Delta function model for the helium trimer: origin of three-body forces

The Dirac bubble potential, previously used to model the helium dimer, is applied to the trimer. It is shown that the quantum mechanical kinetic energy operator for a three-body system contains terms over and above the analogues of classical pairwise contributions. The additional terms, the ‘Borromean couplings’, are responsible for a dramatic increase in the binding energy of the trimer. For example, ⁴He₃ is bounded by two orders of magnitude more strongly than ⁴He₂, 279 mK versus 1.31 mK, respectively, according to our calculations. Moreover, the trimer is considerably more compact than the dimer, with (r₁₂) decreasing to 9.01 Å from 51.9 Å.     

Three-body effects in hydrogen fluoride: survey of potential energy surfaces

The potential energy surface for trimers of hydrogen fluoride is examined for multiple arrangements of the three-molecule cluster. Several established approaches to model the potential energy are examined, including a strictly pairwise additive potential, an established polarizable potential model, another, strictly three-body polarizable model, and a three-body potential recently fitted to accurate ab initio calculations. These potential surfaces are compared to MP2/6-311++G** and SCF/6-311++G**ab initio calculations performed here for each configuration. In each case the overall trimer potential is examined, as well as the three-body contribution to it (obtained by subtracting the sum of the interactions taken pairwise). The effective pair potential has some correspondence to the ab initio calculations, although it generally displays a shallower minimum energy. The established polarizable model has a more repulsive core that compensates for a deeper attractive well that it has adopted to better describe phase-coexistence data. In contrast, the new three-body polarizable model shows better correspondence with the ab initio potential-energy surface.     

The system of differential equations in the momentum space for the three-body problem: Continuous spectrum

A system of differential equations in the momentum space for describing three-body scattering is obtained. Preliminary calculations of the length of boson scattering on a bound bosonic pair are performed. The data obtained are in good agreement with the results of calculations of helium atom scattering on a helium dimer.     

An interionic force law for HgCl2 from first-principles molecular calculations

Mercury dichloride is an ionic compound solidifying into a unique layer structure of rod-like monomers, so that unusual structural and physical properties can be expected for its liquid state. We propose a set of pseudoclassical interionic potentials, including three-body forces and electronic-polarization terms, patterned on the results of relativistic first-principles calculations on the molecular monomer, dimer and trimer. The proposed force law will allow structural studies of the condensed phases by molecular-dynamics simulations, with the main aims of exploring the nature of the short-range and intermediate-range order in the melt and the process of ionization at high pressure and temperature.     

Atom-dimer scattering for confined ultracold fermion gases

We solve the three-body problem of a quasi-one-dimensional ultracold Fermi gas with parabolic confinement length a (perpendicular) and 3D scattering length a. On the two-body level, there is a Feshbach-type resonance at a (perpendicular)/a approximately 1.46, and a dimer state for arbitrary a (perpendicular)/a. The three-body problem is shown to be universal, and described by the atom-dimer scattering length a(ad) and a range parameter b(ad). In the dimer limit a (perpendicular)/a>1, we find a repulsive zero-range atom-dimer interaction. For a (perpendicular)/a<-1, however, the potential has long range, with a(ad)>0 and b(ad)>a(ad). There is no trimer state, and despite a(ad)=0 at a( perpendicular)/a approximately 2.6, there is no resonance enhancement of the interaction.     

Structure and dynamics of few-helium clusters using soft-core potentials

In this work we investigate the structure and dynamics of small clusters of Helium atoms. We consider bound states of clusters having A = 2, 3, 4, 5, 6 atoms and continuum states in the three-atom system. Motivated by the fact that the He-He system has a very large scattering length a compared to the range r ₀ of the He-He potential (r ₀/a < 1/10), we propose the use of a soft-core interparticle potential. We use an attractive gaussian potential that reproduces the values of the dimer binding energy and the atomatom scattering length obtained with one of the widely used He-He interactions, the LM2M2 potential. In addition, we include a repulsive three-body force to reproduce the trimer binding energy. With this model, consisting in the sum of a two- and a three-body potential, we show the spectrum of the four, five, and sixparticle systems and phase-shifts and inelasticities in the three-atom system. Comparisons to calculations using realistic He-He potentials are given. In addition some universal relations are explored.     

Theoretical study of rearrangements in water dimer and trimer

The global minimum and transition states for the acceptor-tunnelling, donor-acceptor interchange and bifurcation tunnelling rearrangements of the water dimer, and the single-flip, bifurcation and concerted proton transfer processes in the water trimer have been reinvestigated. Our analysis of the tunnelling splittings and spectroscopy is based on ab initio calculations at the computational level of second-order M?ller-Plesset (MP2) theory with basis sets of aug-cc-pVXZ quality (X = D, T, Q for the dimer; X = D, T for the trimer). In both water dimer and trimer, the binding energy, barrier heights, intermonomer distances, and harmonic frequencies converge smoothly as the size of the basis set increases. In the water dimer, the binding energy was evaluated as 5.09kcal mol^?1, while the activation energies are 0.52 (acceptor-tunnelling) 0.79 (donor-acceptor interchange), and 1.94 kcal mol^?1 (bifurcation tunnelling) at the MP2/aug-cc-pVQZ level. In the water trimer, the binding energy was evaluated as 16.29 kcal mol^?1, while the activation energies are 0.28 (single-flip), 2.34 (bifurcation), and 26.36 (proton transfer) kcal mol^?1 at the MP2/aug-cc-pVTZ level.     

Efimov Physics in Small Bosonic Clusters

We study small clusters of bosons, A = 2, 3, 4, 5, 6, characterized by a resonant interaction. Firstly, we use a soft-gaussian interaction that reproduces the values of the dimer binding energy and the atom-atom scattering length obtained with LM2M2 potential, a widely used ⁴He-⁴He interaction. We change the intensity of the potential to explore the clusters’ spectra in different regions with large positive and large negative values of the two-body scattering length and we report the clusters’ energies on Efimov plot, which makes the scale invariance explicit. Secondly, we repeat our calculation adding a repulsive three-body force to reproduce the trimer binding energy. In all the region explored, we have found that these systems present two states, one deep and one shallow close to the A ? 1 threshold, and scale invariance has been investigated for these states. The calculations are performed by means of Hyperspherical Harmonics basis set.     

Off-site trimer superfluid on a one-dimensional optical lattice

The Bose-Hubbard model with an effective off-site three-body tunneling,characterized by jumps towards one another,between one atom on a site and a pair atoms on the neighborhood site,is studied systematically on a one-dimensional(1D) lattice,by using the density matrix renormalization group method.The off-site trimer superfluid,condensing at momentum k = 0,emerges in the softcore Bose-Hubbard model but it disappears in the hardcore Bose-Hubbard model.Our results numerically verify that the off-site trimer superfluid phase derived in the momentum space from[Phys.Rev.A81,011601(R)(2010)]is stable in the thermodynamic limit.The off-site trimer superfluid phase,the partially off-site trimer superfluid phase and the Mott insulator phase are found,as well as interesting phase transitions,such as the continuous or first-order phase transition from the trimer superfluid phase to the Mott insulator phase.Our results are helpful in realizing this novel off-site trimer superfluid phase by cold atom experiments.     

Effective pair potentials in fluids in the presence of three-body forces. II

Earlier calculations are extended to the second order in density thus providing the non-additive contributions to the fourth virial coefficient in the presence of a weak three-body force given by the triple-dipole dispersion potential of Axilrod and Teller. We compare the Percus-Yevick approximations of Rushbrooke and Silbert and of Rowlinson at the level of the fourth virial coefficient and find that the former is more accurate. We also compare our calculations of the effective pair potential of liquid argon with the results of Mikolaj and Pings obtained from X-ray diffraction measurements.     

Studies of intermolecular interactions by matrix isolation vibrational spectroscopy: Self-association of water

The mid- and far-infrared spectra of water in argon and nitrogen matrices have been reinvestigated. The water molecule rotates in an argon matrix, but in a nitrogen matrix two low-frequency bands are attributed to libration of the water monomer about its A and C rotational axes. Combinations of these modes with the stretching and bending modes of the water monomer were observed. A detailed concentration-dependence study enabled bands to be attributed to dimer, trimer, and tetramer or higher multimers. The dimer and trimer were both found to have open chain structures, whereas tetramer or higher multimer species appear to be predominantly cyclic. Intermolecular modes, observed for dimer and trimer in the far-infrared spectra, are tentatively assigned.     

Effective Field Theory Analysis of Three-Boson Systems at Next-To-Next-To-Leading Order

We use an effective field theory for short-range forces (SREFT) to analyze systems of three identical bosons interacting via a two-body potential that generates a scattering length, a, which is large compared to the range of the interaction, ?. The amplitude for the scattering of one boson off a bound state of the other two is computed to next-to-next-to-leading order (N²LO) in the ?/a expansion. At this order, two pieces of three-body data are required as input in order to renormalize the amplitude (for fixed a). We apply our results to a model system of three Helium-4 atoms, which are assumed to interact via the TTY potential. We generate N²LO predictions for atom-dimer scattering below the dimer breakup threshold using the bound-state energy of the shallow Helium-4 trimer and the atom-dimer scattering length as our two pieces of three-body input. Based on the convergence pattern of the SREFT expansion, as well as differences in the predictions of two renormalization schemes, we conclude that our N²LO phase- shift predictions will receive higher-order corrections of < 0.2 %. In contrast, the prediction of SREFT for the binding energy of the “deep” trimer of Helium-4 atoms displays poor convergence.     

Adiabatic Representation for Atomic Dimers and Trimers in Collinear Configuration

Physics of Atomic Nuclei - We considered collinear models for a trimer of identical atoms with molecular pair interactions and for an atomic dimer scattered by an atom or tunneling through...     

Condensate fraction and critical temperature of interacting Bose gas in anharmonic trap

The spectral flow of three-body (trimer) states consisting of two heavy (impurity) particles sitting in a condensate of light bosons is considered. Assuming that the condensate is weakly interacting and that an impurity and a boson have a resonant zero-range two-body interaction, we use the Born-Oppenheimer approximation to determine the effective three-body potential. We solve the resulting Schrödinger equation numerically and determine the trimer binding energies as a function of the coherence length of the light bosonic condensate particles. The binding energy is found to be suppressed by the presence of the condensate when the energy scale corresponding to the coherence length becomes of order the trimer binding energy in the absence of the condensate. We find that the Efimov scaling property is reflected in the critical values of the condensate coherence length at which the trimers are pushed into the continuum.     

Water adsorption on the Be(0001) surface: from monomer to trimer adsorption

In this paper, the density functional theory has been used to perform a comparative theoretical study of water monomer, dimer, trimer, and bilayer adsorptions on the Be(0001) surface. In our calculations, the adsorbed water molecules are energetically favoured adsorbed on the atop sites, and the dimer adsorption is found to be the most stable with a peak adsorption energy of ～437 meV. Further analyses have revealed that the essential bonding interaction between the water monomer and the metal substrate is the hybridization of the water 3a₁-like molecular orbital with the (s, p_z) orbitals of the surface beryllium atoms. While in the case of the water dimer adsorption, the 1b₁-like orbital of the H₂O molecule plays a dominant role.     

具有电子推拉结构的多支化分子的光物理特性的研究

利用稳态光谱和飞秒时间分辨荧光亏蚀的技术,研究了不同溶剂中一系列有分子内电荷转移特性的分子的结构与光物理性质的关系,研究体系为三苯胺作为电子给体,2,1,3-苯并噻二唑作为受体的单支分子及其对应的两支和三支分子. 并结合TD-DFT计算进一步解释了实验中所观察到的现象. 三个分子相似的吸收和荧光光谱以及强的溶剂依赖光谱特性表明两支与三支分子激发态与单支分子相似,表明激发态都定域在其中一支上. 激发时多支分子内发生多维电荷转移,然后快速地定域到某一支上发射. 另一方面多支分子相对于单支分子吸收和发射光谱的红     

Adsorption of water monomer and clusters on platinum(111) terrace and related steps and kinks: I. Configurations,energies, and hydrogen bonding

Adsorption and rotation of water monomer, dimer, and trimer on the (111) terrace, (221) and (322) stepped, and (763) and (854) kinked surfaces of platinum were studied by density functional theory calculations using the PW91 approximation to the energy functional. On the (111) terrace, water monomer and the donor molecule of the dimer and trimer adsorb at atop sites. The per-molecule adsorption energies of the monomer, dimer, and trimer are 0.30, 0.45, and 0.48 eV, respectively. Rotation of monomers, dimers, and trimers on the terrace is facile with energy barriers of 0.02 eV or less. Adsorption on steps and kinks is stronger than on the terrace, as evidenced by monomer adsorption energies of 0.46 to 0.55 eV. On the (221) stepped surface the zigzag extended configuration is most stable with a per-molecule adsorption energy of 0.57 eV. On the (322) stepped surface the dimer, two configurations of the trimer, and the zigzag configuration have similar adsorption energies of 0.55 ± 0.02 eV. Hydrogen bonding is strongest in the dimer and trimer adsorbed on the terrace, with respective energies of 0.30 and 0.27 eV, and accounts for their increased adsorption energies relative to the monomer. Hydrogen bonding is weak to moderate for adsorption at steps, with energies of 0.04 to 0.15 eV, as the much stronger water–metal interactions inhibit adsorption geometries favorable to hydrogen bonding. Correlations of hydrogen bond angles and energies with hydrogen bond lengths are presented. On the basis of these DFT/PW91 results, a model for water cluster formation on the Pt(111) surface can be formulated where kink sites nucleate chains along the top of step edges, consistent with the experimental findings of Morgenstern et al., Phys. Rev. Lett., 77 (1996) 703.     

Theoretical study of photoabsorption cross-section of water cluster anions: the size and isomer dependences

Photoabsorption cross-sections of water dimer and trimer anions are calculated with an ab initio molecular orbital method. Because the electron detachment energy of these small water cluster anions is less than 0.3 eV, all of the photoabsorption spectra in the near-infrared and visible region are due to the bound-free transitions. The theoretical spectra of two isomers of dimer anion and three isomers of trimer anion are compared, which suggest the possibility of the identification of the isomer structure by the photoabsorption spectra. The convergence on the basis sets is also examined by adding diffuse functions.     

Six-Bodies Calculations Using the Hyperspherical Harmonics Method

In this work we show results for light nuclear systems and small clusters of helium atoms using the hyperspherical harmonics basis. We use the basis without previous symmetrization or antisymmetrization of the state. After the diagonalization of the Hamiltonian matrix, the eigenvectors have well defined symmetry under particle permutation and the identification of the physical states is possible. We show results for systems composed up to six particles. As an example of a fermionic system, we consider a nucleon system interacting through the Volkov potential, used many times in the literature. For the case of bosons, we consider helium atoms interacting through a potential model which does not present a strong repulsion at short distances. We have used an attractive gaussian potential to reproduce the values of the dimer binding energy, the atom-atom scattering length, and the effective range obtained with one of the most widely used He–He interaction, the LM2M2 potential. In addition, we include a repulsive hypercentral three-body force to reproduce the trimer binding energy.