Statistical Modeling of Gas-Phase Organometallic Reactions Based on Density Functional Theory: Ni+ + C3H8

Density functional theory in its B3LYP variant has been used to explore quantitative details of the adiabatic potential energy surface leading from Ni + + C 3 H 8 reactants through a deep Ni + (C 3 H 8 ) well to NiC 2 H 4 + + CH 4 and NiC 3 H 6 + + H 2 elimination products. The lowest energy path to CH 4 elimination involves facile CC bond insertion followed by a high multicenter transition state (MCTS) leading directly to the exit-channel complex Ni + (C 2 H 4 )(CH 4 ). The lowest energy path to H 2 elimination involves comparably facile secondary CH insertion followed by a comparably high MCTS leading directly to the Ni + (C 3 H 6 )(H 2 ) complex. Primary CH insertion leads to significantly higher barriers to both CH 4 and H 2 elimination; in particular, β-methyl migration is energetically very costly. These results support a mechanism significantly different from the stepwise mechanisms invoked earlier but the same as that found in recent calculations on the Fe + + C 3 H 8 reaction by Holthausen and Koch. The geometries suggest that agostic interactions are important in stabilizing the key MCTSs. We use the B3LYP geometry (moments of inertia) and harmonic vibrational frequencies at each stationary point to construct a detailed rate model of the reaction, applying RRKM theory to each reaction step on the adiabatic ground-state surface. A steady-state approximation holds well and leads to a simple parallel decay model for the long-lived Ni + (C 3 H 8 ) complexes. By adjusting the energies of the key MCTSs downward by 5−7 kcal/mol from the values from B3LYP theory, we can explain the range of experimental time scales, the product branching fractions, total cross section vs kinetic energy, and deuterium isotope effects. Differential centrifugal effects arising from the substantial variation of the mass distribution along the reaction coordinates lead to a strong J -dependence of the Ni + (C 3 H 8 ) decay rate and of product branching fractions as well. The resulting mechanistic picture indicates that at low energy only low- J complexes (formed at small impact parameter) can overcome the centrifugal barriers atop the MCTSs and produce elimination products. High- J complexes live as Ni + (C 3 H 8 ) for nanoseconds−microseconds, repeatedly insert in CC and CH bonds, but eventually revert to Ni + + C 3 H 8 reactants. We suggest possible reasons why the new model cannot explain the bimodal kinetic energy release distribution observed by Bowers and co-workers in the NiC 3 H 6 + + H 2 channel.