Short-range Pair Interactions Research Articles

On the weakness of short-range interactions in Fermi gases

Ultracold quantum gases of equal-spin fermions with short-range interactions are often considered free even in the presence of strongly binding spin-up–spin-down pairs. We describe a large class of many-particle Schrödinger operators with short-range pair interactions, where this approximation can be justified rigorously.

Bose–Einstein condensation for particles with repulsive short-range pair interactions in a Poisson random external potential in

AbstractWe study Bose gases in$d \ge 2$dimensions with short-range repulsive pair interactions at positive temperature, in the canonical ensemble and in the thermodynamic limit. We assume the presence of hard Poissonian obstacles and focus on the non-percolation regime. For sufficiently strong interparticle interactions, we show that almost surely there cannot be Bose–Einstein condensation into a sufficiently localized, normalized one-particle state. The results apply to the canonical eigenstates of the underlying one-particle Hamiltonian.

Towards Efficient Short-Range Pair Interaction on Sunway Many-Core Architecture

The short-range pair interaction consumes most of the CPU time in molecular dynamics (MD) simulations. The inherent computation sparsity makes it challenging to achieve high-performance kernel on the emerging many-core architecture. In this paper, we present a highly efficient short-range force kernel on the Sunway, a novel many-core architecture with many unique features. The parallel efficiency of this algorithm on the Sunway many-core processor is strongly limited by the poor data locality and write conflicts. To enhance the data locality, we adopt a super cluster based neighbor list with an appropriate granularity that fits in the local memory of computing cores. In the absence of a low overhead locking mechanism, using data-privatization force array is a more feasible method to avoid write conflicts, but results in the large overhead of data reduction. We adopt a dual-slice partitioning scheme for both hardware resources and computing tasks, which utilizes the on-chip data communication to reduce data reduction overhead and provide load balancing. Moreover, we exploit the single instruction multiple data (SIMD) parallelism and perform instruction reordering of the force kernel on this many-core processor. The experimental results show that the optimized force kernel obtains a performance speedup of 226x compared with the reference implementation and achieves 20% of peak flop rate on the Sunway many-core processor.

Universal reshaping of arrested colloidal gels via active doping.

Colloids that interact via a short-range attraction serve as the primary building blocks for a broad range of self-assembled materials. However, one of the well-known drawbacks to this strategy is that these building blocks rapidly and readily condense into a metastable colloidal gel. Using computer simulations, we illustrate how the addition of a small fraction of purely repulsive self-propelled colloids, a technique referred to as active doping, can prevent the formation of this metastable gel state and drive the system toward its thermodynamically favored crystalline target structure. The simplicity and robust nature of this strategy offers a systematic and generic pathway to improving the self-assembly of a large number of complex colloidal structures. We discuss in detail the process by which this feat is accomplished and provide quantitative metrics for exploiting it to modulate the self-assembly. We provide evidence for the generic nature of this approach by demonstrating that it remains robust under a number of different anisotropic short-ranged pair interactions in both two and three dimensions. In addition, we report on a novel microphase in mixtures of passive and active colloids. For a broad range of self-propelling velocities, it is possible to stabilize a suspension of fairly monodisperse finite-size crystallites. Surprisingly, this microphase is also insensitive to the underlying pair interaction between building blocks. The active stabilization of these moderately sized monodisperse clusters is quite remarkable and should be of great utility in the design of hierarchical self-assembly strategies. This work further bolsters the notion that active forces can play a pivotal role in directing colloidal self-assembly.

Self-Assembly of Mesophases from Nanoparticles.

A growing number of crystalline and quasi-crystalline structures have been formed by coating nanoparticles with ligands, polymers, and DNA. The design of nanoparticles that assemble into mesophases, such as those formed by block copolymers, would combine the order, mobility, and stimuli responsive properties of mesophases with the electronic, magnetic, and optical properties of nanoparticles. Here we use molecular simulations to demonstrate that binary mixtures of unbound particles with simple short-ranged pair interactions produce the same mesophases as block copolymers and surfactants, including lamellar, hexagonal, gyroid, body-centered cubic, face-centered cubic, perforated lamellar, and semicrystalline phases. The key to forming the mesophases is the frustrated attraction between particles of different types, achieved through control over interparticle size and over strength and softness of the interaction. Experimental design of nanoparticles with effective interactions described by the potentials of this work would provide a distinct, robust route to produce ordered tunable liquid crystalline mesophases from nanoparticles.

Optimized Force Fields for Simulations of Intrinsically Disordered Proteins

Some frequently encountered deficiencies in all-atom molecular simulations, such as nonspecific protein-protein interactions being too strong, and unfolded or disordered states being too collapsed, suggest that proteins are insufficiently well solvated in simulations using current state-of-the-art force fields. In order to address these issues, we make the simplest possible change, by modifying the short-range protein-water pair interactions, and leaving all the water-water and protein-protein parameters unchanged. We find that a modest strengthening of protein-water interactions is sufficient to recover the correct dimensions of intrinsically disordered or unfolded proteins, as determined by direct comparison with small-angle X-ray scattering (SAXS) and Forster resonance energy transfer (FRET) data. The modification also results in more realistic protein:protein affinities, and average solvation free energies of model compounds which are more consistent with experiment. Most importantly, we show that this scaling is small enough not to affect adversely the stability of the folded state, with only a modest effect on the stability of model peptides forming alpha-helix and beta-sheet structures. The proposed adjustment opens the way to more accurate atomistic simulations of proteins, particularly for intrinsically disordered proteins, protein:protein association, and crowded cellular environments.

Balanced Protein-Water Interactions Improve Properties of Disordered Proteins and Non-Specific Protein Association.

Some frequently encountered deficiencies in all-atom molecular simulations, such as nonspecific protein–protein interactions being too strong, and unfolded or disordered states being too collapsed, suggest that proteins are insufficiently well solvated in simulations using current state-of-the-art force fields. To address these issues, we make the simplest possible change, by modifying the short-range protein–water pair interactions, and leaving all the water–water and protein–protein parameters unchanged. We find that a modest strengthening of protein–water interactions is sufficient to recover the correct dimensions of intrinsically disordered or unfolded proteins, as determined by direct comparison with small-angle X-ray scattering (SAXS) and Förster resonance energy transfer (FRET) data. The modification also results in more realistic protein-protein affinities, and average solvation free energies of model compounds which are more consistent with experiment. Most importantly, we show that this scaling is small enough not to affect adversely the stability of the folded state, with only a modest effect on the stability of model peptides forming α-helix and β-sheet structures. The proposed adjustment opens the way to more accurate atomistic simulations of proteins, particularly for intrinsically disordered proteins, protein–protein association, and crowded cellular environments.

Origin of polar distortion inLiNbO3-type “ferroelectric” metals: Role ofA-site instability and short-range interactions

Since conduction electrons of a metal screen effectively the local electric dipole moments, it was widely believed that the ferroelectric-like distortion cannot occur in metals. Recently, metallic LiOsO3, was discovered to be the first clear-cut example of an Anderson-Blount "ferroelectric" metal, which at 140 K undergoes a ferroelectric-like structural transition similar to insulating LiNbO3. This is very surprising because the mechanisms for structural phase transitions are usually quite distinct in metals and insulators. Through performing first principles calculations, here we reveal that the local polar distortion in LiOsO3 is solely due to the instability of the A-site Li atom, in contrast to the LiNbO3 case where the second order Jahn-Teller effect of the B-site Nb ion also plays an additional role. More importantly, the "ferroelectric"-like long range order of the local polar distortion is found to be due to the predominantly ferroelectric short-range pair interactions between the local polar modes which are not screened by conduction electrons. Furthermore, we predict that LiNbO3-type MgReO3 is also a "ferroelectric" metal, but with a much higher structural transition temperature by 391 K than LiOsO3. Our work not only unravels the origin of FE-like distortion in LiNbO3-type "ferroelectric" metals, but also provides clue for designing other multi-functional "ferroelectric" metals.

Riesz External Field Problems on the Hypersphere and Optimal Point Separation

We consider the minimal energy problem on the unit sphere $\mathbb{S}^d$ in the Euclidean space $\mathbb{R}^{d+1}$ in the presence of an external field $Q$, where the energy arises from the Riesz potential $1/r^s$ (where $r$ is the Euclidean distance and $s$ is the Riesz parameter) or the logarithmic potential $\log(1/r)$. Characterization theorems of Frostman-type for the associated extremal measure, previously obtained by the last two authors, are extended to the range $d-2 \leq s < d - 1.$ The proof uses a maximum principle for measures supported on $\mathbb{S}^d$. When $Q$ is the Riesz $s$-potential of a signed measure and $d-2 \leq s <d$, our results lead to explicit point-separation estimates for $(Q,s)$-Fekete points, which are $n$-point configurations minimizing the Riesz $s$-energy on $\mathbb{S}^d$ with external field $Q$. In the hyper-singular case $s > d$, the short-range pair-interaction enforces well-separation even in the presence of more general external fields. As a further application, we determine the extremal and signed equilibria when the external field is due to a negative point charge outside a positively charged isolated sphere. Moreover, we provide a rigorous analysis of the three point external field problem and numerical results for the four point problem.

Neutron scattering studies of short-range order, atomic displacements, and effective pair interactions in a null-matrixNi0.5262Pt0.48crystal

The best known exception to the Heine-Sampson and Bieber-Gauthier arguments for ordering effects in transition metal alloys (similar to the Hume-Rothery rules) is a NiPt alloy, whose phase diagram is similar to that of the CuAu system. Using neutron scattering we have investigated the local atomic order in a null-matrix $^{62}\mathrm{Ni}_{0.52}{\mathrm{Pt}}_{0.48}$ single crystal. In a null-matrix alloy, the isotopic composition is adjusted so that the average neutron scattering length vanishes ($^{62}\mathrm{Ni}$ has a negative scattering length nearly equal in magnitude to that of Pt). Consequently, all contributions to the total scattering depending on the average lattice are suppressed. The only remaining components of the elastic scattering are the short-range order (SRO) and size effect terms. These data permit the extraction of the SRO parameters (concentration-concentration correlations) as well as the displacement parameters (concentration-displacement correlations). Using the Krivoglaz-Clapp-Moss theory, we obtain the effective pair interactions (EPIs) between near neighbors in the alloy. The results can be used by theorists to model the alloy in the context of the electronic theory of alloy phase stability, including a preliminary evaluation of the local species-dependent displacements. Our maps of $V(\mathbf{q})$, the Fourier transform of the EPIs, show very similar shapes in the experimental and reconstructed data. This is of importance when comparing to electronic structure calculations.

Coulomb Fourier transformation: A novel approach to three-body scattering with charged particles

A unitary transformation of the three-body Hamiltonian which describes a system of two charged and one neutral particles is constructed such that the Coulomb potential which acts between the charged particles is explicitly eliminated. The transformed Hamiltonian and, in particular, the transformed short-range pair interactions are worked out in detail. Thereby it is found that, after transformation, the short-range potentials acting between the neutral and either one of the charged particles become simply Fourier transformed but, in addition, multiplied by a function that represents the Coulombic three-body correlations originating from the action of the other charged particle on the considered pair. This function which is universal as it does not depend on any property of the short-range interaction is evaluated explicitly and its singularity structure is described in detail. In contrast, the short-range potential between the charged particles remains of two-body type but occurs now in the ``Coulomb representation.'' Specific applications to Yukawa and Gaussian potentials are given. Since the Coulomb-Fourier-transformed Hamiltonian does no longer contain the Coulomb potential or any other effective interaction of long range, standard methods of short-range few-body scattering theory are applicable.

A Rigorous Derivation¶of the Gross–Pitaevskii Energy Functional¶for a Two-dimensional Bose Gas

We consider the ground state properties of an inhomogeneous two-dimensional Bose gas with a repulsive, short range pair interaction and an external confining potential. In the limit when the particle number $N$ is large but $\bar\rho a^2$ is small, where $\bar\rho$ is the average particle density and $a$ the scattering length, the ground state energy and density are rigorously shown to be given to leading order by a Gross-Pitaevskii (GP) energy functional with a coupling constant $g\sim 1/|\ln(\bar\rho a^2)|$. In contrast to the 3D case the coupling constant depends on $N$ through the mean density. The GP energy per particle depends only on $Ng$. In 2D this parameter is typically so large that the gradient term in the GP energy functional is negligible and the simpler description by a Thomas-Fermi type functional is adequate.

Hydration interactions: aqueous solvent effects in electric double layers

A model for ionic solutions with an attractive short-range pair interaction between the ions is presented. The short-range interaction is accounted for by adding a quadratic nonlocal term to the Poisson-Boltzmann free energy. The model is used to study solvent effects in a planar electric double layer. The counterion density is found to increase near the charged surface, as compared with the Poisson-Boltzmann theory, and to decrease at larger distances. The ion density profile is studied analytically in the case where the ion distribution near the plate is dominated only by counterions. Further away from the plate the density distribution can be described using a Poisson-Boltzmann theory, with an effective surface charge that is smaller than the actual one.

Influence of the distance between ionizable groups on the protonation behavior of various hexaamines

A synthesis route for N,N,N′,N′-tetraaminoethyl-1,2-ethylenediamine, N,N,N′,N′-tetraaminopropyl-1,2-ethylenediamine, N,N,N′,N′-tetraaminopropyl-1,3-propylenediamine and N,N,N′,N′-tetraaminopropyl-1,4-butylenediamine is presented. These molecules differ from each other in the number of carbon atoms between the six amino groups. This results in different protonation behavior. Potentiometric titrations are performed in 0.1 M and 1.0 M KCl, and the six macroscopic protonation constants are obtained from these curves. An Ising model with a limited number of microscopic protonation constants and short-ranged pair interactions describes the protonation behavior quantitatively. The results are compared to those of other, similar molecules. The advantage of the Ising model over empirical relations such as the Taft equations is the more systematic approach with which the titration curves of more complex molecules can be described. The values for the Ising model parameters obtained here can be used to predict the protonation behavior of more complex, in particular larger, polyamines.

A lattice-gas model for alkali-metal fullerides: body-centred-cubic structure

A Coulomb lattice-gas model with a host-lattice screening mechanism is adapted to describe the ordering phenomena in alkali-metal fullerides of body-centred-cubic structure. It is assumed that the electric charge of an alkali ion residing at a tetrahedral interstitial site is completely screened by its first-neighbour molecules. The electronic energy of the ion is also taken into consideration as a charged spherical shell. By means of these assumptions an effective (short-range) pair interaction between two alkali ions is obtained. The resultant lattice-gas model is analysed by using two- and six-sublattice mean-field approximations. The thermodynamic properties are summarized in phase diagrams for different shell radii.

Effect of potential energy topography on dynamics and phase behaviour of clusters

Clusters of seven identical particles, bound by pairwise Morse potentials, simulated at constant energy, exhibit zones of dynamic coexistence of solid-like and liquid-like forms if the range parameter ρ0 = βr0 of the potential is large, corresponding to a short-range pair interaction. However no such phase coexistence occurs for longer-range Morse potentials, according to the criterion of bimodality (or unimodality, for no coexistence) of the distribution of short-time average vibrational temperatures. The difference is due to the smoother topography of the multidimensional potential surface generated by the longer-range pair potentials, particularly in the higher-energy reaches of that surface.

The effect of charge transfer on the transition temperatures of binary alloys

Abstract A Short range pair interactions are derived in order to calculate the Madelung energy of random binary alloys. It is pointed out that the energy contribution due to charge fluctuations is proportional to the on-site term in mean field theory. The effect of charge transfer on phase transitions is then demonstrated in the case of Cu x Au1−x systems. In our example, it is found that by including charge corrections the transition temperatures are in better agreement with experiment than when using the bare generalized peturbation method pair interactions.

Unbinding of three strings in the Born-Oppenheimer approximation

The unbinding transition of three strings, fluctuating without overhangs in two dimensions, is considered in the Born-Oppenheimer approximation. The calculation, which is extremely simple, gives some insight into the physical considerations that determine the universality class. In the case of short-range pair interactions the unbinding transition is predicted to be universal, with the same critical exponents as in the unbinding of two strings. For strings bound by short-range three-body interactions the unbinding transition is nonuniversal. Both of these predictions are in agreement with recent exact studies.

Gaussian multipoles in practice: Electrostatic energies for intermolecular potentials

AbstractA method is presented for calculating the total electrostatic interaction energies between molecules from ab initio monomer wave functions. This approach differs from existing methods, such as Stone's distributed multipole analysis (DMA), in including the short‐range penetration energy as well as the long‐range multipolar energy. The monomer charge densities are expressed as distributed series of atom‐centered functions which we call Gaussian multipoles; these are analogous to the distributed point multipoles used in DMA. Our procedure has been encoded in the GMUL program. Calculations have been performed on the formamide/formaldehyde complex, a model system for NH …︁ O hydrogen bonding in biological molecules, and also on guanidinium/benzene, modeling amino/aromatic interactions in proteins. We find that the penetration energy can be significant, especially in its contribution to the variation of the electrostatic energy with interaction geometry. A hybrid method, which uses Gaussian multipoles for short‐range atom pair interactions and point multipoles for long‐range ones, allows the electrostatic energies, including penetration, to be calculated at a much reduced cost. We also note that the penetration energy may provide the best route to an atom–atom anisotropic model for the exchange‐repulsion energy in intermolecular potentials. © 1994 by John Wiley &amp; Sons, Inc.

Isotopic shift of helium melting pressure: Path integral Monte Carlo study.

We compute by a path integral Monte Carlo calculation the isotropic shift of helium melting pressure in the temperature range (T&gt;100 K) where a discrepancy between theory and experiment has been recently reported. We use a realistic Aziz pair potential together with Bruch-McGee three-body forces for the interaction. The isotopic shift predicted in this work is in agreement with experiment; its measurement provides a good test of the interatomic potential of helium, as the isotopic shift is sensitive to the kinetic energy, which is determined by the short-range pair interaction.