Modified Morse potential

The attractive energies 4D(cr/r)6 and ae2/2 r4 have two important effects on the vibrational energy transfer (a) they speed up the approaching collision partners so that the kinetic energy of the relative motion is increased, and (b) they modify the slope of the repulsive part of the interaction potential on which the transition probability depends. By letting m °°, we have completely ignored the second effect while we have over-emphasized the first. Note that Equation 12 is identical to an expression we could obtain when the interaction potential is assumed as U(r) = A [exp (— r/a)] — (ae2/2aA) — D. Similarly, if we assume a modified Morse potential of the form... 

Other three-parameter functions can be used, and the same relationship between E and AE can be derived—e.g., Varshnis second potential function, which is a modified Morse potential (21) and Linnetts mixed exponential and inverse power of the internuclear distance (12). 

Starting from the modified Morse potential of Chiu, et al., the new water forcelield is optimized using the bulk NVT and NPT states and the interfacial state. This potential is chosen as the initial starting guess, rather than an arbitrary starting point. 

The atomistic methods usually employ atoms, molecules or their group and can be classified into three main categories, namely the quantum mechanics (QM), molecular dynamics (MD) and Monte Carlo (MC). Other atomistic modeling techniques such as tight bonding molecular dynamics (TBMD), local density (LD), dissipative particle dynamics (DPD), lattice Boltzmann (LB), Brownian dynamics (BD), time-dependent Ginzbuig-Lanau method, Morse potential function model, and modified Morse potential fimction model were also applied afterwards. 

Modified Morse Potentials and Tersoff-Breimer potential 1.08 Predicting the elastic properties of SWCNTs based on the classical Cauchy-Bom rule... 

It is difficult to point to the basic reason why the average-potential model is not better applicable to metallic solutions. Shimoji60 believes that a Lennard-Jones 6-12 potential is not adequate for metals and that a Morse potential would give better results when incorporated in the same kind of model. On the other hand, it is possible that the main trouble is that metal solutions do not obey a theorem of corresponding states. More specifically, the interaction eAB(r) may not be expressible by the same function as for the pure components because the solute is so strongly modified by the solvent. This point of view is supported by considerations of the electronic models of metal solutions.46 The idea that the solvent strongly modifies the solute metal is reached also through a consideration of the quasi-chemical theory applied to dilute solutions. This is the topic that we consider next. 

For comparison with our results in table 3, which presents values of 20 adjusted parameters with 15 parameters constrained to define the rotational g factor, Dulick et alii [115] required also 20 adjusted parameters, with a constrained parameter T> for the equilibrium binding energy for a function of potential energy having a modified Morse form. The latter parameter is specified as... 

A postulated advantage of accurate prediction of wave numbers of transitions far above the measured range through representing potential energy in a modified Morse form is plainly illusory. 

The above data have been analyzed theoretically within the same model as described for the chemical shift tensor (5iso In order to understand the chemical shift observed within the KDP family, we concentrate here on the polarizability modified double-well potential of the protons, which has been modelled by two back-to-back Morse potentials (see Chap. 1 in this volume). The separation between the protons and the centre of the left (/) or right (r) PO4 shell... 

The author examines with success the efficiency of the methods by their applications to bound states for the one-dimensional harmonic oscillator, anharmonic oscillators, the Morse potential, and the modified Poschl-Teller potential in quantum mechanics. 

The authors in this paper present an explicit symplectic method for the numerical solution of the Schrodinger equation. A modified symplectic integrator with the trigonometrically fitted property which is based on this method is also produced. Our new methods are tested on the computation of the eigenvalues of the one-dimensional harmonic oscillator, the doubly anharmonic oscillator and the Morse potential. 

Electronic levels and vibrational constants are based on the review of Rosen (1 ) as modified by the additional data of Novikov and Gurvich (7 ). Vibrational constants are adjusted for natural isotopic abundances. B is calculated from r which is estimated by comparison of the bond lengths of MX2(M-Mg, Ca, Sr, Ba and X=F, Cl) with those of MgCl, CaCl and MF(M Mg, Ca, Sr, Ba). The value of is estimated from the Morse potential function. 

Figure 2.4 Classification of negative-ion Morse potential energy curves originally presented by Herschbach in 1966. The curves are calculated from actual data. The empty spaces are impossible combinations. These classifications have been modified so that they are symmetrical and all combinations are possible [34, 36].

Figure 7.11 Original Hershbach ionic morse potential energy curves and the modified HIMPEC [2, 3], The curves are calculated for the current best available data. The multiple curves for 02(—) and I2( ) are given to illustrate the relative positions of the curves. The specific example is the curve that is solid.

Herschbach ionic Morse potential energy curves. A classification of negative-ion potential energy curves originally proposed by Herschbach and recently modified. 

Dimensionless constant that modifies the attraction of the Morse potential of anions. 

The most frequently used model potentials are Rigid sphere, point center of repulsion, Sutherland s model, Lennard-Jones potential, modified Buckingham potential, Kihara potential, Morse potential. Their advantages and disadvantages are thoroughly discussed elsewhere [39] [28]. 

A somewhat modified version of the Morse potential was proposed [7] in the... 

Modified Hooke s law corrected with cubic (as in the MM2-based force fields [8]) and further extensions to quartic terms (as in MM3 [9], CFF [10], and MMFF [11] force fields see Eq. (3) [9]) or other expansions [12] have been developed to mimic the Morse potential and are used to speed up convergence in very distorted starting geometries, while keeping a proper description of the potential energy. 

Le Roy et al. [OSRloy] give an alternative treatment of the frequency data (Direct-potential fit) which is based on the eigenvalues of the radial Schrddinger equation. The potential is expressed in form of a modified Morse function where the exponent is written in form of a power series expansion. The coefficients and those in the non-adiabatic correction terms are determined in a direct fit to the experimental eigenvalue differences, see [05Roy] for details and results. 

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