Linear free energy relationships for polyhalogenated alkane transformation by electron-transfer mediators in model aqueous systems

Linear free energy relationships (LFERs) based on Marcus theory were generated for transformation of C-1- and C-2-polyhalogenated alkanes (PHAs or R-X, where X = H, F, Cl, Br) in model aqueous systems containing bulk reductants and the electron-transfer mediators iron porphyrin or mercaptojuglone (5-hydroxy-2-mercapto-1,4-naphthoquinone). The model systems are representative of common natural environments where iron species and natural organic matter serve as electron shuttles from bulk reductants to pollutants such as PHAs. Seven ab initio computational theories were tested for their ability to generate rapid, accurate, and precise estimates of the R-X bond dissociation energy, the largest energetic term in the Marcus equation. The descriptors for the LFERs were computed using B3LYP/6-311++g(d, p) theory/basis set. The LFERs that had the highest correlation coefficients for the two model systems were log(k(FcP)) = -0.0777(+/-0.0105)D(R-X)' -0.00804(+/-0.00961)Delta G(o)' + 21.7(+/-2.82) (adj r(2) = 0.946; n = 16) and log(k(Jug)) = -0.103(+/-0.0308)-D(R-X)' - 0.00958(+/-0.00513)LUMO + 22.7(+/-9.72) (adj r(2) = 0.955; n = 12). D(R-X)' is the bond dissociation energy of the R-X bond that dissociates the transition state, Delta G degrees' is the standard free energy of one-electron reduction, LUMO is the energy of the lowest unoccupied molecular orbital of the PHA, and the numbers in parentheses are 95% confidence limits of the regression coefficient estimates. All coefficients were significant at 90% confidence. These results support earlier hypotheses based on PHA kinetic results, reaction intermediates, and products in the model systems that the initial, rate-limiting step in the reaction in both model systems is a dissociative one-electron transfer. The study supports previous studies that showed, for electron-transfer reactions involving homolytic bond dissociation, the overall reorganization energy term in the Marcus equation is composed primarily of the bond dissociation energy. Correlation of rate constants of polyhalogenated aliphatic compounds measured in related aqueous systems with D(R-X)' and Delta G degrees' suggests one-electron transfer may, at least partially, limit disappearance rates in those systems.