Morse Potential Energy Research Articles

The statistical properties of q-deformed Morse potential for some diatomic molecules via Euler–MacLaurin method in one dimension

In this paper, we present a closed-form expression of the vibrational partition function for the one-dimensional q-deformed Morse potential energy model. Through this function, the related thermodynamic functions are derived and studied in terms of the parameters of the model. Especially, we plotted the q-deformed vibrational partition function and vibrational specific heat for some diatomic molecule systems such as \(\text {H}_{2}\), HCl, LiH, and CO. The idea of a critical temperature \(T_{C}\) is introduced in relation to the specific heat.

Nonadiabatic Dynamics via the Symmetrical Quasi-Classical Method in the Presence of Anharmonicity.

The symmetrical quasi-classical (SQC) method recently proposed by Miller and Cotton allows one to simulate nonadiabatic dynamics based on an algorithm with classical-like scaling with respect to system size. This is made possible by casting the electronic degrees of freedom in terms of mapping variables that can be propagated in a classical-like manner. While SQC was shown to be rather accurate when applied to benchmark models with harmonic electronic potential energy surfaces, it was also found to become inaccurate and to suffer numerical instabilities when applied to anharmonic systems. In this paper, we propose an extended SQC (E-SQC) methodology for overcoming those discrepancies by describing the anharmonic nuclear modes, which are coupled to the electronic degrees of freedom, in terms of classical-like mapping variables. The accuracy of E-SQC relative to standard SQC is demonstrated on benchmark models with quartic and Morse potential energy surfaces.

A convenient and accurate wide-range parameter relationship between Buckingham and Morse potential energy functions

ABSTRACTThis study explores the close-range, short-range and long-range relationships between the parameters of the Morse and Buckingham potential energy functions. The results show that the close-range and short-range relationships are valid for bond compression and for very small changes in bond length, respectively, while the long-range relationship is valid for bond stretching. A wide-range relationship is proposed to combine the comparative advantages of the close-range, short-range and long-range parameter relationships. The wide-range relationship is useful for replacing the close-range, short-range and long-range parameter relationships, thereby preventing the undesired effects of potential energy jumps resulting from functional switching between the close-range, short-range and long-range interaction energies.

Application of Morse potential in nonlinear dynamics of microtubules

We here present a model of nonlinear dynamics of microtubules using modified extended tanh-function method as a mathematical tool. Interaction between neighbouring dimers belonging to a single protofilament is commonly modelled by a harmonic potential. In this paper, we introduce a more realistic Morse potential energy instead. We obtained three solitary waves as before, when the harmonic potential was used. However, the Morse potential allows transition from the state when elastic term in the expression for total energy is bigger than the inertial one to the state when the inertial potential is bigger. Also, three new solutions were obtained.

Insights into reactive scattering of Pu + H2 at low energies

The corrosion of metal interfaces, due to continuous exposure to gaseous hydrogen atmosphere, significantly limits the applications of plutonium-based nuclear materials in the related fields. In this work, we simplify the situations by considering the fundamental reactions of Pu atom with a single H2 molecule, and investigate from a theoretical perspective collision dynamics of Pu + H2 at low energies based on ab initio potential energy surfaces. Trajectory calculation analysis shows that three main channels, the formation of the PuH2, the PuH fragment, and the fragmentation, exhibit different energy-dependent cross sections, from which we observed that the PuH2 formation is non-threshold reaction, whereas the other two channels are featured by pronounced threshold effects, which is in consistent with experimental observations. In addition, we find that three-body effects can play a decisive role in the reactions since the simplified Morse potential energy surfaces can even yield spurious results in some situations.

Studies on complex π-π and T-stacking features of imidazole and phenyl/p-halophenyl units in series of 5-amino-1-(phenyl/p-halophenyl)imidazole-4-carboxamides and their carbonitrile derivatives: Role of halogens in tuning of conformation

5-amino-1-(phenyl/p-halophenyl)imidazole-4-carboxamides (N-phenyl AICA) (2a-e) and 5-amino-1-(phenyl/p-halophenyl)imidazole-4-carbonitriles (N-phenyl AICN) (3a-e) had been synthesized. X-ray crystallographic studies of 2a-e and 3a-e had been performed to identify any distinct change in stacking patterns in their crystal lattice. Single crystal X-ray diffraction studies of 2a-e revealed π-π stack formations with both imidazole and phenyl/p-halophenyl units in anti and syn parallel-displaced (PD)-type dispositions. No π-π stacking of imidazole occurred when the halogen substituent is bromo or iodo; π-π stacking in these cases occurred involving phenyl rings only. The presence of an additional T-stacking had been observed in crystal lattices of 3a-e. Vertical π-π stacking distances in anti-parallel PD-type arrangements as well as T-stacking distances had shown stacking distances short enough to impart stabilization whereas syn-parallel stacking arrangements had got much larger π-π stacking distances to belie any syn-parallel stacking stabilization. DFT studies had been pursued for quantifying the π-π stacking and T-stacking stabilization. The plotted curves for anti-parallel and T-stacked moieties had similarities to the ‘Morse potential energy curve for diatomic molecule’. The minima of the curves corresponded to the most stable stacking distances and related energy values indicated stacking stabilization. Similar DFT studies on syn-parallel systems of 2b corresponded to no π-π stacking stabilization at all. Halogen-halogen interactions had also been observed to stabilize the compounds 2d, 2e and 3d. Nano-structural behaviour of the series of compounds 2a-e and 3a-e were thoroughly investigated.

Photoelectron recoil in CO in the x-ray region up to 7 keV

Carbon $1s$ photoelectron spectra of CO molecules in gas phase were recorded in the tender x-ray energy range, from 2.3 to 6.9 keV. The intensity ratios of individual peaks from $\ensuremath{\nu}=0$ to 3 within the vibrational progression of the C $1s$ photoelectron spectrum were determined at the various photon energies and are shown to be strongly affected by the photoelectron recoil effect. The experimental vibrational intensity ratios are compared with theoretical predictions at different levels of accuracy. Developments of the recoil model, using generalized Franck-Condon factors, rovibrational coupling, Morse potential energy curves, and accurate angular averaging are presented and applied to the analysis of the experimental results.

Mass spectrometric determination of Morse parameters for the fifty-four superoxide states dissociating to the lowest limit.

Superoxide is the most significant homonuclear diatomic anion in biochemistry. Theory predicts 12 doublet (X, A-K) and 12 quartet (a-l) electronic states split by spin orbital coupling into 54 states dissociating to the (3) P(O) + (2) P(O(-) ) limit. Dissociation energies for the 27 bonding states with positive electron affinities have been determined from mass spectrometric data. However, the 27 antibonding states with negative electron affinities have not been experimentally characterized. The electron affinity of the hydrogen atom per electron, the Hylleraas, is the fundamental measure of electron correlation. It has been used to assign and evaluate experimental electron affinities of atoms and diatomic molecules. The 27 negative electron affinities of oxygen are estimated from the 27 positive values and the Hylleraas. These values are used to determine frequencies and internuclear separations by fitting theoretical electron impact distributions to the gas-phase mass spectrometric atomic oxygen anion distribution peaking at about 6.5 eV. The dissociation energies, internuclear distances and frequencies giving the first complete set of Morse potential energy curves for the 54 superoxide states dissociating to the lowest limit are reported from mass spectrometric data. The potentials are compared to theoretical and empirical literature curves. The existence of the 27 bonding and 27 antibonding spin orbital coupling superoxide states dissociating to (3) P(O) + (2) P(O(-) ) is established from mass analyzed thermal, photon, and electron ionization data. There are electron affinities from 0 to 0.15 eV, and onsets and peaks for dissociative electron attachment that cannot be explained by the 54 states. These support the existence of the 36 superoxide spin states dissociating to [(1) D(O) + (2) P(O(-) )] and [(1) S(O) + (2) P(O(-) )] predicted by quantum mechanics. Copyright © 2016 John Wiley & Sons, Ltd.

Solutions of the Dirac equation with the Morse potential energy model in higher spatial dimensions

Analytical solutions of the Dirac equation with the Morse potential energy model in higher spatial dimensions have been explored. We present the bound-state energy equation and the corresponding upper and lower radial wave functions. We find that the behavior of the higher-dimensional relativistic vibrational energies remains similar to that of the three-dimensional molecular system for the \( {\rm X}^2\sum^+\) state of the CP molecule. This symmetry phenomenon will break at the critical point through which the system undergoes a phase transition from a stable to an unstable state.

Prediction of Molecular Interaction between Platelet Glycoprotein Ibα and von Willebrand Factor using Molecular Dynamics Simulations.

The molecular mechanism of the unique interaction between platelet membrane glycoprotein Ibα (GPIbα) and von Willebrand Factor (VWF), necessary for platelet adhesion under high shear stress, is yet to be clarified. The molecular dynamics simulation using NAMD (Nanoscale Molecular Dynamics) package with the CHARMM 22 (Chemistry at Harvard Macromolecular Mechanics) force field were used to predict dynamic structural changes occurring in the binding site of A1 domain of VWF and N terminus domain of GPIbα under water soluble condition. The mean distance between the mass center of A1 domain of VWF and GPIbα in the stable form was predicted as 27.3 Å. The potential of mean force between the A1 domain of VWF and GPIbα were calculated in conditions of various distances of the mass center between them. All the calculated values were fitted to the Morse potential energy function curve. The maximum adhesive force between A1 domain of VWF and GPIbα was predicted as 62.3 pN by differentiating the potential of mean force with respect to the molecular distance. The molecular dynamics simulation is useful for predicting the dynamic structure changes of protein bonds involved in platelet adhesion and for predicting the adhesive forces generated between their interactions.

A combined DFT/HREELS study of the vibrational modes of terphenylthiol SAMs

Self-assembled monolayers of p-terphenylthiol (TPT, HS-(C6H4)2-C6H5) deposited onto gold can serve as model systems for aromatic lithography resists. Such thin molecular films are suitably probed using high resolution electron energy loss spectroscopy, due to its high surface sensitivity. Extended energy loss spectra were measured at different probing energies. The TPT monolayer overlapping ν(CH) stretching modes could be modelled by a single effective anharmonic oscillator sustained by a Morse potential energy curve, thanks to the resonant excitation of the associated overtone series at 6 eV. A remarkably good agreement was obtained between the TPT monolayer energy loss spectrum and the computer-simulated infrared vibrational spectrum of the isolated TPT molecule. Density Functional Theory calculations for TPT, fully deuterated TPT and benzenethiol isolated molecules were performed with the exchange correlation functional B3LYP and a dispersion correction, using a triple ζ+ polarisation basis set. By comparing the vibrational patterns obtained for these parent systems, (re-)assignments of all the features observed in the TPT self-assembled monolayer energy loss spectrum are discussed. The obtained vibrational assignments can be confidently transposed to other related systems, such as benzenethiol and biphenyl self-assembled monolayers.

Studies on the π–π stacking features of imidazole units present in a series of 5-amino-1-alkylimidazole-4-carboxamides

Reaction of 2-ethoxymethyleneamino-2-cyanoacetamide with primary alkyl amines in acetonitrile solvent affords 1-substituted-5-aminoimidazole-4-carboxamides. Single crystal X-ray diffraction studies of these imidazole compounds show that there are both anti-parallel and syn-parallel π–π stackings between two imidazole units in parallel-displaced (PD) conformations and the distance between two π–π stacked imidazole units depends mainly on the anti/ syn-parallel nature and to some extent on the alkyl group attached to N-1 of imidazole; molecules with anti-parallel PD-stacking arrangements of the imidazole units have got vertical π–π stacking distance short enough to impart stabilization whereas the imidazole unit having syn-parallel stacking arrangement have got much larger π–π stacking distances. DFT studies on a pair of anti-parallel imidazole units of such an AICA lead to curves for ‘π–π stacking stabilization energy vs. π–π stacking distance’ which have got similarity with the ‘Morse potential energy diagram for a diatomic molecule’ and this affords to find out a minimum π–π stacking distance corresponding to the maximum stacking stabilization energy between the pair of imidazole units. On the other hand, a DFT calculation based curve for ‘π–π stacking stabilization energy vs. π–π stacking distance’ of a pair of syn-parallel imidazole units is shown to have an exponential nature.

Solutions of the Klein–Gordon equation with the Morse potential energy model in higher spatial dimensions

We solve the Klein–Gordon equation with the Morse potential energy model to obtain the relativistic bound state energy equation in D spatial dimensions. We find that the inter-dimensional degeneracy symmetry exists for the molecular system represented by the Morse potential model. For a fixed vibrational quantum number and various rotational quantum numbers, the relativistic energies for the X1Σ+ state of the ScI molecule diverge as D increases. We observe that the behavior of the relativistic vibrational energies in higher dimensions remains similar to that of the three-dimensional system.

Molecular spinless energies of the modified Rosen–Morse potential energy model in higher spatial dimensions

We solve the Klein–Gordon equation with the modified Rosen–Morse potential energy model in D spatial dimensions. The bound state energy equation has been obtained by using the supersymmetric WKB approximation approach. We find that the inter-dimensional degeneracy symmetry exists for the molecular system represented by the modified Rosen–Morse potential. For fixed vibrational and rotational quantum numbers, the relativistic energies for the 61Πu state of the 7Li2 molecule and the X3Π state of the SiC radical increase as D increases. We observe that the behavior of the relativistic vibrational energies in higher dimensions remains similar to that of the three-dimensional system.

D-dimensional energies for lithium dimer and silicon carbide radical

By using the supersymmetric shape invariance approach, we solve the Schrödinger equation with the modified Rosen–Morse potential energy model in D spatial dimensions. We find that the inter-dimensional degeneracy symmetry exists for the molecular system represented by the modified Rosen–Morse potential energy model. The rotation-vibrational energies for the 61Πu state of the 7Li2 molecule and the X3Π state of the SiC radical are observed to increase as D increases in the presence of a fixed vibrational quantum number and rotational quantum number. It is found that the behavior of the vibrational energies in higher dimensions remains similar to that of the three-dimensional system for these two molecular states.

D-dimensional energies for scandium monoiodide

We solve the Schrodinger equation with the Morse potential energy model in \(D\) spatial dimensions. The bound state rotation–vibrational energy spectra have been obtained by using the supersymmetric shape invariance approach. For a fixed vibrational quantum number and various rotational quantum numbers, the energies for the \(\hbox {X}^{1}\Sigma ^{+}\) state of ScI molecule increase as \(D\) increases. We observe that the behavior of the vibrational energies in higher dimensions remains similar to that of the three-dimensional system. The dimensional scaling method resembles a translation transformation from the higher dimensions to the actual three dimensions.

Universal scaling of potential energy functions describing intermolecular interactions. I. Foundations and scalable forms of new generalized Mie, Lennard-Jones, Morse, and Buckingham exponential-6 potentials.

Based on the formulation of the analytical expression of the potential V(r) describing intermolecular interactions in terms of the dimensionless variables r* = r/r(m) and ɛ* = V/ɛ, where r(m) is the separation at the minimum and ɛ the well depth, we propose more generalized scalable forms for the commonly used Mie, Lennard-Jones, Morse, and Buckingham exponential-6 potential energy functions. These new generalized forms have an additional parameter from the original forms and revert to the original ones for some choice of that parameter. In this respect, the original forms of those potentials can be considered as special cases of the more general forms that are introduced. We also propose a scalable, non-revertible to the original one, 4-parameter extended Morse potential.

D-dimensional energies for cesium and sodium dimers

We solve the Schrödinger equation with the improved Rosen−Morse potential energy model in D spatial dimensions. The D-dimensional rotation-vibrational energy spectra have been obtained by using the supersymmetric shape invariance approach. The energies for the 33[Formula: see text]g+ state of the Cs2 molecule and the 51Δg state of the Na2 molecule increase as D increases in the presence of fixed vibrational quantum number and various rotational quantum numbers. We observe that the change in behavior of the vibrational energies in higher dimensions remains similar to that of the three-dimensional system.

Diatomic molecule energies of the modified Rosen−Morse potential energy model

We solve the Schrödinger equation with the modified Rosen−Morse empirical potential model to obtain rotation-vibrational energy spectra and unnormalized radial wave functions. The vibrational energy levels calculated with the modified Rosen−Morse potential model for the 61Πu state of the 7Li2 molecule and the X3Π state of the SiC radical are in better agreement with the Rydberg−Klein−Rees data than the predictions of the Morse potential model.

A study on predicting coalbed methane production depending on reservoir properties

This paper presents a study on predicting coalbed methane (CBM) production based on reservoir properties. Two hundred numerical models with different reservoir properties which are generated by a Monte Carlo method are numerically simulated using a compositional simulator. Empirical equations are built to estimate the gas recovery, peak gas rate, time to peak gas rate and gas production decline rates by analysing the relationships between reservoir properties and gas production rates. The peak gas rate, time to peak gas rate and gas production decline rates are used in the rate–time fit equation to predict the gas production rate. Results show that the combination of the modified Morse potential energy equation and the exponential decline equation can be used to fit the gas production for the entire production period of CBM wells. The regression coefficients between the calculated and numerical simulated gas recovery, logarithmic peak gas rate and logarithmic time to peak gas rate are 0.82, 0.86 and 0.80, respectively. New relationships between the time to peak gas rate and the decline parameters are presented in this paper.