Pair Potential Function Research Articles

A cutoff-based method with charge-distribution-data driven pair potentials for efficiently estimating electrostatic interactions in molecular systems.

We introduce a simple cutoff-based method for precise electrostatic energy calculations in the molecular dynamics (MD) simulations of point-particle systems. Our method employs a theoretically derived smooth pair potential function to define electrostatic energy, offering stability and computational efficiency in MD simulations. Instead of imposing specific physical conditions, such as dielectric environments or charge neutrality, we focus on the relationship represented by a single summation formula of charge-weighted pair potentials. This approach allows an accurate energy approximation for each particle, enabling a straightforward error analysis. The resulting particle-dependent pair potential captures the charge distribution information, making it suitable for heterogeneous systems and ensuring an enhanced accuracy through distant information inclusion. Numerical investigations of the Madelung constants of crystalline systems validate the method's accuracy.

On the adaptation of reference sets using niching and pair-potential energy functions for multi-objective optimization

Multi-objective evolutionary algorithms (MOEAs) have shown a good capability to approximate the Pareto front (PF) of complex multi-objective optimization problems (MOPs). Recently, several decomposition-based, indicator-based, and reference set-based MOEAs have been proposed to tackle MOPs with four or more objective functions, known as many-objective optimization problems (MaOPs). Some well-known MOEAs from these design strategies use a predefined reference set generated with uniformly distributed weight vectors on a unit simplex. These MOEAs have demonstrated good convergence, coverage, and uniformity of solutions on MOPs with regular PF shapes, i.e., simplex-like shapes. However, it has been shown that their performance degrades on MOPs with irregular PF shapes. In this paper, we proposed a pluggable reference set adaptation method based on niching and pair-potential energy functions (PPFs), called AdaK, to enhance the performance of these MOEAs on MOPs with irregular PF shapes while maintaining their good behavior on MOPs with regular PF shapes. Our adaptation method was validated by plugging it into three well-known MOEAs that use a predefined weight vector-based reference set. We perform an empirical study using different PPFs for our adaptation method on the DTLZ, WFG, Minus-DTLZ, Minus-WFG, IMOP, and VNT test suites. Our experimental results show the capability of our adaptation method to promote an invariant performance regardless of the PF shape. Additionally, we show that MOEAs with our adaptation method have a competitive performance against state-of-the-art MOEAs.

On the utilization of pair-potential energy functions in multi-objective optimization

On the utilization of pair-potential energy functions in multi-objective optimization

A continuum-molecular model for anisotropic electrically conductive materials

An anisotropic model for two-dimensional electrical conduction, elasticity and fracture is proposed in the peridynamic theoretical framework. Material points interact through elastic non-central pair potentials and inelastic pair potential functions of pairwise elastic and inelastic deformation measure, allowing to obtain a bond-based type model for conductive Cauchy orthotropic media without restrictions in the number of independent material constants. The elasticity of pair interactions can be described mechanistically by equivalent normal and shear springs, whose stiffness varies continuously with the spatial orientation of the ligament and, preserving the elastic symmetries of the material, depends on four material parameters defining in-plane orthotropic classical elasticity. The macroscopic anisotropic conductivity is described instead by continuous functions of the micro-conductive properties of the interparticles interactions. Moreover, non-uniform material toughness is modeled adopting an anisotropic energetic failure criterion related to direction-dependent fracture energy functionals. The accuracy of the proposed model has been assessed by several problems including the anisotropic electrical conduction in multi-phases laminae with a central hole and evolving cracks, and the fracture and damage sensing in cortical bone considering different orientation of the material reference system.

Development of Finnis-Sinclair potential of metal Nb and the influence of potential function form on the properties of material

<sec>Researchers’ work on computational materials is often hampered by the lack of suitable intera tomic potentials. In this paper, under the framework of Finnis-Sinclair (FS) potentials, the process of fitting, testing and correction of interatomic potential is given in detail by developing the FS potential for metal Nb. First, the relationship between the interatomic potential and the macroscopic properties of the material is established. Then, the Finnis-Sinclair potential of metal Nb is fitted by reproducing the experimental data, such as the cohesive energy, bulk modulus, surface energy, vacancy formation energy and equilibrium lattice constant, and the fitting mean square error is less than 10<sup>–7</sup>. In order to test the interatomic potential, the elastic constant, shear modulus and Cauchy pressure of metal Nb are calculated by the constructed interatomic potential. In addition, how the form of the interatomic potential function affects the interstitial performance is discussed, and the constructed interatomic potential is modified according to the results of density functional theory (DFT) of the interstitial formation energy. The treatment of cutoff distance is also discussed. In the paper, the results are as follows. 1) The original form of FS potential is not suitable for extending the atomic interaction to the third nearest neighbor. Through analysis and test, it is found that when the modified electron density function is in the form of the fourth power and the form of the pair potential function is in the form of the sixth power polynomial, the interatomic potential can better describe the interatomic interaction; 2) The result of interstitial formation energy is taken as the target value to modify the behavior of the pair potential function in the near distance, and the modified interatomic potential gives the interstitial formation energy close to the result of DFT. When the interstitial energy calculated by the interatomic potential is larger than the target value, the pair potential curve of near distance will be softened by the superposition of a polynomial term, otherwise, the pair potential curve will be stiffened; 3) When the physical quantity under equilibrium state is used as the fitting data, the fitted potential parameters and the elastic constant results will not be affected, while adjusting the curve form of the potential function, as long as none of the function value, the slope and the curvature of the function curve is changed at each neighbor position. The magnitude of interstitial energy will be affected by changing the shape of the curve that is less than the first neighbor range; 4) Under the cutoff strategy in this paper, changing the cutoff distance has almost no influence on the calculated results of potential parameters or crystal properties, but has a slight influence on the mean square error of the fitting results. </sec><sec>The results of this paper provide some information for the construction of interatomic potentials database, and lay a foundation for constructing the Nb-related interatomic potential of alloy. And it also provides a method and basis for developing and improving the quality of interatomic potential.</sec>

Local energy optimality of periodic sets

We study the local optimality of periodic point sets in $\mathbb{R}^n$ for energy minimization in the Gaussian core model, that is, for radial pair potential functions $f_c(r)=e^{-c r}$ with $c>0$. By considering suitable parameter spaces for $m$-periodic sets, we can locally rigorously analyze the energy of point sets, within the family of periodic sets having the same point density. We derive a characterization of periodic point sets being $f_c$-critical for all $c$ in terms of weighted spherical $2$-designs contained in the set. Especially for $2$-periodic sets like the family $\mathsf{D}^+_n$ we obtain expressions for the hessian of the energy function, allowing to certify $f_c$-optimality in certain cases. For odd integers $n\geq 9$ we can hereby in particular show that $\mathsf{D}^+_n$ is locally $f_c$-optimal among periodic sets for all sufficiently large~$c$.

Size and Structure Dependence of the Anomalous Bulk Modulus for FCC Metallic Nanoparticles

The purpose of this work is to develop a theoretical model to calculate the bulk moduli of FCC nanoparticles that account for their size and structure. The bulk modulus for spherical nanoparticles has been derived from the cohesive energy which had been calculated by summing up the potential energy function of every pair of atoms of these metallic nanoparticles. The ab initio pair potential energy function has been formed by inverting the cohesive energy function proposed by (Rose et al., 1981), using the Chen-Mobius method. The results show that, as the size decreases, the bulk modulus decreases for spherical nanoparticles, which agrees with previous experimental and theoretical predictions. The results also predicted an “amorphous” structure for ultra-small nanoparticles and were consistent with previous experimental work.

Adhesive contact of a diamond sphere with an iron substrate caused by interatomic interaction

By incorporating the adhesive force as a body force in the finite element method, the adhesive contact between a diamond sphere and the iron substrate is studied. The adhesive force is derived from Morse potential by integrating the pair potential function over the spherical domain. Based on the tensile behaviors of iron nanowires, the elastic and elastoplastic material parameters are obtained for the substrate. As the radius of the sphere is larger than 320 nm and the maximum depth of indentation is one-tenth of the radius of the sphere, the adhesion caused by interatomic interaction between diamond and iron is small enough to ignore. Then take the sphere whose radius is 20 nm as an example, the results of a single load–unload cycle and multiple load–unload cycles are discussed. In the contact process between the sphere and the surface, the phenomena jump-to-contact and jump-off-contact were observed. Further, the stress distributions inside the substrate and the pressure distribution are investigated. With the analysis of the results, the proposed method can be used to simulate the mechanical behaviors under micro-nano scale contact.

Vibrational Dynamics of Pd39Ni10Cu30P21Bulk Metallic Glass

In the present study, we report the vibrational dynamics of Pd39Ni10Cu30P21 bulk metallic glass in terms of the phonon Eigen frequencies of the localized collective excitations using Show’s optimized model pseudopotential at room temperature. While theoretical effective atom model (EAM) with Wills-Harrison (WH) approach are used for the computation of the interatomic pair potential (PP) and pair correlation function (PCF). The phonon dispersion curves are computed through Hubbard-Beeby (HB) approach. Various elastic and thermodynamic properties have been reported from the elastic limit of the phonon dispersion curves. The screening dependency on the aforesaid properties is studied by adopting different kinds of local field correction functions

Structural and Collective Dynamics of Bi50Zn50 of binary metallic glass

In the present paper, structural properties, collective dynamics and elastic properties have been studied of Bi50Zn50 liquid metallic glass at a wide range of temperatures. Ashcroft and Langreth binary structure factor have been used to study for static structure factor and pair correlation function for present alloy. The collective excitation has been studied for longitudinal and transverses phonon modes based on our well-established model potential along with Hubbard and Beeby (HB) approach. These frequencies are expressed in terms of many-body correlation functions of atoms as well as of interatomic potential. The important ingredients in the present study are the pair-potential and pair-correlation functions. The local field correlation functions due to Hartree (H) and Farid et al (F) are employed to investigate the influence of the screening effects on the vibrational dynamics of Bi50Zn50 liquid metallic glass. The results for bulk modulus (BT), modulus of rigidity (G), Poisson’s ratio (ξ), Young’s modulus (Y), Debye temperature (ƟD), the propagation velocity of elastic waves and dispersion curves are reported. Good agreement with the experiment is observed for the structure factors and elastic properties results are consistent and confirm the applicability of model potential and self-consistent phonon theory for such studies.

A three-dimensional anisotropic point process characterization for pharmaceutical coatings

Spatial characterization and modeling of the structure of a material may provide valuable knowledge on its properties and function. Especially, for a drug formulation coated with a polymer film, understanding the relationship between pore structure and drug release properties is important to optimize the coating film design. Here, we use methods from image analysis and spatial statistics to characterize and model the pore structure in pharmaceutical coatings. More precisely, we use and develop point process theory to characterize the branching structure of a polymer blended film with data from confocal laser scanning microscopy. Point patterns, extracted by identifying branching points of pore channels, are both inhomogeneous and anisotropic. Therefore, we introduce a directional version of the inhomogeneous K-function to study the anisotropy and then suggest two alternative ways to model the anisotropic three-dimensional structure. First, we apply a linear transformation to the data such that it appears isotropic and subsequently fit isotropic inhomogeneous Strauss or Lennard-Jones models to the transformed pattern. Second, we include the anisotropy directly in a Lennard-Jones and a more flexible step-function model with anisotropic pair-potential functions. The methods presented will be useful for anisotropic inhomogeneous point patterns in general and for characterizing porous material in particular.

Thermophysical properties of krypton-helium gas mixtures from ab initio pair potentials.

A new potential energy curve for the krypton-helium atom pair was developed using supermolecular ab initio computations for 34 interatomic distances. Values for the interaction energies at the complete basis set limit were obtained from calculations with the coupled-cluster method with single, double, and perturbative triple excitations and correlation consistent basis sets up to sextuple-zeta quality augmented with mid-bond functions. Higher-order coupled-cluster excitations up to the full quadruple level were accounted for in a scheme of successive correction terms. Core-core and core-valence correlation effects were included. Relativistic corrections were considered not only at the scalar relativistic level but also using full four-component Dirac-Coulomb and Dirac-Coulomb-Gaunt calculations. The fitted analytical pair potential function is characterized by a well depth of 31.42 K with an estimated standard uncertainty of 0.08 K. Statistical thermodynamics was applied to compute the krypton-helium cross second virial coefficients. The results show a very good agreement with the best experimental data. Kinetic theory calculations based on classical and quantum-mechanical approaches for the underlying collision dynamics were utilized to compute the transport properties of krypton-helium mixtures in the dilute-gas limit for a large temperature range. The results were analyzed with respect to the orders of approximation of kinetic theory and compared with experimental data. Especially the data for the binary diffusion coefficient confirm the predictive quality of the new potential. Furthermore, inconsistencies between two empirical pair potential functions for the krypton-helium system from the literature could be resolved.

A multi-state modified embedded atom method potential for titanium

The continuing search for broadly applicable, predictive, and unique potential functions led to the invention of the multi-state modified embedded atom method (MS-MEAM) (Baskes et al 2007 Phys. Rev. B 75 094113). MS-MEAM replaced almost all of the prior arbitrary choices of the MEAM electron densities, embedding energy, pair potential, and angular screening functions by using first-principles computations of energy/volume relationships for multiple reference crystal structures and transformation paths connecting those reference structures. This strategy reasonably captured diverse interactions between atoms with variable coordinations in a face-centered-cubic (fcc)-stable copper system. However, a straightforward application of the original MS-MEAM framework to model technologically useful hexagonal-close-packed (hcp) metals proved elusive. This work describes the development of an hcp-stable/fcc-metastable MS-MEAM to model titanium by introducing a new angular function within the background electron density description. This critical insight enables the titanium MS-MEAM potential to reproduce first principles computations of reference structures and transformation paths extremely well. Importantly, it predicts lattice and elastic constants, defect energetics, and dynamics of non-ideal hcp and liquid titanium in good agreement with first principles computations and corresponding experiments, and often better than the three well-known literature models used as a benchmark. The titanium MS-MEAM has been made available in the Knowledgebase of Interatomic Models (https://openkim.org/) (Tadmor et al 2011 JOM 63 17).

Lennard-Jones type pair-potential method for coarse-grained lipid bilayer membrane simulations in LAMMPS

Lipid bilayer membranes have been extensively studied by coarse-grained molecular dynamics simulations. Numerical efficiencies have been reported in the cases of aggressive coarse-graining, where several lipids are coarse-grained into a particle of size 4∼6nm so that there is only one particle in the thickness direction. Yuan et al. proposed a pair-potential between these one-particle-thick coarse-grained lipid particles to capture the mechanical properties of a lipid bilayer membrane, such as gel–fluid–gas phase transitions of lipids, diffusion, and bending rigidity Yuan et al. (2010). In this work we implement such an interaction potential in LAMMPS to simulate large-scale lipid systems such as a giant unilamellar vesicle (GUV) and red blood cells (RBCs). We also consider the effect of cytoskeleton on the lipid membrane dynamics as a model for RBC dynamics, and incorporate coarse-grained water molecules to account for hydrodynamic interactions. The interaction between the coarse-grained water molecules (explicit solvent molecules) is modeled as a Lennard-Jones (L-J) potential. To demonstrate that the proposed methods do capture the observed dynamics of vesicles and RBCs, we focus on two sets of LAMMPS simulations: 1. Vesicle shape transitions with enclosed volume; 2. RBC shape transitions with different enclosed volume. Finally utilizing the parallel computing capability in LAMMPS, we provide some timing results for parallel coarse-grained simulations to illustrate that it is possible to use LAMMPS to simulate large-scale realistic complex biological membranes for more than 1 ms. Program summaryProgram Title: fluidmembraneProgram Files doi:http://dx.doi.org/10.17632/4v53nkv5hc.1Licensing provisions: GNU GPLv3Programming language: C++.Nature of problem:A pair-potential function for simulating the shape transition of fluid vesicles and the resting shapes of red blood cells.Program Solution method:Nosé-Hoover thermostat and Berendsen pressure coupling algorithms.External routines/libraries: LAMMPSSubprograms used: create_rbc_with_water (MATLAB), bond_harmonic1 (C++), in_example (LAMMPS input script).

Theoretical Model to Estimate the Distribution of Radon in Alveolar Membrane Neighborhood

Radon is a naturally occurring radioactive gas which tends to concentrate indoors, easily emanates from the ground into the air, where it disintegrates and emits radioactive particles. It can enter the human body through breathing or ingesting mostly water. When radon inhaled, travels through the respiratory tract to alveoli where the majority is expelled into the environment. Moreover, when ingested in water, it passes into the intestine where it is absorbed and driven from the bloodstream to the lungs; in these organs, due to differences in partial pressures, it is transported to alveoli by simple diffusion process. When radon is not removed, it decays in short-lived solid disintegration products (218Po and 214Po) with high probability of being deposited in biological tissues, causing DNA damage because of the densely ionizing alpha radiation emitted. We propose a semi-empirical, smooth, and continuous pair potential function in order to model the molecular interactions between radon and lung alveolar walls; we use Molecular Dynamics (MD) to determine the gas distribution in an alveolar neighborhood wall, and estimate the quantity thereof it diffuses through the alveolar membrane as a concentration function.

State-of-the-art ab initio potential energy curve for the krypton atom pair and thermophysical properties of dilute krypton gas.

A new reference krypton-krypton interatomic potential energy curve was developed by means of quantum-chemical ab initio calculations for 36 interatomic separations. Highly accurate values for the interaction energies at the complete basis set limit were obtained using the coupled-cluster method with single, double, and perturbative triple excitations as well as t-aug-cc-pV5Z and t-aug-cc-pV6Z basis sets including mid-bond functions, with the 6Z basis set being newly constructed for this study. Higher orders of coupled-cluster terms were considered in a successive scheme up to full quadruple excitations. Core-core and core-valence correlation effects were included. Furthermore, relativistic effects were studied not only at a scalar relativistic level using second-order direct perturbation theory, but also utilizing full four-component and Gaunt-effect computations. An analytical pair potential function was fitted to the interaction energies, which is characterized by a depth of 200.88 K with an estimated standard uncertainty of 0.51 K. Thermophysical properties of low-density krypton were calculated for temperatures up to 5000 K. Second and third virial coefficients were obtained from statistical thermodynamics. Viscosity and thermal conductivity as well as the self-diffusion coefficient were computed using the kinetic theory of gases. The theoretical results are compared with experimental data and with results for other pair potential functions from the literature, especially with those calculated from the recently developed ab initio potential of Waldrop et al. [J. Chem. Phys. 142, 204307 (2015)]. Highly accurate experimental viscosity data indicate that both the present ab initio pair potential and the one of Waldrop et al. can be regarded as reference potentials, even though the quantum-chemical methods and basis sets differ. However, the uncertainties of the present potential and of the derived properties are estimated to be considerably lower.

Real-time SAXS study of a strain gauge based on a self-assembled gold nanoparticle monolayer

A strain gauge based on a monolayer of colloidal gold nanoparticles deposited on a flexible Mylar foil by a modified Langmuir-Schaefer method was tested in situ under external uniaxial stress by the small-angle X-ray scattering (SAXS) technique. Simultaneously, the stress-strain curve of the foil was measured. A high-flux laboratory X-ray source allowed fast data collection with 10s temporal resolution. The monolayer exhibits a linear response in terms of the interparticle distances up to the 13% substrate strain while keeping its full integrity. This result indicates the dominant role of the pair potential function between the nanoparticle surfactant molecules and molecules of the substrate and compares well with previous quasi-static measurements of a similar strain gauge, suggesting none or negligible effect of the transient strain phenomena longer than the sampling interval on the gauge response. Keeping a constant strain on finishing the stretching, fast transient effects with characteristic times down to the limit imposed by the X-ray detector time resolution were not observed either during the SAXS pattern collection. A different stress behavior of the interparticle distance in the direction perpendicular to stretching comparing with a monolayer of colloidal iron-oxide nanoparticles studied previously reveals the surfactant effect on the gauge response controlled by the interparticle pair potential function. The results obtained suggest that the colloidal gold-nanoparticle monolayer on a flexible substrate is a prospective strain gauge with a very fast linear response in a broad strain range.

Ab initio Intermolecular Potential Energy Surface and Calculation of Second Virial Coefficients for the Cl2–Cl2 Dimer

The results presented in this paper are the ab initio intermolecular potentials and the second virial coefficient, B 2 ( T ) of the dimer Cl 2 -Cl 2 . These ab initio potentials were proposed by the quantum chemical calculations at high level of theory CCSD (T) with basis sets of Dunning’s valence correlation-consistent aug-cc-pV m Z ( m = 2, 3); these results were extrapolated to complete basis set limit aug-cc-pV23Z. The ab initio energies of complete basis set limit aug-cc-pV23Z resulted from the exponential extrapolation were used to construct the 5-site pair potential functions. The second virial coefficients for this dimer were predicted from those with four-dimensional integration. The second virial coefficients were also corrected to first-order quantum effects. The results turn out to be in good agreement with experimental data, if available, or with those from empirical correlation. The quality of ab initio 5-site potentials proved the reliability for prediction of molecular thermodynamic properties.

The foundation and study of a new type of lattice inversion potential for Iridium

In this paper, the lattice cohesive curve of iridium is investigated through first-principles calculations. The double-exponential function to fit the curve is presented. The inversion pair potential curve is generated through Chen’s inversion method. The accurate pair potential function is obtained through fitting by the new double-exponential function. The phonon spectra are calculated using the inversion potential data, the embedded atom method (EAM) potential theory and first-principles method, respectively, to verify the reliability of the inversion potential. The method combining Boltzmann statistics equation with accuracy fitting of lattice cohesive energy curve is proposed to calculate the thermal expansion coefficient. In addition, the bulk modulus and Grüneisen constant in the room temperature are calculated. The results are in good agreement with experiment results, which imply that the inversion potential is effective and accurate.

Far-field compression for fast kernel summation methods in high dimensions

Abstract We consider fast kernel summations in high dimensions: given a large set of points in d dimensions (with d ≫ 3 ) and a pair-potential function (the kernel function), we compute a weighted sum of all pairwise kernel interactions for each point in the set. Direct summation is equivalent to a (dense) matrix–vector multiplication and scales quadratically with the number of points. Fast kernel summation algorithms reduce this cost to log-linear or linear complexity. Treecodes and Fast Multipole Methods (FMMs) deliver tremendous speedups by constructing approximate representations of interactions of points that are far from each other. In algebraic terms, these representations correspond to low-rank approximations of blocks of the overall interaction matrix. Existing approaches require an excessive number of kernel evaluations with increasing d and number of points in the dataset. To address this issue, we use a randomized algebraic approach in which we first sample the rows of a block and then construct its approximate, low-rank interpolative decomposition. We examine the feasibility of this approach theoretically and experimentally. We provide a new theoretical result showing a tighter bound on the reconstruction error from uniformly sampling rows than the existing state-of-the-art. We demonstrate that our sampling approach is competitive with existing (but prohibitively expensive) methods from the literature. We also construct kernel matrices for the Laplacian, Gaussian, and polynomial kernels—all commonly used in physics and data analysis. We explore the numerical properties of blocks of these matrices, and show that they are amenable to our approach. Depending on the data set, our randomized algorithm can successfully compute low rank approximations in high dimensions. We report results for data sets with ambient dimensions from four to 1,000.