Potential, centrifugal Morse

The two cases which arise in diatomic molecules are rotational predissociation and electronic predissociation the latter case applies only to excited electronic states. We deal first with rotational predissociation, with can arise for either ground or excited states. The potential energy curve shown for a Morse oscillator in section 6.8 is for a rotationless (./ = 0) molecule. For a rotating molecule, however, we must add a centrifugal term to the potential,... 

Figure 6.27. Morse potential for J = 0 and J = 10, showing the presence of the centrifugal barrier in the J = 10 case, and a quasibound level, QB.

The microwave experiment studies rotational structure at a given vibrational level. The spectra are analyzed in terms of rotational models of various symmetries. The vibration of a diatomic molecule is, for instance, approximated by a Morse potential and the rotational frequencies are related to a molecular moment of inertia. For a rigid classical diatomic molecule the moment of inertia I = nr2 and the equilibrium bond length may be calculated from the known reduced mass and the measured moment, assuming zero centrifugal distortion. 

These estimates bracket the NASA-JPL and lUPAC recommendations of 6.5x10 and 7.7 x 10 cm molecule s [9,60]. It is therefore possible fo reconcile fhe thermochemistry proposed here with the observed lO + NO2 recombination kinetics while employing reasonable input parameters for the unimolecular model. Nevertheless it must be stressed, as emphasized earlier [16], that there is considerable uncertainty in some of the input parameters to an RRKM analysis, especially the Frot term. It is of interest to compare the present kinetic calculations with the Multiwell [61] Master Equation calculations on this system by Golden [16]. He used a Morse potential to locate the centrifugal maximum, and from the bond extension Frot 2.1 is derived, about 1/7 of fhaf used here. On the other hand, the higher Eo value yields a density of sfafes larger by a facfor of 6, and fhese two factors largely cancel. 

Moments of inertia at fixed geometries are calculated by changing only the bond distance in the reaction coordinate. The potential energy surface along the reaction coordinate is modeled by a Morse function including the centrifugal barrier [48]... 

Fig. 5.14. Quantum defect plots for the centrifugally distorted nf series in Ba+ (a) shows the ordinary QDT plot, while (b) shows the plot obtained from the same experimental data using the generalised theory in the text. Note that the lowest point in the nf channel lies off the graph this is normal, since it has no node except at the origin and the corresponding wavefunction lies mostly in the non-Coulombic part of the potential (c) shows how the energy of the bound state can also be obtained by fitting a Morse potential to the Hartree-Fock potential of the inner well (after J.-P. Connerade [217]).

Another system which has been treated in a rather complete manner is the dissociation of HOOH (Brouwer et al., 1987). The rates as well as the product energy distributions were calculated. As with the NO2 reaction, the interaction potential was assumed to have no barriers so that Ef for each HOOH reaction channel is assumed to be associated with the centrifugal barrier. In order to calculate this barrier, the reaction is treated as a triatomic dissociation, ABC AB + C. The effective rotational constant, at the centrifugal barrier is calculated according to formulas derived by Troe (1983). In addition, the model was simplified by replacing two adjustable parameters, a (from the interpolation function) and B (from the Morse potential), by their ratio, a/p. A value of 0.44 was found to adequately account for the data. Figure 7.25 shows the comparison of the SACM k E) curves with those obtained from experiments or trajectory calculations. 

Let us try this. An ideal experimental range for us would be a molecule with a Morse-like potential energy (p. 169), because here the problem is exactly solvable, yet preserves some important realistic features (e.g., dissociation). Unfortunately, evenif we approximated Uk(R) = E j R) + H j j R) by a Morse curve, after adding the centrifugal term J J + l)h /(l/juR ) the curve will no longer be of the... 

---