Half collisions

Photodissociation has been referred to as a half-collision. The molecule starts in a well-defined initial state and ends up in a final scattering state. The intial bound-state vibrational-rotational wavefunction provides a natural initial wavepacket in this case. It is in connection with this type of spectroscopic process that Heller [1-3] introduced and popularized the use of wavepackets. 

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. 

The right-hand side of Eq. 7.2 may alternatively contain a molecule, AB, instead of a free pair, A + B such processes are sometimes referred to as half-collisions. 

The simplest system for addressing the dynamics of barrier reactions is of the type [ABA] — AB + A. This system is the half-collision of the A + BA full collision (see Fig. 14). It involves one symmetrical stretch (Qs), one asymmetrical stretch (QA), and one bend (q) it defines a barrier along the reaction coordinate. 

M. Garcia-Sucre, G. Raseev, and G. C. Ross, Eds., Half Collision Resonances in Molecules Experimental and Theoretical Approaches, American Institute of Physics, New York, 1991. 

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). 

From this starting point, the authors develop equations leading to the evaluation of the real symmetric K matrix to specify the scattering process on the repulsive surface and propose its determination by a variational method. Furthermore, they show explicitly the conditions under which their rigorous equations reduce to the half-collision approximation. A noteworthy result of their approach which results because of the exact treatment of interchannel coupling is that only on-the-energy-shell contributions appear in the partial linewidth. Half-collision partial linewidths are found not to be exact unless off-the-shell contributions are accidentally zero or (equivalently) unless the interchannel coupling is zero. The extension of the approach to indirect photodissociation has also been presented. The method has been applied to direct dissociation of HCN, DCN, and TCN and to predissociation of HCN and DCN (21b). 

Although theoretical techniques for the characterization of resonance states advanced, the experimental search for reactive resonances has proven to be a much more difficult task [32-34], The extremely short lifetime of reactive resonances makes the direct observation of these species very challenging. In some reactions, transition state spectroscopy can be employed to study resonances through "half-collision experiments," where even very short-lived resonances may be detected as peaks in a Franck-Condon spectrum [35-38]. Neumark and coworkers [39] were able to assign peaks in the [IHI] photodetachment spectrum to resonance states for the neutral I+HI reaction. Unfortunately, transition state spectroscopy is not always feasible due to the absence of an appropriate Franck-Condon transition or due to practical limitations in the required level of energetic resolution. The direct study of reactive resonances in a full collision experiment, such as with a molecular beam apparatus, is the traditional and more usual environment to work. Unfortunately, observing resonance behavior in such experiments has proven to be exceedingly difficult. The heart of the problem is not a... 

Fig. 1.4 Schematic illustration of a full collision (a) and a half collision (b).

Furthermore, the total energy Ef in half collisions can be relatively easily controlled by variation of the photolysis wavelength. This is essential for the detection of resonances and other structures which require high... 

Resonances in full and in half collisions (Poliak, Child, and Pechukas 1980 Poliak 1981 Poliak and Child 1981 Marston and Wyatt 1984a,b, 1985 Schinke, Weide, Heumann, and Engel 1991). 

If the interaction potential V/ depends only on R, energy cannot flow between the translational and the vibrational modes the full or half collision is elastic (no final state interaction). The resulting quantum mechanical or classical equations of motion separate in two uncoupled blocks and the motions in R and r evolve independently of each other. 

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. 

The first point to be considered is how this kind of half collision is connected to other types of collisional experiments. As already mentioned, in order to describe a collision the parameters of the entrance channel have to be known and those of the output channels have to be precisely measured. In the van der Waals method they can, in principle, all be known, but only a few can be varied. 

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