A Generalized Structure-Activity Relationship for the Decomposition of (Substituted) Alkoxy Radicals

A novel and readily applicable Structure-Activity Relationship (SAR) for predicting the barrier height Eb to decomposition by (beta) C-C scission of (substituted) alkoxy radicals is presented. Alkoxy radicals are pivotal intermediates in the atmospheric oxidation of (biogenic) volatile organic compounds, and their fate is therefore of crucial importance to the understanding of atmospheric VOC degradation mechanisms. The SAR is based on available theoretical energy barriers and validated against barriers derived from experimental data. The SAR is expressed solely in terms of the number(s) Ni of alkyl-, hydroxy- and\or oxo-substituents on the (alpha) and (beta)carbons of the breaking bond: Eb (kcal/mol) =17.5-2.1 × N(alpha)(alk)-3.1 ×N(beta)(alk)-8.0 × N(alpha),(beta)(OH)-8.0 × N(beta)(O=)-12 × N(alpha) (O=). For barriers below 7 kcal/mol, an additional, second-order term accounts for the curvature. The SAR reproduces the available experimental and theoretical data within 0.5 to 1 kcal/mol. The SAR generally allows conclusive predictions as to the fate of alkoxy radicals; several examples concerning oxy radicals from prominent atmospheric VOC are presented. Specific limitations of the SAR are also discussed. Using the predicted barrier height Eb, the high-pressure rate coefficient for alkoxy decomposition k^(infinity)diss (298 K) can be obtained from k^(infinity)diss (298 K) = L × 1.8 × 10^13 exp(-Eb/RT) s^-1, with L the reaction path degeneracy.