Morse dissociation energy

The Morse oscillator model is often used to go beyond the harmonic oscillator approximation. In this model, the potential Ej(R) is expressed in terms of the bond dissociation energy Dg and a parameter a related to the second derivative k of Ej(R) at Rg k = ( d2Ej/dR2) = 2a2Dg as follows ... 

C d Hie dissociation energy of die pure covalent Morse potential... 

It is also assumed that the repulsive terms in the two Morse curves are approximately the same, leading to an equation that relates the difference in the equilibrium distances to the ratio of the dissociation energies ... 

The three parameters in the Morse function D, B, re are positive and are usually chosen to fit the bond dissociation energy, the harmonic vibrational frequency and the equilibrium bond length. At r = re, the Morse function V = 0. As r — D, V approaches D. For r re, V is large and positive, corresponding to short range repulsion. Although the Morse function has been used extensively, its representation of the potential away from re is not satisfactory. Several modifications have been proposed in Morse function. 

Figure 1.3 Potential curve of a molecule (ground state of HC1). The full curve is the Morse potential of Eq. (1.6). The dashed curve is the harmonic approximation. De is the dissociation energy, and re is the equilibrium separation.

Fig. 4 Morse curves of the reactants and products at zero driving force (z is the elongation of the RX distance from equilibrium, P = V(,(2Jt p/ )Rx) with Vq representing the vibration frequency, p the reduced mass of the two atoms of the R—X bond, and the RX bond dissociation energy).

Even for potential energy the other approach [93] required one parameter additional to oiu-s, apart from Dq, the latter quantity, equilibrium binding energy, is stated to be based on thermochemical data, but the cited source [95] indicates a value of dissociation energy 29q <2.84eV to arise from spectral analysis. Such an upper limit must be understood to provide an asymptotic limit for V(i ) at large i in a formula of Morse type because an attempted evaluation of 29e from only infrared spectral data is unreliable. The stated reason for the choice... 

Morse potential phys chem An approximate potential associated with the distance r between the nuclei of a diatomic molecule in a given electronic state it is V(r) = D 1 - expl - a(r - rj where q is the equilibrium distance, D is the dissociation energy, and n is a constant. mors po.ten-chol mosaic gold See stannic sulfide. mo za-ik. gold ... 

Here, De is the bond dissociation energy, re is the equilibrium bond length, and a is a constant that characterizes the steepness of the potential and determines the vibrational frequencies. The advantage of using the Morse potential to improve upon harmonic-oscillator-level predictions is that its energy levels and wavefunctions are also known exactly. The energies are given in terms of the parameters of the potential as follows ... 

The initial exploration in this unit requires the students to compare the trajectories calculated for several different energies for both Morse oscillator and harmonic oscillator approximations of a specific diatomic molecule. Each pair of students is given parameters for a different molecule. The students explore the influence of initial conditions and of the parameters of the potential on the vibrational motion. The differences are visualized in several ways. The velocity and position as a function of time are plotted in Figure 2 for an energy approximately 50% of the Morse Oscillator dissociation energy. The potential, kinetic and total energy as a function of time are plotted for the same parameters in Figure 3. 

Figure 2. Internuclear separation (top panel) and velocity (bottom panel) as a function of time for a Morse (dashed line) and harmonic (solid line) oscillator having the same total energy, ca. 50% of the dissociation energy of the Morse potential. Note the rapid change in velocity at the inner turning point and slow change in velocity at the outer turning point for an anharmonic oscillator.

Fig. 9.30. Morse curves for the reactants and products at zero driving force (v, elongation of the R-X distance from the equilibrium B = iz (2jt2p /Drx)1/2 uq, vibration frequency p, reduced mass Dm, bond dissociation energy). (Reprinted with permission of J. M. Saveant, J. Am. Chem. Soc. 109 6788 copyright 1992 American Chemical Society.)...

The attractive Morse potential has three variable parameters which can be fitted to the dissociation energy, the harmonic force constant and the equilibrium distance. The hi er force constants are then in error, but zsHulburt mdHirschfelder 123) showed these can be corrected by multiplying the repulsive part of the potential by a polynomial as follows... 

It is possible to set up a. similar empirical model based on a Morse function. However the Morse function gives a poor correlation of bond length with vibrational frequency and dissociation energy whereas the internuelear potential function used here gives a much better correlation of these quantities, which I feel is the reason for the usefulness of the function in describing hydrogen bond properties,... 

Figure 10.5—Morse diagram. The segments within the boundaries of the envelope show the possible energy levels of the bond. This envelope also explains the significant increase of the bond length x as its energy approaches the level of the dissociation energy.

Figure 2 depicts the vibrogram corresponding to the dynamics on the ground state of iodine, modeled by a Morse potential with the equilibrium distance r = 2.67 A and the dissociation energy D = 12,542 cm 1 [14, 108]. The periodic orbit and its repetitions clearly appear in the vibrogram. The classical... 

Note that the value of the anharmonicity constant can thus be derived from a comparison between the fundamental n = 0 to n = 1 absorption band frequency and the first and subsequent overtone band positions. Given the form of the Morse Curve, Xe can be calculated from De, and hence an estimate of the bond dissociation energy... 

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