Ab Initio Calculation of Inner-Sphere Reorganization Energies of Arenediazonium Ion Couples

Abstract

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.

Sandmeyer reactions. Part 7.1 An investigation into the reduction steps of Sandmeyer hydroxylation and chlorination reactions

“…Recent work which reports calculation of the barriers to self exchange in ArN 2 ϩ /ArN 2 ؒ couples by a variety of theoretical methods supports a strong substituent dependence. 71 The unsubstituted couple PhN 2 ϩ /PhN 2 ؒ is therefore expected to exhibit a self-exchange rate much reduced in comparison with that ca. 10 8 dm 3 mol Ϫ1 s Ϫ1 shown by the couple PhCN/ PhCN Ϫ which, though isoelectronic, does not undergo substantial structural or orbital reorganisation 72 and, given a reaction constant > 5 for self-exchange in ArN…”

Are Reactions Between Metal Cyanides and Aryl Diazonium Ions Really Outer-Sphere Electron Transfer Processes?

“…As a consequence, a previously reported method of extraction of self-exchange reorganization energies for benzenediazonium salts by using Marcus theory and assuming that the primary reaction proceeds according to eq cannot be valid. The fact that the self-exchange energies obtained by and large agree with ab initio calculations , and calculations based on ESR spectra of benzenediazenyl radicals thus remains unexplained.…”

“…In fact, the results are by and large in agreement with ab initio calculations, showing that substantial changes do occur in the C−N and the N−N bond lengths as well as the C−N−N bond angle upon ET. For example, the C−N−N bond angle is found to be 180° in ZC 6 H 4 N 2 + and ∼120° in ZC 6 H 4 N 2 • . , Moreover, structural changes have also been deduced from measurement of ESR spectra of various aryldiazenylradicals at low temperatures …”

Aryldiazenyl Radicals from Arylazo Sulfones: Visible Light‐Driven Diazenylation of Enol Silyl Ethers

“…This approach led to carbodiazenylations (where two aryl moieties are tethered to the nucleophile) or made use of different intermediates such as the aryldiazene cation radical . The intermediacy of an aryldiazenyl radical ( I , Scheme ), however, is a rare occurrence . The main reason is the poor stability at room temperature in solution of this intermediate since it is known that loss of dinitrogen took place to give an aryl radical with a fragmentation rate constant in the 0.4–4.0×10 5 s −1 range .…”