Photodissociation of triatomic molecules

The potential surfaces associated with polyatomic molecules become progressively more complex as the number of atoms N, and hence degrees of freedom, increases (3A 5 for linear and 3A — 6 for non-linear 

As mentioned earlier, a useful concept when considering photodissociation is to think of the process as a half collision. The fragments are thought of as departing from a point on a potential surface that would have been reached by a collision between the fragments, had they been travelling towards each other with the appropriate impact parameter, etc. We shall make use of this concept in the discussion that follows, but a more detailed account of recoil dynamics will be given in Part 5 on bimolecular collisions. 

For triatomic and larger polyatomic molecules, the molecular fragments produced may be internally excited (electronic, vibrational and rotational), i.e. 

The energy distribution in the BC fragment can be obtained directly using either LIF, REMPI, IR emission, or by measuring the kinetic energy of the recoiling atom. The latter approach is particularly favourable when H atoms are formed, for, as we have seen, the H atom will receive most of the kinetic energy. 

To illustrate our present level of understanding of the photodissociation dynamics of triatomic molecules we will describe work on a few selected molecules and start by considering the simplest of all stable triatomic molecules, i.e. water. 

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Bersohn, R. (1984). Final state distributions in the photodissociation of triatomic molecules, J. Phys. Chem. 88, 5145-5149. 

Heather, R.W. and Light, J.C. (1983a). Photodissociation of triatomic molecules Rotational scattering effects, J. Chem. Phys. 78, 5513-5530. 

Schinke, R. (1986c). The rotational reflection principle in the direct photodissociation of triatomic molecules. Close-coupling and classical calculations, J. Chem. Phys. 85, 5049-5060. 

Untch, A., Hennig, S., and Schinke, R. (1988). The vibrational reflection principle in direct photodissociation of triatomic molecules Test of classical models, Chem. Phys. 126, 181-190. 

Note added in proof a theoretical analysis of the polarization of fluorescence from the diatomic fragments formed in the photodissociation of triatomic molecules has been developed by Macpherson, Simons and Zare ). 

There have been several high quality 3D calculations on the photodissociation of triatomic molecules using non-reactive potential energy surfaces [47-51]. Indeed, Segev and Shapiro calculated [47] the photoabsorption spectrum for the process... 

The photochemical processes of triatomic molecules have been extensively studied in recent years, particularly those of water, carbon dioxide, nitrous oxide, nitrogen dioxide, ozone, and sulfur dioxide, as they are important minor constituents of the earth s atmosphere. (Probably more than 200 papers on ozone photolysis alone have been published in the last decade.) Carbon dioxide is the major component of the Mars and Venus atmospheres. The primary photofragments produced and their subsequent reactions are well understood for the above-mentioned six triatomic molecules as the photodissociation involves only two bonds to be ruptured and two fragments formed in various electronic states. The photochemical processes of these six molecules are discussed in detail in the following sections. They illustrate how the knowledge of primary products and their subsequent reactions have aided in interpreting the results obtained by the traditional end product analysis and quantum yield measurements. 

The concepts of laser chemistry are developed along the lines of unimolecular reactions, or, in other words, dissociative processes in the most common sense. The discussion evolves from the photodissociation of diatomic molecules through triatomic species up to larger polyatomic entities (Chapters 15 to 17). Suitable coverage is also given to multiphoton and photoionization processes, which involve the subtle inclusion of intermediate and continuum states (Chapter 18). The part on unimolecular reactions concludes with a discus-... 

The effect of conical intersections on the state-specific and state-to-state reactive and nonreactive scattering attributes was demonstrated with the aid of an extended two coordinate quasi Jahn-Teller (JT) model. In recent years, the photodissociation dynamics of triatomic molecules, for example O3 and H2S, have been studied by calculating the diabatic electronic states and their couplings employing an ah initio approach. The reactive scattering dynamics of insertion reactions, for example, C - - H2, ... 

Since nuiny processses demonstrate substantial quantum effects of tunneling, wave packet break-up and interference, and, obviously, discrete energy spectra, symmetry induced selection rules, etc., it is clearly desirable to develop meAods by which more complex dynamical problems can be solved quantum mechanically both accurately and efficiently. There is a reciprocity between the number of particles which can be treated quantum mechanically and die number of states of impcxtance. Thus the ground states of many electron systems can be determined as can the bound state (and continuum) dynamics of diatomic molecules. Our focus in this manuscript will be on nuclear dynamics of few particle systems which are not restricted to small amplitude motion. This can encompass vibrational states and isomerizations of triatomic molecules, photodissociation and exchange reactions of triatomic systems, some atom-surface collisions, etc. 

E. J. Heller, Quantum corrections to classical photodissociation models, J. Chem. Phys. 68 2066 (1978) Photofragmentation of triatomic molecules, J. Chem. Phys. 68 3891 (1978). 

Pack R T 1976 Simple theory of diffuse vibrational structure in continuous UV spectra of polyatomic molecules. I. Collinear photodissociation of symmetric triatomics J. Chem. Phys. 65 4765... 

Figure C3.5.7. Possible modes of vibrational wavepacket (smootli Gaussian curve) motion for a highly vibrationally excited diatomic molecule produced by photodissociation of a linear triatomic such as Hglj, from [8].

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

Figure 4.27 The impulsive3 model of the photodissociation of a triatomic molecule ABC— A ABC...

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 photofragmentation that occurs as a consequence of absorption of a photon is frequently viewed as a "half-collision" process (16)- The photon absorption prepares the molecule in assorted rovibrational states of an excited electronic pes and is followed by the half-collision event in which translational, vibrational, and rotational energy transfer may occur. It is the prediction of the corresponding product energy distributions and their correlation to features of the excited pes that is a major goal of theoretical efforts. In this section we summarize some of the quantum dynamical approaches that have been developed for polyatomic photodissociation. For ease of presentation we limit consideration to triatomic molecules and, further, follow in part the presentation of Heather and Light (17). 

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. 

Beswick and Gelbart (55) published an interesting paper concerned with the bending contribution to rotational distribution. They considered the photodissociation of a triatomic molecule ABC + hv A + BC applicable to both linear and bent molecules. The Hamiltonian is expressed in terms of so-called dis-... 

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,... 

We consider the photodissociation of a linear triatomic molecule, ABC — A + BC(n), where n specifies the final vibrational state. The appropriate Jacobi coordinates R and r are defined in Figure 2.1 and the nuclear Hamiltonian is given in (2.39). For simplicity, we assume that only one chemical dissociation channel exists. Figures 1.11 and 2.3 depict typical potential energy surfaces appropriate for this section. 

For simplicity and clarity of presentation we restrict the following derivation to the photodissociation of the linear triatomic molecule ABC as outlined in Section 2.4. The Jacobi coordinates R and r are defined in Figure 2.1 and (2.39) gives the corresponding Hamiltonian H for the motion of the nuclei. 

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). 

We consider the photofragmentation of a triatomic molecule, ABC — A + BC(j), within the model outlined in Section 3.2. The vibrational coordinate of BC is fixed and the total angular momentum is zero. According to (5.23), the classical approximation of the partial photodissociation cross section for producing BC in rotational state j is given by... 

The photodissociation of symmetric triatomic molecules of the type ABA is particularly interesting because they can break apart into two identical ways ABA — AB + A and ABA — A + BA. Figure 7.18(a) shows a typical PES as a function of the two equivalent bond distances. It represents qualitatively the system IHI which we will discuss in some detail below. We consider only the case of a collinear molecule as illustrated in Figure 2.1. The potential is symmetric with respect to the C -symmetry line 7 IH = i HI and has a comparatively low barrier at short distances. The minimum energy path smoothly connects the two product channels via the saddle point. A trajectory that starts somewhere in the inner region can exit in either of the two product channels. However, the branching ratio ctih+i/cti+hi obtained by averaging over many trajectories or from the quantum mechanical wavepacket must be exactly unity. 

Before we start a more quantitative discussion it is worthwhile thinking about which coordinates to use for interpretation of rotational excitation. Let us consider the photodissociation of a triatomic molecule, C1NO —> Cl + NO(j), for example. Researchers with a background in electronic structure calculations and spectroscopy normally use bond coordinates, i.e., the two bond distances i ciN and I no and the C1NO bond angle a [see Figure 10.1(a)]. These are the appropriate coordinates for... 

For simplicity we consider the photodissociation of a triatomic molecule, ABC —> A + BC(j), as described in Section 3.2. Let us assume that the PES in the excited electronic state is isotropic, i.e., it depends only on the Jacobi coordinate R, but not on the orientation angle 7. Then, the... 

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