The impulsive model

It is worthwhile, however, pointing out that the existence of a long-lived intermediate state and the absence of a barrier in the exit channel do not necessarily imply statistical product state distributions. The fragment distributions in the dissociation of weakly bound van der Waals molecules are usually neither thermal nor statistical, despite the extremely long lifetime of the complex. We will come back to this in Chapter 12. 

In the pure impulsive model, the total excess energy Eexcess partitions into translational energy of both products, as well as vibrational and rotational energy of the diatomic fragment. In a modified version, Busch and Wilson (1972a) assumed that the B-C bond is infinitely stiff such that vibrational energy transfer is prohibited. Employing conservation of 

Because of its simplicity the impulsive model is very appealing and frequently employed to model measured rotational state distributions (Dugan and Anthony 1987 Levene and Valentini 1987 Butenhoff, Car-leton, and Moore 1990). In most applications, however, it is necessary to incorporate at least one fit parameter or some dynamical constraints in order to obtain agreement with experimental results, for example, the equilibrium angle in the excited electronic state or the point at which the repulsive force vector intersects the BC-axis. The impulsive model is not an a priori theory. 

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The fraction of the available energy residing in the CH2I radicals is much larger than that in the CH3 radicals dissociated from CH3I, which is only 12% (834). Qualitatively, this difference in the energy partitioning can be understood from (11-23) based on the impulsive model (see p. 93). 

Fig. 10.19. Schematic illustration of the impulsive model for the dissociation of a triatomic molecule, ABC —> A + BC(j). The heavy arrows indicate the repulsive force between atom A and its nearest neighbor, B, which generates rotation of BC about its center-of-mass.

The main drawback of the impulsive model is the neglect of the a dependence of the interaction potential (Schinke 1989a). When the fragments separate the diatomic molecule starts to rotate and at the same time a decreases as indicated in Figure 10.19. Each PES shows some an-... 

Fig. 10.20. Rotational state distribution of CN following the photodissociation of C1CN at 191.5 nm. Comparison between exact close-coupling calculations using the full ab initio PES of Waite and Dunlap (1986) (solid curve) and the impulsive model (IM, dashed curve). Adapted from Schinke (1990).

The impulsive model is only applicable if the dissociative PES depends so weakly on the bond angle that the torque —dV/da can be safely neglected. 

The impulsive model is applicable in the case of H2OA because the dependence of the PES on the HOH bending angle is indeed very weak throughout the bond fission. 

Schinke, R. (1989a). Rotational excitation in direct photodissociation and its relation to the anisotropy of the excited state potential energy surface How realistic is the impulsive model , Comments At. Mol. Phys. 23, 15-44. 

The impulse model is applied to the interpretation of experimental results of the rotational and translational energy distributions and is effective for obtaining the properties of the intermediate excited state [28, 68, 69], where the impulse model has widely been used in the desorption process [63-65]. The one-dimensional MGR model shown in Fig. 1 is assumed for discussion, but this assumption does not lose the essence of the phenomena. The adsorbate-substrate system is excited electronically by laser irradiation via the Franck-Condon process. The energy Ek shown in Fig. 1 is the excess energy surpassing the dissociation barrier after breaking the metal-adsorbate bond and delivered to the translational, rotational and vibrational energies of the desorbed free molecule. 

In the impulse model, the excess energy Ek is transferred to an NO molecule as the momentum p0 given only to an N atom. Here, p0 is normal to the surface and Ek = p /2m, where m is mass of the N atom. Recoil of substrate Pt atoms can be ignored, because the mass of a Pt atom is much larger than that of an N atom. After desorption the momentump0 is converted to the linear momentum of the center of mass, P, and the linear momentum of the internal coordinate, p. A relationship p0 = m dri/df is satisfied in the impulse model and it can be approximated to dr2/df = 0 at the moment of the Pt-N bond breaking, where and r2 are the position vectors of N and O atoms, respectively, in an adsorbed NO molecule. 

In another limiting form of the impulsive model, the rigid radical limit, the alkyl radical is assumed to recoil as a rigid body, so that only rotational excitation can occur. The extent of excitation is determined by conservation of energy as well as linear and angular momentum. The result is... 

The refined model is also a classical mechanical model of the reactive collision event, in which both the long-range polarization and short-range repulsive forces are taken into account. In doing so, the model assumes that the repulsive forces are impulsive at the reaction radius , and for this reason the model is referred to as the impulsive model . 

Fig. 18. CO vibrational population distributions obtained from the experiment (open circles and solid curve), the ciuve-crossing model by Fisher and Smith (solid circles and dashed curve), and the impulsive model by Levine and Bernstein (triangles and dotted curve). Reprinted with permission from Chem. Pfys. Lett., 42, 78 (1976). Copyright by North-HoUand Publishing Company.

Two models for determining PEDs for dissociation along repulsive potentials are discussed here. The impulsive model is a very crude classical model whose major virtue is its simplicity. A more sophisticated model is the transition-state mapping model. Finally, we mention the use of classical trajectories in determining PEDs. 

A linear molecule is thus not expected to produce any rotationally excited products. This model predicts for the case of the NO2 dissociation, that 71.5% of the available energy is released as translational energy compared to the observed 60% when NO2 is photodissociated at 28,800 cm (Busch and Wilson, 1972). Such discrepancies are not unexpected in view of its simplicity. As pointed out by Schinke (1992) the impulsive model would be strictly applicable only if the dissociative potential energy surface depends so weakly on the bond angle that the torque —dVIda. can be safely neglected. This is almost never true. 

Figure 9.18 The 02( S v = 12) product rotational distribution obtained by LIF from the photodissociation of O3 at 248 nm. The solid lines are the calculated statistical PST distribution and the impulsive model prediction. Taken and adapted with permission from Daniels and Wiesenfeld (1993).

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