Application of the Group Additivity Method to Alkyl Radicals:  An ab Initio Study

The geometries and standard enthalpies of formation (Δ<sub>f</sub><i>H</i>°) of 4 paraffins and 31 alkyl radicals at 298 K were obtained by means of complete basis set 4 (CBS-4) ab initio molecular orbital theory. A comparison of the geometry of a molecule and the radicals derivable from it via elimination of a H atom from different positions suggests that only a negligible change occurs in the geometry of the groups immediately adjacent to the radical center. The CBS-4 Δ<sub>f</sub><i>H</i>°s scaled by an empirical correction display an average deviation of 0.4 kcal mol<sup>-1</sup> from the experimental data. Group values (GVs) were evaluated from the corrected ab initio Δ<sub>f</sub><i>H</i>°s by simultaneous parameter estimation. The group additivity (GA) rule was checked by a statistical analysis of the theoretical data. The derived GVs describe the corrected ab initio Δ<sub>f</sub><i>H</i>°s with an average deviation of less than 0.3 kcal mol<sup>-1</sup>, which indicates that the GA rule is applicable to alkyl radicals, and the Δ<sub>f</sub><i>H</i>°s of alkyl radicals can be predicted with an accuracy similar to that attained with existing experimental methods. New values of radical, radical-adjacent, and (C)<sub>2</sub>−C−Ċ−(C) gauche GVs are suggested; together with the accepted alkane GVs, these yield accurate Δ<sub>f</sub><i>H</i>°s of alkyl radicals within estimated errors of 0.5 kcal mol<sup>-1</sup>. Application of the GVs derived from small species is predicted to perform less satisfactorily in the estimation of Δ<sub>f</sub><i>H</i>°s of C<sub>4</sub>−C<sub>6</sub> species:  the average deviation increases from 0.3 to 0.6 kcal mol<sup>-1</sup>, while the correlation of the individual deviations and carbon numbers of the alkyl radicals changes from nearly zero to −0.36.