Long-range Interaction Potential Research Articles

Range Separation of the Interaction Potential in Intermolecular and Intramolecular Symmetry-Adapted Perturbation Theory.

Symmetry-adapted perturbation theory (SAPT) is a popular and versatile tool to compute and decompose noncovalent interaction energies between molecules. The intramolecular SAPT (ISAPT) variant provides a similar energy decomposition between two nonbonded fragments of the same molecule, covalently connected by a third fragment. In this work, we explore an alternative approach where the noncovalent interaction is singled out by a range separation of the Coulomb potential. We investigate two common splittings of the 1/r potential into long-range and short-range parts based on the Gaussian and error functions, and approximate either the entire intermolecular/interfragment interaction or only its attractive terms by the long-range contribution. These range separation schemes are tested for a number of intermolecular and intramolecular complexes. We find that the energy corrections from range-separated SAPT or ISAPT are in reasonable agreement with complete SAPT/ISAPT data. This result should be contrasted with the inability of the long-range multipole expansion to describe crucial short-range charge penetration and exchange effects; it shows that the long-range interaction potential does not just recover the asymptotic interaction energy but also provides a useful account of short-range terms. The best consistency is attained for the error-function separation applied to all interaction terms, both attractive and repulsive. This study is the first step toward a fragmentation-free decomposition of intramolecular nonbonded energy.

Stochastic differential equations for infinite particle systems of jump type with long range interactions

Infinite-dimensional stochastic differential equations (ISDEs) describing systems with an infinite number of particles are considered. Each particle undergoes a Lévy process, and the interaction between particles is determined by the long-range interaction potential. The potential is of Ruelle's class or logarithmic. We discuss the existence and uniqueness of strong solutions of the ISDEs.

Light bullets in a nonlocal Rydberg medium with PT-symmetric moiré optical lattices

Realizing stable light bullets in high dimensions is a long-standing goal in the study of nonlinear optics. Here, we propose a scheme for the creation of stable light bullets (LBs) in a cold Rydberg atomic gas system with PT symmetry moiré optical lattices. Depending on the synergetic local and nonlocal Kerr nonlinearities, and PT symmetry moiré optical lattices, we obtain an appropriate nonlocal Rydberg long-range interaction and PT symmetry potential which can compensate for the diffraction and dispersion of the probe field. Numerical results show that different spatial and temporal distributions of LBs, including fundamental, multi-pole solitons, and vortical ones are uncovered, and their stabilities are evaluated through linear-stability analysis and direct simulation with perturbation. Furthermore, the solitons exhibit a quasi-elastic collision in the transversal direction during propagation. Our study provides a new route for manipulating LBs via controlled optical nonlinearities and PT symmetry moiré optical lattices in cold Rydberg gases.

Kinetic theory of one-dimensional inhomogeneous long-range interacting N-body systems at order 1/N^{2} without collective effects.

Long-range interacting systems irreversibly relax as a result of their finite number of particles, N. At order 1/N, this process is described by the inhomogeneous Balescu-Lenard equation. Yet, this equationexactly vanishes in one-dimensional inhomogeneous systems with a monotonic frequency profile and sustaining only 1:1 resonances. In the limit where collective effects can be neglected, we derive a closed and explicit 1/N^{2} collision operator for such systems. We detail its properties, highlighting in particular how it satisfies an H theorem for Boltzmann entropy. We also compare its predictions with direct N-body simulations. Finally, we exhibit a generic class of long-range interaction potentials for which this 1/N^{2} collision operator exactly vanishes.

Superglass formation in an atomic BEC with competing long-range interactions

The complex dynamical phases of quantum systems are dictated by atomic interactions that usually evoke an emergent periodic order. Here, we study a quantum many-body system with two competing and substantially different long-range interaction potentials where the dynamical instability towards density order can give way to a superglass phase, i. e., a superfluid disordered amorphous solid, which exhibits local density modulations but no long-range periodic order. We consider a two-dimensional BEC in the Rydberg-dressing regime coupled to an optical standing wave resonator. The dynamic pattern formation in this system is governed by the competition between the two involved interaction potentials: repulsive soft-core interactions arising due to Rydberg dressing and infinite-range sign changing interactions induced by the cavity photons. The superglass phase is found when the two interaction potentials introduce incommensurate length scales. The dynamic formation of this peculiar phase without any externally added disorder is driven by quantum fluctuations and can be attributed to frustration induced by the two competing interaction energies and length scales.

Superballistic and superdiffusive scaling limits of stochastic harmonic chains with long-range interactions

We consider one-dimensional infinite chains of harmonic oscillators with random exchanges of momenta and long-range interaction potentials which have polynomial decay rate |x|−θ , x → ∞, θ > 1 where is the interaction range. The dynamics conserve total momentum, total length and total energy. We prove that the systems evolve macroscopically on superballistic space-time scale when 1 < θ < 3, when θ = 3, and hyperbolic space-time scale (yɛ −1, tɛ −1) when θ > 3. Combining our results and the results in (Suda 2021 Ann. Inst. Henri Poincare B 57 2268–2314), we show the existence of two different space-time scales on which the systems evolve. In addition, we prove the fluctuations of the normal modes of the superballistic wave equation, which are analogues of the Riemann invariants and capture fluctuations along the characteristics. For the normal modes, the space-time scale is superdiffusive when 2 < θ ⩽ 4 and diffusive when θ > 4.

Зависимость энергии отдачи от кристаллографических направлений при бомбардировке монокристалла медленными ионами

Calculations of the recoil energy under bombardment of the surface edge (001) for the vanadium mono-crystal by K+ ions (E0 = 10―50 eV) with the initial motion trajectories lying in planes perpendicular to the plane (001) and parallel to the planes (100) and (110), passing along the crystallographic directions [010] and [110], respectively, have been made by the method of molecular dynamics using a long-range interaction potential. Anisotropy of maximum energy transfer to one of the group of (3―5) atoms simultaneously participating in the interaction, depending on the ion motion trajectory, has been revealed. The energy spray thresholds for specified directions have been determined.

Dependence of the recoil energy on crystallographic directions under bombardment of a mono-crystal by slow ions

Calculations of the recoil energy under bombardment of the surface edge (001) for the vanadium mono-crystal by K+ ions (E_0=10-50 eV) with the initial motion trajectories lying in planes perpendicular to the plane (001) and parallel to the planes (100) and (110), passing along the crystallographic directions [010] and [110], respectively, have been made by the method of molecular dynamics using a long-range interaction potential. Anisotropy of maximum energy transfer to one of the group of (3-5) atoms simultaneously participating in the interaction, depending on the ion motion trajectory, has been revealed. The energy spray thresholds for specified directions have been determined Keywords: ion bombardment, single crystal, crystallographic directions, recoil energy, sputtering thresholds.

Stability of Lipid Coatings on Nanoparticle-Decorated Surfaces.

Lipid membranes supported on solid surfaces and nanoparticles find multiple applications in industrial and biomedical technologies. Here, we explore in silico the mechanisms of the interactions of lipid membranes with nanostructured surfaces with deposited nanoparticles and explain the characteristic particle size dependence of the uniformity and stability of lipid coatings observed in vitro. Simulations are performed to demonstrate the specifics of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) lipid membrane adhesion to hydrophilic and hydrophobic nanoparticles ranging in size from 1.5 to 40 nm using an original coarse-grained molecular dynamics model with implicit solvent and large simulation boxes (scales up to 280 × 154 × 69 nm3). We find that one of the major factors that affects the uniformity and stability of lipid coatings is the disjoining pressure in the water hydration layer formed between the lipid membrane and hydrophilic solid surface. This effect is accounted for by introducing a special long-range lipid-solid interaction potential that mimics the effects of the disjoining pressure in thin water layers. Our simulations reveal the physical mechanisms of interactions of lipid bilayers with solid surfaces that are responsible for the experimentally observed nonmonotonic particle size dependence of the uniformity and stability of lipid coatings: particles smaller than the hydration layer thickness (<2-3 nm) or larger than ∼20 nm are partially or fully enfolded by a lipid bilayer, whereas particles of the intermediate size (5-20 nm) cause membrane perforation and pore formation. In contrast, hydrophobic nanoparticles, which repel the hydration layer, tend to be encapsulated within the hydrophobic interior of the membrane and coated by the lipid monolayer. The proposed model can be further extended and applied to a wide class of systems comprising nanoparticles and nanostructured substrates interacting with lipid and surfactant bilayers and monolayers.

Statistical quantum mechanical approach to diatom-diatom capture dynamics and application to ultracold KRb + KRb reaction.

A general and rigorous quantum method is proposed for studying capture dynamics between two diatomic molecules in full dimensionality. By solving the time-independent Schrödinger equation with proper boundary conditions, this method is ideally suited for studying quantum dynamics of cold and ultracold reactions. To illustrate its applicability, the capture dynamics between ultracold KRb molecules is characterized in full six dimensions for the first time using a first-principles based long-range interaction potential. The calculated capture rates for collisions involving distinguishable and indistinguishable 40K87Rb molecules are in good agreement with the experiment and exhibit clear Wigner threshold behaviors. Predictions for ultracold collisions between internally excited 40K87Rb suggest minor changes in the loss rate, consistent with experimental observations in similar systems.

Long-range interaction of Li(2S2)−Li(2S2)−Li+(1S1)

The long-range interactions among two- or three-atom systems are of considerable importance in the cold and ultracold research areas for many-body systems. For an ion and an atom, the long-range interaction potential is dominated by the induction (or polarization) potential resulting from the (classical) effect of the ion's electric field on the atom and the leading term of the induction potential is much stronger than the (quantum mechanical) dispersion (or van der Waals) interaction. The present paper focuses on the long-range interaction of the $\mathrm{Li}(2\phantom{\rule{0.16em}{0ex}}^{2}S)\ensuremath{-}\mathrm{Li}(2\phantom{\rule{0.16em}{0ex}}^{2}S)\ensuremath{-}{\mathrm{Li}}^{+}(1\phantom{\rule{0.16em}{0ex}}^{1}S)$ system, to see what changes this induction effect (originating in the electric field of the ${\mathrm{Li}}^{+}$ ion) yields in the long-range additive and nonadditive interactions of this three-body system. Using perturbation theory for energies, we evaluate the coefficients ${C}_{n}$ in the potential energy for the three well-separated constituents, where $n$ refers to the corresponding order in inverse powers of distance, obtaining the additive interaction coefficients ${C}_{4}, {C}_{6}, {C}_{7}, {C}_{8}, {C}_{9}$ and the nonadditive interaction coefficients ${C}_{7}, {C}_{9}$. The obtained coefficients ${C}_{n}$ are calculated with highly accurate variationally generated nonrelativistic wave functions in Hylleraas coordinates. Our calculations may be of interest for the study of three-body recombination and for constructing precise potential energy surfaces. We also provide precise evaluations of the long-range potentials for the two-body $\mathrm{Li}(2\phantom{\rule{0.16em}{0ex}}^{2}S)\ensuremath{-}{\mathrm{Li}}^{+}(1\phantom{\rule{0.16em}{0ex}}^{1}S)$ system. For both the two-body and three-body cases, we provide results for the like-nuclei cases of $^{6}\mathrm{Li}$ and $^{7}\mathrm{Li}$.

Non-adiabatic quantum dynamics of the ultracold Li+LiNa→ Li2+Na chemical reaction

SynopsisWe report non-adiabatic dynamics of the Li+LiNa→Li2+Na chemical reaction at cold and ultracold temperatures employing accurate ab initio electronic potential energy surfaces in a quantum dynamics formulation employing a diabatic representation. Results are compared against those from a single adiabatic ground state potential energy surface and a universal model based on the long-range interaction potential. We discuss signatures of non-universal behavior in the total rate coefficients as well as strong non-adiabatic effects in the state-to-state rotationally resolved rate coefficients.

Accurate non-bonded potentials based on periodic quantum mechanics calculations for use in molecular simulations of materials and systems.

Molecular dynamics simulations require accurate force fields (FFs) to describe the physical and chemical properties of complex materials and systems. FF parameters for valence interactions can be determined from high-quality Quantum Mechanical (QM) calculations. However, it has been challenging to extract long-range nonbonded interaction potentials from QM calculations since there is no unambiguous method to separate the total QM energy into electrostatics (polarization), van der Waals (vdW), and other components. Here, we propose to use density functional theory with dispersion corrections to obtain the equation of state for single element solid systems (of H, C, N, O, F, Cl, Br, I, P, He, Ne, Ar, Kr, Xe, and Rn) from which we obtain the pure 2-body vdW nonbonded potentials. Recently, we developed the polarizable charge equilibration (PQEq) model based on QM polarization energy of electric probe dipoles with no contributions from vdW. Together, the vdW and PQEq interactions form the nonbonded potential of our new transferrable reactive FF (RexPoN). They may also be useful to replace the nonbonded parts of standard FFs, such as OPLS, Amber, UFF, and CHARMM. We find that the individual 2-body vdW potential curves can be scaled to a universal vdW potential using just three specific atomic parameters. This simplifies extension to the rest of the periodic table for atoms that do not exhibit molecular packing. We validate the accuracy of these nonbonded interactions for liquid water, energetic, and biological systems. In all cases, we find that our new nonbonded potentials provide good agreement with QM and experimental data.

Inverse scattering in the Stark effect

We study one of the multidimensional inverse scattering problems for quantum systems governed by the Stark Hamiltonians. By applying the time-dependent method developed by Enss and Weder (1995 J. Math. Phys. 36 3902–21), we prove that the high-velocity limit of the scattering operator uniquely determines the short-range interaction potentials. Moreover, we prove that, when a long-range interaction potential is given, the high-velocity limit of the Dollard-type modified scattering operator uniquely determines the short-range part of the interactions. We allow the potential functions to belong to very broad classes. These results are improvements on the previous results obtained by Adachi and Maehara (2007 J. Math. Phys. 48 042101; Adachi et al 2013 Inverse Problems 29 085012).

A multiscale study of misfit dislocations in PbTe/PbSe(001) heteroepitaxy

Abstract

Fast decay of eigenfunction correlators in long-range continuous random alloys

Abstract We study random Anderson Hamiltonians in Euclidean spaces with a long-range particle-media interaction potential {\mathfrak{u}(r)=r^{-A}} . Improving earlier results, for any {A&gt;2d} , we establish spectral and strong dynamical localization with sub-exponential decay of eigenfunction correlators, both in the strong disorder regime and at low energies.

Reskit: A toolkit to determine the poles of an S-matrix

We present the python package reskit, developed to calculate the coefficients of an analytical continuation of the S-matrix of a physical system by means of Padé approximants and, from this fit, determine the complex poles of this S-matrix.The current implementation of the program is restricted to elastic scattering, i.e. cases in which all channels have the same energy. It has been tested using as input ab initio scattering data for electron–molecule collisions obtained for energies along the real axis. The identification and characterisation of the resonances present in the systems using reskit is described and discussed. Program summaryProgram Title:reskitProgram Files doi:http://dx.doi.org/10.17632/p47yys8wpm.1Licensing provisions: MITProgramming language: Python 2.7Nature of problem: the S-matrix of a system is usually calculated as a function of real energy (for example by varying the kinetic energy of a projectile in a scattering process). Locating its complex poles requires some type of extrapolation on the Riemann sheets relating the total energy, in the complex plane, to the momentum. The program determines the complex poles of the fitted polynomial S-matrix that identify its resonant, bound and virtual states.Solution method: the program is based on the method developed by Rakityansky and collaborators [1] in which a Padé approximant is used to fit provided S-matrix data, determined as a function of a real energy. Expressing the S-matrix in the Jost form, the generally complex poles of the S-matrix can be found by determining the stability of the roots of the determinant of the Jost matrix as S-matrix data for an increasing number of energies are used for the fit.Additional comments including restrictions and unusual features: the current implementation requires that all channels/states have the same energy and that no long-range Coulomb interaction potential is present. The first of these restrictions results in a simplified S-matrix that is defined solely as a function of the momentum in the complex plane.[1] P. Ogunbade, S. Rakityansky, S-matrix parametrization as a way of locating quantum resonances and bound states: multichannel case, in: Proceedings of the 2nd South Africa - JINR SYMPOSIUM, Models and Methods in Few- and Many-Body Systems, JINR, 2010, 52–61.

Next-order asymptotic expansion for N-marginal optimal transport with Coulomb and Riesz costs

Motivated by a problem arising from Density Functional Theory, we provide the sharp next-order asymptotics for a class of multimarginal optimal transport problems with cost given by singular, long-range pairwise interaction potentials. More precisely, we consider an N-marginal optimal transport problem with N equal marginals supported on Rd and with cost of the form ∑i≠j|xi−xj|−s. In this setting we determine the second-order term in the N→∞ asymptotic expansion of the minimum energy, for the long-range interactions corresponding to all exponents 0<s<d. We also prove a small oscillations property for this second-order energy term. Our results can be extended to a larger class of models than power-law-type radial costs, such as non-rotationally-invariant costs. The key ingredient and main novelty in our proofs is a robust extension and simplification of the Fefferman–Gregg decomposition [20], [26], extended here to our class of kernels, and which provides a unified method valid across our full range of exponents. Our first result generalizes a recent work of Lewin, Lieb and Seiringer [36], who dealt with the second-order term for the Coulomb case s=1,d=3.

Range-Separated Tensor Format for Many-Particle Modeling

We introduce and analyze the new range-separated (RS) canonical/Tucker tensor format which aims for numerical modeling of the 3D long-range interaction potentials in multiparticle systems. The main idea of the RS tensor format is the independent grid-based low-rank representation of the localized and global parts in the target tensor, which allows the efficient numerical approximation of $N$-particle interaction potentials. The single-particle reference potential, described by the radial basis function $p(\|x\|)$, $x \in \mathbb{R}^d$, say $p(\|x\|)=1/\|x\|$ for $d=3$, is split into a sum of localized and long-range low-rank canonical tensors represented on a fine 3D $n\times n\times n$ Cartesian grid. The smoothed long-range contribution to the total potential sum is represented on the 3D grid in $O(n)$ storage via the low-rank canonical/Tucker tensor. We prove that the Tucker rank parameters depend only logarithmically on the number of particles $N$ and the grid size $n$. Agglomeration of the short-rang...

A pseudo-thermodynamic description of dispersion for nanocomposites

Dispersion in polymer nanocomposites is determined by the kinetics of mixing and chemical affinity. Compounds like reinforcing filler/elastomer blends display some similarity to colloidal solutions in that the filler particles are close to randomly dispersed through processing. It is attractive to apply a pseudo-thermodynamic approach taking advantage of this analogy between the kinetics of mixing for polymer compounds and thermally driven dispersion for colloids. In order to demonstrate this pseudo-thermodynamic approach, two polybutadienes and one polyisoprene were milled with three carbon blacks and two silicas. These samples were examined using small-angle x-ray scattering as a function of filler concentration to determine a pseudo-second order virial coefficient, A2, which is used as an indicator for compatibility of the filler and polymer. It is found that A2 follows the expected behavior with lower values for smaller primary particles indicating that smaller particles are more difficult to mix. A2 is analogous to the excluded volume and long-range interaction potential for non-equilibrated nanocomposites. The measured values of A2 can be used to specify repulsive interaction potentials for coarse grain DPD simulations of filler/elastomer systems. In addition, new methods to quantify the filler percolation threshold and filler mesh size as a function of filler concentration are obtained. The results represent a new approach to understanding and predicting dispersion in polymer nanocomposites based on a thermodynamic analogy.