D2 and HD Reactions

Since 1971, persistent efforts have been made to relate the experimental results from the F + H2, D2 and HD reactions to potential surfaces via trajectory calculations.All surfaces have been of the repulsive type and favor collinear approach of F to H2. The calculated results lead to rather large /y , even on the repulsive surfaces, because of the mixed energy release that is characteristic of the F-H-H mass combination, i.e., the H H repulsive energy is released while the Rhf distance is still extended, which for collinear collisions corresponds to trajectories that cut the corner of the potential energy surface. However, the surfaces do differ in specific ways and the calculations illustrate various consequences emanating from these small differences. It is beyond the scope of this discussion to consider the individual potential surfaces and attention will be focused on the calculations that permit comparisons with energy disposal data (see Table 2.20). The collinear ab initio surface was fitted to a semiempirical expression that subsequently was used in a one-dimensional trajectory calculation to obtain 

The numbers listed in the reaction column are the magnitude and position, of the potential barrier in the collinear entrance 

Nearly all of the surfaces examined have the same difficulties 

Most of the calculations have predicted a dependence of the reaction cross section and energy disposal upon the Ha rotational state. By studying the infrared chemiluminescence from normal and para hydrogen at 77 K and 290 K, the energy disposal for/na = has been obtained. 

The HF product rotational excitation was invariant with however, the /v did change as follows J = 0(0.70), J = 1(0.67), and J = 2(0.69). Since the trajectory calculations did not give the correct vibrational distribution of the HF product, only the calculated mean value, /y , can be compared to the experimental results which, of course, include the complete HF(t = 1, 2, and 3) distribution. The /y values are available for / = 0, 1, and 2 from three 

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We have given a detailed review of the RDEQ theory and applications recently and so here we present a brief review of the theory and suggest some new extensions of it in Section 2. Some new tests of the theory are presented for the Mu+H2 reaction as well as preliminary results for excited bending state resonances in H+H2 in Section 3. A review of calculations on the 0( P)+H2 D2 and HD reactions is also given there. 

HD reaction produces Iboth NH and ND and is thus equivalent to two separate reactions). Recently, studies of reaction (8) and the N + D2 and HD reactions have Ibeen made at low temperatures using the CRESU technique. Careful consideration was given to the difference in reactivity of the ortho and para forms of H2 and to the influence of the fine structure states of the N ions on the derived Ae for the reactions (see Marquette et al 1985 and the paper by Rowe in these Proceedings). 

This question was addressed by use of classical trajectory techniques with an ion-quadrupole plus anisotropic polarizability potential to determine the collision rate constant (k ). Over one million trajectories with initial conditions covering a range of translational temperature, neutral rotor state, and isotopic composition were calculated. The results for the thermally average 300 K values for are listed in the last column of Table 3 and indicate that reaction (11) for H2/H2, D2/D2, and HD /HD proceeds at essentially the classical collision rate, whereas the reported experimental rates for H2/D2 and D2/H2 reactions seem to be in error as they are significantly larger than k. This conclusion raises two questions (1) If the symmetry restrictions outlined in Table 2 apply, how are they essentially completely overcome at 300 K (2) Do conditions exist where the restriction would give rise to observable kinetic effects ... 

The orientation in the adsorption of HD at room temperature is explained by the thermodynamic facility, and the orientation at — 40°C is referable to kinetic facility in the adsorption. In agreement with these facts, the hydrogenation of 1,3-butadiene with H2, D2, and HD was performed on ZnO at room temperature and at -40°C (76). Contrary to expectation, the reaction of butadiene with HD on ZnO resulted in giving exactly the same orientation at room temperature and at -40°C, as shown in Fig. 25 (76). The isotope... 

In addition to reactions (a)-(d), ideas on tunneling have been also used (see references cited in ref. 53) to explain isotopic effects in the exchange reactions of Cl and F atoms with H2, D2 and HD molecules, in the reactions... 

The diffusion coefficient of D atoms in a D2 crystal (measured in the same way as described above) is also temperature-independent in the range 1.9 to 4.2 K, though it is 4 orders of magnitude smaller than for H in H2 [Lee et al., 1987 Miyazaki et al., 1989], In mixed crystals of D2 and HD (from 20 1 to 7 1) a decrease in the D-atom concentration coincides with an increase in that of H, so that the total concentration remains constant. This means that the conversion is due to the diffusion-limited exchange reaction... 

The assumption was made that all the species of hydrogen have identical solubilities. As the authors point out, only the rates for D2 and HD are directly comparable, as p-H2 conversion may occur in some collisions of insufficient energy to cause exchange. The lower rate constant for HD relative to D2 is apparent rather than real as only half the exchange reactions of HD with H20 result in a loss of HD, the true rate constant for HD is twice that shown in the preceding table. 

How the D2 and D2O reactions of [p-N2H2 Ru(PCy3)(S4) 2l also allow rationalization of the other constraints of the N2 dependent HD formation (156)... 

Jenkinson and Dyne (3) used deuterated cyclohexane to differentiate between Reactions 1 and 2. From the formation of D2 and HD in diluted hydrocarbon solution they concluded that the former reaction is much less important than the radical process. This is in net contradiction with the results obtained with scavengers that show about equal importance for both reactions (7, 16). This work will show that the apparent difficulty is because of the isotopic effect. 

The ion-molecule reactions of H2, D2, and HD have been extensively studied ... 

In anticipation of our impending separation my brother and I continued our planned work at a furious pace. We compared the rates of the thermal reconversion of parahydrogen and orthodeuterium with that of the H2 + D2 = 2HD reaction ( ) and showed that the effect on the rates of the differences in the zero-point energies of the hydrogen molecules H2, D2 and HD are almost completely compensated by corresponding differences in the zero-point of the respective tri-atomic activated complexes H, H2D, HD2 and D3. 

Other work is, however, not in agreement with this finding. For X = Br, investigation of the reactions of the hot atoms, reactions (38) and (39), has bem carried out by photolysis of mixtures of DBr, H2, and Br2 in the absence of added moderator. Hot hydrogen atoms with an average translational energy of about 1 eV were produced by the sequence (46) and (47). Yidds of D2 and HD as a function of the composition of the reaction mixture were interpreted using a... 

The overall reaction for the HD loss is exothermic by 30.2 kcal moP and the corresponding free energies of reaction AG (298.15 K) are —33.1 kcal moP In comparison with the D2 elimination, the HD channel is much favored both thermodynamically and dynamically. This is comparable with the experimental gain for D2 and HD in a ratio of 70( 15) 100 [17, 18]. 

Their model is simple enough to be tractable, yet realistic enough to be a reasonable approximation to the physical situation. The system chosen was the reaction of Ar" with H2, D2, and HD. The model is as follows. The reactants approach under the influence of the ion-induced-dipole potential during the collision, the ion and each atom are treated as hard spheres the argon hydride ion is deemed to have been formed if the relative translational energy between the two nuclei is less than the bond dissociation energy finally, the products separate subject to the relevant ion-induced-dipole potential, t... 

A hierarchy of reduced dimensionality exact quantum theories of reactive scattering is presented for the vibrational state-to-state cumulative reaction probability and vibrational state-to-state thermal rate constant. The central approximation in these theories is the adiabatic treatment of the bending motion of the reactive species in the strong interaction region of configuration space. Applications of the theories are made to the reactions MU+H2, 0( P)+H2, D2 and HD... 

The reactions of 0( P) with H2 D2 and HD have become one of the most intensively studied set of reactions both experimentally and theoreti cally. Theoretically there have b ej several three-dimensional quasiclassical trajectory studies collinear exact quantum... 

This method combines the Doppler-shift and ion TOP techniques in an orthogonal manner such that the three-dimensional velocity distribution of the reaction product can be measured directly in the c.m. system (e.g. see Liu (2001)). The method has been applied to a signihcant number of reactions involving 0( D) and S( D) atoms with H2, D2 and HD molecules. Figure 23.19 illustrates the basic concepts of this novel method. 

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