Photodissociation of vibrationally excited states

Theoretically, the calculation of photodissociation cross sections for excited vibrational states proceeds in exactly the same way as for the dissociation of the lowest level. The basic quantities are the photodissociation amplitudes (2.68) with the initial wavefunction being 

In this chapter we will focus on the following questions  

1) How does the absorption spectrum reflect the nodal structure of the wavefunction of the parent molecule in the electronic ground state  

2) How does the initial excitation influence the final product state distributions and the chemical branching provided two different dissociation channels can be accessed  

We first briefly discuss in Section 13.1 the one-dimensional case and a simple two-dimensional model. The photodissociation of highly excited vibrational states of H2O and HOD, for which both experimental and theoretical results are available, will be reviewed in more detail in Sections 13.2 and 13.3. 

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In particular, Shapiro and others calculated state-to-state photodissociation cross sections from vibrationally excited states of HCN and DCN [58], N2O [59], and O3 [60]. Eor instance, the detailed product-vibrational state distributions and absorption spectra of HCN(DCN) were compared [58]. These results were obtained employing a half-collision approximation, where the photodissociation could be depicted as consisting of two steps, that is, absorption of the photon and the dissociation, as well as an exact numerical integration of the coupled equations. In particular, it was predicted that large isotope effects can be obtained in certain regions of the spectrum by photodissociation of vibrationally excited molecules. 

Vander Wal, R.L., Scott, J.L., and Crim, F.F. (1991). State resolved photodissociation of vibrationally excited water Rotations, stretching vibrations, and relative cross sections, J. Chem. Phys. 94, 1859-1867. 

The reaction of DN3 along its X A surface requires the absorption of IR photons and shows product state selectivity [2]. The overtone photodissociation of vibrationally excited XN3 (X = H, D) under collisionless conditions proceeds via the reaction channels ... 

The degree of vibrational excitation in a newly formed bond (or vibrational mode) of the products may also increase with increasing difference in bond length (or normal coordinate displacement) between the transition state and the separated products. For example, in the photodissociation of vinyl chloride [9] (reaction 7), the H—Cl bond length at the transition state for four-center elimination is 1.80 A, whereas in the three-center elimination, it is 1.40 A. A Franck-Condon projection of these bond lengths onto that of an HCl molecule at equilibrium (1.275 A) will result in greater product vibrational excitation from the four-center transition state pathway, and provides a metric to distinguish between the two pathways. 

Vibrationally mediated photodissociation (VMP) can be used to measure the vibrational spectra of small ions, such as V (OCO). Vibrationally mediated photodissociation is a double resonance technique in which a molecule first absorbs an IR photon. Vibrationally excited molecules are then selectively photodissociated following absorption of a second photon in the UV or visible [114—120]. With neutral molecules, VMP experiments are usually used to measure the spectroscopy of regions of the excited-state potential energy surface that are not Franck-Condon accessible from the ground state and to see how different vibrations affect the photodissociation dynamics. In order for VMP to work, there must be some wavelength at which vibrationally excited molecules have an electronic transition and photodissociate, while vibrationally unexcited molecules do not. In practice, this means that the ion has to have a... 

The V (OCO) ion has a structured electronic photodissociation spectrum, which allows us to measure its vibrational spectrum using vibrationally mediated photodissociation (VMP). This technique requires that the absorption spectrum (or, in our case, the photodissociation spectrum) of vibrationally excited molecules differ from that of vibrationally unexcited molecules. The photodissociation spectrum of V (OCO) has an extended progression in the V OCO stretch, indicating that the ground and excited electronic states have different equilibrium V "—OCO bond lengths. Thus, the OCO antisymmetric stretch frequency Vj should be different in the two states, and the... 

The theory of photodissociation described in Section III requires vibrational frequencies of the excited state to predict internal energies of photofragments. In connection with planned applications of this theory to C2N2, ab initio multiconfiguration... 

The general theory for the absorption of light and its extension to photodissociation is outlined in Chapter 2. Chapters 3-5 summarize the basic theoretical tools, namely the time-independent and the time-dependent quantum mechanical theories as well as the classical trajectory picture of photodissociation. The two fundamental types of photofragmentation — direct and indirect photodissociation — will be elucidated in Chapters 6 and 7, and in Chapter 8 I will focus attention on some intermediate cases, which are neither truly direct nor indirect. Chapters 9-11 consider in detail the internal quantum state distributions of the fragment molecules which contain a wealth of information on the dissociation dynamics. Some related and more advanced topics such as the dissociation of van der Waals molecules, dissociation of vibrationally excited molecules, emission during dissociation, and nonadiabatic effects are discussed in Chapters 12-15. Finally, we consider briefly in Chapter 16 the most recent class of experiments, i.e., the photodissociation with laser pulses in the femtosecond range, which allows the study of the evolution of the molecular system in real time. 

As in Example 4.2, the branching ratio between the two product channels can be controlled by appropriate vibrational pre-excitation of HOD [16]. For example, when the initial state is a vibrationally excited state of HOD corresponding to four quanta in the HO-D stretch, the channel D + OH is exclusively populated in a subsequent unimolecular photodissociation reaction induced by a UV-photon. The energy of the UV-photon must, however, lie within a rather narrow energy range. 

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