Even-odd product variation of the C_n⁺ + D₂ (n = 4-9) reaction: Complexity of the linear carbon cation electronic states

We have studied reactions between linear C_n⁺ (n = 4-9) and D₂, using ion mobility mass spectrometry techniques and quantum chemical calculations in order to understand the complex reactivity of the linear cluster cations. Only linear C_nD⁺ products were observed for the odd (n = 5, 7, 9) linear clusters, while C_nD₂⁺ was the main product for the even clusters. For the reaction rate constants determined for these two channels, we obtained the following two features: (1) the rate constant decreases with the size n, and (2) even-sized clusters have lower rate constants than neighboring odd-sized clusters. In the theoretical calculations using the CCSD(T) and B3LYP methods with the cc-pVTZ basis, we found that a low lying ²Σ state in odd clusters may play an important role in these reactions. This opposes the previous interpretation that the ²Π_g/u state is the dominant electronic state for linear C_n⁺ (n = 4-9) clusters. We showed that a barrierless radical abstraction forming C_nD⁺ occurs through a direct head on approach for the ²Σ state C_n⁺. In contrast, a carbene-like insertion forming C_nD₂⁺ occurs through a sideways approach for the ²Π_g/u state C_n⁺. We have concluded that the higher rate constants for the odd clusters come from the existence of symmetry broken ²Σ states which are absent in even linear clusters.