Impulsive model

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). 

The fj that appears in the atomic fragments (X) is large, and suggests that an impulsive model for dissociation is the correct theoretical interpretation of the results. In fact, the spectator model appears to predict the fj that are observed. 

Fig. 6.7. Left-hand side Rotational excitation function J(70) and weighting function W(70) for the dissociation of ClNO(Si). Right-hand side Calculated final rotational state distribution of NO for an excess energy of 1 eV. The dashed curves represent the same quantities calculated, however, within the so-called impulsive model (IM) which we will discuss in Section 10.4. Reproduced from Schinke et al. (1990).

As in Chapter 9 we discuss first the elastic limit (no exit channel excitation) in Section 10.1 and subsequently the more interesting inelastic case in Section 10.2. In Section 10.3 we consider the decay of long-lived resonance states and the impact of exit channel dynamics on the product distributions. A simple approximation, the so-called impulsive model, which is frequently employed to analyze experimental distributions in the absence of a PES, is discussed critically in Section 10.4. The chapter ends with a more qualitative assessment of thermal broadening of rotational state distributions in Section 10.5... 

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... 

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.

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. 

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. 

McClelland, G.M. and Herschbach, D.R. (1987). Impulsive model for angular momentum polarization in chemical reactions, J. Phys. Chem., 91, 5509-5515. 

It is also important that the influence of the desorption dynamics on the nuclear motion is discussed. Zimmermann and Ho [65] discuss rotational excitation in photodesorption using a simple impulse model. In particular, rotational energy distributions with two spin-orbit states of NO desorption of on-top species from the Pt( 111) surface and from the oxidized Ni(0 01) surface are analyzed. Furthermore, they also discuss velocity distributions [66] and rotational-translational correlations [67]. Murata and Fukutani [28, 68, 69] analyze the experimental data using a simple impulse model without any fitting parameter. The results are described in the present text in detail, and the procedure is quite different from that derived by Zimmermann and Ho [65]. 

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. 

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