Reactive scattering resonances are quasi-bound quantum states that form and decay during the course of a chemical reaction. They have no classical analogue, but they have been seen in quantum reactive scattering calculations since the early 1970s, and the importance of resonances in nuclear and electronic collisions has been appreciated for longer still. However, it is only comparatively recently that a resonance has been conclusively identified in a full-collision (crossed molecular beam) experiment on a chemical reaction.
The reaction in question is F + HD to HF + D, in which a light H atom is transferred between two heavier atoms (F and D). The following figure shows the measured differential cross section for this reaction as a function of the collision energy, along with a simulated differential cross section from our research group. The experimental measurements were made by Liu and coworkers in a crossed molecular beam apparatus, and the simulation involved performing quantum reactive scattering calculations on an ab initio electronic potential energy surface:
The key feature in this figure is the pronounced backward scattering (180 degree) peak at a collision energy of around 0.5 kcal/mol, which shifts sideways with increasing collision energy. This peak is not seen in a classical trajectory simulation, which predicts essentially zero reactivity for this reaction below a threshold of 1 kcal/mol. The origin of the peak is therefore quantum mechanical, and a detailed analysis of the quantum scattering calculation has shown that it is due to a reactive scattering resonance.
The underlying resonance (quasi-bound quantum state) wavefunction is shown in the following figure. This wavefunction was calculated by Rex Skodje, who applied his spectral quantization method to the FHD system to help interpret the experimental results. The resonance wavefunction is shown in red as a function of the F to HD distance R and the HD bond length r, and it is superimposed on light blue contours of the Stark-Werner F + HD potential energy surface:
One can see from this figure that the quasi-bound state is trapped on the product side of the reaction barrier by the small kinematic skewing angle of the F + HD system, and that it has three nodes in the product HF stretching coordinate. The resonance wavefunction therefore corresponds to HF(v'=3), but since its energy lies below the HF(v'=3) + D asymptote it can only decay predissociatively into product states with lower values of the HF vibrational quantum number. This is the classic signature of a Feshbach resonance.
A fuller discussion of this resonance and its effect on various experimental observables can be found in the three papers we have published in collaboration with Skodje and Liu: J. Chem. Phys. 112, 4536 (2000), Phys. Rev. Lett. 85, 1206 (2000), and Phys. Chem. Comm. 5, 27 (2002).