Bond dissociation energies (BDEs) and radical stabilization energies (RSEs) associated with a series of 22 monosubstituted methyl radicals ( • CH 2 X) have been determined at a variety of levels including, CBS-RAD, G3(MP2)-RAD, RMP2, UB3-LYP and RB3-LYP. In addition, W1′ values were obtained for a subset of 13 of the radicals. The W1′ BDEs and RSEs are generally close to experimental values and lead to the suggestion that a small number of the experimental estimates warrant reexamination. Of the other methods, CBS-RAD and G3(MP2)-RAD produce good BDEs. A cancellation of errors leads to reasonable RSEs being produced from all the methods examined. CBS-RAD, W1′ and G3(MP2)-RAD perform best, while UB3-LYP performs worst. The substituents (X) examined include lone-pair-donors (X ) NH 2 , OH, OCH 3 , F, PH 2 , SH, Cl, Br and OCOCH 3 ), π-acceptors (X ) BH 2 , CHdCH 2 , CtCH, C 6 H 5 , CHO, COOH, COOCH 3 , CN and NO 2 ) and hyperconjugating groups (CH 3 , CH 2 CH 3 , CF 3 and CF 2 CF 3 ). All substituents other than CF 3 and CF 2 CF 3 result in radical stabilization, with the vinyl (CHdCH 2 ), ethynyl (CtCH) and phenyl (C 6 H 5 ) groups predicted to give the largest stabilizations of the π-acceptor substituents examined and the NH 2 group calculated to provide the greatest stabilization of the lone-pair-donor groups. The substituents investigated in this work stabilize methyl radical centers in three general ways that delocalize the odd electron: π-acceptor groups (unsaturated substituents) delocalize the unpaired electron into the π-system of the substituent, lone-pair-donor groups (heteroatomic substituents) bring about stabilization through a three-electron interaction between a lone pair on the substituent and the unpaired electron at the radical center, while alkyl groups stabilize radicals via a hyperconjugative mechanism. Polyfluoroalkyl substituents are predicted to slightly destabilize a methyl radical center by inductively withdrawing electron density from the electron-deficient radical center.

The G3-RAD, G3X-RAD, G3͑MP2͒-RAD, and G3X͑MP2͒-RAD, procedures, designed particularly for the prediction of reliable thermochemistry for free radicals, are formulated and their performance assessed using the G2/97 test set. The principal features of the RAD procedures include ͑a͒ the use of B3-LYP geometries and vibrational frequencies ͑in place of UHF and UMP2͒, including the scaling of vibrational frequencies so as to reproduce ZPVEs, ͑b͒ the use of URCCSD͑T͒ ͓in place of UQCISD͑T͔͒ as the highest-level correlation procedure, and ͑c͒ the use of RMP ͑in place of UMP͒ to approximate basis-set-extension effects. G3-RAD and G3X-RAD are found to perform well overall with mean absolute deviations ͑MADs͒ from experiment of 3.96 and 3.65 kJ mol Ϫ1 , respectively, compared with 4.26 and 4.02 kJ mol Ϫ1 for standard G3 and G3X. G3-RAD and G3X-RAD successfully predict heats of formation with MADs of 3.68 and 3.11 kJ mol Ϫ1 , respectively ͑compared with 3.93 and 3.60 kJ mol Ϫ1 for standard G3 and G3X͒, and perform particularly well for radicals with MADs of 2.59 and 2.50 kJ mol Ϫ1 , respectively ͑compared with 3.51 and 3.18 kJ mol Ϫ1 for standard G3 and G3X͒. The G3͑MP2͒-RAD and G3X͑MP2͒-RAD procedures give acceptable overall performance with mean absolute deviations from experiment of 5.17 and 4.92 kJ mol Ϫ1 , respectively, compared with 5.44 and 5.23 kJ mol Ϫ1 for standard G3͑MP2͒ and G3X͑MP2͒. G3͑MP2͒-RAD and G3X͑MP2͒-RAD give improved performance over their standard counterparts for heats of formation ͑MADsϭ4.73 and 4.44 kJ mol Ϫ1 , respectively, versus 4.94 and 4.64 kJ mol Ϫ1 ). G3͑MP2͒-RAD shows similar performance to G3͑MP2͒ for radical heats of formation ͑MADϭ5.10 versus 5.15 kJ mol Ϫ1 ) while G3X͑MP2͒-RAD performs significantly better than G3X͑MP2͒ ͑MADϭ4.67 versus 5.19 kJ mol Ϫ1 ).

The effects of the R- and Z-substituents on radical stability in the reversible addition fragmentation chain transfer (RAFT) polymerization process have been studied via high level ab initio molecular orbital calculations. Radical stabilization energies (RSEs) of the RAFT-adduct radicals CH3SC•ZSR and corresponding leaving group radicals R• have been calculated for various combinations of Z = H, Cl, C⋮CH, CHCH2, CN, CF3, NH2, CH3, Ph, Bz, naphthyl, OCH3, OCH2CH3, OCH(CH3)2, and OC(CH3)3 and R = CH2CN, C(CH3)2CN, Bz, CH(Ph)CH3, C(Ph)(CH3)2, CH2COOCH3, CH(COOCH3)CH3, CH2OCOCH3, and CH2CH3. The results were used in combination with the corresponding values of the enthalpies of the fragmentation reactions, CH3SC•(Z)SR → CH3SC(Z)S + •R and CH3SC•(Z)SR → •CH3 + SC(Z)SR, to examine the effects of the substituents on the stability of both the RAFT-adduct radicals and the corresponding thiocarbonyl compounds. The RAFT-adduct radicals are stabilized by electron donation from the two sulfur substituents, and this stability can be further enhanced by unsaturated π-accepting substituents (such as CN, phenyl, and naphthyl). In contrast, lone pair donor Z-substituents (such as Cl, NH2, and OCH3) have a much smaller effect on radical stability. The R-group, which can modify the donation ability of the SR-group, has a minimal effect on the stability of the RAFT-adduct as it is buffered by the second sulfur substituent. However, these orbital interactions do affect the strength of the breaking S−R bond, and this provides an important contribution to the trends in the fragmentation enthalpies. Steric effects on radical stability are also important, with bulky R- and Z-groups inducing conformational changes that interfere with these orbital interactions, sometimes with unexpected consequences. The substituent effects on the RAFT agents are qualitatively different; the agents are strongly stabilized by the lone pair donor Z-substituents and strongly destabilized by electron withdrawing groups (such as CN and CF3) in the R- and Z-positions. Moreover, steric effects are generally more significant, with bulky R- and Z-groups destabilizing the RAFT agent more than the corresponding RAFT-adduct radicals. As part of this work, the accuracy of the low-cost RMP2/6-311+G(3df,2p) method for studying addition−fragmentation processes in RAFT polymerization was evaluated.

Geometries, frequency factors, barriers, and reaction enthalpies have been calculated at a variety of levels of theory for methyl radical addition to CH 2 dCH 2 , CH 2 dCHCH 3 , CHtCH and CHtCCH 3 , with a view to selecting reliable computational procedures for studying radical addition to carbon-carbon double and triple bonds. Reaction rates for both the addition and reverse (β-scission) reactions were also calculated using various transition-state-theory-based procedures, applied at a number of theoretical levels. In general it was found that the geometries, frequency factors and temperature corrections are relatively insensitive to the level of theory, but barriers and reaction enthalpies require a careful choice of theoretical level. Nonetheless, suitable lower-cost alternatives to the high-level W1 results are provided by G3X-RAD and G3(MP2)-RAD. Although errors are somewhat increased, the RMP2/6-311+G(3df,2p) (for addition to alkenes) or B3-LYP/6-311+G-(3df,2p) (for addition to alkynes) levels of theory also provide a reasonable approximation to the high-level methods. The CBS-QB3 procedure also produces very good reaction enthalpies, but shows a systematic error in the reaction barriers. It appears that the correction for spin contamination in the addition transition structures may be overestimated in standard CBS-QB3 and better results are obtained if the spin-correction term is omitted (U-CBS-QB3). † Part of the special issue "Fritz Schaefer Festschrift". § On postdoctoral leave from FESC-UNAM (Me ´xico).

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The structures and reactivities of the alkoxy radicals methoxy (CH 3 O·), ethoxy (CH 3 CH 2 O·), 1-propoxy (CH 3 CH 2 CH 2 O·), 2-propoxy ((CH 3 ) 2 CHO·), 2-butoxy (CH 3 CH 2 CH(CH 3 )O·), tert-butoxy ((CH 3 ) 3 CO·), prop-2-enoxy (CH 2 =CHCH 2 O·), and but-3-en-2-oxy (CH 2 =CHCH(CH 3 )O·) have been investigated at the B3-LYP/6-31G(d) and CBS-RAD levels of theory. Enthalpies of formation (∆ f H 298 o ) were calculated with CBS-RAD for all the alkoxy radicals, the carbonyl and radical products of β-scission reactions, and the transition structures leading to them. The mean absolute deviation between the predicted and available experimental ∆ f H 298 o values is 5.4 kJ mol -1 . Eyring (∆H 0 ‡ , ∆H 298 ‡ , ∆G 298 ‡ ) and Arrhenius (log A, E a ) activation parameters for both the forward (β-scission) and reverse (radical addition to carbonyl) pathways were calculated. Agreement with available experimental data is very good, generally within 1-5 kJ mol -1 for E a , and 0.5 for log A. The transition structures are found to be substantially polarized, with the departing radical slightly positive, the O atom negative, and the rest of the molecule positive. The barriers for the β-scission reactions decrease with decreasing endothermicity and with decreasing ionization energy of the departing radical.Résumé : Faisant appel à des calculs théoriques aux niveaux B3-LYP/6-31G(d) et CBS-RAD de la théorie, on a étudié les structures et les réactivités des radicaux alkoxy, méthoxy (CH 3 O·), éthoxy (CH 3 CH 2 O·), 1-propoxy (CH 3 CH 2 CH 2 O·), 2-propoxy [(CH 3 ) 2 CHO·], 2-butoxy [CH 3 CH 2 CH(CH 3 )O·], tert-butoxy [(CH 3 ) 3 CO·], prop-2-énoxy (CH 2 =CHCH 2 O·) et but-3-én-2-oxy [CH 2 =CHCH(CH 3 )O·]. On a calculé les enthalpies de formation, ∆ f H 298 o , au niveau CBS-RAD de la théorie pour tous les radicaux alkoxy, tous les produits carbonylés et tous les produits radicalaires provenant de réac-tions de β-scission et toutes les structures de transition qui y conduisent. La déviation absolue moyenne entre les valeurs prédites et les valeurs de ∆ f H 298 o expérimentales disponibles est de 5,4 kJ mol -1 . On a aussi calculé les paramètres d'activation d'Eyring (∆H 0 ‡ , ∆H 298 ‡ , ∆G 298 ‡ ) et d'Arrhenius (log A, E a ) pour la réaction vers la droite (β-scission) et pour la réaction inverse (addition d'un radical sur le carbonyle). L'accord entre les valeurs calculées et les valeurs expéri-mentales disponibles est bon, généralement entre 1 et 5 kJ mol -1 pour les valeurs de E a et de 0,5 pour le log A. On a trouvé que les structures de transition sont assez polarisées alors que le radical qui se détache est légèrement positif, l'atome d'oxygène est négatif et que le reste de la molécule est positif. Les barrières aux réactions de β-scission diminuent avec une augmentation du caractère endothermique et avec une diminution de l'énergie d'ionisation du radical qui se détache.

We have investigated and compared the ability of numerical and Gaussian-type basis sets combined with density functional theory (DFT) to accurately describe the geometries, binding energies, and electronic properties of aluminum clusters, Al12XHn (X = Al, Si; n = 0, 1, 2). DFT results are compared against high-level benchmark calculations and experimental data where available. Properties compared include geometries, binding energies, ionization potentials, electron affinities, and HOMO-LUMO gaps. Generally, the PBE functional with the double numerical basis set with polarization (DNP) performs very well against experiment and the analytical basis sets for considerably less computational expense.

The heats of formation at 0 K (Δf H 0) of 29 small (containing up to 3 heavy atoms) open-shell molecules, with accurately known experimental values, have been calculated using a number of high-level theoretical procedures. The theoretical methods examined include variants of Gaussian-n (G2, G2-RAD(RMP2), G2-RAD(B3-LYP), G2-RAD(QCISD), G3, G3-RAD, G3X, G3X-RAD, G3(MP2), G3(MP2)-RAD, G3X(MP2) and G3X(MP2)-RAD), CBS (CBS-APNO, CBS-Q, CBS-RAD and CBS-QB3), and Martin extrapolation (Martin-2, Martin-3, W1, W1‘, W1h, W2h and W2) procedures. The open-shell systems include doublet radicals (•BeH, •CH, •CH3, •NH2, •OH, •SiH3, •PH2, •SH, •N2 +, •NO, •ONO, •O2 -, •CN, •CO+, •CS+, •CCH, •CHO, •OOH, •CHCH2, •CH2CH3, •CH2OH, •OCH3, •SCH3 and •COCH3) and triplet biradicals (:CH2, :NH, :SiH2, :O2, and :S2). The results for these systems are used to assess the performance of the various theoretical methods. The smallest mean absolute deviations (MADs) from experiment are found with the G3-RAD, G3X-RAD, G3X, W1h, W2, W1, and W2h procedures with MADs lying in the range 2.0−2.5 kJ mol-1. The smallest values for the largest deviation (LD) from experiment are found with the G3X, G3X-RAD, W2, and W2h procedures and are ±6.4 kJ mol-1. A selection of the most accurate theoretical procedures (G3-RAD, G3X-RAD, G3X, W1h, W2, W1, and W2h) is used to predict the heats of formation for several radicals (•OF, •CH2CHCH2, •CH2CN, •CH2COOH, and •CH2C6H5) for which there are greater uncertainties associated with the experimental values.