The fundamental physics of radical-molecule reactivity: New quantum chemical approaches

A complete methodology for quantifying the activation barriers of radical-molecule abstraction reactions is derived from first principles with the dual intentions of analytical prediction and conceptual understanding. Radical molecule reactions, which span twelve orders of magnitude in reactivity and are relevant to myriad branches of chemistry from biological systems to chemical lasers, have recently been shown by Donahue et al. to be strongly dependent upon system parameters evaluated at infinite separation. The research here presented supports this reactivity dependence and improves upon the original model by evaluating the specific two-state coupling between reactant and product wave functions.; The overall reaction is treated by means of a linear curve-crossing model and the energy evolution evaluated separately in the approach/withdrawal and transfer regions to produce a modular description of the total adiabatic reaction coordinate. Properties of the isolated product and reactant wave functions are utilized to determine the energetic boundary conditions of the linear crossing. The adiabatic excited states are evaluated as mixed ionic-covalent states which reflect the relative interaction strengths of the ionic and triplet configurations with the ground state. Ground state energies are determined by consideration of the repulsive frontier orbital interaction between the abstracting radical and abstracted atom.; A new, total-system diabatic orbital basis set is constructed as a linear combination of isolated two atom bonding and anti-bonding orbitals. The orbitals of this basis set are then isolated as the structural precursors to the adiabatic wave function which yields the reactive barrier and the state to state overlap is determined by explicit integration.; A new analytic function, the pseudo-hyperbola, is derived for the purpose of imposing energetic constraints upon the adiabatic surfaces in the crossing region. The single adjustable parameter of the pseudo-hyperbola (which reduces to the hyperbola in the symmetric case) is determined by matching the adiabatic-diabatic splitting at the boundary conditions to the prediction of second-order, non-degenerate perturbation theory under a generalized coupling potential. The derived barriers reproduce experimentally measured hydrogen transfer reactions to within near chemical accuracy (1.5 kcal) and strongly support plenary reactivity control by excited state properties among homologous reactive series.; Finally, it is demonstrated how the various functional parameters of the derived model may be related to empirically observed reactivity trends and thereby used to justify them mathematically.