Insertion reactions are characterised by having a deep well on the potential energy surface that corresponds to a covalently-bound collision complex. Typical examples are provided by the reactions of electronically excited carbon (1D), nitrogen (2D), oxygen (1D) and sulphur (1D) atoms with H2. The first of these reactions proceeds via singlet CH2, the second via the NH2 radical, the third via the water molecule, and the last via H2S, all four of which are very strongly bound relative to the reactants with well depths of over 4 eV:
The exact quantum mechanical treatment of these reactions is complicated by the need to converge all of the bound and low-lying resonance states of the collision complex. However, the very existence of these resonance states suggests that an exact quantum mechanical treatment may not be necessary: if the resonances are sufficiently long lived, a simple statistical description of their formation and decay into reactant and product channels may be enough to give satisfactory results. We have recently developed the theory of such a statistical model and used it to study all four of the above insertion reactions.
The following figure shows one of our results. It compares exact quantum mechanical (QM), statistical (SM) and experimental (Exp) differential cross sections for the S(1D) + H2 reaction at a collision energy of 97 meV. The exact quantum mechanical results were calculated by Honvault and Launay, and the experimental measurements were made by Lee and Liu:
It can be seen from the figure that the S(1D) + H2 reaction behaves perfectly statistically at this collision energy, and that the quantum dynamics on the ground adiabatic (1A') potential energy surface is all that is needed to explain the experimental results: the quantum scattering, statistical, and experimental angular distributions for this reaction are all on top of one another.
More details are given in J. Chem. Phys. 119, 12895 (2003), which also contains results for the C(1D) + H2, N(2D) + H2 and O(1D) + H2 reactions and references to earlier work on the statistical model (which was first introduced in the nuclear physics literature in the 1950s).