Revisiting the Hammond postulate: The role of reactant and product ionic states in regulating barrier heights, locations, and transition state frequencies

Radical-molecule reaction barriers are often the product of an avoided curve crossing between two states: the reactant ground state, which ultimately correlates with a product ionic state, and a reactant ionic state, which ultimately correlates with the product ground state. The energy, location, and loose-mode frequencies of the transition state are controlled by this interaction. The curve crossing itself is constrained by long-range Coulombic forces acting primarily on the ionic states as the reactants approach each other. The crossing height is in essence a geometric mean of the ionic surface heights; a low ionic state energy in either the reactants or the products will force a low reaction barrier. The crossing location is controlled primarily by any asymmetry in the reactant and product ionic heights, while the interaction distance of the transition state is controlled by a balance in gradients on the ground and ionic states. The frequencies related to translation of the separated reagents within the center of mass frame of reference are controlled by the same physics controlling the barrier height, as is the imaginary frequency associated with the reaction itself. This drives a tight correlation between barrier heights. transition state frequencies (and thus preexponential terms), and the imaginary frequency (and thus the tunneling term). This is demonstrated by analyzing a series of H atom transfers from a mainfold of alkanes to a mainfold of atoms. The Hammond postulate-reaction enthalpy controls transition state location-does not correspond to the mechanism controlling either barrier height or location, but rather appears to work in cases where ionization potential correlates with bond strengths.