Photodissociation Final state distribution

Photodissociation combines aspects of both molecular spectroscopy and molecular scattering. The spectroscopist is essentially interested in the first step of Equation (1.1), i.e., the absorption spectrum. In the past six decades or so methods of ever increasing sophistication have been developed in order to infer molecular geometries from structures in the absorption or emission spectrum (Herzberg 1967), whereas the fate of the fragments, i.e., the final state distribution is of less relevance in spectroscopy. The decay of the excited complex is considered only inasfar as the widths of the individual absorption lines reflect the finite lifetime in the excited state and therefore the decay rate of the excited molecule. 

In the time-independent approach one has to calculate all partial cross sections before the total cross section can be evaluated. The partial photodissociation cross sections contain all the desired information and the total cross section can be considered as a less interesting by-product. In the time-dependent approach, on the other hand, one usually first calculates the absorption spectrum by means of the Fourier transformation of the autocorrelation function. The final state distributions for any energy are, in principle, contained in the wavepacket and can be extracted if desired. The time-independent theory favors the state-resolved partial cross sections whereas the time-dependent theory emphasizes the spectrum, i.e., the total absorption cross section. If the spectrum is the main observable, the time-dependent technique is certainly the method of choice. 

Despite the many theoretical predictions of inelastic resonances (mainly observed in calculations with reduced dimensionality Manz 1989, for example) we do not know of an unambiguous experimental observation of resonances in atom-molecule or molecule-molecule gas-phase collisions. In contrast to full atom-molecule collisions pronounced resonance-like structures are actually rather common features in bound-continuum absorption spectra (Robin 1974, 1975, 1985 Okabe 1978 Fano and Rao 1986). In fact, all sharp structures in UV absorption spectra can be considered as resonances and therefore photodissociation provides ideal opportunities to investigate resonance phenomena, such as the lifetime, the decay mechanism, and the final state distributions of the fragments, on a very detailed basis. 

The photodissociation of H20(A) represents a very special example of rotational excitation the initial FC distribution, which reflects solely the bending motion in the parent molecule, remains unchanged because the torque —dV/dj is essentially zero along the reaction path. In most other cases, however, the coupling between translation and rotation is substantial and the final state distribution of the fragment reflects the net result of this coupling. 

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 ... 

Band, Y.B., Freed, K.F., and Kouri, D.J. (1981). Half-collision description of final state distributions of the photodissociation of polyatomic molecules, J. Chem. Phys. 74, 4380-4394. 

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

As long as the photodissociation reaction is fairly direct, the time-dependent formulation is fruitful and provides insight into both the process itself and the relationship of the final-state distributions to the absorption spectrum features. Moreover, solution of the time-dependent Schrodinger equation is feasible for these short-time evolutions, and total and partial cross sections may be calculated numerically.5 Finally, in those cases where the wavepacket remains well localized during the entire photodissociation process, a semi-classical gaussian wavepacket propagation will yield accurate results for the various physical quantities of interest.6... 

We have used the laser resonance-enhanced multiphoton ionization (REMPI) method to probe the final state distributions of S atoms formed in the 193-nm photodissociation of several organosulfur molecules and radicals [58-60], Using the rate-equation scheme and calibrating with the known photodissociation cross sections for the formation of S( P2,i,o, >2) in the 193-nm photodissociation of CS2, we have estimated the absolute cross sections for the photodissociation of organosulfur radicals HS [59,60] and CH3S [58,60] leading to the formation of S( P2,i,o o)-... 

The final rotational state distributions of the products in the fragmentation of a polyatomic molecule contain additional clues about the intra- and intermolecular dynamics, especially about the coupling in the exit channel. In realistic as well as model studies it has been observed that the rotational state distributions of the photodissociation products reflect the angular dependence of the wave function at the transition state and the anisotropy of the PES in the exit channel [4, 9, 10]. HO2 is no exception. 

A much clearer picture evolves when one decomposes the total spectrum into the partial photodissociation cross sections a(, n,j) for absorbing a photon with wavelength A and producing NO in a particular vibrational-rotational state with quantum numbers (n,j). Experimentally this is accomplished by measuring so-called photofragment yield spectra. The idea is, in principle, simple the NO product is probed by laser-induced fluorescence (LIF). However, instead of scanning the wavelength Alif of the probe laser (in order to determine the final rotational state distribution) one fixes Alif to a particular transition NO(2n, nj) —>... 

The main purpose of this chapter is to emphasize the intimate relation between the topology of the dissociative PES and the vibrational excitation of the fragment molecule. In Sections 9.1 and 9.2 we consider exclusively direct processes. The photodissociation of symmetric molecules with two equivalent product channels is the topic of Section 9.3. Finally, vibrational state distributions following the decay of a long-lived intermediate complex will be discussed in Section 9.4. The theory... 

The photodissociation of symmetric molecules such as H2O, H2S, and O3 illustrates particularly clearly the close relation between the change of the molecular configuration along the dissociation path and the final vibrational state distribution. Figure 9.9 shows the two-dimensional PES... 

While all examples discussed in the foregoing sections belong to the category of direct photodissociation we consider in this section three cases of indirect bond fission and the subsequent vibrational state distributions. We will focus our attention on the question, how do the final distributions reflect the fragmentation mechanism ... 

Rotational excitation as a consequence of overall rotation of the parent molecule before the photon is absorbed does not reveal much dynamical information about the fragmentation process. It generally increases with the magnitude of the total angular momentum J and thus increases with the temperature of the molecular sample. In order to minimize the thermal effect and to isolate the dynamical aspects of photodissociation, experiments are preferably performed in a supersonic molecular beam whose rotational temperature is less than 50 K or so. Broadening of final rotational state distributions as a result of initial rotation of the parent molecule will be discussed at the end of this chapter. 

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