Quasi-diatomic model

Even though the dissociation process is not direct, predissociation is fast enough that the essential elements of the rotational distribution are explained by a quasi-diatomic model. 

One of the earliest models is the quasi-diatomic model (10-13). This model is based on the assumption that the normal modes describing the state(s) of the photofragments are also the normal modes of the precursor molecule. This means, for example, that in the photodissociation of a linear triatomic molecule ABC A + BC (e.g., photodissociation of ICN - I + CN), the diatomic oscillator BC is- assumed to be a normal mode vibration in the description of the initial state of the triatomic molecule ABC. This means that the force constant matrix describing the vibrational motion of the molecule ABC can be written in the form (ignoring the bending motion) ... 

Most of the theoretical papers dealing with the photodissociation of polyatomic molecules are included in Table 9 under specific headings. Lee et introduced the multidimensional reflection (MR) approximation to replace the quasi-diatomic model often used in the theoretical descriptions of polyatomic molecule photodissociation. They utilized the results of the MR approximation to examine the dependence of the extinction coefficient on i max— V, where is the frequency of maximum absorption, to obtain the slope and orientation of the co-ordinate of steepest descent on the upper state surface and to explain the dependence of the absorption cross-section from initially excited vibrational states on the orientation of this co-ordinate. 

X 10 s, assuming a quasi-diatomic model for the rotating photo-excited parent molecule. 

The direct dissociation as discussed for ICN is also observed in other reactions. However, once we go beyond a quasi-diatomic model, the motion of the other degrees of freedom needs to be addressed. 

When the quasi-diatomic Franck-Condon model was compared with the experimental results it was found that it could predict the observed vibrational distribution as well as the observation that the translational energy is much greater than the rotational energy. The theory could not, however, predict the observed proportionality between the average rotational energy and the available energy. A simple classical description of the impulsive dissociation of a rotating molecule does predict this observed linear proportionality. 

Note that in a sudden transition, eq. 3 is a more general relation than the Golden role (see, e.g., reference 15). In that circumstance the Golden rule appears as a special case of the FC factor, corresponding to small V and the applicability of perturbation theory. In order to evaluate the FC factor, Berry used the dressed oscillator model which, in principle, coincides with the previously described quasi-diatomic method. 

A widely-used model in this class is the direct-interaction with product repulsion (DIPR) model [173—175], which assumes that a generalised force produces a known total impulse between B and C. The final translational energy of the products is determined by the initial orientation of BC, the repulsive energy released into BC and the form of the repulsive force as the products separate. This latter can be obtained from experiment or may be assumed to take some simple form such as an exponential decay with distance. Another method is to calculate this distribution from the quasi-diatomic reflection approximation often used for photodissociation [176]. This is called the DIPR—DIP model ( distributed as in photodissociation ) and has given good agreement for the product translational and rotational energy distributions from the reactions of alkali atoms with methyl iodide. 

The preceding presentation describes how the collision impact parameter and the relative translational energy are sampled to calculate reaction cross sections and rate constants. In the following, Monte Carlo sampling of the reactant s Cartesian coordinates and momenta is described for atom + diatom collisions and polyatomic + polyatomic collisions. Initial energies are chosen for the reactants, which corresponds to quantum mechanical vibrational-rotational energy levels. This is the quasi-classical model [2-4]. 

The earliest interfragment model was developed by Holdy, Klotz, and Wilson and its predictions were compared with the then available data for the near u.v. photodissociation of ICN (though these have since been questioned, see section S). Like many of the models which followed it, both semi-classical and quantum mechanical, it incorporated the quasi-diatomic approximation. This assumed that the molecular vibrational motion could be separated into pure bond vibrations, and that in the dissociation of a triatomic molecule, e.g. 

In 1973 Simons and Tasker combined the two distinct approadies into a single model which retained the quasi-diatomic approximation, but assumed... 

The energy disposal and effective upper state lifetimes have been reproduced using classical trajectory calculations a quasi-diatomic assumption was made to determine the slope of the section through the upper potential energy surface along the N—a bond from the shape of the u.v. absorption profile. The only adjustable parameter was the assumption of a parallel transition in the quasi-diatomic molecule. In contrast, a statistical adiabatic channel model which assumed dissociation via unimolecular decomposition out of vibrationally and rotationally excited level in the ground electronic state (following internal con-... 

It is generally believed that the polarizabilities of monatomic ions and molecules are independent of field direction. For undistorted quasi-spherical molecules (e.g. CH4, CC14, etc.) the same is usually assumed. When two such atoms are held together, as in a diatomic molecule, the new system is not isotropically polarizable. The model discussed by Silberstein (1917) makes this understandable. If a unit field acts along the line of centres A-B it will induce primary moments parallel to itself in both A and B, and likewise if it acts at 90° to A-B. Each primary moment will induce a secondary moment in its neighbour in the first case the secondary moments will add to the primary moments, but in the second they will subtract. Hence b along the line of centres exceeds that across it, and the polarizability of A-B is an anisotropic property. A similar situation is to be expected with the majority of polyatomic ions or molecules (see Table 21). 

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