Morse Potential Function Research Articles

On the Nonlinear Stochastic Dynamics of an Atomic Force Microscope Cantilever

AbstractAtomic force microscopy (AFM) serves characterization and actuation in nanoscale applications. We study the stochastic dynamics of an AFM cantilever under tip-sample interactions represented by the Lennard–Jones and Morse potential energy functions. In both cases, we also study the contrasting dynamic effects of additive (external) and multiplicative (internal) noise. Moreover, for multiplicative noise, we study the two sub-cases arising from the Itô and Stratonovich interpretations of stochastic integrals. In each case, we also investigate the stochastic stability of the system by tracing the time evolution of the maximal Lyapunov exponent. Additionally, we obtain stationary probability densities for the unforced dynamics using stochastic averaging.

Accuracy of the new modified Morse potential energy function for ground and excited states of diatomic molecules

This paper presents a detailed study on the performance of the new modified Morse potential in representing the vibrational motion of several diatomic molecules. The matrix Numerov method has been used to solve the time-independent Schrödinger equation for the new modified Morse potential, Morse potential, and Varshni potential. The vibrational energy eigenvalues of the 20 diatomic molecules in various electronic states were calculated. The vibrational energy eigenvalues and anharmonicity constants calculated using the new modified Morse potential were closer to the experimental values for all 20 molecules than the eigenvalues calculated from the Morse and Varshni potential functions.

Formation Control Over Delaunay Triangulation Networks With Guaranteed Collision Avoidance

This article addresses the collision avoidance of networked swarms of mobile agents. A gradient-based control scheme with artificial potential fields guides all the agents into a distance-based formation. While, in the relevant literature, unbounded forces are used to achieve collision avoidance, this article shows a way to guarantee collision avoidance that respects control input limitations. To this end, it is proposed to use Morse potential functions, and it is shown how to parameterize them appropriately. The results are extended to the case that a switching proximity communication network in form of a Delaunay triangulation is applied to the networked system. It is shown that under which conditions the collision avoidance is preserved among the overall network. The proposed method is evaluated experimentally with mobile robots.

Study on macroscopic thermodynamic properties of ClO molecule based on the improved Hulburt–Hirschfelder potential energy function

AbstractThe improved Hulburt–Hirschfelder potential energy function is used as a proposal to emulate the behavior of intramolecular motion of a gas composed of diatomic molecules. In this work, the rovibrational energies of ClO molecule in the ground electronic state are obtained by solving the one‐dimensional Schrödinger equation with the improved Hulburt–Hirschfelder potential energy curve. And then, the molar heat capacities, molar entropies, molar enthalpies and reduced Gibbs free energies of ClO macroscopic gas are calculated by the quantum statistical ensemble theory. The results are compared with those calculated by using RKR potential energy curve from experiment and Morse potential energy function. It is found that the macroscopic thermodynamic properties of ClO calculated by the improved Hulburt–Hirschfelder potential energy function are closer to the experimental values, which provides a new way to calculate the macroscopic thermodynamic quantities of diatomic gas based on molecular microscopic information.

Refined models of coordination between Al3+/Mg2+ and enzyme in molecular dynamics simulation in terms of ABEEM polarizable force field

MFX (AlF30, AlF4− and MgF3−) as transition state analogues of phosphoryl transfer enzymes (enzyme-MFX-TSAs) is of great significance for study of the catalytic mechanism of phosphoryl transfer enzymes. Bonded model and non-bonded model based on the ABEEM polarizable force field (ABEEM PFF) are developed and applied to study the coordination of enzyme-MFX-TSAs. The bond stretching of the bond containing metal is simulated by Morse potential energy function, because the change of chemical bond is described more accurately in a large range. The charge distribution of the system is distributed to multiple-charge-sites, including atomic site, σ bond site, π bond site and lone pair electron site. Partial charge can fluctuate according to the surrounding environment and molecular conformation. The reasonable charge distribution of 68 model molecules can be obtained, and the energy minimizations are performed in vacuum. Then, with the same parameters the charge distribution and the charge transfer of four complexes are obtained, and the energy minimization and molecular dynamics simulation in NVT ensemble are carried out in vacuum and explicit water solution. The results verify the correctness, rationality and transferability of the new parameters of ABEEM PFF, and the bonded model simulates more reasonable charge distribution and geometry. The parameters determined in this paper make up the blank of the parameters of MFX and phosophoryl transfer enzymes containing Mg2+. The development of ABEEM PFF provides a refined tool for MFX-TSAs to study the catalytic mechanism of phosphoryl transfer enzymes.

Designing the nonlinear mechanical response of graphyne structures: A finite element structural mechanics approach

Over recent decades, the exploration of various allotropes of carbon at the nanoscale has attracted a significant amount of research interest. The demand for the synthesis of novel carbon-based nanostructures has resulted in the discovery of graphynes, i.e. one-atom-thick planar crystal lattice sheets of benzene rings connected by acetylene bonds. In this study, computer modelling and simulations were applied to characterise the full tensile and elastoplastic mechanical behaviour of such structures. Using a nonlinear finite element-based structural mechanics method, which is based on Morse potential functions, several parametric studies were performed, and various illustrative size-dependent diagrams were obtained, enabling the suitable and accurate design of graphyne-based material components based on key mechanical properties such as stiffness, tensile strength, and fracture strain. The four well-known types of graphyne sheets were numerically investigated: graphyne-1, also known as graphyne; graphyne-2, also known as graphdiyne; graphyne-3; and graphyne-4. The predictions of the mechanical properties of graphene were compared with other corresponding estimations to validate the research results.

Nonlinear Finite Element Analysis of γ-Graphyne Structures under Shearing.

In this study, a nonlinear, spring-based finite element approach is employed in order to predict the nonlinear mechanical response of graphyne structures under shear loading. Based on Morse potential functions, suitable nonlinear spring finite elements are formulated simulating the interatomic interactions of different graphyne types. Specifically, the four well-known types of γ-graphyne, i.e., graphyne-1 also known as graphyne, graphyne-2 also known as graphdiyne, graphyne-3, and graphyne-4 rectangular sheets are numerically investigated applying appropriate boundary conditions representing shear load. The obtained finite element analysis results are employed to calculate the in-plane shear stress–strain behaviour, as well as the corresponding mechanical properties as shear modulus and shear strength. Comparisons of the present graphyne shearing response predictions with other corresponding estimations are performed to validate the present research results.

Transport properties of two-component radium – halogen dilute gas media

Based on state-of-the-art ab initio potential energy functions and classical kinetic theory, some transport properties (diffusion, viscosity and thermal conductivity coefficients) of two-component dilute gas media of radium and halogen (F, Cl, Br, I) atoms were predicted as functions of the translation temperature up to 3000 K. Calculations were performed by sequential analytical and (or) numerical computations of deflection angle, cross-section and collision integrals. A detailed methodology for the calculation of the transport properties using the Morse potential was developed. Some numerical difficulties arising due to the singularity of the integrands and discontinuous character of the variable of integration are considered. The dependence of transport properties on isotope mass is also shown. Possible errors introduced by using the model Morse potential function instead of the real potential for the interaction between atoms are estimated. These data can be useful for the planning of the experiments on the direct laser cooling of the monohalides of alkaline earth metals.

Accuracy of the New Modified Morse Potential Energy Function for Ground and Excited States of Diatomic Molecules

Accuracy of the New Modified Morse Potential Energy Function for Ground and Excited States of Diatomic Molecules

Eigensolution to Morse potential for Scandium and Nitrogen monoiodides

The solutions for Morse potential energy function under the influence of Schr¨odinger equation are examined using supersymmetric approach. The energy equation obtained was used to generate eigenvalues forX1 +state of scandium monoiodide (ScI) and X3 state of nitrogen monoiodide (NI) respectively were obtained by imputing their respective spectroscopic parameters. The calculated results for the two molecules aligned excellently with the predicted/observed values.

An approach to determine the diatomic vibrational energy levels: application to LiH, NO and CO molecules

This work presents the systematic calculation of vibrational energy levels, for diatomic molecules through an alternative approach, reposed on the Floquet representation analysis. The Morse potential function has been employed to solve the Schrodinger equation, and to obtain the vibrational energy levels of diatomic systems. As an illustration, the numerical energy values of some molecules have been computed, and compared to those of literature, revealing a good agreement, and showing the accuracy of our approach.

On the derivation of coefficient of Morse potential function for the silicene: a DFT investigation.

In this paper, the structural and mechanical properties of silicene are investigated by the density functional theory calculations. To calculate Young's, bulk, and shear moduli and Poisson's ratio of the silicene, the optimized unit cells containing two atoms are proposed and the effect of chirality on the elastic properties of silicene is examined. It is shown that the silicene has an isotropic behavior, while graphene has an anisotropic behavior. The results showed that calculated moduli for the silicene are significantly lower than those of graphene in zigzag and armchair directions, while Poisson's ratio of silicene is higher than that of graphene. The paper describes one common type of inharmonic interatomic potentials used for constructing nonlinear models of the material using the modified Morse potential function. Using this concept, the effects of chirality on dissociation energy, inflection point, and coefficients of the modified Morse potential function are studied. Comparison of the cutoff distance value in the modified Morse potential showed that inflection point values for the armchair and zigzag graphene are highly direction-dependent, whereas these values have negligible difference for silicene.

Microscopic Study on the Mechanism of Tool Bond Wear in Cutting Ni–Fe-Cr-Co–Cu Series Nickel-Base Superalloy

In the process of nickel-based alloy machining, chips are easy to bond on the tool surface, which weaken the tool performance and make the tool wear. Therefore, it is very important to study the mechanism of tool bond wear in the process of nickel-based superalloy machining. In order to reflect the wear process of the tool from the perspective of micro cutting, the molecular dynamics simulation model for cutting Ni–Fe-Cr-Co–Cu nickel-based alloy with SiC tool was established. The Morse potential functions between the tool and workpiece are calculated, and the simulation results are analyzed visually. It is found that the bond wear is the main wear form of tool in the process of cutting nickel-based alloy, and the wear processes are divided into three stages: contact, adhesion and shedding. The stress and strain in the cutting area are calculated and it is found that the bond occurs when the tool-workpiece extrusion is strong. Through the calculation of radial distribution function and formation energy, it is found that Ni-Si compound is formed on the tool surface, and the newly generated Ni-Si compound reduces the tool performance compared with the silicon carbide structure. This study provides a more complete microscopic explanation of the tool wear mechanism, which is helpful to find a method to prolong tool life.

Systematic Parameterization and Simulation of Boronic Acid-β-Lactamase Aqueous Solution in Developing the ABEEMσπ Polarizable Force Field.

Boronic acid, an inhibitor of β-lactamase, has begun to be applied to the treatment of biological infections and tumors. Scientists are working to develop new and more effective boronic acid. Molecular dynamics (MD) simulation provides a powerful auxiliary tool for drug design. However, the current force fields have no boron-related parameters. In this work, an atom-bond electronegativity equalization method at the σπ level (ABEEMσπ) polarizable force field (ABEEMσπ PFF) of boronic acid and β-lactamase has been developed to determine the potential functions and parameters. The interaction between boron and serine in β-lactamase is regarded as a bonded mode. The interaction between them is simulated by the Morse potential energy function, which is close to the experimental change of the stretching potential energy in a large range. The potential energy surfaces of the bond length, bond angle, and dihedral angle of boronic acid-β-lactamase have the same stability point and change trend as M06-2X/6-311G**. For 47 boronic acid-β-lactamase training molecules, the linear correlation coefficient (R) of the charge distribution between the ABEEMσπ PFF and HF/STO-3G is greater than 0.96. Attributed to the fact that the charge distribution of the ABEEMσπ PFF can fluctuate with the change of geometry and environment, the polarization effect and charge-transfer effect are well reflected. The binding ability of different boronic acids with the same β-lactamase is different. A total of 10 boronic acid-β-lactamase model molecules and 10 boronic acid-β-lactamase and water complexes are simulated. The order of binding energy of five large model molecules calculated by the ABEEMσπ PFF is consistent with that of the MP2 method. The binding energies of boronic acid-β-lactamase and water complexes are close to those of the MP2 method. The results of MD simulation of five aqueous boronic acid-β-lactamase complexes in the NVT ensemble verify the rationality of boron-related parameters of the ABEEMσπ PFF, which have a good application prospect. This study lays a solid theoretical foundation for further study of the inhibition of boronic acid on β-lactamase.

Characteristics of sound side knee loading parameters of 53 trans-tibial amputees

This paper deals with a numerical model for the buckling and post-buckling analysis of single-wall carbon nanotubes. Reasons of efficiency lead to the choice of a simple molecular statics model, wherein binary, ternary and quaternary atomic interactions are accounted for and described using Morse and cosine potential functions. The equations of the model are discussed in depth and the parameters of the potential functions are justified in the light of a comparison with ab-initio results. Several case studies regarding zigzag and armchair tubes of different aspect ratios, under compression, bending and torsion, are addressed with the aim of investigating the efficacy of the model and the role of the quaternary interactions, in contexts of both global and local behaviours.

An atomistic-based finite element progressive fracture model for silicene nanosheets

A progressive finite element method is proposed herein to investigate the fracture of silicene nanosheets. By treating a silicene nanosheet as a buckled frame structure, its mechanical behavior is simulated using the modified Morse potential function. The interatomic force per atom is calculated for all atoms as a set of inharmonic oscillator networks, which are described by the modified Morse potential function, while the nonlinear behavior is defined by these interatomic forces with an iterative solution procedure as strain increases. The nonlinear stress–strain relationships of the armchair and zigzag silicene nanosheets are also obtained for pristine and defective cases including the tensile strength and ultimate strain. For the silicene with both configurations, i.e., armchair and zigzag, a sudden drop is seen in the stress–strain diagram, showing that both of them represent the brittle behavior. Moreover, it is concluded that the tensile strength and ultimate strain of the armchair silicenes are slightly larger than those of the zigzag one. It is also seen that the mechanical properties of the silicene are significantly affected by the single-vacancy and Stone–Wales defects. The computed results reveal that single-vacancy defects can reduce the ultimate strain of silicene by approximately 7.3% with respect to that of pristine silicene, whereas the effect of Stone–Wales defects is less significant.

A New Generalized Morse Potential Function for Calculating Cohesive Energy of Nanoparticles

A new generalized Morse potential function with an additional parameter m is proposed to calculate the cohesive energy of nanoparticles. The calculations showed that a generalized Morse potential function using different values for the m and α parameters can be used to predict experimental values for the cohesive energy of nanoparticles. Moreover, the enlargement of the attractive force in the generalized potential function plays an important role in describing the stability of the nanoparticles rather than the softening of the repulsive interaction in the cases when m > 1.

A new modified Morse potential energy function for diatomic molecules

A new modified Morse potential is introduced to describe the vibrational motion of diatomic molecules. The vibrational energy eigenvalues for the ground state of the H2 and N2 molecules are obtained by numerically solving the time-independent Schrödinger equation using a Python program and the Matrix Numerov method for the case of the Morse potential, Hulbert-Hirschfelder potential, and the modified Morse potential functions. The comparison of the vibrational energy eigenvalues and the anharmonicity constant obtained for the modified Morse potential function reveals better agreement with the experimental data than the other potential functions. Also, the proposed modified Morse potential function fits the RKR potential energy curve more closely than the Morse potential function and Hulbert-Hirschfelder potential function, especially in the region where the potential extends to near the dissociation limit.

Simulation of water internal pressure within temperature range of 0–370 °C

We have chosen Morse and Rydberg potential energy functions in order to approximate water internal pressure (Pi) over a large temperature range using physically sound models. We have found that these functions adequately reproduce the water internal pressure curve within the range of 0–250 °C. In order to adequately calculate water Pi within the range of 0–370 °C, we have used modified Morse and Rydberg functions. These functions are capable of reproducing the temperature dependence of water Pi within the range of 0–370 °C with average error being 1% and maximal error not exceeding 5%. The functions of Morse and Rydberg and their modifications allowed us to calculate two components of the internal pressure of water: the repulsion pressure and the attractive pressure. The analysis of changes in the repulsion pressures and the attraction of water in the entire investigated temperature range are performed.

Evaluation of the Morse potential function coefficients for germanene by the first principles approach

In this paper, first principles calculations are used to investigate atomic structure and mechanical properties of germanene nanosheet. By applying uniaxial and biaxial tensile strains as well as shear strain, the tensile and shear properties of the germanene nanosheet, including Young’s and bulk moduli, Poisson’s ratio, and shear moduli are computed. Furthermore, the parameters of the modified Morse potential function are calculated for Ge–Ge interaction in the germanene nanosheet. Also, the mechanical behavior of germanene nanosheet is studied under tensile loading at large strains extended to the plastic range. Based on the simulations, Young’s modulus of the armchair and zigzag germanene nanosheet are computed as 52.8 and 49.9N/m, respectively. Besides, the values of Poisson’s ratio of the armchair and zigzag germanene nanosheet are obtained as 0.35 and 0.29, respectively.