computational cost scales as the third power of the number of monomers and is competitive in accuracy in the tests presented here with even the electrostatically embedded three-body approximation.

Skyrme pseudo-potential-based EDF parametrization for spuriousity-free MR EDF calculations

First exploratory steps toward a pseudo-potential-based Skyrme energy density functional for spuriousity-free multi-reference calculations are presented. A qualitatively acceptable fit can be accomplished by adding simple three- and four-body contact terms to the standard central plus spin–orbit two-body terms. To achieve quantitative predictive power, higher-order terms, e.g. velocity-dependent three-body terms, will be required.

Molecular Density Functional Theory of Water

Three-dimensional implementations of liquid-state theories offer an efficient alternative to computer simulations for the atomic-level description of aqueous solutions in complex environments. In this context, we present a (classical) molecular density functional theory (MDFT) of water that is derived from first principles and is based on two classical density fields, a scalar one, the particle density, and a vectorial one, the multipolar polarization density. Its implementation requires as input the partial charge distribution of a water molecule and three measurable bulk properties, namely, the structure factor and the k-dependent longitudinal and transverse dielectric constants. It has to be complemented by a solute-solvent three-body term that reinforces tetrahedral order at short-range. The approach is shown to provide the correct 3-D microscopic solvation profile around various molecular solutes, possibly possessing H-bonding sites, at a computer cost two to three orders of magnitude lower than with explicit simulations.

Many-body dispersion interactions from the exchange-hole dipole moment model

In this article, we present the extension of the exchange-hole dipole moment model (XDM) of dispersion interactions to the calculation of two-body and three-body dispersion energy terms to any order, 2(l)-pole oscillator strengths, and polarizabilities. By using the newly-formulated coefficients, we study the relative importance of the higher-order two-body and the leading non-additive three-body (triple-dipole) interactions in gas-phase as well as in condensed systems. We show that the two-body terms up to R(-10), but not the terms of higher-order, are essential in the correct description of the dispersion energy, while there are a number of difficulties related to the choice of the damping function, which precludes the use three-body triple-dipole contributions in XDM. We conclude that further study is required before the three-body term can be used in production XDM density-functional calculations and point out the salient problems regarding its use.

Weak response of cold symmetric nuclear matter at three-body cluster level

We studied the Fermi and Gamow-Teller responses of cold symmetric nuclear matter within a unified dynamical model, suitable to account for both short- and long-range correlation effects. The formalism of correlated basis functions has been used to construct two-body effective interactions and one-body effective weak operators. The inclusion of the three-body cluster term allowed for incorporating in the effective interaction a realistic model of three- nucleon forces, namely the UIX potential. Moreover, the sizable unphysical dependence of the effective weak operator is removed once the three-body cluster term is taken into account.

The Interpretation of Diffraction Patterns of Two Prototypical Protic Ionic Liquids: a Challenging Task for Classical Molecular Dynamics Simulations

In this study, we discuss the performance of classical molecular dynamics in predicting the experimental X-ray diffraction patterns of liquid ethylammonium nitrate (one of the simplest protic room-temperature ionic liquid showing amphiphilic behavior) and of its hydroxy derivative (2-ethanolammonium nitrate, 2-HOEAN). Newly recorded energy-dispersive X-ray diffraction structure factors are compared with the corresponding quantities extracted from molecular dynamics simulations. Other useful theoretical and experimental indicators are used as a probe of the local structure of the title ionic liquids. We shall show that the use of a general purpose, two-body terms only, force field, such as OPLS/AA is able to describe most of the structural experimental data. However, we shall also point out that an improved description of some key structural features observed in the X-ray radial distribution function, can be obtained very easily by adding a general three-body potential energy term instead of changing the two-body potential parameters, in order to optimize the agreement with experimental data. This three-body term turns out to be naturally able to describe the complex polarization effects due to hydrogen bonding without requiring a quanto-mechanical treatment or a polarizable force field. In addition the present model turns out to be able to account for the presence of a low-Q peak in the scattering patterns of EAN, which has been commonly interpreted as a manifestation of the amphiphilic nature of this compound.

First-Order Phase Transitions in Optical Lattices with Tunable Three-Body Onsite Interaction

We study the two-dimensional Bose-Hubbard model in the presence of a three-body interaction term, both at a mean-field level and via quantum Monte Carlo simulations. The three-body term is tuned by coupling the triply occupied states to a trapped universal trimer. We find that, for a sufficiently attractive three-body interaction, the n=2 Mott lobe disappears and the system displays first-order phase transitions separating the n=1 from the n=3 lobes and the n=1 and n=3 Mott insulator from the superfluid. We also analyze the effect of finite temperature and find that transitions are still of first order at temperatures T~J, where J is the hopping matrix element.

A Computational Study of Anion-Modulated Cation−π Interactions

The interaction of anions with cation-π complexes formed by the guanidinium cation and benzene was thoroughly studied by means of computational methods. Potential energy surface scans were performed in order to evaluate the effect of the anion coming closer to the cation-π pair. Several structures of guanidinium-benzene complexes and anion approaching directions were examined. Supermolecule calculations were performed on ternary complexes formed by guanidinium, benzene, and one anion and the interaction energy was decomposed into its different two- and three-body contributions. The interaction energies were further dissected into their electrostatic, exchange, repulsion, polarization and dispersion contributions by means of local molecular orbital energy decomposition analysis. The results confirm that, besides the electrostatic cation-anion attraction, the effect of the anion over the cation-π interaction is mainly due to polarization and can be rationalized following the changes in the anion-π and the nonadditive (three-body) terms of the interaction. When the cation and the anion are on the same side of the π system, the three-body interaction is anticooperative, but when the anion and the cation are on opposite sides of the π system, the three-body interaction is cooperative. As far as we know, this is the first study where this kind of analysis is carried out with a structured cation as guanidinium with a significant biological interest.

Fully ab initio protein‐ligand interaction energies with dispersion corrected density functional theory

Dispersion corrected density functional theory (DFT-D3) is used for fully ab initio protein-ligand (PL) interaction energy calculation via molecular fractionation with conjugated caps (MFCC) and applied to PL complexes from the PDB comprising 3680, 1798, and 1060 atoms. Molecular fragments with n amino acids instead of one in the original MFCC approach are considered, thereby allowing for estimating the three-body and higher many-body terms. n > 1 is recommended both in terms of accuracy and efficiency of MFCC. For neutral protein side-chains, the computed PL interaction energy is visibly independent of the fragment length n. The MFCC fractionation error is determined by comparison to a full-system calculation for the 1060 atoms containing PL complex. For charged amino acid side-chains, the variation of the MFCC result with n is increased. For these systems, using a continuum solvation model with a dielectricity constant typical for protein environments (ϵ = 4) reduces both the variation with n and improves the stability of the DFT calculations considerably. The PL interaction energies for two typical complexes obtained ab initio for the first time are found to be rather large (-30 and -54 kcal/mol).

Nuclear matter equation of state and three-body forces

The energy per particle, symmetry energy, pressure, and free energy are calculated for symmetric nuclear matter using BHF approach with modern nucleon-nucleon CD-Bonn, Nijm1, Argonne v18, and Reid 93 potentials. To obtain saturation in nuclear matter we add three-body interaction terms which are equivalent to a density-dependent two-nucleon interaction a la Skyrme force. Good agreement is obtained in comparison with previous theoretical estimates and experimental data.

Examination of the hydrogen-bonding networks in small water clusters (n = 2–5, 13, 17) using absolutely localized molecular orbital energy decomposition analysis

Using the ωB97X-D and B3LYP density functionals, the absolutely localized molecular orbital energy decomposition method (ALMO-EDA) is applied to the water dimer through pentamer, 13-mer and 17-mer clusters. Two-body, three-body, and total interaction energies are decomposed into their component energy terms: frozen density interaction energy, polarization energy, and charge transfer energy. Charge transfer, polarization, and frozen orbital interaction energies are all found to be significant contributors to the two-body and total interaction energies; the three-body interaction energies are dominated by polarization. Each component energy term for the two-body interactions is highly dependent on the associated hydrogen bond distance. The favorability of the three-body terms associated with the 13- and 17-mer structures depends on the hydrogen-donor or hydrogen-acceptor roles played by each of the three component waters. Only small errors arise from neglect of three-body interactions without two adjacent water molecules, or beyond three-body interactions. Interesting linear correlations are identified between the contributions of charge-transfer and polarization terms to the two and three-body interactions, which permits elimination of explicit calculation of charge transfer to a good approximation.

Ab initio shell model with a core: Extending the No Core Shell Model to heavier nuclei

The No Core Shell Model (NCSM) is an ab initio method for calculating the properties of atomic nuclei, starting with the fundamental interactions among the nucleons and treating all A nucleons as being active. This approach has been successfully applied to nuclei with A ≤ 20, but it is difficult to treat heavier mass nuclei with existing computer technology, because of the extemely large basis spaces required to obtain converged results. In this presentation we outline a new formalism for extending the NCSM to heavier mass nuclei. It involves using the NCSM approach to determine the core, one-body and two-body (and perhaps also three-body) terms, which are the usual input for standard shell model (SSM) calculations. Such SSM calculations can be easily performed for sd- and pf-shell nuclei. As a test of this new formalism, we apply it to nuclei in the 0p-shell, for which exact NCSM calculations can also be performed for making comparisons. Results are given both for energy spectra and electromagnetic properties.

Effects of three-body interactions in the parametric and modulational instabilities of Bose–Einstein condensates

The parametric modulational instability for a discrete nonlinear Schrödinger equation with a cubic–quintic nonlinearity is analyzed. This model describes the dynamics of BECs, with both two- and three-body interatomic interactions trapped in an optical lattice. We identify and discuss the salient features of the three-body interaction in the parametric modulational instability. It is shown that the three-body interaction term can both, shift as well as narrow the window of parametric instability, and also change the behavior of a modulationally stable and parametrically unstable BEC with attractive two-body interaction. We explore this instability through the multiple-scale analysis and identify it numerically. The effect of the three body losses have also been investigated.

LOCV CALCULATIONS FOR POLARIZED LIQUID 3He: THE EFFECT OF THREE-BODY CLUSTER ENERGY

We have used the lowest order constrained variational (LOCV) method to calculate some of the ground state properties of the polarized liquid 3 He by inclusion of the three-body cluster energy contribution. It is shown that the contribution of the three-body cluster term for the ground state energy of this system is substantial, especially at high densities. It is also shown that the inclusion of the three-body energy contribution improves our result for the binding energy of the liquid 3 He . It is seen that the magnitude of the three-body cluster energy decreases by increasing the polarization. The magnetic susceptibility of the liquid 3 He has also been computed, showing no spontaneous ferromagnetic phase transition.

Interatomic potentials for the vibrational properties of III-V semiconductor nanostructures

We derive interatomic potentials for zinc blende InAs, InP, GaAs, and GaP semiconductors with possible applications in the realm of nanostructures. The potentials include bond stretching interaction between the nearest and next-nearest neighbors, a three-body term, and a long-range Coulomb interaction. The optimized potential parameters are obtained by (i) fitting to bulk phonon dispersions and elastic properties and (ii) constraining the parameter space to deliver well-behaved potentials for the structural relaxation and vibrational properties of nanostructure clusters. The targets are thereby calculated by density functional theory for clusters of up to 633 atoms. We illustrate the new capability by the calculation Kleinman and Gr\"uneisen parameters and of the vibrational properties of nanostructures with 3 to 5.5 nm diameter.