Rotational product distributions

Figure 19. Comparison of the quantum (filled circles, long dashes) and the classical (solid lines) rotational product distributions of C>2(n = 0) following the dissociation of HO2 for four energies as indicated the precise energies of the corresponding quantum resonances are 0.1513, 0.2517, 0.3507, and 0.4471 eV, respectively. Also shown are the distributions obtained from PST (short dashes). All distributions are normalized so that the areas under the curves are equal. The arrows on the 7 axis indicate the highest accessible state at the respective energy and the vertical bars on the classical curves indicate7sACM, the highest populated state according to the SACM. (Reprinted, with permission of the American Institute of Physics, from Ref. 37.)...

The dynamics of a reaction that proceeds directly over the transition state is expected to be qualitatively different from that of a resonance-mediated reaction. In particular, one expects that the branching ratios into the product rovibrational states will be very different between the direct and the resonant mechanisms. For example, if a given Feshbach resonance corresponds to trapping on the v = 1 vibrationally adiabatic curve, then one might expect that the population of the v = l vibrational state of the product molecule may be greatly enhanced by the resonant mechanism. Similarly, the rotational product distribution resulting from the fragmentation of a resonance molecule may show a quite distinct pattern from that of a direct reaction. Indeed, Liu and coworkers [94], and Nesbitt and coworkers [95] have noted distinct rotational patterns in the F+HD resonant reaction. 

The quantum product state distributions from the reaction show a similar dichotomy for EC<1 kcal/mol and EC>1 kcal/mol. Focusing on the rotational state distribution for the dominant HF(tf = 2) product, in Figure 3.5 we show the ICS for F+HD HF(v = 2,/ ) as a function off and Ec. The scattering calculations show a clear change in the rotational product distribution between low- and high-energy scatterings. The rotational distribution at low... 

In order to evaluate partial photodissociation cross sections (vibrational and rotational product distributions) i.e. ABC + hv A + BC n,K) the wave function can be projected onto the different rovibrational eigenstates of the molecular fragment BC at fixed distance R between the two fragments. The chosen R should be on the asymptote of the potential energy surface where the two fragments do not interact. Balint-Kurti et at [87] have shown that the partial cross section is given by... 

The general conclusion from these comparisons for Hp is that the different DW theories give qualitatively similar results for relative quantities such as state-to-state differential cross sections and rotational product distributions. Howover. the absolute values of cross sections are different in the various DW theories, the order being SSDW < VADW < RADW < CADW s exact. This order Illustrates that as systematically better approximations (based on physical understanding) are made to the exact wavefunction the T matrix element (16). the magnitudes of the... 

All the DW calculations discussed above have been for the reactant molecule In its ground state, with v=0. j=0. The first DW calculations for a rotationally or vibrationally excited reactant molecule were carried out by the VADW method (Clary and Connor [23.241). Figure 4 compares with the exact results [731. the VADW rotational product distributions for i=0.1,2 for H- -H2(j) on PK [241. There Is close agreement between the two calculations. The effect of vibrational excitation [231 for the H2(v=2.j=0) molecule is illustrated in Figure 5 (also for PK). which plots a(v=2. j=0 4 v <2) against translational energy where... 

Figure 2 Accurate quantum. RADW and VADW rotational product distributions P(0.0 OJ ) for H+H2 on PK at Etr = 0.327 eV plotted against rotational energy.

Figure 4 Accurate quantum and VADW rotational product distributions P(0.j O.j ) for or PK at Etot = 0.60 eV plotted against rotational...

There has recently been considerable theoretical Interest In the H+D2 reaction. Two Important experiments have measured vibrational-rotational product distributions under nearly single collision conditions (41,58). The experiments are performed at Etr = 1 3 smaller product... 

Figure 9 Rotational product distributions into v =0 for H+D2 from collisions with Etr = 0.55 and 1.3 eV.

Figure 14 VADW rotational product distributions for H+FpCv=0. j-0) on a LEPS surface at Etr = V plotted against rotational energy. The...

Figure 18 VADW. quasiclassical (QC) and experimental (AL) rotational product distributions of OH(v = 1) for the 0( P)+HC( CH3) 3 reaction at Etr - 29.2 kJ mor plotted against rotational energy.

The rotational product distribution of resonances above the reaction threshold also proves to be more complicated than the non-reactive case. While the selection rule A/ = 1,2 was quite successful for the decay of product state resonances in the Cl + HF(v = 0) manifold when />10, this prediction showed serious error for reactive channel decay. Thus, if we consider the pre-reactive R(3,0,ll) complex at =3.79 kcal/mol, we see it decays dominantly into the y = 10 level in the entrance channel consistent with the selection rule. However, the decay into the product channel is distributed more broadly over the v = 3, / = 0-7 levels. This behavior is intuitive since the decay of a pre-complex into products or a post-complex into reagents involves the rearrangement of atoms and the scrambling of orbital angular momentum. 

---