Conical Intersections and Activation Energies

1. Addition of Peroxyl Radicals to Alkenes and the Reaction of Oxygen with Alkyl Radicals Moray Stark Department of Chemistry University of York, York, YO10 5DD, UK Addition of Peroxyl Radicals to Alkenes One of the most studied examples of radical reactions with alkenes is peroxyl radical addition, investigated in detail by Waddington et al.eg.1 (acetyl and alkylperoxyl radicals) and Baldwin and Walker et al. eg.2 (hydroperoxyl radicals). k1 k2 Hydroperoxyl + Ethene k-1 Transition State Adduct Hydroxyl + Ethene Oxide Epoxides are the dominant product of these reactions, with the initial addition being the rate determining step (k2 >> k-1).1,2 Frontier Orbital Description of Radical Addition to Alkenes This dependence of activation energy for the However, the radical in the 2A’ first addition reaction on the energy of the first excited state correlates with the excited state of the radical is what would be 2A’ ground state of the Cs saddle expected if the radical and alkene approached point (an ROHF representation of this in the same plane (Cs symmetry). is shown here). The peroxyl radical 2A” ground state correlates with an energetically unfavourable 2A” excited state of the Cs saddle point for the addition. Activation Energy vs. Alkene Ionisation Energy It is well known that one of the factors controlling This identifies the addition as an the rate of addition of peroxyl radicals to alkenes electrophilic reaction; the greater is the ionisation energy of the alkene; the reaction the charge transfer to the radical being faster the lower the alkene ionisation energy.1,2 during the reaction, the faster the rate. Conical Intersections and Activation Energies If the radical and alkene approach in the The conical intersection guarantees same plane (Cs symmetry), then the 2A” that for a particular relative orientation and 2A’ surfaces cross at a conical and separation of the radical and intersection. alkene, the energy of the system must be higher than the reactants. The transition state for the addition reaction has C1 symmetry, and is The proximity of the transition state to reached from the conical intersection the conical intersection ensures that it by moving along the symmetry breaking too has an energy higher than the co-ordinate of the branching space. reactants, with a barrier height related to the energy of the first excited state of the radical. Charge Transfer During Reaction The parabola model of Pearson and Parr allows Shown here is how the system’s the degree of charge transfer at the transition energy varies with charge transfer state for the addition to be estimated by using for the addition of acetylperoxyl the ionisation energies (I) and electron affinities radicals to 2-methyl-2-butene. (A) of the isolated reactants.3 The energy released (EC) by the charge transfer (NC) can be viewed as the driving force for the reaction. Reaction of Oxygen with Alkyl Radicals Alkyl radicals react with oxygen to give alkylperoxyl radicals Ab-initio studieshave shown that which at low pressure or high temperature can decompose to alkylperoxyl radicals decompose an alkene and hydroperoxyl radical. directly to the alkene + HO2 via a 2A” transition state and not via the However, there has been controversy over the mechanism of hydroperoxylalkyl radical as once this decomposition, as the reverse reaction, HO2 + alkene, gives thought.8 the epoxide + OH and not the alkylperoxyl radical as might be expected on the grounds of reversibility.eg.2,7 This mechanism is combined here with the above description for peroxyl radical addition to alkenes. Activation Energy vs. Charge Transfer Energy The energy released by charge transfer to The relationship also suggests that the radical as it approaches the alkene (EC) the activation energy for a reaction correlates very well with the activation energy involving no charge transfer would for the reaction4 (as indeed do data for nitrate be 80 - 90 kJ mol-1. radical addition).5 Coincidentally, 80 - 90 kJ mol-1 is This suggests that the energy released by also typical of the energy required to charge transfer lowers the barrier for the promote these radicals to their first addition approximately in proportion, electronically excited states.6 becoming barrierless for EC 60 kJ mol-1. Potential Energy Diagram for Ethyl + Oxygen Discussion of this class of reaction has centred on A potential energy diagram for this the most studied example, ethyl + oxygen, with system is suggested here, based on disagreement over not just the mechanism, but the above mechanism, and with also of barrier heights for key steps in the reaction. barrier heights chosen to be as compatible as possible with experimental observations. References (1) Ruiz Diaz, R.; Selby, K.; Waddington, D. J. J. Chem. Soc. Perkin Trans. 21977, 360. (5) Wayne, R. P. et al. Atmos. Environ. 1991, 25A, 1. (2) Stothard, N. D.; Walker, R. W. J. Chem. Soc. Faraday Trans.1990, 86, 2115. (6) Stark, M. S. J. Am. Chem. Soc.2000, 122, 4162. (3) Parr, R. G.; Pearson, R. G. J. Am. Chem. Soc.1983, 105, 7512. (7) Wagner, A. F.; Slagle, I. R.; Sarzynski, D.; Gutman, D. J. Phys. Chem. 1990, 94, 1853. (4) Stark, M. S. J. Phys. Chem.1997, 101, 8296. (8) Quelch, G. E.; Gallo, M. M.; Schaefer, H. F. J. Am. Chem. Soc.1992, 114, 8239.