Superposition Approximation Research Articles

Structure of the simple harmonic-repulsive system in liquid and glassy states studied by the triple correlation function

An efficient description of the structures of liquids and, in particular, the structural changes that happen with liquids on supercooling remains to be a challenge. The systems composed of soft particles are especially interesting in this context because they often demonstrate non-trivial local orders that do not allow to introduce the concept of the nearest-neighbor shell. For this reason, the use of some methods, developed for the structure analysis of atomic liquids, is questionable for the soft-particle systems. Here we report about our investigations of the structure of the simple harmonic-repulsive liquid in 3D using the triple correlation function (TCF), i.e., the method that does not rely on the nearest neighbor concept. The liquid is considered at reduced pressure (P = 1.8) at which it exhibits remarkable stability against crystallization on cooling. It is demonstrated that the TCF allows addressing the development of the orientational correlations in the structures that do not allow drawing definite conclusions from the studies of the bond-orientational order parameters. Our results demonstrate that the orientational correlations, if measured by the heights of the peaks in the TCF, significantly increase on cooling. This rise in the orientational ordering is not captured properly by the Kirkwood’s superposition approximation. Detailed considerations of the peaks’ shapes in the TCF suggest the existence of a link between the orientational ordering and the slowdown of the system’s dynamics. Our findings support the view that the development of the orientational correlations in liquids may play a significant role in the liquids’ dynamics and that the considerations of the pair distribution function may not be sufficient to understand intuitively all the structural changes that happen with liquids on supercooling. In general, our results demonstrate that the considerations of the TCF are useful in the discussions of the liquid’s structures beyond the pair density function and interpreting the results obtained with the bond-orientational order parameters.

Axisymmetric Stokes flow due to a point-force singularity acting between two coaxially positioned rigid no-slip disks

Abstract

First-Principles Collision Cross Section Measurements of Large Proteins and Protein Complexes.

Rotationally averaged collision cross section (CCS) values for a series of proteins and protein complexes ranging in size from 8.6 to 810 kDa are reported. The CCSs were obtained using a native electrospray ionization drift tube ion mobility-Orbitrap mass spectrometer specifically designed to enhance sensitivity while having high-resolution ion mobility and mass capabilities. Periodic focusing (PF)-drift tube (DT)-ion mobility (IM) provides first-principles determination of the CCS of large biomolecules that can then be used as CCS calibrants. The experimental, first-principles CCS values are compared to previously reported experimentally determined and computationally calculated CCS using projected superposition approximation (PSA), the Ion Mobility Projection Approximation Calculation Tool (IMPACT), and Collidoscope. Experimental CCS values are generally in agreement with previously reported CCSs, with values falling within ∼5.5%. In addition, an ion mobility resolution (CCS centroid divided by CCS fwhm) of ∼60 is obtained for pyruvate kinase (MW ∼ 233 kDa); however, ion mobility resolution for bovine serum albumin (MW ∼ 68 kDa) is less than ∼20, which arises from sample impurities and underscores the importance of sample quality. The high resolution afforded by the ion mobility-Orbitrap mass analyzer provides new opportunities to understand the intricate details of protein complexes such as the impact of post-translational modifications (PTMs), stoichiometry, and conformational changes induced by ligand binding.

On the nature of the structural transitions between anti-Mackay stacking, chiral stacking and their thermal stability in AgCu nanoalloys

AgCu nanoalloys are known to exhibit a size dependent transition to the chiral stacking from the anti-Mackay stacking. In the current work, the role of composition on the structural transitions between the anti-Mackay and the chiral stacking in AgCu nanoalloys has been studied computationally using a combination of global optimization searches and heating simulations. It is observed that in addition to the size, composition also affects the surface stacking in these nanoalloys. Further, results show that the nature of the recently reported thermally induced transition to the chiral stacking is strongly dependent on the Cu content in the AgCu nanoalloys. The amount of Cu in the nanoalloy affects both the transition temperature and the “sharpness” of the transition. By analyzing the frequencies of the vibrational modes calculated using the Harmonic Superposition Approximation (HSA), the thermal stability of the chiral stacking is attributed to the vibrational entropic contribution. Finally, the findings in the current work have been consolidated in the form of a size-composition map. By referring to this size-composition map, the preference for the chiral stacking can be understood for the nanoalloys belonging to the size window between the “magic” sized nanoalloys.

New Protocol for Predicting the Ligand-Binding Site and Mode Based on the 3D-RISM/KH Theory.

An efficient algorithm to find the binding position and mode of small ligands bound at an active site of protein is proposed based on the spatial distribution function (SDF) obtained from the three-dimensional reference interaction site model (3D-RISM) theory with the Kovalenko-Hirata (KH) closure relation. The ligand examined includes hydrophobic, acidic, and basic molecules and zwitterions. Eighteen different types of proteins, which serve as targets for those ligands, are selected to examine the robustness of the algorithm. An imaginary atom, referred to as an "anchor site", is defined at the center of geometry of a ligand molecule that serves as a center for searching the binding position and mode of the ligand molecule in the translational and rotational spaces. The probable binding sites (PBSs) are identified based on the SDFs of the ligand molecules around the protein, and the PBS is ranked according to the peak height of SDF. The deviations from the mean height of the peak values of SDFs for 50 PBSs are analyzed based on the z-score, which is a measure of prominence of the site. The PBS found at the closest distance from the anchor site of the crystal structure is referred to as the "nearest site". The orientation of the ligand molecule at each PBS is explored by changing the Euler angles, and the most probable binding mode is determined based on the superposition approximation. The binding position of ligand molecules is successfully predicted as one of the distinct peaks in SDF of the anchor site, with a few exceptions. The binding mode of the ligand molecule predicted based on the superposition approximation is consistent with the X-ray crystal structure in nine systems, a half of the systems investigated. The significance of the results is discussed in detail. An application of the new protocol to fragment-based drug discovery is suggested.

Spatial population dynamics: Beyond the Kirkwood superposition approximation by advancing to the Fisher–Kopeliovich ansatz

The superior Fisher–Kopeliovich closure is applied to the hierarchy of master equations for spatial moments in population dynamics for the first time. As a consequence, the density, pair and triplet distribution functions of entities are calculated within this closure for a birth–death model with nonlocal dispersal and competition in continuous space. The new results are compared with those obtained by “exact” individual-based simulations as well as by the inferior mean-field and Kirkwood superposition approximations. It is shown that the Fisher–Kopeliovich approach significantly improves the quality of the description in a wide range of varying parameters of the model.

Distortion of the Ligand Environment of Gd3+ and Eu2+ Ions in Garnets: Y3Al5O12, Lu3Al5O12, and Y3Ga5O12

Using experimental second-rank parameters of the spin Hamiltonian of the rhombic centers Gd3+ and Eu2+ in three garnets and the superposition approximation formalism, relaxation of the nearest environment of impurity ions is estimated.

Adatom pair distribution up to half coverage: O-Pd(100)

The superposition approximation and the Born–Green–Yvon (BGY) equation allows calculation of pair distributions in thermal equilibrium from pair potentials. A 2-d variant can be used to derive adatom pair distributions from arbitrary analytical pair potentials. As practical example substrate mediated elastic interactions, fitted previously to first principles (FP) calculations, are used to derive adatom pair distributions of O-Pd(100). The evaluation method utilizes the particle-hole symmetry of the pair interaction lattice gas Hamiltonian. The nonlinear BGY-type integral equation is solved numerically up to half coverage using power series expansion of coverage.The resulting adatom pair- and three-body distributions are used to analyze the short-range order of adatoms. A Monte Carlo (MC) simulation was performed in parallel to compare the current model with established methods. MC derived pair distributions fit well to those found with the analytical model, except in the high coverage region. The Fourier transformed pair correlations are compared with experimental LEED spot data and provide additional insight.Due to significant attraction the model predicts formation of 3rd and 4th nearest neighbors (n.n.) at small 3rd n.n. chains. A long range order of adatoms like a p(2 × 2) lattice is not found with the current model but a glassy structure is proposed as also indicated by the equilibrium Monte Carlo configurations. The glassy structure is assumed to contain fluctuations explaining broad p(2 × 2) LEED spots in the 0.25 monolayer region. The assumptions and limitations of the model towards higher coverages are discussed and open questions are formulated.

Density functional approach to the description of the structure of dimer nanoparticles at liquid-liquid interfaces.

An extension of the density functional approach from our recent work (Phys. Chem. Chem. Phys., 2019, 21, 3073-3082) is developed. It permits us to study the microscopic structure and thermodynamic properties of chain particles at the interface between two partially miscible liquids. Explicit calculations are carried out for a binary symmetric mixture of hard-sphere Yukawa fluids and dimers built of hard-sphere segments. The model is simple, but it captures the interplay between localization of dimers at the interface and their orientation and assembly into layers. The segment density profiles are combined with the site superposition approximation to interpret angle-dependent local densities of dimers. Emphasis is put on self-organization of dimers. The evolution of the interfacial structure of dimers and of fluid species with the amount of added dimers and of the supporting mixture density is explored. Preferential orientations of dimers in the outer and inner layers of the interface are discovered. Changes of the interface width upon changing the parameters of the system are discussed. Similarities and differences between the properties of the interface hosting diatomic and spherical particles are explained.

Искажение лигандного окружения ионов Gd-=SUP=-3+-=/SUP=- и Eu-=SUP=-2+-=/SUP=- в гранатах: Y-=SUB=-3-=/SUB=-Al-=SUB=-5-=/SUB=-O-=SUB=-12-=/SUB=-, Lu-=SUB=-3-=/SUB=-Al-=SUB=-5-=/SUB=-O-=SUB=-12-=/SUB=-, Y-=SUB=-3-=/SUB=-Ga-=SUB=-5-=/SUB=-O-=SUB=-12-=/SUB=-

Using the second-rank spin Hamiltonian experimental parameters of the rhombic Gd3+ and Eu2+ centers in three garnets, as well as the superposition approximation formalism, estimations of the relaxation of the impurity ions nearest environment have been made.

Continuum Approximations to Systems of Correlated Interacting Particles

We consider a system of interacting particles with random initial conditions. Continuum approximations of the system, based on truncations of the BBGKY hierarchy, are described and simulated for various initial distributions and types of interaction. Specifically, we compare the Mean Field Approximation (MFA), the Kirkwood Superposition Approximation (KSA), and a recently developed truncation of the BBGKY hierarchy (the Truncation Approximation - TA). We show that KSA and TA perform more accurately than MFA in capturing approximate distributions (histograms) obtained from Monte Carlo simulations. Furthermore, TA is more numerically stable and less computationally expensive than KSA.

Definition and Time Evolution of Correlations in Classical Statistical Mechanics.

The study of dense gases and liquids requires consideration of the interactions between the particles and the correlations created by these interactions. In this article, the N-variable distribution function which maximizes the Uncertainty (Shannon’s information entropy) and admits as marginals a set of (N−1)-variable distribution functions, is, by definition, free of N-order correlations. This way to define correlations is valid for stochastic systems described by discrete variables or continuous variables, for equilibrium or non-equilibrium states and correlations of the different orders can be defined and measured. This allows building the grand-canonical expressions of the uncertainty valid for either a dilute gas system or a dense gas system. At equilibrium, for both kinds of systems, the uncertainty becomes identical to the expression of the thermodynamic entropy. Two interesting by-products are also provided by the method: (i) The Kirkwood superposition approximation (ii) A series of generalized superposition approximations. A theorem on the temporal evolution of the relevant uncertainty for molecular systems governed by two-body forces is proved and a conjecture closely related to this theorem sheds new light on the origin of the irreversibility of molecular systems. In this respect, the irreplaceable role played by the three-body interactions is highlighted.

Conformational diversity in deprotonated water clusters and anharmonic infrared spectra

ABSTRACTInfrared spectroscopy has become a powerful tool for structural assignment of ionic compounds in the gas phase. Using the reactive OSS2 potential, the stable conformers of deprotonated water clusters (HO)OH− have been explored for n = 6–9 and n = 20 using different computational approaches, namely conventional molecular dynamics, replica-exchange molecular dynamics (REMD), and the harmonic superposition approximation (HSA). The stable structures generally exhibit a rather open character, the missing proton giving rise to either a well-localised hydroxide ion or, occasionally, to a bihydroxide anion with one proton shared between two oxygens. At finite temperature, the predictions of REMD and HSA agree reasonably well with one another. The anharmonic infrared absorption spectra obtained from the equilibrium samples of conformers were also determined from the three methods. At 100 K, the spectra resulting from conventional MD sampling are found to be possibly unreliable owing to isomerisation over times scales that exceed fluxional motion which we evaluate to be on the order of a few tens of picoseconds.

Characterization and modeling of dual material double gate tunnel field effect transistor using superposition approximation method

SummaryTunnel field effect transistors are used for ultra‐low power application since it is challenging to operate CMOS at very low supply voltage. As tunnel field effect transistor has a very low subthreshold slope due to band to band tunneling (BTBT) mechanism, it has the potential to operate at very low operating voltage. It is necessary that the devices utilized in implantable bio‐medical applications and Internet of Everything (IoE) need to consume very low power. This work presents an analysis of Dual Material Double Gate Tunnel Field effect transistor (DMDG‐TFET). An analytical two dimensional (2D) model has been developed to obtain the analytical expressions for drain current. The 2D Poisson's equation has been used to calculate surface potential in the silicon channel using the superposition approximation, as it considers the short channel effects in the calculation of the current when compared to parabolic approximation. To validate the model, analytical results have been confirmed by comparing with the Sentaurus TCAD simulation results. A reduced subthreshold slope of 31.2 mV/decade is obtained in this paper. It shows that DMDG TFET is a promising candidate for ultra‐low power applications. The subthreshold swing obtained using superposition approximation is more optimized than that of parabolic approximation technique.

Can nanoscale surface charge heterogeneity really explain colloid detachment from primary minima upon reduction of solution ionic strength?

This study theoretically examined colloid detachment from primary minima with ionic strength (IS) reduction on heterogeneous collector surfaces. The chemically and physically heterogeneous collector surfaces were modeled as a planar surface carrying nanoscale patches of different zeta potentials and nanoscale pillars/hemispheroids, respectively. The surface element integration technique was used to calculate interaction energies between colloid and collector surfaces. Two boundary conditions for the double-layer interaction energy were considered, namely constant surface potential (CSP), and linear superposition approximation (LSA). In contrast to prevailing opinions in the literature, our results show that colloids attached on the chemically heterogeneous surface cannot be detached by IS reduction under CSP condition due to an increase of the adhesive force/torque with decreasing IS. Detachment from chemically heterogeneous surfaces by IS reduction can occur under LSA condition only when the flow velocity is very high. In contrast, the presence of nanoscale physical heterogeneity can cause colloid detachment from primary minima by IS reduction under both CSP and LSA conditions at flow velocities commonly used in experimental studies because of a significant reduction in the adhesive forces/torques.

Electrostatic interaction between dissimilar colloids at fluid interfaces.

The electrostatic interaction between two nonidentical, moderately charged colloids situated in close proximity of each other at a fluid interface is studied. By resorting to a well-justified model system, this problem is analytically solved within the framework of linearized Poisson-Boltzmann density functional theory. The resulting interaction comprises a surface and a line part, both of which, as functions of the interparticle separation, show a rich behavior including monotonic as well as nonmonotonic variations. In almost all cases, these variations cannot be captured correctly by using the superposition approximation. Moreover, expressions for the surface tensions, the line tensions and the fluid-fluid interfacial tension, which are all independent of the interparticle separation, are obtained. Our results are expected to be particularly useful for emulsions stabilized by oppositely charged particles.

Phase Separation in AgCu and AgNi Core–Shell Icosahedral Nanoparticles: A Harmonic Thermodynamics Study

AbstractThe temperature dependence of equilibrium chemical ordering in Ag‐rich AgCu and AgNi icosahedral nanoalloys is numerically studied within the harmonic superposition approximation to the partition function. The nanoalloys are modeled by an atomistic force field derived from the second‐moment approximation to the tight‐binding model. It is found that the equilibrium chemical ordering consists of phase‐separated arrangements of the core–shell type, at least up to room temperature for AgCu and up to 600 K for AgNi. This result is rationalized in terms of the concept of preferred nucleation sites for phase separation, such as the central site in the icosahedron.

Approximate expressions for the surface charge density/surface potential relationship and double-layer potential distribution for a spherical or cylindrical colloidal particle based on the modified Poisson-Boltzmann equation

Approximate expressions for the surface charge density/surface potential relationship and double-layer potential distribution are derived for a spherical or cylindrical colloidal particle in an electrolyte solution. The obtained expressions are based on an approximate form of the modified Poisson-Boltzmann equation taking into account the ion size effects through the Carnahan-Starling activity coefficients of electrolyte ions. We further derive approximate expression for the effective surface potentials of a spherical or cylindrical particle and for the electrostatic interaction energy between two spherical or cylindrical particles on the basis of the linear superposition approximation.

Implicit Solvation Using the Superposition Approximation (IS-SPA): An Implicit Treatment of the Nonpolar Component to Solvation for Simulating Molecular Aggregation.

Nonpolar solute-solvent interactions are the driving force for aggregation in important chemical and biological phenomena including protein folding, peptide self-assembly, and oil-water emulsion formation. Currently, the most accurate and computationally efficient description of these processes requires an explicit treatment of all solvent and solute atoms. Previous computationally feasible implicit solvent models, such as solute surface area approaches, are unsuccessful at capturing aggregation features including both structural and energetic trends while more theoretically rigorous approaches, such as Reference Interaction Site Model (RISM), are accurate but extremely computationally demanding. Our approach, denoted Implicit Solvation using the Superposition Approximation (IS-SPA), builds on previous theory utilizing the Kirkwood superposition approximation to approximate the mean force of the solvent from solute parameters. We introduce and verify a parabolic first solvation shell truncation of atomic solvation, fitting water distributions around a molecule, and a Monte Carlo integration of the mean solvent force. These extensions allow this method to be implemented as an efficient nonpolar implicit solvent model for molecular simulation. The approximations in IS-SPA are first explored and justified for the homodimerization of an array of different sized Lennard-Jones spheres. The accuracy and transferability of the approach are demonstrated by its ability to capture the position and relative energies of the desolvation barrier and free energy minimum of alkane homodimers. The model is then shown to reproduce the phase separation and solubility of cyclohexane and water. These promising results, coupled with 2 orders of magnitude speed-up for dilute systems as compared to explicit solvent simulations, demonstrate that IS-SPA is an appealing approach to boost the time- and length-scale of molecular aggregation simulations.

Experimental investigation of triplet correlation approximations for fluid water

Triplet correlations play a central role in our understanding of fluids and their properties. Of particular interest is the relationship between the pair and triplet correlations. Here we use a combination of Fluctuation Solution Theory and experimental pair radial distribution functions to investigate the accuracy of the Kirkwood Superposition Approximation (KSA), as given by integrals over the relevant pair and triplet correlation functions, at a series of state points for pure water using only experimental quantities. The KSA performs poorly, in agreement with a variety of other studies. Several additional approximate relationships between the pair and triplet correlations in fluids are also investigated and generally provide good agreement for the fluid thermodynamics for regions of the phase diagram where the compressibility is small. A simple power law relationship between the pair and triplet fluctuations is particularly successful for state points displaying low to moderately high compressibilities.