Ab initio calculations of the transition state energy and position for the reaction H+C(2)H(5)R->HH+C(2)H(4)R, with R=H, CH3, NH2, CN, CF3, C5H6: Comparison to Marcus' theory, Miller's theory, and Bockris' model

Some years ago, Murdoch proposed that one can use the Marcus equation to predict the position of the transition state for chemical reactions. A slightly different equation was proposed by Miller. In this paper, ab initio calculations are used to test Murdoch's and Miller's proposal for a series of hydrogen abstraction reactions: H + CH(3)CH(2)R --> H-2 + CH(2)CH(2)R, with R = H, CH3, CN, CF3, C5H5. We find that in all cases the reactions have late or very late transition states. If we define chi as a dimensionless reaction coordinate which goes from 0 at the reactants to 1 at the products, we find that the chi of the transition state varies from 0.63 to 0.86, for the cases here. In contrast, the Marcus equation and Miller's equation give quantitatively incorrect results, i.e., early to middle transition states (chi = 0.44-0.51). There does not appear to be any correlation between the positions of the transition state estimated from the ab initio calculations and those predicted by the Marcus equation or Miller's equation. Interestingly, the Hammond hypothesis gives a reasonable fit to the data. The energy of the transition state is reasonably well predicted by the Marcus equation, however. Detailed analysis of our results indicates that Pauli repulsions (i.e. electron-electron repulsions) play a key role in determining the position of the transition state. The Pauli repulsions are ignored in Marcus' model.