Background of the problem:

The reaction between methyl iodide (CH₃I) and the cyanide ion (CN⁻) is particularly intriguing, as it leads to the formation of two isomeric products, methyl isocyanide (NCCH₃) and methyl cyanide (CNCH₃), along with iodide (I⁻) as a byproduct. To explore the reaction dynamics, Carrascosa et al. conducted crossed-beam velocity map imaging experiments, which revealed a high degree of internal excitation in the products across three distinct collision energies.

Due to the inability to experimentally determine the reaction barriers for the formation of the two isomers, a statistical branching ratio of [NCCH₃]/[CNCH₃] = 1 was assumed, based on the assumption of similar barrier heights. However, a separate investigation using high-level ab initio electronic structure calculations provided further insight into the thermodynamics of the system.

This theoretical study found that NCCH₃ is thermodynamically more stable than CNCH₃ by 24.6 kcal/mol, as calculated at the CCSD(T)-F12b/aug-cc-pVQZ level of theory. The difference in activation barriers between the two pathways was found to be negligible.

Additionally, alternative reaction pathways such as proton abstraction and iodine abstraction may also influence the reaction dynamics. These channels lead to the formation of HCN/HNC + CH₂I⁻ and ICN⁻/INC⁻ + CH₃, respectively. Notably, the latter pathway involving iodine abstraction was observed at higher collision energies, suggesting its increased relevance under such conditions.

Why did we study this reaction?

1. A key challenge in this reaction is that the experiment lacked the capability to determine the product branching ratio, i.e., [NCCH₃]/[CNCH₃]

2. Why is the energy released in the reaction predominantly distributed into the internal modes (e.g., vibration, rotation) of the products?

Classical Trajectory Simulations

We carried out direct dynamics simulations of this reaction at all experimental collision energies, ie. 0.3 eV, 0.7 eV and 1.1 eV. The energy gradients required to integrate the equation of motions were calculated on the fly at the B3LYP/aug-cc-pVDZ (ECP) level of theory using the VENUS-NWChem software package.

The time required to integrate these trajectories was too high to get statistically meaningful results. It took us one and a half years to generate only 1500 trajectories! Moreover, the reaction has 1-3% reactivity, which only made 41 reactive trajectories for overall analysis. Still, we proved that experimentally observed dominance of the direct rebound mechanism (see Anim1 for mechanism)  and non-statistical branching ratios of formed products, ie. [NCCH₃]/[CNCH₃] ≠ 1 at all collision energies.

However, the determination of the product's internal energy distribution requires a strong statistical assessment. This objective was hard to achieve by DFT direct dynamics. Hence, we decided to run direct dynamics using a semi-empirical quantum chemistry method called Parameterised Model 7 (PM7). We can see in Fig. 1 the mapping of the potential energy profile PM7 over DFT. The mapping shows good agreement between the barrier heights calculated by both methods. We generated a total of 60,000 trajectories using the semi-empirical direct dynamics method. This time, although the overall reactivity remained the same, the data obtained were statistically more reliable.

The internal energy and scattering angle distribution at all collision energies are shown in Fig. 2.  This completes our third objective, high internal excitation of products and backscattering, which significantly matches the experiments.

Key outcomes of the study 

1. The product branching ratios are non-statistical.

2. The simulations confirm high internal excitation of the formed products.

3. Direct rebound mechanism is dominant at all collision energies.