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) ... 

The low frequency (vw 100 cm-1) stretching force constants, k , in Table 6 are in all cases, except HCN HF and CH3CN HF, calculated from the centrifugal distortion parameter, Dj, using a pseudo-diatomic model in which the monomers of the complex are treated as point masses m, and m2 ... 

At liquid-helium temperatures, hydrogenated ZnO samples exhibit an 0-H stretch mode at a frequency of 3326 cm at liquid-helium temperatures (Fig 1). The IR peak corresponding to this mode broadens and shifts to higher frequency when the sample is warmed to room temperature. Deuterated ZnO samples, at liquid-helium temperatures, have an 0-D stretch mode at 2470 cm . The ratio of the 0-H and 0-D frequencies are in good agreement with a simple diatomic model. More importantly, the frequency ratio is nearly identical to that of 0-H and 0-D complexes in GaP. ° Our observed 0-H mode is different from those observed by Lavrov et al. and Nickel and Fleischer. ... 

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. 

Figure 9.2 Diatomic model of molecular vibration. The centre of gravity does not change during the stretching vibration.

It is helpful to have basic knowledge of the relationship between vibrational frequencies and bond strength and atomic masses. We may use the relationship in understanding and assigning positions of characteristic bands in spectra. This relationship can be illustrated with the simplest vibration of a diatomic model. Classical mechanics shows the vibrational frequency relationship. 

Evidently, p(Jn, R) is an analog of classical momentum, which is in general complex valued. Therefore, the distribution of turning points in the complex / -plane depends strongly on the nature of the potential /(/ ). Conversely, this distribution provides the information on the nature of U(R). As shown by Connor and co-workers (Connor, 1972, 1976 Connor and Mackay, 1979 Connor et al., 1980), such a method provides a powerful technique for the study of diatomic interactions via comparison of the theoretical study of positions and residues of Regge poles for diatomic model potentials and the scattering experimental data. 

Rossky and Chiles refer to this as the ISF-PY approximation. They have applied this closure to a Lennard-Jones 12-6 diatomic model representative... 

Studies of this system show a broad range of control over the I to I product ratio. For example, a superposition of ,> and 3> (the first and third vibrational states of the ground-electronic-state potential energy surface) allows an increase of the yield of I from 30%, the value attained by excitation with one frequency, to more than 70%. Furthermore, using a diatomic model for CH3I, BS were able to define conditions which reduce the I yield to zero or increase it fully to one. 

Molecular dynamics studies of diatomic model detonations were first carried out by Karo and Hardy in 1977 [14]. They were soon followed by other groups [15, 16]. These early studies employed predissociative potentials, in which the reactant dimer molecules are metastable and can dissociate exothermically. More realistic models, combining an endothermic dissociation of reactants with an exothermic formation of product molecules, were introduced by White and colleagues at the Naval Research Laboratory and U.S. Naval Academy, first using a LEPS (London-Eyring-Polanyi-Sato) three-body potential for nitric oxide [17], and later a Tersoff-type bond-order potential [18] for a generic AB model, loosely based on NO [19, 20]. 

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

The "statistical formulation (67.Ill) cannot be applied to unimolecular reactions for which the classical activation energy and the reaction heat are equal (E = Q) without introducing some additio-nal assumptions which are necessary for the definition of the transition state. One usually considers the "activated complex (AB) as a rotating "diatomic molecule in which the centrifugal force is balanced by an attractive dipole-induced dipole or dispersion force /HO/. This "diatomic model implies that the angular momentum... 

Using (11 to 13.IV) we will consider in Sec.2.2.3.IV the recombination reactions for which the "diatomic"model is more justified than for unimolecular decay reactions. 

A "diatomic model for radical-radical recombination seems to be a good approximation as well. Therefore, lor such reactions the maximum of the effective potential energy (8.IV), including a centrifugal potential, allows us to define a transition state (or "activated complex). This provides the possibility for an application of either the colli-sional or statistical formulations of the theory of chemical reaction rates these formulations will be compared in the following sections. 

For an electronically adiabatic reaction (X= 1), this equation turns into the expression (24.IV) of the simple collision theory. In this case the "diatomic" model will be valid only if, after the very fast "non-adiabatic" collision of the radicals CH, the reaction is com-... 

The same interpretation results from the above approximate treatment of radical recombination reactions, using the "diatomic" model, where the collision diameter d is related to the high temperature approximation of expression OOliV) for the rotational partition function of product molecule AB, being in a state which should be considered a.non-stationary transition state. 

For atom-atom recombination reactions there exists no difficulty for a separation of the angular momentum p in a classical consideration, already made in Sec.3.II. Using the "diatomic"model, this consideration may be extended to radical-radical recombination where the interaction at large separation is mainly due to dispersion forces hence, the attractive potential has the form (32.IV) and the effective potential energy (56.11) (with r = x) becomes... 

On the basis of the diatomic model, these conclusions may be extended to the radical-radical recombination reactions as far as this model represents an acceptable approximation. Therefore, for such re-... 

The situation is quite different in bimolecular reactions with an activation energy (E >0). In particular, the "diatomic" model is certainly a bad approximation for radical-radical rebinding along a double bond in which the maximum of the effective potential (35 IV) lies near the saddle-point of the potential energy surface /141/, In this case no central forces govern the nuclear motion hence, the total angular momentum is not a constant, which means that the reaction cannot be rotationally adiabatic. Therefore, in this situation the statistical theory cannot correctly reproduce the results of the simple collision theory. 

Because of the cancellations described in the preceding paragraphs, it is often possible to obtain close approximations to the true isotope effects in reactions of polyatomic molecules using models for calculation that are much simpler than the molecules themselves. Even the diatomic model, A—B, with which we began our discussion, is frequently successful. For some reactions, however, it can be seriously misleading. This is especially true in the treatment of proton transfers, where it does not consider the base (or solvent molecule) that must be present to remove the proton (Westheimer, 1961). 

To demonstrate the maximum control afforded in the diatomic case we redid the CH3 I comp.utations including only the third vibrational state in the sum Eq. (10) defining j In this way the CHg radical is essentially replaced by a single particle, equivalent in mass to F. This provides a diatomic model akin to FI. The results are shown in Fig. 3 for a different choice of initial states as compared to Fig. 2. The ability to reduce the I yield to zero, or increase it fully to one, is clearly evident. 

---