# Vibrational state dependency of the reaction cross section

I'm reading p.1238 of Mcquarrie's Physical Chemistry: A Molecular Approach textbook.

In the last line of the page, the author explains that the value of the reaction cross section in the constant total energy depends strongly on the vibrational state of the reactant. Of course, it means that not only translational kinetic energy but also internal energy(such as vibrational state) contributes to the value of the reaction cross section values.

However, the book puts a limit on the 'constant total energy'. If both translational kinetic energy and vibrational energy contribute to the reaction cross section value, does the explanation in the book imply that vibrational energy contributes more to the reaction cross section value than translational kinetic energy?

If that's true, is there a way to explain the difference in contribution qualitatively? Or is it just a matter of quantitative differences?

Vibrations are very important for reactions. In the particular example of $$\ce{H2+(g) + He}$$

• vibrational levels 0-3 have an energy less than E0 (minimum energy for reaction), so additional transitional energy is needed to induce reaction. That’s why we see a threshold.
• vibrational levels > 4 already have more than E0 energy so they react even with no additional energy

The greater the vibrational energy level of $$\ce{H2+}$$ the easier it will be for the substitution reaction, and this makes sense considering the transition state diagram

You may also be interested in the "harpoon" reaction which demonstrates how vibrations are important 1.

This reaction is known as a harpoon reaction because an electron is first transferred from M in $$\ce{M...XR}$$ or $$\ce{[M...XR]^*}$$ to $$\ce{RX}$$ and thereby forms the ionic transition state $$\ce{M+...RX-}$$. The negatively charged $$\ce{RX-}$$ is unstable and can dissociate, forming the products $$\ce{M+X-}$$ and $$\ce{R}$$.

These type of reactions are, in general, valuable for studying how rovibrational states affect the reaction probabilities because they can be triggered by light, and are small enough to model with extremely accurate theories.

In particular, the reaction probability has notable "resonances" spaced precisely 10.9 $$cm^{-1}$$ apart. These resonances are most likely due to low frequency bending mode of the T-shaped complex.

References:

1. Skowronek, S., Jiménez, J. B. & González Ureña, A. Resonances in the Ba...FCH3+hv→BaF+CH3 reaction probability. J. Chem. Phys. 111, 460–463 (1999).