Reactive resonances

Of course, the distinction between reactive- and bound-state wave functions becomes blurred when one considers very long-lived reactive resonances, of the sort considered in Section IV.B, which contain Feynman paths that loop many times around the CL Such a resonance, which will have a very narrow energy width, will behave almost like a bound-state wave function when mapped onto the double space, since e will be almost equal to Fo - The effect of the GP boundary condition would be therefore simply to shift the energies and permitted nodal structures of the resonances, as in a bound-state function. For short-lived resonances, however, Te and To will differ, since they will describe the different decay dynamics produced by the even and odd n Feynman paths separating them will therefore reveal how this dynamics is changed by the GP. The same is true for resonances which are long lived, but which are trapped in a region of space that does not encircle the Cl, so that the decay dynamics involves just a few Feynman loops around the CL... 

The F + H2 — HF + FI reaction is one of the most studied chemical reactions in science, and interest in this reaction dates back to the discovery of the chemical laser.79 In the early 1970s, a collinear quantum scattering treatment of the reaction predicted the existence of isolated resonances.80 Subsequent theoretical investigations, using various dynamical approximations on several different potential energy surfaces (PESs), essentially all confirmed this prediction. The term resonance in this context refers to a transient metastable species produced as the reaction occurs. Transient intermediates are well known in many kinds of atomic and molecular processes, as well as in nuclear and particle physics.81 What makes reactive resonances unique is that they are not necessarily associated with trapping... 

One property of the F + HD reaction which is particularly unique is the nearly complete absence of direct reaction pathway at energies below about Ec = 1 kcal/mol.26,27,31 At these low energies the reaction, and all of its observable characteristics, is mediated through a reactive resonance. The total DCS presented so far is a highly averaged quantity, the actual data obtained from the Doppler-selected TOF measurement is however the state-to-state DCS. To illustrate the effect of reactive resonance at the state-to-state level of details, let us focus on the low energy reaction. Figure 20... 

The possibility of the existence of short-lived reactive resonances has been discussed often over the years. The early advances in this field were largely theoretical and based on the analysis of quantum reaction dynamics using approximate PESs.5-10 These studies provided much insight into the dynamical origin of complex formation. However, they were speculative... 

Fig. 1. A schematic diagram of the relationship between adiabatic potential curves and reactive resonances, (a) shows the conventional Feshbach resonance trapped in a well of an adiabatic curve, (b) illustrates barrier trapping, which occurs near the energy of the barrier maximum of an adiabatic curve.

The simple INR concept has succeeded beautifully for many problems in atomic and nuclear physics. Unfortunately, the INR picture is seldom valid for reactive resonances, which, on the contrary, tend to be broad and overlapping. The breakdown of the INR idealization for reactive resonances was appreciated long ago in terms of the impact parameter averaging implicit in reactive collisions.38 If we imagine that an isolated reactive resonance corresponds to a vibrational state of an intermediate molecule, then the rotational energy levels built on that state have energies given by... 

Cross-sections for reactive scattering may exhibit a structure due to resonance or to other dynamical effects such as interference or threshold phenomenon. It is useful to have techniques that can identify resonance behavior in a system and distinguish it from other sorts of dynamics. Since resonance is associated with dynamical trapping, the concept of the collision time delay proves quite useful in this regard. Of course since collision time delay for chemical reactions is typically in the sub-picosecond domain, this approach is, at present, only useful in analyzing theoretical scattering results. Nevertheless, time delay is a valuable tool for the theoretical identification of reactive resonances. 

Perhaps the first clear observation of a reactive resonance in a collision experiment was recently made for the F + HD —> HF + D reaction.65-67 This reaction was one isotopomer of the F + H2 system studied in the landmark molecular beam experiments of Lee and co-workers in 1985.58 Unlike the F + H2 case, no anomalous forward peaking of the product states was reported, and results for F + HD were described as the most classical-like of the isotopes considered. Furthermore, a detailed quantum mechanical study68 of F + HD —> HF + D reaction on the accurate Stark-Werner (SW)-PES69 failed to locate resonance states. Therefore, it was surprising that the unmistakable resonance fingerprints emerged so clearly upon re-examination of this reaction. 

To uniquely associate the unusual behavior of the collision observables with the existence of a reactive resonance, it is necessary to theoretically characterize the quantum state that gives rise to the Lorentzian profile in the partial cross-sections. Using the method of spectral quantization (SQ), it is possible to extract a Seigert state wavefunction from time-dependent quantum wavepackets using the Fourier relation Eq. (21). The state obtained in this way for J = 0 is shown in Fig. 7 this state is localized in the collinear F — H — D arrangement with 3-quanta of excitation in the asymmetric stretch mode, and 0-quanta of excitation in the bend and symmetric stretch modes. If the state pictured in Fig. 7 is used as an initial (prepared) state in a wavepacket calculation, one observes pure... 

Fig. 7. The probability density of the reactive resonance at Ec = 0.52 kcal/mol. In (a) the F-H-D collinear subspace is shown using the Jacobi coordinates (R,r). In (b), the probability density is sliced r = 2 Bohr and is shown in the (R, 7) coordinates. The plot clearly shows a state with 3 nodes along the asymmetric stretch and 0 nodes in the...

In summary, the reactive resonance for the F + HD —> HF + D reaction is found to leave clear signatures on a variety of collision observables. The resonance state itself is readily extracted from the quantum dynamics on the SW-PES, and the scattering observables are found to correlate well with the predictions of theory. 

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