Morse potentials, intermolecular

Although two-parameter models are rather restrictive, three-parameter models of the intermolecular potential have been developed which provide reasonable descriptions of the thermodynamic behavior of solids. Examples include the Morse potential, the exponential-six potential, and, more recently, a form proposed by Rose et al. (1984) for metals. 

Here Eh and a are the parameters of a normal Morse potential, and m = mh mi in the framework of the model discussed). Although this combined potential (4.3.26) provides plausible estimates, it can hardly be substantiated in terms of the theory of intermolecular interactions and contains, in addition, only biquadratic anharmonic... 

C.L. Kong. Combing Rules for Intermolecular Potential Parameters. II. Rules for the Lennard-Jones (12-6) Potential and the Morse Potential. J. Chem. Phys., 59 2464-2467,1973. 

The Lennard-Jones potential is a rather crude representation of an actual intermolecular potential, chosen more often for computational simplicity than chemical accuracy. More accurate for many chemical purposes is the Morse potential... 

The MEP for dissociation of the dimer is defined by the condition that at every intermolecular distance R, 6X and 02 take the values so as to minimize the energy the potential along this MEP is modelec by a Morse potential with De = 4.3-4.5 kcal/mol and a = 1.45-1.55 A. The onedimensional barrier for interconversion and the corresponding correlation between d2 and 0, are presented in Figure 8.11a. The concerted rotation... 

There is no strict equilibrium bond length R for the hard sphere or square well potentials, because there is no unique value of R at which the potential energy reaches a minimum. The square well, like the Morse potential, does have a dissociation energy. For intermolecular bonds, we shall label this dissociation energy (the well-depth) by e, rather than by D, which we use for dissociation of a chemical bond. 

The Morse potential itself is not a good model here, because the exponential dependence of the curve at large R is not very similar to the R power law. Instead, the Lennard-Jones 6-12 potential tends to be the model potential of choice for intermolecular interactions ... 

The semiempirical methods combine experimental data with theory as a way to circumvent the calculational difficulties of pure theory. The first of these methods leads to what are called London-Eyring-Polanyi (LEP) potential energy surfaces. Consider the triatomic ABC system. For any pair of atoms the energy as a function of intermolecular distance r is represented by the Morse equation, Eq. (5-16),... 

We are now prepared to set down the effective quantum numbers for use of the selection rule expression of eq. 5. Application of the analytical expression for vibrational predissociation rates of A-B C for a wide variety of van der Waals molecules bound by Morse intermolecular potential functions like those shown in Fig. 2 reveals the effective translational quantum number change... 

We obtain Rg Cr) after specifying the form of the intermolecular potential for A-H B which we will approximate by the Morse function of equation (2). The analytical form of the R (r) Morse oscillator wavefunction is given elsewhere.An example of Ro(r) i.e. for the u =0 level) together with V(r) for a typical A-H B complex is shown in Fig. 5. One can see that RqCt) resembles an harmonic oscillator wavefunction which is localized near the van der Waals bond length. 

F. A. Morse, R. B. Bernstein, and H. U. Hostettler, Evaluation of the intermolecular potential well depth from observations of rainbow scattering Cs-Hg and K-Hg, J. Chem. Phys. 36 1947 (1962). 

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