Ab initio calculation of inner-sphere reorganization energies of arenediazonium ion couples

The geometries of a series of substituted arenediazonium cations (p-NO2, p-CN, p-Cl, p-F, p-H, m-CH3, p-CH3, p-OH, p-OCH3, p-NH2) and the corresponding diazenyl radicals were optimized at the HF/6-31G, MP2/6-31G, B3LYP/6-31G, B3LYP/TZP, B3PW91/TZP, and CASSCF/6-31G levels of theory. Inner-sphere reorganization energies for the single electron-transfer reaction between the species were computed from the optimized geometries according to the NCG method and compared to experimental values determined by Doyle et al. All levels of theory predicted a CNN bond angle of 180 degrees in the cation. A bent neutral diazenyl radical was predicted at all levels of theory excepting B3LYP/TZP and B3PW91/TZP for the p-Cl-substituted compound. Inner-sphere reorganization energies determined at the HF, MP2, and CASSCF levels of theory correlated poorly with both experimental results and calculated geometries. Density functional methods correlated best with the experimental values, with B3LYP/6-31G yielding the most promising results, although the ROHF/6-31G survey also showed some promise. B3LYP/6-31G calculations correctly predicted the order of the inner-sphere reorganization energies for the series, excluding the halogen-substituted compounds, with values ranging from 42.8 kcal x mol(-1) for the p-NO2-substituted species to 55.1 kcal x mol(-1) for NH2. The magnitudes of these energies were lower than the experimental by a factor of 2. For the specific cases examined, the closed-shell cation geometries showed the expected geometry about the CNN bond, with variations in the CN and NN bond lengths correlating with the electron-donating/withdrawing capacity of the substituent. As predicted by Doyle et al., a large geometry change was observed upon reduction. The neutral diazenyl radicals showed a nominal CNN bond angle of 120 degrees and variations in the CN and NN bond lengths also correlated with the electron-donating/withdrawing capacity of the substituent. Changes in theta(CNN) and r(CN) both correlated well with calculated lambda(inner). The key parameters influencing inner-sphere reorganization energy were the CN and NN bond lengths and the CNN bond angle. This influence is explained qualitatively via resonance models produced from NRT analysis and is related to the amount of CN double bond character. Based on these observations, B3LYP/6-31G calculations are clearly the most amenable for calculating inner-sphere reorganization energies for the single electron-transfer reaction between cation/neutral arenediazonium ion couples.