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 correspondin g diazenyl radicals were optimized at the HF/6-31G*, MP2/6-31G*, B3LYP/6-31 G*, 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 NC G 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 excep ting B3LYP/TZP and B3PW91/TZP for the p-Cl-substituted compound. Inner-sphe re reorganization energies determined at the HF, MP2, and CASSCF levels of theory correlated poorly with both experimental results and calculated geom etries. Density functional methods correlated best with the experimental va lues, with B3LYP/6-31G* yielding the most promising results, although the R OHF/6-31G* survey also showed some promise. B3LYP/6-31G* calculations corre ctly predicted the order of the inner-sphere reorganization energies for th e series, excluding the halogen-substituted compounds, with values ranging from 42.8 kcal mol(-1) for the p-NO2-substituted species to 55.1. kcal mol( -1) for NH2. The magnitudes of these energies were lower than the experimen tal by a factor of 2. For the specific cases examined, the closed-shell cat ion geometries showed the expected geometry about the CNN bond, with variat ions in the CN and NN bond lengths correlating with the electron-donating/w ithdrawing capacity of the substituent. As predicted by Doyle et al., a lar ge geometry change was observed upon reduction. The neutral diazenyl radica ls 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 correlat ed well with calculated lambda (inner). The key parameters influencing inne r-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 c haracter. Based on these observations, B3LYP/6-31G* calculations are clearl y the most amenable for calculating inner-sphere reorganization energies fo r the single electron-transfer reaction between cation/neutral arenediazoni um ion couples.