Morse Potential Research Articles

Internal conversion rates from the extended thawed Gaussian approximation: Theory and validation.

The theoretical prediction of the rates of nonradiative processes in molecules is fundamental in assessing their emissive properties. In this context, global harmonic models have been widely used to simulate vibronic spectra as well as internal conversion rates and to predict photoluminescence quantum yields. However, these simplified models suffer from the limitations that are inherent to the harmonic approximation and can have a severe effect on the calculated internal conversion rates. Therefore, the development of more accurate semiclassical methods is highly desirable. Here, we introduce a procedure for the calculation of nonradiative rates in the framework of the time-dependent semi-classical Extended Thawed Gaussian Approximation (ETGA). We systematically investigate the performance of the ETGA method by comparing it to the adiabatic and vertical harmonic methods, which belong to the class of widely used global harmonic models. Its performance is tested in potentials that cannot be treated adequately by global harmonic models, beginning with Morse potentials of varying anharmonicity followed by a double well potential. The calculated radiative and nonradiative internal conversion rates are compared to reference values based on exact quantum dynamics. We find that the ETGA has the capability to predict internal conversion rates in anharmonic systems with an appreciable energy gap, whereas the global harmonic models prove to be insufficient.

A potential well model for host-guest chemistry in double-network hydrogels toward mechanochemical coupling and toughening

Different from conventional single-network hydrogels, double-network (DN) hydrogels have attracted great research interest due to their ultra-high toughness; however, the working principles behind their complex mechanochemical coupling have not been fully understood. In this study, an extended potential well model is formulated to investigate the host-guest chemistry and the free-energy trap effect, coupled in DN hydrogels undergoing mechanochemical toughening. According to the Morse potential and mean field model, the newly established potential well model can describe the coupled binding of the host brittle network and guest ductile network in the DN hydrogels. A free-energy equation is further proposed to describe the working principles of the mechanochemical coupling and toughening mechanisms using the depth, width, and trap number of potential wells, which determine the barrier energy of the host brittle network, the mesh size of guest ductile network, and the mechanochemical host-guest interactions of these two networks, respectively. Finally, the effectiveness of the proposed model is verified using finite-element analysis (FEA) and experimental results of various DN hydrogels reported in the literature. Using the potential well model, which has host-guest chemistry from both brittle and ductile networks, this study clarifies the linking of mechanochemical coupling and toughening mechanisms in DN hyrdogels.

Semi-infinite Quantum Wells In a Position-Dependent Mass Background

Using a point canonical transformation starting from the constant-mass Schrödinger equation for the Morse potential, it is shown that a semi-infinite quantum well model with a non-rectangular profile associated with a position-dependent mass that becomes infinite for some negative value of the position, while going to a constant for a large positive value of the latter can be easily derived. In addition, another type of semi-infinite quantum well associated with the same position-dependent mass is constructed and solved by starting from the Rosen-Morse II potential instead of the Morse one.

Theoretic measure and thermal properties of a standard Morse potential model.

Since the proposition of the standard form of Morse potential [Formula: see text] model over the years, there has not been much attention on the potential. Its application to different studies such as the thermodynamic properties and information theory are yet to be reported to the best of our understanding. In this study, the solutions of the radial Schrödinger equation for the standard Morse potential is obtained using supersymmetric approach. The effect of the quantum number on the energy eigenvalue for the standard Morse potential is examined numerically for the hydrogen molecule (H2), lithium molecule (Li2), and potassium molecule (K2). Using the energy equation and the wave function obtained, the theoretic measures and thermodynamic properties of hydrogen, lithium, and potassium molecules are calculated via maple program. It has been shown that the energy of the standard Morse potential is fully bounded for the three molecules studied. A higher concentration of electron density corresponds to a strongly localized distribution in the position configuration. The Beckner, Bialynicki-Birula, and Mycieslki (BBM) inequality is satisfied for both the ground state and the first excited state. Finally, the product of uncertainty obtained obeyed the Heisenberg uncertainty relation.

Effect of Interatomic Potential on Simulation of Fracture Behavior of Cu/Graphene Composite: A Molecular Dynamics Study

Interatomic interaction potentials are compared using a molecular dynamics modeling method to choose the simplest, but most effective, model to describe the interaction of copper nanoparticles and graphene flakes. Three potentials are considered: (1) the bond-order potential; (2) a hybrid embedded-atom-method and Morse potential; and (3) the Morse potential. The interaction is investigated for crumpled graphene filled with copper nanoparticles to determine the possibility of obtaining a composite and the mechanical properties of this material. It is observed that not all potentials can be applied to describe the graphene–copper interaction in such a system. The bond-order potential potential takes into account various characteristics of the bond (for example, the angle of rotation and bond lengths); its application increases the simulation time and results in a strong interconnection between a metal nanoparticle and a graphene flake. The hybrid embedded-atom-method/Morse potential and the Morse potential show different results and lower bonding between graphene and copper. All the potentials enable a composite structure to be obtained; however, the resulting mechanical properties, such as strength, are different.

Exact solution and coherent states of an asymmetric oscillator with position-dependent mass

We revisit the problem of the deformed oscillator with position-dependent mass [da Costa et al., J. Math. Phys. 62, 092101 (2021)] in the classical and quantum formalisms by introducing the effect of the mass function in both kinetic and potential energies. The resulting Hamiltonian is mapped into a Morse oscillator by means of a point canonical transformation from the usual phase space (x, p) to a deformed one (xγ, Πγ). Similar to the Morse potential, the deformed oscillator presents bound trajectories in phase space corresponding to an anharmonic oscillatory motion in classical formalism and, therefore, bound states with a discrete spectrum in quantum formalism. On the other hand, open trajectories in phase space are associated with scattering states and continuous energy spectrum. Employing the factorization method, we investigate the properties of the coherent states, such as the time evolution and their uncertainties. A fast localization, classical and quantum, is reported for the coherent states due to the asymmetrical position-dependent mass. An oscillation of the time evolution of the uncertainty relationship is also observed, whose amplitude increases as the deformation increases.

Bounce corrections to gravitational lensing, quasinormal spectral stability, and gray-body factors of Reissner-Nordström black holes

Gravitational lensing in the weak field limit, quasinormal spectra, and gray-body factors are investigated in the Reissner-Nordstr\"om spacetime corrected by bounce parameters. Using the Gauss-Bonnet theorem, we analyze the effects of bounce corrections to the weak gravitational deflection angle and find that the divergence of the deflection angle can be suppressed by a bounce correction in the Reissner-Nordstr\"om spacetime. We also notice that the bounce correction plays the same role as the Morse potential in the deflection angle. Moreover, we derive the perturbation equations with spin-dependent effective potentials and discuss the quasinormal spectral stability. We observe that the quasinormal spectra have the same behavior in large bounce parameters for different multiple numbers and they decrease significantly if the bounce parameter is much bigger than the charge. We further study the transmission probability of particles scattered by the effective potentials and reveal that the bounce correction introduced into the Reissner-Nordstr\"om spacetime increases the gray-body factors of perturbation fields.

Petviashvili Method for the Fractional Schrödinger Equation

In this paper, we extend the Petviashvili method (PM) to the fractional nonlinear Schrödinger equation (fNLSE) for the construction and analysis of its soliton solutions. We also investigate the temporal dynamics and stabilities of the soliton solutions of the fNLSE by implementing a spectral method, in which the fractional-order spectral derivatives are computed using FFT (Fast Fourier Transform) routines, and the time integration is performed by a 4th order Runge–Kutta time-stepping algorithm. We discuss the effects of the order of the fractional derivative, α, on the properties, shapes, and temporal dynamics of the soliton solutions of the fNLSE. We also examine the interaction of those soliton solutions with zero, photorefractive and q-deformed Rosen–Morse potentials. We show that for all of these potentials, the soliton solutions of the fNLSE exhibit a splitting and spreading behavior, yet their dynamics can be altered by the different forms of the potentials and noise considered.

Molecular dynamics simulation-based microstructure evolution and subsurface damage of Fe-Ni alloy grinding

PurposeMolecular dynamics is an emerging simulation technique in the field of machining in recent years. Many researchers have tried to simulate different processing methods of various materials with the theory of molecular dynamics (MD), and some preliminary conclusions have been obtained. However, the application of MD simulation is more limited compared with traditional finite element model (FEM) simulation technique due to the complex modeling approach and long computation time. Therefore, more studies on the MD simulations are required to provide a reliable theoretical basis for the nanoscale interpretation of grinding process. This study investigates the crystal structures, dislocations, force, temperature and subsurface damage (SSD) in the grinding of iron-nickel alloy using MD analysis.Design/methodology/approach In this study the simulation model is established on the basis of the workpiece and single cubic boron nitride (CBN) grit with embedded atom method and Morse potentials describing the forces and energies between different atoms. The effects of grinding parameters on the material microstructure are studied based on the simulation results.FindingsWhen CBN grit goes through one of the grains, the arrangement of atoms within the grain will be disordered, but other grains will not be easily deformed due to the protection of the grain boundaries. Higher grinding speed and larger cutting depth can cause greater impact of grit on the atoms, and more body-centered cubic (BCC) structures will be destroyed. The dislocations will appear in grain boundaries due to the rearrangement of atoms in grinding. The increase of grinding speed results in the more transformation from BCC to amorphous structures.Originality/valueThis study is aimed to study the grinding of Fe-Ni alloy (maraging steel) with single grit through MD simulation method, and to reveal the microstructure evolution within the affected range of SSD layer in the workpiece. The simulation model of polycrystalline structure of Fe-Ni maraging steel and grinding process of single CBN grit is constructed based on the Voronoi algorithm. The atomic accumulation, transformation of crystal structures, evolution of dislocations as well as the generation of SSD are discussed according to the simulation results.

Soliton Dynamics Analysis of Peyrard-Bishop-Dauxois DNA Model Using 4th Order Morse Potential Approach

Research has been carried out to analyze the dynamics of the soliton DNA of the Peyrard-Bishop-Dauxois (PBD) model with 4th-order-approximation Morse Potential. The aim of research is to know physical changes of PBD model with 4th-order-approximation Morse Potential on stable and unstable state in describing denaturation process of DNA. The Process was carried out by finding a numerical solution of the 4th-order NLS as stable equation using finite-difference method. Then, the result was be simulated on Matlab. The results show that on the stable state, expand Morse Potential for 4th-order than for 3th-order rastically increased amplitude of oscillation from 1,89 pm to 16 pm. On the first unstable state, the stable equation was multiplied by (1+ ) where the value of = 0.25. On the second unstable state, the stable equation was multiplied two times by (1+ ) where the value of = 0.25. On three of them, amplitude of oscillation decreased from 16 pm, 2,9 pm to 2,5 pm. Comparing to previous order, there is a new addtion to the 4th-order Morse Potential coefficient which have physical meaning that larger expansion requires larger dissociation energy as well. So it can be concluded that the PBD model of DNA is descriptively able to explain the biological phenomenon of denaturation in DNA.

Thermal properties and quantum information theory with the shifted Morse potential

By employing the Nikiforov–Uvarov functional analysis (NUFA) method, we solved the radial Schrödinger equation with the shifted Morse potential model. The analytical expressions of the energy eigenvalues, eigenfunctions and numerical results were determined for selected values of the potential parameters. Variations of different thermodynamic functions with temperature were discussed extensively. Different quantum information-theoretic measures, including Shannon entropy, Fisher information and Fisher–Shannon product of the shifted Morse potential, were investigated numerically and graphically in position and momentum spaces for the ground and the first excited states. The quantum information theories considered satisfied their corresponding inequalities, including Bialynicki–Birula–Mycielski, Stam–Cramer–Rao inequalities and the Fisher–Shannon product relation.

Relative energies without electronic perturbations via alchemical integral transform.

We show that the energy of a perturbed system can be fully recovered from the unperturbed system's electron density. We derive an alchemical integral transform by parametrizing space in terms of transmutations, the chain rule, and integration by parts. Within the radius of convergence, the zeroth order yields the energy expansion at all orders, restricting the textbook statement by Wigner that the p-th order wave function derivative is necessary to describe the (2p + 1)-th energy derivative. Without the need for derivatives of the electron density, this allows us to cover entire chemical neighborhoods from just one quantum calculation instead of single systems one by one. Numerical evidence presented indicates that predictive accuracy is achieved in the range of mHa for the harmonic oscillator or the Morse potential and in the range of machine accuracy for hydrogen-like atoms. Considering isoelectronic nuclear charge variations by one proton in all multi-electron atoms from He to Ne, alchemical integral transform based estimates of the relative energy deviate by only few mHa from corresponding Hartree-Fock reference numbers.

Relativistic solutions of the morse potential via the formula method

The Dirac equation is solved using the Formula method. A non-relativistic mapping gives energy eigenvalues, in this limit, for a Hamiltonian including the Morse potential. The energies of the H2, LiH, HCl, CO, ScH, ScN, ScF and I2 molecules for both low and high-lying states are computed. Our results are found to be consistent with the literature. Also, new high-lying states for the Morse potential are also reported in the present study. The results of this study indicate that for the energy Eigen values of the H2 molecule, the deviation from the literature becomes more pronounced for the states (n, l) = (5, 20) and (6, 20).

Vibrational levels of a generalized Morse potential.

A Generalized Morse Potential (GMP) is an extension of the Morse Potential (MP) with an additional exponential term and an additional parameter that compensate for MP's erroneous behavior in the long range part of the interaction potential. Because of the additional term and parameter, the vibrational levels of the GMP cannot be solved analytically, unlike the case for the MP. We present several numerical approaches for solving the vibrational problem of the GMP based on Galerkin methods, namely, the Laguerre Polynomial Method (LPM), the Symmetrized LPM, and the Polynomial Expansion Method (PEM), and apply them to the vibrational levels of the homonuclear diatomic molecules B2, O2, and F2, for which high level theoretical near full configuration interaction (CI) electronic ground state potential energy surfaces and experimentally measured vibrational levels have been reported. Overall, the LPM produces vibrational states for the GMP that are converged to within spectroscopic accuracy of 0.01 cm-1 in between 1 and 2 orders of magnitude faster and with much fewer basis functions/grid points than the Colbert-Miller Discrete Variable Representation (CN-DVR) method for the three homonuclear diatomic molecules examined in this study. A Python library that fits and solves the GMP and similar potentials can be downloaded from https://gitlab.com/gds001uw/generalized-morse-solver.

Laser-induced dynamic alignment of the HD molecule without the Born-Oppenheimer approximation.

Laser-induced molecular alignment is well understood within the framework of the Born-Oppenheimer (BO) approximation. Without the BO approximation, however, the concept of molecular structure is lost, making it hard to precisely define alignment. In this work, we demonstrate the emergence of alignment from the first-ever non-BO quantum dynamics simulations, using the HD molecule exposed to ultrashort laser pulses as a few-body test case. We extract the degree of alignment from the non-BO wave function by means of an operator expressed in terms of pseudo-proton coordinates that mimics the BO-based definition of alignment. The only essential approximation, in addition to the semiclassical electric-dipole approximation for the matter-field interaction, is the choice of time-independent explicitly correlated Gaussian basis functions. We use a variational, electric-field-dependent basis-set construction procedure, which allows us to keep the basis-set dimension low while capturing the main effects of electric polarization on the nuclear and electronic degrees of freedom. The basis-set construction procedure is validated by comparing with virtually exact grid-based simulations for two one-dimensional model systems: laser-driven electron dynamics in a soft attractive Coulomb potential and nuclear rovibrational dynamics in a Morse potential.

Microscopic deformation and failure modes of high‐functionality epoxy resins from bond breaking molecular dynamics simulations and experimental investigation

AbstractThe material behavior of the API‐60 epoxy resin was investigated using atomistic molecular dynamics simulations. In this study, a hybrid, reactive force field (M‐GAFF2), which combined Morse and harmonic bond potentials from GAFF2, was developed to understand the elastic/plastic response of the cured epoxy polymer. We found that elastic deformation was caused by epoxy network rearrangement at low strain while plastic deformation was observed by stretching and breaking covalent bonds after the yield point. Ab initio calculations at the CASPT2(2,2)/6‐311+G** level of theory were performed to compute parameters for M‐GAFF2. These are necessary for breaking covalent bonds in the epoxy network backbone when they are deformed. The M‐GAFF2 was effective in revealing the ductile‐like deformation behavior of the crosslinked epoxy polymer at the microscopic level, including elastic/plastic deformations and progressive failure. The effect of testing temperature at 300 and 400 K and degree of cure (DoC) on tensile properties such as Young's modulus, ultimate strength, and failure strain was evaluated to verify the feasibility of the M‐GAFF2 in different thermodynamic constraints. This new approach is easy to use for nonequilibrium MD simulations and computationally efficient for studying the microscopic deformation and failure behavior of thermosetting polymers at the atomistic scale.

Molecular Dynamics Study: Correlation of Heat Conduction Across S-L Interfaces Between Constant Heat Flux and Shear Applied to Liquid Systems

Heat conduction (HC) at solid-liquid (S-L) interfaces play a significant role in the performance of engineering systems. Thus, this study investigates HC at S-L interfaces and its correlation between constant heat flux (CHF) and shear applied to liquid (SAL) systems using non-equilibrium molecular dynamics simulation. The S-L interface consists of solids with the face-centred cubic (FCC) lattice of (110), (111) and (100) planes facing the liquid. The solid is modelled by Morse potential whereas the liquid is modelled by Lennard Jones potential. The interaction between solid-liquid was modelled by Lorentz-Bertholet combining rules. The temperature and heat flux of the system is evaluated to correlate the HC at the S-L interface which reflect by the interfacial thermal resistance (ITR). The results suggest that the surfaces of FCC influence ITR at the S-L interface. The (110) surface for both cases of CHF and SAL has the lowest ITR as compared to other surfaces. In general, ITR for the case of SAL is higher than the CHF. SAL disturbs the adsorption behaviour of liquid at the S-L interfaces, thus reducing the HC. In conclusion, the surface of FCC and liquid experiencing shear do influence the characteristics of HC at the S-L interface.

Non-reversible Metastable Diffusions with Gibbs Invariant Measure II: Markov Chain Convergence

This article considers a class of metastable non-reversible diffusion processes whose invariant measure is a Gibbs measure associated with a Morse potential. In a companion paper (Lee and Seo in Probab Theory Relat Fields 182:849–903, 2022), we proved the Eyring–Kramers formula for the corresponding class of metastable diffusion processes. In this article, we further develop this result by proving that a suitably time-rescaled metastable diffusion process converges to a Markov chain on the deepest metastable valleys. This article is also an extension of (Rezakhanlou and Seo in https://arxiv.org/abs/1812.02069, 2018), which considered the same problem for metastable reversible diffusion processes. Our proof is based on the recently developed resolvent approach to metastability.

Non-relativistic molecular modified shifted Morse potential system

A shifted Morse potential model is modified to fit the study of the vibrational energies of some molecules. Using a traditional technique/methodology, the vibrational energy and the un-normalized radial wave functions were calculated for the modified shifted Morse potential model. The condition that fits the modified potential for molecular description were deduced together with the expression for the screening parameter. The vibrational energies of SiC, NbO, CP, PH, SiF, NH and Cs2 molecules were computed by inserting their respective spectroscopic constants into the calculated energy equation. It was shown that the calculated results for all the molecules agreement perfectly with the experimental RKR values. The present potential performs better than Improved Morse and Morse potentials for cesium dimer. Finally, the real Morse potential model was obtained as a special case of the modified shifted potential.

Rigid Procedure to Calculate the Melting Point of Metal Using the Solid-Liquid Phase (Coexistence) Method

Melting point, particularly metal, is one of the important data for many applications. For developing new materials, adequate theories for melting point are very crucial. The determination of melting point using the popular phase-change curve method is very easy but usually overestimate. In current work, we determine the melting point of a pure metal (iron) using the method of solid-liquid phase coexistence. For this goal, molecular dynamics simulation was applied to obtain data of trajectories of atoms. Simulation (LAMMPS) and data analysis (OVITO) procedures are strictly applied to obtain the accurate melting point of iron based on the obtained trajectories data. For initial structure design of simulation, we used the ATOMSK program. The melting point of iron obtained using the phase change curve (PCC) method is about 2750 K < TPCC < 3250 K and using the coexistence phase (CP) method is TCP = 2325 K. A more accurate calculation needs to include defects factor in the simulated material and calculation. In this research we use the Morse potential to represent all of the atomic interaction among atoms of Fe material.