Half-collision process

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). 

In this section we will provide the formalism for an extension of the Born-Oppenheimer adiabatic approximation that deals with unstable autoioniz-ing molecules and takes into account the coupling between electronic and nuclear motion. The new formalism will be applied in two cases (i) full collision process of vibrational excitation of H2 molecule by electron impact [8], (ii) half collision process of interatomic Coulombic decay of electronically excited Ne cationic dimer [9,10]. 

We will demonstrate here an application of the complex analogue of the Born-Oppenheimer approximation to a half collision process, namely, to the reaction... 

Studies on orthokinetic flocculation (shear flow dominating over Brownian motion) show a more ambiguous picture. Both rate increases (9,10) and decreases (11,12) compared with orthokinetic coagulation have been observed. Gregory (12) treated polymer adsorption as a collision process and used Smoluchowski theory to predict that the adsorption step may become rate limiting in orthokinetic flocculation. Qualitative evidence to this effect was found for flocculation of polystyrene latex, particle diameter 1.68 pm, in laminar tube flow. Furthermore, pretreatment of half of the latex with polymer resulted in collision efficiencies that were more than twice as high as for coagulation. 

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. 

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. 

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). 

The final application of classical S-matrix theory to be discussed is the description of photodissociation of a complex (e.g. triatomic) molecule. The completely classical description, essentially the half-collision model of Holdy, Klutz and Wilson,54 is discussed first, and then the semiclassical version of the theory is presented. A completely quantum mechanical description of the process has been developed in detail recently by Shapiro,55 The quantity of interest is the transition dipole,... 

The distinction between direct dissociation processes discussed in the present section and indirect dissociation or predissociation processes discussed in Section 7.3 to Section 7.14 is that in a direct process photoexcitation occurs from a bound state (typically v = 0 of the electronic ground state) directly to a repulsive state (or to an energy region above the dissociation asymptote of a bound state) whereas in an indirect process the photoexcitation is to a nominally bound vibration-rotation level of one electronically excited state which in turn is predissociated by perturbative interaction with the continuum of another electronic state. Direct dissociation, often termed a half collision is much faster and dynamically simpler than indirect dissociation. In a direct dissociation process the distance between atoms increases monotonically and the time required for the two atoms to separate is shorter than a typical vibrational or rotational period (Beswick and Jortner, 1990). 

In gas-phase dynamics, the discussion is focused on the TD quantum wave packet treatment for tetraatomic systems. This is further divided into two different but closed related areas molecular photofragmentation or half-collision dynamics and bimolecular reactive collision dynamics. Specific methods and examples for treating the dynamics of direct photodissociation of tetraatomic molecules and of vibrational predissociation of weakly bound dimers are given based on different dynamical characters of these two processes. TD methods such as the direct projection method for direct photodissociation, TD golden rule method and the flux method for predissociation are presented. For bimolecular reactive scattering, the use of nondirect product basis and the computation of the initial state-selected total reaction probabilities by flux calculation are discussed. The descriptions of these methods are supported by concrete numerical examples and results of their applications. 

We discussed also the relation between collisional relaxation and processes occuring in half-collisions (dissociation of molecules and of... 

The second step, the fragmentation, is of completely different nature. It is motion of heavy nuclei against each other on an excited state potential surface. Because the break up of the excited molecule to products resembles the second half of a reaction collision, photodissociation processes are sometimes called half collisions . 

Molecular photodissociation is an ideal process for such studies and has been examined in considerable detail. This unimolecular event is sometimes considered as a half collision, where the absorption of a photon excites the system to a repulsive state that flies apart. A number of radiation sources have been employed for such photoly-... 

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. 

Figure 22.5 shows a pictorial representation of the so-called two-vector correlation, both in photodissociation (half-collisions) and in atom-exchange reactions (full collisions). The important point to consider is that photodissociation is an anisotropic process in which the polarization of the electric field Sp of the photolysis laser defines a direction with respect to which the vector describing both products and parent molecule can be correlated. As a consequence, one can measure and analyse the correlation between the parent transition dipole moment fi and the recoil photofragment velocity vector, i.e. the v correlation. Thus, the angular distribution of the photofragments I 6) can be described in the form (Zare, 1972)... 

Van der Waals hetero-clusters are ideal model systems for the detailed study of a variety of photophysical and photochemical processes such as energy transfer, vibrational predissociation, fine-structure relaxation, and half-collision chemical reactions. In addition, the spectroscopy of these species provides central information on intermolecular forces and their additivity properties. 

Ultrashort pulses are able to prepare localized wave packets which (for short times) move in the average classically. This motion clearly defines a reaction path for the case that the reaction starts right at the transition state and the molecular fragments evolve into the arrangement channels. In this sense the laser induced process is a half collision , since the first part of a full collision where the atomic and molecular species approach each other is missing. 

Tiny microparticles came together to form microagglomerates, and these in turn formed larger clots, which then formed larger bodies, the diameter of which was initially measured in centimetres but later increased to metres such planetary building blocks are known as planetesimals . Computer simulations indicate that these existed around four and a half billion years ago (Wetherhill, 1981). Planetesimals grew to form bodies which were several kilometres across, and there were often collisions in which larger bodies were swallowed up by smaller ones a process which is not unknown in modern economics ... 

Triplet-triplet annihilation In concentrated solutions, a collision between two molecules in the Ti state can provide enough energy to allow one of them to return to the Si state. Such a triplet-triplet annihilation thus leads to a delayed fluorescence emission (also called delayed fluorescence of P-type because it was observed for the first time with pyrene). The decay time constant of the delayed fluorescence process is half the lifetime of the triplet state in dilute solution, and the intensity has a characteristic quadratic dependence with excitation light intensity. 

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