Triatomic molecule, photodissociation, initial

B. Detailed Definition of the Initial Wavepacket for Photodissociation of a Triatomic Molecule... 

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) ... 

A detailed analysis of the rotational degrees of freedom and of bending motion has been carried out by Freed and Band (2) and by Morse and Freed (52-54). The former authors considered the photodissociation of a linear triatomic molecule. In that work the rotational part of the initial wavefunction is written in the form... 

This expression has been analyzed for the dissociation of ICN. The initial thermal distribution corresponds to large j. A distribution peaked around j 25 was obtained, in good agreement with experimental data. The analysis has been generalized to describe the case of a bent triatomic molecule (53,5A). Moreover, these authors consider the scalar coupling which corresponds to indirect photodissociation. 

Let us, for illustration purposes, consider the dissociation of a triatomic molecule as sketched in Figure 1.4. In an ideal experiment one would measure differential photodissociation cross sections with full specification of the initial state and full resolution of the final state,... 

Let us again consider the photodissociation of the linear triatomic molecule with coordinates R and r (Figure 2.1). We want to solve the time-dependent Schrodinger equation (4.1) with the Hamiltonian given in (2.39) and the initial condition (4.4). 

As mentioned above, the interpretation of the asymmetry of a a E)/E for a triatomic molecule is much more difficult than for a diatomic molecule. However, the asymmetry is a relevant phenomenological parameter which characterizes the XS in addition to the centre, the width and the amplitude. The isotopic (isotopologue) dependence of these four parameters is of special interest when dealing with the photodissociation processes [9,15]. In fact, this aspect was our initial motivation when starting this study and will be treated in the future. Below, we characterize the XS asymmetry of three important molecules O3, SO2 and CO2. 

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