Vibrational and rotational product state distributions

The OH radical is produced in a particular vibrational and rotational quantum state specified by the quantum numbers n and j. The corresponding energies are denoted by tnj. The probabilities with which the individual quantum states are populated are determined by the forces between the translational mode (the dissociation coordinate) and the internal degrees of freedom of the product molecule along the reaction path. Final vibrational and rotational state distributions essentially reflect the dynamics in the fragment channel. They are one major source of information about the dissociation process. 

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In this chapter we elucidate the state-specific perspective of unimolec-ular decomposition of real polyatomic molecules. We will emphasize the quantum mechanical approach and the interpretation of the results of state-of-the-art experiments and calculations in terms of the quantum dynamics of the dissociating molecule. The basis of our discussion is the resonance formulation of unimolecular decay (Sect. 2). Summaries of experimental and numerical methods appropriate for investigating resonances and their decay are the subjects of Sects. 3 and 4, respectively. Sections 5 and 6 are the main parts of the chapter here, the dissociation rates for several prototype systems are contrasted. In Sect. 5 we shall discuss the mode-specific dissociation of HCO and HOCl, while Sect. 6 concentrates on statistical state-specific dissociation represented by D2CO and NO2. Vibrational and rotational product state distributions and the information they carry about the fragmentation step will be discussed in Sect. 7. Our description would be incomplete without alluding to the dissociation dynamics of larger molecules. For them, the only available dynamical method is the use of classical trajectories (Sect. 8). The conclusions and outlook are summarized in Sect. 9. 

In this section, we shall focus exclusively on the scalar properties of the fragments and consider the vibrational and rotational product state distributions (PSD s) following the dissociations of HCO, NO2, and H2CO discussed in Sects. 5 and 6. An in-depth introduction to the vast and fascinating field of product state analysis can be found in Ref. 20 (Chapters 9, 10, and 11). Recently, the PSD s of several representative groups of molecules were reviewed in Ref. 306. 

Figure 12. Potential energy contour plots for He + I Cl(B,v = 3) and the corresponding probability densities for the n = 0, 2, and 4 intermolecular vibrational levels, (a), (c), and (e) plotted as a function of intermolecular angle, 0 and distance, R. Modified with permission from Ref. 40. The I Cl(B,v = 2/) rotational product state distributions measured following excitation to n = 0, 2, and 4 within the He + I Cl(B,v = 3) potential are plotted as black squares in (b), (d), and (f), respectively. The populations are normalized so that their sum is unity. The l Cl(B,v = 2/) rotational product state distributions calculated by Gray and Wozny [101] for the vibrational predissociation of He I Cl(B,v = 3,n = 0,/ = 0) complexes are shown as open circles in panel (b). Modified with permission from Ref. [51].

The use of molecular and atomic beams is especially useful in studying chemiluminescence because the results of single molecular interactions can be observed without the complications that arise from preceding or subsequent energy-transfer coUisions. Such techniques permit determination of active vibrational states in reactants, the population distributions of electronic, vibrational, and rotational excited products, energy thresholds, reaction probabihties, and scattering angles of the products (181). 

Electronic excitation from atom-transfer reactions appears to be relatively uncommon, with most such reactions producing chemiluminescence from vibrationaHy excited ground states (188—191). Examples include reactions of oxygen atoms with carbon disulfide (190), acetylene (191), or methylene (190), all of which produce emission from vibrationaHy excited carbon monoxide. When such reactions are carried out at very low pressure (13 mPa (lO " torr)), energy transfer is diminished, as with molecular beam experiments, so that the distribution of vibrational and rotational energies in the products can be discerned (189). Laser emission at 5 p.m has been obtained from the reaction of methylene and oxygen initiated by flash photolysis of a mixture of SO2, 2 2 6 (1 )-... 

Gray and Wozny [101, 102] later disclosed the role of quantum interference in the vibrational predissociation of He Cl2(B, v, n = 0) and Ne Cl2(B, v, = 0) using three-dimensional wave packet calculations. Their results revealed that the high / tail for the VP product distribution of Ne Cl2(B, v ) was consistent with the final-state interactions during predissociation of the complex, while the node at in the He Cl2(B, v )Av = — 1 rotational distribution could only be accounted for through interference effects. They also implemented this model in calculations of the VP from the T-shaped He I C1(B, v = 3, n = 0) intermolecular level forming He+ I C1(B, v = 2) products [101]. The calculated I C1(B, v = 2,/) product state distribution remarkably resembles the distribution obtained by our group, open circles in Fig. 12(b). 

Photodissociation dynamics [89,90] is one of the most active fields of current research into chemical physics. As well as the scalar attributes of product state distributions, vector correlations between the dissociating parent molecule and its photofragments are now being explored [91-93]. The majority of studies have used one or more visible or ultraviolet photons to excite the molecule to a dissociative electronically excited state, and following dissociation the vibrational, rotational, translational, and fine-structure distributions of the fragments have been measured using a variety of pump-probe laser-based detection techniques (for recent examples see references 94-100). Vibrationally mediated photodissociation, in which one photon... 

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). 

Excitation of ClNO(Ti) in any one of the three vibrational bands yields exclusively NO products in vibrational state n — n (Qian et al. 1990). The left-hand side of Figure 9.12 depicts the results of a three-dimensional wavepacket calculation including all three degrees of freedom and using an ab initio PES (Solter et al. 1992). This calculation reproduces the absorption spectrum and the final vibrational and rotational distributions of NO in good agreement with experiment. 

Up to now we have exclusively considered the scalar properties of the photodissociation products, namely the vibrational and rotational state distributions of diatomic fragments, i.e., the energy that goes into the various degrees of freedom. Although the complete analysis of final state distributions reveals a lot of information about the bond breaking and the forces in the exit channel, it does not completely specify the dissociation process. Photodissociation is by its very nature an anisotropic process — the polarization of the electric field Eo defines a unique direction relative to which all vectors describing both the parent molecule and the products can be measured. These are ... 

For the determination of product vibrational and rotational distributions, we must consider the time for vibrational or rotational relaxation by gas-phase collisions. This is not as strongly dependent on the nature of the products as it is for electronic quenching. Rotational relaxation is a much more efficient process than vibrational relaxation, requiring typically less than one hundred collisions to rotationally relax a molecule compared with several thousand collisions to bring about vibrational relaxation [76]. Thus, primary product vibrational energy distributions may be determined at pressures greater than 10-4 Torr, whilst much lower pressures are required to observe unrelaxed rotational state distributions. 

Quantum mechanical and classical calculations have been performed [245] for H + Cl2 on a recently optimised extended LEPS surface [204]. The quantum mechanical results were transformed to three dimensions by the information theoretic procedure and are in good agreement with the distributions determined in the chemiluminescence experiments. However, three-dimensional trajectory calculations on the surface consistently underestimate (FR) at thermal energies and it is concluded that the LEPS surface which was optimised using one-dimensional calculations does not possess the angular dependence of the true three-dimensional surface. This appears to result from the lack of flexibility of the LEPS form. Trajectory studies [196] for H + Cl2 on another LEPS surface find a similar disposal of the enhanced reagent energy as was found for H + F2. The effect of vibrational excitation of the Cl2 on the detailed form of the product vibrational and rotational state distributions was described in Sect. 2.3. 

Angular scattering measurements [336] for Ba + 02 indicate that the reaction proceeds via a long-lived collision complex and that the product recoil distributions are well described by statistical models using a loose transition state with 0.40. The BaO product vibrational and rotational distributions have been determined by laser-induced fluorescence methods, showing that about two-thirds of the available... 

The measured vibrational and rotational distributions for the ground state CaO product from the reaction Ca (3P) + 02, indicate that its... 

Laser-fluorescence measurements [386] of the ground state MX products of the reactions of Y and Sc with F2, Cl2, Br2 and I2 were analysed assuming Boltzmann vibrational and rotational distributions for the MX product, giving TVib values in the range 2150—2850 K and Ttoi values between 1425 and 1700 K for this family of reactions. This indicates a rather low conversion ( 15%) of the reaction energy into internal energy of the MX product, although it should be emphasised that the above results depend on the spectroscopic and thermodynamic data for the metal monohalides which are not very well established. 

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