Flux-velocity contour map

In a crossed-beam experiment the angular and velocity distributions are measured in the laboratory coordinate system, while scattering events are most conveniently described in a reference frame moving with the velocity of the centre-of-mass of the system. It is thus necessary to transfonn the measured velocity flux contour maps into the center-of-mass coordmate (CM) system [13]. Figure B2.3.2 illustrates the reagent and product velocities in the laboratory and CM coordinate systems. The CM coordinate system is travelling at the velocity c of the centre of mass... 

Fig. 21. The product D-atom velocity-flux contour map, d

Figure 5. Center-of-mass velocity flux contour map n-H2i 1.84 kcal/mol, with three-dimensional perspective.

Fig. 11. HCCO product flux (velocity-angle) contour map from the 0(3P) + C2H2 reaction at Ec = 9.5kcalmol 1 (a). 3D perspective (b).

Fig. 16. Flux (velocity-angle) contour maps of the vinoxy (CH2CHO), acetyl (CH3CO), and ketene (CH2CO) products from the 0(3P) + C2H4 reaction at Ec = 12.9 kcal mol-1.

Fig. 5-10 Flux (velocity-angle) contour map for the KI product from the reaction K -f CH31 -KI + CH3. (Adapted from Rulis and Bernstein [33] and Levine and Bernstein [34].)...

In the two systems discussed thus far, the product scattering is very anisotropic. This indicates the lifetime of a molecular collision is very short relative to rotation of the complex formed between reactants (i.e., < --10" sec). If this were not the case, the scattering of product would be symmetric about the center of mass since all information about initial geometry of the collision would be lost after a few rotations. In fact, long-lived complexes have been observed in many cases. For example, the flux (velocity-angle) contour map for CsF formed in the reaction... 

Fig. 6-10 Flux velocity-angle contour map for DF obtained from the reaction F + D2 DF + D. The initial relative translational energy was 1.68 kcal/mole. The circles represent the largest possible value of the final velocity of DF consistent with the vibrational quantum number v. [Adapted from Y. T. Lee, in Physics of Electronic and Atomic Collisions, VII ICPEAC 1971, Fig. 4a. Reproduced by permission of copyright owner, North-Holland Publishing Co., Amsterdam.]...

Figure 2 Left Measured (dots) and calculated (solid line - see text) HCl product laboratory angular distribution from the Cl + H2 reaction at Ec = 24.5 kJ/mol and corresponding Newton diagram. Right HCl product center-of-mass flux (velocity-angle) contour map.

Figure 5 Center-of-mass flux (velocity-angle) contour maps of the HOD and CO2 products from the OH + D2 and OH + CO reactions with three-dimensional perspective.

To each internal state of the products there corresponds a velocity whose mag-nitnde is determined from conservation of energy and whose direction is to be measured. Both experiment and theory can provide such resolution, as shown in Figure 5.12. But this requires a separate plot for each final quantum state. Instead, we represent this information on a single plot in such a way that the major dynamical features of the reaction are immediately evident. We do so in the form of a product flux contour map, a map showing the distribution of the final velocity vectors. We develop the concept of a Newton sphere by means of an example. Consider the elementary reaction... 

Crossed-beam experiments naturally produce flux velocity-angle contour maps, which can be measured with considerable detail. Applications include a variety of atom-diatom reactions, ion-molecule reactions, complex mode reactions, diatom atom reactions, etc. Examples are to be found throughout the text. For the special case when the reaction is photoinitiated we return to this... 

Figure 6.12 Flux (velocity-angle) contour map (upper half only) for the Dl product of the D + I2 reaction, for Ej = 9kcal mol See also Problem P. The extensive "sideward" scattering has been interpreted in terms of a preferred bent geometry for the transition state. This behavior is consistent with molecular orbital considerations (Section 5.1.5.1). [Adapted from J. D. McDonald etal., J. Chem. Phys. 56,769 (1972).]...

The usual flux velocity-angle contour map is of this quantity in a (0, ) polar coordinate system. Experimentally, it is easier to determine the relative values of the cross-section for different velocities. The results are then presented as a distribution P(6,u ) a a(9,u ) that can be normalized by integration over aU scattering angles and velocities,/du f d oE P(6, u )= 1. 

The CM distributions for the HF products are summarized graphically in Figure 5, a contour map of the velocity flux distribution as a function of the CM scattering angle 6. The v ... 

The ultimate desirable outcome in any chemical reaction dynamic experiment is the measurement of flux-velocity contour maps for quantum-state-selected products from photofragmentation, or inelastic and reactive collisions processes for which the initial state is also well defined. From such contour maps, complete information on the chemical process can be deduced in favourable cases. 

Fig. 8.11. Contour map of the angle-velocity flux distributions for DCl in the D + CI2 reaction. The radius vector is proportional to the velocity of the Cl. Contours are drawn at relative intensities of 0.1, 0.5, 0.8, and 1.0. [Adapted from D. R. Herschbach, Disc. Faraday Soc. 55, 233 (1973).]...

Contour maps for the angle-velocity flux of ArD+ produced in this reaction have been computed on the basis of a highly approximate potential-energy surface. The model treats Ar+ as a hard sphere and Dg as a pair of hard spheres nearly in contact. The relative motion prior to Ar -Da collision is governed by the ion-induced-dipole potential between Ar+ and D2. During collision the ion and each atom are treated as hard spheres. An ArD+ ion is presumed to have formed if the relative translational energy of the nuclei is less than the bond dissociation energy. As the products... 

Figure 6.10 (cont.) Contour map the flux (velocity-angle) distribution for the Kl product of the K + I2 reaction. The initial velocities are shown in the center-of-mass system where the velocity of the heavy I2 is necessarily small compared to that of K. All Kl molecules with the same final velocity u, will lie on a circle centered at the c.m. ( ). The dashed circle corresponds to the highest recoil velocity allowed by conservation of energy, and hence to internally cold Kl molecules. The closer the point is to the c.m., the higher is the internal energy of the Kl product. Kl scattered at a given direction 9 with respect to the direction of the incident K atom will appear on a given ray (from the c.m.). The maximal scattering is into the contour (arbitrarily) labeled 10. Contrast with the location of the same contour in Figure 6.11. [Adapted from K. T. Gillen, A. M. Rulis, and R. B. Bernstein, J. Chem. Phys. 54, 2831 (1971).]...

FIGURE 11.8 Center-of-mass velocity contour flux map for the reaction of phenyl radicals (left 0°) with acetylene (a), ethylene (h), and D6-henzene (c) to form phenylacetylene (a), styrene (h), and D5-diphenyl (c) (right 180°). The colors connect data points with an identical flux and range from red (highest flux) to yellow (lowest flux). The units of axis are given in ms (see legend). 

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