High-level ab initio molecular orbital theory is used to obtain benchmark values for the ferricenium/ferrocene (Fc(+)/Fc) couple, the IUPAC recommended reference electrode for nonaqueous solution. The gas-phase ionization energy of ferrocene is calculated using the high-level composite method, G3(MP2)-RAD, and two higher-level variants of this method. These latter methods incorporate corrections for core correlation and, in the case of the highest level considered, use (RO)CCSD(T)/6-311+G(d,p) in place of (RO)CCSD(T)/6-31G(d) as the base level of theory. All methods provide good agreement with one another and the corresponding experimental values. Solvation energies have been calculated using PCM, CPCM, SMD, and COSMO-RS. Using G3(MP2)-RAD-Full-TZ gas-phase energies and COSMO-RS solvation energies, the absolute redox potentials of the Fc(+)/Fc couple have been calculated as 4.988, 4.927, and 5.043 V in acetonitrile, 1,2-dichloroethane, and dimethylsulfoxide solutions, respectively.

The performance of a variety of DFT functionals (BLYP, PBE, B3LYP, B3P86, KMLYP, B1B95, MPWPW91, MPW1B95, BB1K, MPW1K, MPWB1K, and BMK), together with the ab initio methods RHF, RMP2, and G3(MP2)-RAD, and with ONIOM methods based on combinations of these procedures, is examined for calculating the enthalpies of a range of radical reactions. The systems studied include the bond dissociation energies (BDEs) of R-X (R = CH3, CH2F, CH2OH, CH2CN, CH2Ph, CH(CH3)Ph, C(CH3)2Ph; X = H, CH3, OCH3, OH, F), RCH(Ph)-X (R = CH3, CH3CH2, CH(CH3)2, C(CH3)3, CH2F, CH2OH, CH2CN; X = H, F), R-TEMPO (R = CH3, CH2CH3, CH(CH3)2, C(CH3)3, CH2CH2CH3, CH2F, CH2OH, CH2CN, CH(CN)CH3, CH(Cl)CH3; TEMPO = 2,2,6,6,-tetramethylpiperidin-1-yloxyl) and HM1M2-X (M1, M2 = CH2CH(CH3), CH2CH(COOCH3), CH2C(CH3)(COOCH3); X = Cl, Br), the beta-scission energies of RXCH2* and RCH2CHPh* (R = CH3, CH2CH3, CH(CH3)2, C(CH3)3; X = O, S, CH2), and the enthalpies of several radical addition, ring-opening, and hydrogen- and chlorine-transfer reactions. All of the DFT methods examined failed to provide an accurate description of the energetics of the radical reactions when compared with benchmark G3(MP2)-RAD values, with all methods tested showing unpredictable deviations of up to 40 kJ mol-1 or more in some cases. RMP2 also shows large deviations from G3(MP2)-RAD in the absolute values of the enthalpies of some types of reaction and, although it fares somewhat better than the DFT methods in modeling the relative values, it fails for substituents capable of strongly interacting with the unpaired electron. However, it is possible to obtain cost-effective accurate calculations for radical reactions using ONIOM-based procedures in which a high-level method, such as G3(MP2)-RAD, is only used to model the core reaction (which should contain all substituents alpha to the reaction center), and the full system is modeled using a lower-cost procedure such as RMP2.

High-level ab initio calculations have been used to determine the oxidation and reduction potentials of a large number of nitroxides including derivatives of piperidine, pyrrolidine, isoindoline, and azaphenalene, substituted with COOH, NH2, NH3+, OCH3, OH, and NO2 groups, with a view to (a) identifying a low-cost theoretical procedures for the determination of electrode potentials of nitroxides and (b) studying the effect of substituents on these systems. Accurate oxidation and reduction potentials to within 40 mV (3.9 kJ mol(-1)) of experimental values were found using G3(MP2)-RAD//B3-LYP/6-31G(d) gas-phase energies and PCM solvation calculations at the B3-LYP/6-31G(d) level. For larger systems, an ONIOM method in which G3(MP2)-RAD calculations for the core are combined with lower-cost RMP2/6-311+G(3df,2p) calculations for the full system, was able to approximate G3(MP2)-RAD values (to within 1.6 kJ mol(-1)) at a fraction of the computational cost. The overall ring structure has more effect on the electrode potentials than the inclusion of substituents. Azaphenalene derivatives display the lowest oxidation potentials and least negative reduction potentials and are thus the most promising target to function as antioxidants in biological systems. Piperidine and pyrrolidine derivatives have intermediate oxidation potentials but on average pyrrolidine derivatives display more negative reduction potentials. Isoindoline derivatives show higher oxidation potentials and more negative reduction potentials. Within a ring, the substituents have a relatively small effect with electron donating groups such as amino and hydroxy groups stabilizing the oxidized species and electron withdrawing groups such as carboxy groups stabilizing the reduced species, as expected.

Standard ab initio molecular orbital theory and density functional theory calculations have been used to calculate absolute one-electron reduction potentials of several para-quinones in acetonitrile. The high-level composite method of G3(MP2)-RAD is used for the gas-phase calculations and a continuum model of solvation, CPCM, has been employed to calculate solvation energies. To compare the theoretical reduction potentials with experiment, the reduction potentials relative to a standard calomel electrode (SCE) have also been calculated and compared to experimental values. The average error of the calculated reduction potentials using the proposed method is 0.07 V without any additional approximation. An ONIOM method in which the core is studied at G3(MP2)-RAD and the substituent effect of the rest of the molecule is studied at R(O)MP2/6-311+G(3df,2p) provides an accurate low-cost alternative to G3(MP2)-RAD for larger molecules.