Long-range Terms Research Articles

Periodic ab initio estimates of the dispersive interaction between molecular nitrogen and a monolayer of hexagonal BN

The ab initio determination of the leading long-range term of pairwise additive dispersive interactions, based on the independent analysis of the response properties of the interacting objects, is here considered in the case where these are part of a periodic system. The interaction of a nitrogen molecule with a thin film of hexagonal BN has been chosen as a case study for identifying some of the problems involved, and for proposing techniques for their solution. In order to validate the results so obtained, the interaction energy between N(2) and a BN monolayer at different distances has been estimated following a totally different approach, namely by performing post-Hartree-Fock (MP2) supercell calculations using the Crystal+Cryscor suite of programs. The results obtained with the two approaches closely agree over a long range, while the limit of validity of the purely dispersive regime can be clearly assessed.

Ordered interfaces for dual easy axes in liquid crystals

Using nCB films adsorbed on MoS 2 substrates studied by x-ray diffraction, optical microscopy and Scanning Tunneling Microscopy, we demonstrate that ordered interfaces with well-defined orientations of adsorbed dipoles induce planar anchoring locked along the adsorbed dipoles or the alkyl chains, which play the role of easy axes. For two alternating orientations of the adsorbed dipoles or dipoles and alkyl chains, bi-stability of anchoring can be obtained. The results are explained using the introduction of fourth order terms in the phenomenological anchoring potential, leading to the demonstration of first order anchoring transition in these systems. Using this phenomenological anchoring potential, we finally show how the nature of anchoring in presence of dual easy axes (inducing bi-stability or average orientation between the two easy axes) can be related to the microscopical nature of the interface. Introduction Understanding the interactions between liquid crystal (LC) and a solid substrate is of clear applied interest, the vast majority of LC displays relying on control of interfaces. However this concerns also fundamental problems like wetting phenomena and all phenomena of orientation of soft matter bulk induced by the presence of an interface. In LCs at interfaces, the so-called easy axes correspond to the favoured orientations of the LC director close to the interface. If one easy axis only is defined for one given interface, the bulk director orients along or close to this axis [1]. It is well known that, in anchoring phenomena, two major effects compete to impose the anchoring directions of a liquid crystal, first, the interactions between molecules and the interface, second, the substrate roughness whose role has been analyzed by Berreman [2]. The influence of adsorbed molecular functional groups at the interface is most often dominant with, for example in carbon substrates, a main influence of unsaturated carbon bonds orientation at the interface [3]. In common LC displays, there is one unique easy axis, but modifications of surfaces have allowed for the discovery of promising new anchoring-related properties. For instance, the first anchoring bi-stability has been established on rough surfaces, associated with electric ordo-polarization [4] and the competition between a stabilizing short-range term and a destabilizing long-range term induced by an external field, can induce a continuous variation of anchoring orientation [5]. More recently, surfaces with several easy axes have been studied extensively. It has been shown that control of a continuous variation of director pretilt, obtained in several systems [6, 7], is associated with the presence of two different easy axes, one perpendicular to the substrate (homeotropic) and one planar [7, 8]. Similar models can explain the continuous evolution of anchoring between two planar orientations observed on some crystalline substrates [9]. However, in the same time, two easy axes can also lead to anchoring bi-stability [10, 11] or discontinuous transitions of anchoring [9], which is not compatible with the model established to interpret observed control of pretilt. In order to be able to predict if bi-stability or continuous combination of the two easy axes occurs for one given system, it becomes necessary to understand the microscopic origin of the easy axes.

Kinetic investigation of the relationship between the efficiency of columns and their diameter

Abstract Many brands of packing materials made of fine particles are now available in both conventional (4.6 mm i.d.) and narrow-bore (2.1 mm i.d.) columns. It is a general observation that the efficiency of the former tends to be markedly higher than that of the latter. This report provides a detailed illustration of the characteristics of this enigma. The corrected reduced plate heights of three brands of columns packed with shell particles in 4.6 and 2.1 mm I.D. columns were measured. The brands were the 1.7 and 2.6 μm Kinetex-C 18 (Phenomenex, Torrance, CA, USA), the 2.7 μm Poroshell120-C 18 (Agilent Technologies, New Castle, DE, USA), and the 2.7 μm Halo-C 18 (Advanced Material Technologies, Wilmington, DE, USA). The extra-column contributions were minimized by optimizing the configuration of the instrument (injection volume < 1.0 μL, 115 μm needle seat capillary, 80 μm connecting tubes, no heat exchanger, 0.8 μL detection cell). The correct peak variances were derived from the numerical integration of the first and second order moments of the experimental band profiles. These experimental results confirm that the kinetic performance of narrow-bore columns is inferior to that of conventional columns for all three brands of shell particles. We demonstrate that this difference is accounted for by a contribution to the column HETP of the long-range eddy diffusion term that is larger in the 2.1 than in the 4.6 mm I.D. columns. While the associated relative velocity biases are of comparable magnitude in both types of columns, the characteristic radial diffusion lengths are of the order of 100 and 40 μm in the wall regions of narrow-bore and conventional columns, respectively.

Bose condensation in flat bands

We derive effective Hamiltonians for lattice bosons with strong geometrical frustration of the kinetic energy by projecting the interactions on the flat lowest Bloch band. Specifically, we consider the Bose Hubbard model on the one dimensional sawtooth lattice and the two dimensional kagome lattice. Starting from a strictly local interaction the projection gives rise to effective long-range terms stabilizing a supersolid phase at densities above nu_c=1/9 of the kagome lattice. In the sawtooth lattice on the other hand we show that the solid order, which exists at the magic filling nu_c=1/4, is unstable to further doping. The universal low-energy properties at filling 1/4+delta nu are described by the well known commensurate-incommensurate transition. We support the analytic results by detailed numerical calculations using the Density Matrix Renormalization Group and exact diagonalization. Finally, we discuss possible realizations of the models using ultracold atoms as well as frustrated quantum magnets in high magnetic fields. We compute the momentum distribution and the noise correlations, that can be extracted from time of flight experiments or neutron scattering, and point to signatures of the unique supersolid phase of the kagome lattice.

An assessment on the use of the debye-hückel equation for the thermodynamic modeling of aqueous systems containing polymers and salts

In this work, a study on the role of the long-range term of excess Gibbs energy models in the modeling of aqueous systems containing polymers and salts is presented. Four different approaches on how to account for the presence of polymer in the long-range term were considered, and simulations were conducted considering aqueous solutions of three different salts. The analysis of water activity curves showed that, in all cases, a liquid-phase separation may be introduced by the sole presence of the polymer in the long-range term, regardless of how it is taken into account. The results lead to the conclusion that there is no single exact solution for this problem, and that any kind of approach may introduce inconsistencies.

Discrete vortex solitons in dipolar Bose–Einstein condensates

We analyse the existence, stability and dynamics of localized discrete modes with intrinsic vorticity S = 1 and S = 2 in the disc-shaped dipolar Bose–Einstein condensate loaded into a deep two-dimensional optical lattice. The condensate, which features the interplay of local contact and nonlocal dipole–dipole (DD) interactions between atoms, is modelled by the 2D discrete Gross–Pitaevskii equation which includes the long-range DD term. Various species of discrete vortex solitons, which are known in the model of the condensate with local interactions, are found to exist in the presence of the DD interaction too. In locally self-attractive condensates, the isotropic DD repulsion, which corresponds to the orientation of atomic dipoles perpendicular to the confinement plane, helps to extend the region of the vortex stability, while in the case of anisotropic DD interactions, corresponding to the in-plane orientation of the dipoles, vortices are unstable. In the former case, those vortices which are unstable may evolve into robust ring-shaped breathers. The attractive isotropic DD interaction can create localized vortices in the condensate with the local self-repulsion, but they all are unstable, evolving into single-peak asymmetric structures.

Simplified Theory for DNA Melting Maps

DNA melting maps on DNA stretched on surfaces or in nanochannels give a coarse grained picture of the underlying sequence with potential applications in studies of structural variations and for identification of (micro)organisms.The underlying mechanism is based on the difference in free energies associated with breaking AT and GC basepairs so that DNA melts first in AT-rich regions and only at higher temperature in GC-rich regions. With a suitable choice of dye the melted regions and the unmelted regions can readily be distinguished.The Poland-Scheraga (PS)model is an Ising model with a long-range term due to the entropy associated with the single-stranded regions and, although computationally slow (∼ square of the number of basepairs), has proven to well reproduce melting data. However, by adapting our algorithms to the resolution of the experimental melting mapping (1kbp) we can make them computationally more efficient.We combine a transfer matrix approach and an exact Poland-type algorithm to study opening probabilities along DNA. We systematically explore different degrees of simplifications such as capping the long-range interactions or using a coarse-grained effective-medium approach. We evaluate our simplifications against exact solutions to the PS model for known sequences (figure).View Large Image | View Hi-Res Image | Download PowerPoint Slide

Uniform energy and density distribution: diblock copolymers’ functional

We study a nonlocal variational problem arising in diblock copolymers models, whose energy is given by the Cahn–Hilliard functional plus a long-range interaction term. We prove that minimizers develop uniform energy and density distributions, thus justifying partially the highly regular microphase separation observed in diblock copolymers’ melts. We also give a new proof of the scaling law for the minimum energy. This work extends the techniques introduced in [1] where analogous results are proved for the sharp interface limit of the functional considered.

An Implementation of the Smooth Particle Mesh Ewald Method on GPU Hardware.

The smooth particle mesh Ewald summation method is widely used to efficiently compute long-range electrostatic force terms in molecular dynamics simulations, and there has been considerable work in developing optimized implementations for a variety of parallel computer architectures. We describe an implementation for Nvidia graphical processing units (GPUs) which are general purpose computing devices with a high degree of intrinsic parallelism and arithmetic performance. We find that, for typical biomolecular simulations (e.g., DHFR, 26K atoms), a single GPU equipped workstation is able to provide sufficient performance to permit simulation rates of ≈50 ns/day when used in conjunction with the ACEMD molecular dynamics package (1) and exhibits an accuracy comparable to that of a reference double-precision CPU implementation.

Symmetric Electrolyte Nonrandom Two-Liquid Activity Coefficient Model

The electrolyte nonrandom two-liquid (eNRTL) model is reformulated as a symmetric activity coefficient model with the reference states chosen to be pure liquids for solvents and pure fused salts for electrolytes. These reference states are consistently used in the local interaction term, represented by a reformulated NRTL expression, and the long-range interaction term, represented by an extended symmetric Pitzer−Debye−Huckel expression. Retaining the local electroneutrality and like-ion repulsion hypotheses, the new symmetric electrolyte NRTL model yields simpler activity coefficient expressions for both molecular and ionic species. The utility of the model is demonstrated with vapor−liquid equilibrium, liquid−liquid equilibrium, and solid−liquid equilibria of several mixed solvent electrolyte systems.

Precision measurements of thepp→π+pnandpp→π+dreactions: Importance of long-range and tensor force effects

Inclusive measurements of pion production in proton-proton collisions in the forward direction were undertaken at 400 and 600 MeV at the cooler synchrotron (COSY) at Forschungszentrum Julich using the Big Karl spectrograph. The high resolution in the pi(+) momentum ensured that there was an unambiguous separation of the pp ->pi(+)d/pi(+)pn channels. Using these and earlier data, the ratio of the production cross sections could be followed through the Delta region and compared with the predictions of final state interaction theory. Deviations are strongly influenced by long-range terms in the production operator and the tensor force in the final pn system. These have been investigated in a realistic pp ->pi(+)d/pi(+)pn calculation that includes S reversible arrow D channel coupling between the final nucleons. A semiquantitative understanding of the observed effects is achieved. .

Symmetric Nonrandom Two-Liquid Segment Activity Coefficient Model for Electrolytes

The nonrandom two-liquid segment activity coefficient model (NRTL-SAC) [Chen, C.-C.; Song, Y. Solubility Modeling with a Nonrandom Two-Liquid Segment Activity Coefficient Model. Ind. Eng. Chem. Res. 2004, 43, 8354−8362] has been shown to be a simple and practical thermodynamic model for correlating and predicting phase behavior for complex pharmaceutical molecules. The model was later extended for electrolytes [Chen, C.-C.; Song, Y. Extension of Non-Random Two-Liquid Segment Activity Coefficient Model for Electrolytes. Ind. Eng. Chem. Res. 2005, 44, 8909−8921]. However, the electrolyte model was presented as an unsymmetric activity coefficient model with aqueous phase infinite dilution reference state. Such an unsymmetric model becomes rather cumbersome to use when dealing with nonaqueous solvents. In this work, we present a symmetric electrolyte NRTL-SAC model which simplifies the long-range interaction term. We further examine the utility of the model in predicting salt solubilities in nonaqueous solven...

Charge-transfer in Symmetry-Adapted Perturbation Theory

In Symmetry-Adapted Perturbation Theory the charge-transfer energy is normally absorbed into the induction energy, but it can be treated separately. There are two contributions: the long-range or polarization term, which ignores effects due to exchange of electrons between the interacting molecules, and an exchange term. The sum of the two is much smaller than the polarization term, by up to an order of magnitude. The net contribution to hydrogen bond energies is a few kJ mol −1 at equilibrium, and is approximately proportional to the exchange-repulsion energy at other geometries and no more than 10% of it in magnitude.

Query structuring and expansion with two-stage term dependence for Japanese web retrieval

In this paper, we propose a new term dependence model for information retrieval, which is based on a theoretical framework using Markov random fields. We assume two types of dependencies of terms given in a query: (i) long-range dependencies that may appear for instance within a passage or a sentence in a target document, and (ii) short-range dependencies that may appear for instance within a compound word in a target document. Based on this assumption, our two-stage term dependence model captures both long-range and short-range term dependencies differently, when more than one compound word appear in a query. We also investigate how query structuring with term dependence can improve the performance of query expansion using a relevance model. The relevance model is constructed using the retrieval results of the structured query with term dependence to expand the query. We show that our term dependence model works well, particularly when using query structuring with compound words, through experiments using a 100-gigabyte test collection of web documents mostly written in Japanese. We also show that the performance of the relevance model can be significantly improved by using the structured query with our term dependence model.

Generalized ensemble methods for de novo structure prediction

Current methods for predicting protein structure depend on two interrelated components: (i) an energy function that should have a low value near the correct structure and (ii) a method for searching through different conformations of the polypeptide chain. Identification of the most efficient search methods is essential if we are to be able to apply such methods broadly and with confidence. In addition, efficient search methods provide a rigorous test of existing energy functions, which are generally knowledge-based and contain different terms added together with arbitrary weights. Here, we test different search methods with one of the most accurate and predictive energy functions, namely Rosetta the knowledge-based force-field from Baker's group [Simons K, Kooperberg C, Huang E, Baker D (1997) J Mol Biol 268:209-225]. We use an implementation of a generalized ensemble search method to scale relevant parts of the energy function. This method, known as Hamiltonian Replica Exchange Monte Carlo, outperforms the original Monte Carlo Simulated Annealing used in the Rosetta package in terms of sampling low-energy states. It also outperforms another widely used generalized ensemble search method known as Temperature Replica Exchange Monte Carlo. Our results reveal clear deficiencies in the low-resolution Rosetta energy function in that the lowest energy structures are not necessarily the most native-like. By using a set of nonnative low-energy structures found by our extensive sampling, we discovered that the long-range and short-range backbone hydrogen-bonding energy terms of the Rosetta energy discriminate between the nonnative and native-like structures significantly better than the low-resolution score used in Rosetta.

The 20th anniversary of the three-nucleon analyzing power puzzle – A personal recollection

The history of the three-nucleon analyzing power puzzle is described by an experimentalist who has been collaborating with few-body theoreticians in trying to unravel the physics of this long-standing phenomenon. Although surprising effects have been discovered along the way, the puzzle is still unexplained. Hopefully, some of the long-range three-nucleon force terms predicted by chiral effective field theory in N3LO will eventually solve the puzzle.

Subleading contributions to the chiral three-nucleon force: Long-range terms

We derive the long-range contributions to the tree-nucleon force at next-to-next-to-next-to-leading order in the chiral expansion. We give both momentum- and coordinate-space representations.

An extension of the Pitzer equation for the excess Gibbs energy of aqueous electrolyte systems to aqueous polyelectrolyte solutions

Pitzer's equation for the excess Gibbs energy of aqueous solutions of low-molecular electrolytes is extended to aqueous solutions of polyelectrolytes. The model retains the original form of Pitzer's model (combining a long-range term, based on the Debye–Hückel equation, with a short-range term similar to the virial equation where the second osmotic virial coefficient depends on the ionic strength). The extension consists of two parts: at first, it is assumed that a constant fraction of the monomer units of the polyelectrolyte is dissociated, i.e., that fraction does not depend on the concentration of the polyelectrolyte, and at second, a modified expression for the ionic strength (wherein each charged monomer group is taken into account individually) is introduced. This modification is to account for the presence of charged polyelectrolyte chains, which cannot be regarded as punctual charges. The resulting equation was used to correlate osmotic coefficient data of aqueous solutions of a single polyelectrolyte as well as of binary mixtures of a single polyelectrolyte and a salt with low-molecular weight. It was additionally applied to correlate liquid–liquid equilibrium data of some aqueous two-phase systems that might form when a polyelectrolyte and another hydrophilic but neutral polymer are simultaneously dissolved in water. A good agreement between the experimental data and the correlation result is observed for all investigated systems.

Bootstrap approximations in contractor renormalization

We propose a bootstrap method for approximating the long-range terms in the contractor renormalization method. The idea is tested on the two-dimensional Heisenberg antiferromagnet and the frustrated ${J}_{2}\text{\ensuremath{-}}{J}_{1}$ model. We obtain renormalization group flows that directly reveal the N\'eel phase of the unfrustrated Heisenberg antiferromagnet and the existence of a phase transition in the ${J}_{2}\text{\ensuremath{-}}{J}_{1}$ model for weak frustration. However, we find that this bootstrap method is dependent on blocking and truncation schemes. For this reason, we discuss these dependencies and unresolved issues that researchers who use this approach must consider.

Long-range analysis of density fitting in extended systems

Density fitting scheme is analyzed for the Coulomb problem in extended systems from the correctness of long-range behavior point of view. We show that for the correct cancellation of divergent long-range Coulomb terms it is crucial for the density fitting scheme to reproduce the overlap matrix exactly. It is demonstrated that from all possible fitting metric choices the Coulomb metric is the only one which inherently preserves the overlap matrix for infinite systems with translational periodicity. Moreover, we show that by a small additional effort any non-Coulomb metric fit can be made overlap-preserving as well. The problem is analyzed for both ordinary and Poisson basis set choices. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008