DOI: 10.1002/cphc.200500308 Homolysis of N-alkoxyamines: A Computational Study Anouk Gaudel-Siri, Didier Siri,* and Paul Tordo[a] During nitroxide-mediated polymerization (NMP) in the presence of a nitroxide R2(R1)NOC, the reversible formation of N-alkoxyamines [PON(R1)R2] reduces significantly the concentration of polymer radicals (PC) and their involvement in termination reactions. The control of the livingness and polydispersity of the resulting polymer depends strongly on the magnitude of the bond dissociation energy (BDE) of the CON(R1)R2 bond. In this study, theoretical BDEs of a large series of model N-alkoxyamines are calculated with the PM3 method. In order to provide a predictive tool, correlations between the calculated BDEs and the cleavage temperature (Tc ), and the dissociation rate constant (kd ), of the N-alkoxyamines are established. The homolytic cleavage of the NOC bond is also investigated at the B3P86/6-311 + + G(d,p)//B3LYP/631G(d), level. Furthermore, a natural bond orbital analysis is carried out for some N-alkoxyamines with a OCON(R1)R2 fragment, and the strengthening of their CON(R1)R2 bond is interpreted in terms of stabilizing anomeric interactions. Introduction Controlled/“living” radical polymerizations enable the design of polymers with complex architectures and polydispersities well below the theoretical limit for conventional free-radical polymerization processes. Among controlled/“living” radical polymerization procedures, nitroxide-mediated polymerization[1] (NMP) is based on the reversible trapping of growing polymer radicals by a stable nitroxide to form dormant N-alkoxyamines (Scheme 1). The thermally labile N-alkoxyamines decompose on heating to release nitroxide molecules and reactive polymeric chains that may add monomers before recombining with the nitroxide to give N-alkoxyamines with higher molecular weights. Scheme 1. Controlled/“living” polymerization in the presence of nitroxide. The process is based on the persistent radical effect[2] and the efficiency of the control depends on the ratio of the dissociation and recombination rate constants, kd/kc [Eq. (1)]: o kd =kc ¼ ðAd =Ac ÞexpðDHr =RTÞ ð1Þ where Ad and Ac are the Arrhenius prefactors for the N-alkoxyamine dissociation and recombination, respectively. It is commonly assumed that Ad/Ac is roughly constant for a set of similar compounds. Thus, the polymerization process is partly controlled by the magnitude of DHr8, which is the bond dissociation enthalpy (BDE) of the NOC bond. If the NOC bond is too labile, the polymerization process is not controlled; whereas it is inhibited if the NOC bond is too strong. The experi- 430 mental determination of BDE (NOC) for a given N-alkoxyamine is a tedious task that requires the determination of Ead and Eac, the activation energies for the N-alkoxyamine dissociation and recombination respectively. So, the strength of the NOC bond is often indirectly studied with the help of kd or the cleavage temperature Tc. The determination of kd requires many kinetic runs at a given temperature and, to determine Tc values, a precise protocol[3m] using electron spin resonance (ESR) was followed: the temperature of the sample was increased stepwise by 5 8C, and the rough Tc corresponds to the temperature where the ESR signal of the nitroxide appears. Cleavage temperatures of N-alkoxyamines are also directly correlated to the strength of the NOC bond, since the stronger the NOC bond is, the higher the temperature of dissociation should be. Eac for the combination of carbon-centered radicals with nitroxides are small and, if we assume that they are not significantly influenced by the structure of the trapped radical,[4] then Equation (2) is obtained: log kd / E ad =RT / BDE ðNOCÞ=RT ð2Þ A correlation similar to Equation (2) between the experimental values of logkd and Tc has already been reported.[3m] [a] Dr. A. Gaudel-Siri,+ Prof. D. Siri, Prof. P. Tordo UMR-CNRS 6517, Universit$s d’Aix-Marseille 1 et 3 Facult$ des Sciences de St-J$r*me, Case 521 13397 Marseille Cedex 20 (France) Fax: (+ 33) 491-288-841 E-mail: didier.siri@up.univ-mrs.fr [+] Current address: UMR-CNRS 6178, Universit$ Paul C$zanne-Aix-Marseille Facult$ des Sciences et Techniques, Case D12 13397 Marseille Cedex 20 (France) : 2006 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim ChemPhysChem 2006, 7, 430 – 438 Homolysis of N-alkoxyamines Many experimental[3] but few theoretical[3a, f–g, j–k, m–o, 5] studies have been performed to estimate factors influencing the BDE (NOC) of N-alkoxyamines. Experimental results show that narrow polydispersities and high polymerization rates depend on the ease of the NOC bond homolysis.[3f] Both experimental and theoretical results have established that the more stabilized the released radical is, or the more destabilized the starting N-alkoxyamine is, the easier is the dissociation of the NO C bond.[3b, f, m, 5] Nitroxides such as 2,2,6,6-tetramethylpiperidine1-oxyl (TEMPO, I), di-tert-butylnitroxide (DTBN, II), and N,N-(2methylpropyl-1)-(1-diethylphosphono-2,2-dimethyl-propyl-1)-Noxyl (SG1, III) (Scheme 2) have been extensively used for NMP of styrene. Nitroxide III was shown to be efficient also during Scheme 2. Chemical structures of the nitroxides I–XII. the NMP of various acrylic monomers. Nevertheless, to extend NMP to other types of monomers, or to improve the previous reported results, the development of appropriate nitroxides is still a challenge. Molecular modeling could be of great help to estimate, before their synthesis, the efficiency of new nitroxides for NMP. Moreover, a rapid procedure to estimate a priori the BDE (NOC) or the dissociation rate constant kd of new Nalkoxyamines may help organic and polymer chemists in the design of suitable controllers. The present work is a theoretical study of the dissociation reactions of various N-alkoxyamines. In the first section, we give the results of our BDE (NOC) calculations for various Nalkoxyamines. We show that good correlations exist between their calculated BDE (NOC) and their Tc and kd values. These correlations provide a valuable tool for evaluating the ability of new nitroxides to control the NMP of styrene and acrylate monomers. Furthermore, for N-alkoxyamines, the competition between two different dissociation pathways is studied and shows the limitations of NMP procedures. The results are completed by a natural bond orbital (NBO) analysis[6] for three Nalkoxyamines. The NBO analysis allows the separation of the energy contributions due to hyperconjugation from those caused by electrostatic and steric interactions, so that the influence of hyperconjugative interactions can be studied separately. three other main reasons supported the choice of the PM3 method: * * * the better description[9] of nitroxides and N-alkoxyamines obtained with PM3, compared to MNDO,[10a] AM1,[10b] or SAM1[10c] the satisfactory parametrization of the phosphorus atom in PM3 among semiempirical methods, PM3 gives the most satisfying calculated bond lengths and BDEs. In a recent study[11a] with a series of 28 compounds, the mean absolute error value for the calculated BDEs of XX and XY bonds was 7 kJ mol1 at the B3P86/6-311G(2d,2p)//PM3 level and 10 kJ mol1 at the B3P86/ 6-311G(2d,2p)//AM1 level. This result can be accounted for by the better accuracy of the PM3 calculated bond lengths. In the first step, for each N-alkoxyamine, the lowest-energy geometry was determined by simulated annealing[12] and highest occupied molecular orbital/lowest unoccupied molecular orbital (HOMO/ LUMO) configuration interaction. The energy of the radical species was calculated with a minimal configuration interaction over the HDOMO (highest doubly occupied MO), singly occupied MO SOMO, and LUMO frontier orbitals. All minima were confirmed by the calculation of vibrational frequencies. Bond dissociation enthalpies were calculated from Equations (3) and (4): BDECO ð298 KÞ ¼ DHf o ðnitroxideÞ þ DHf o ðRC ÞDHf o ðN-alkoxyamineÞ ð3Þ BDENO ð298 KÞ ¼ DHf o ðaminylÞ þ DHf o ðROC ÞDHf o ðN-alkoxyamineÞ ð4Þ where the energy of the open-shell species is recalculated with a minimal configuration interaction over the two SOMOs (keywords OPEN(2,2) C.I. = 2) in order to minimize size-consistency problems. Density functional theory (DFT) calculations were performed with the Gaussian 03 package.[13] In some recent studies,[4a, 11] various standard functionals have been tested to calculate the BDEs of C X and XY bonds belonging to a large panel of compounds. The best results were obtained with the B3P86 functional and the best correlation constants between the experimental and calculated values were obtained[11c] at the B3P86/6-311 + + G(d,p)//B3LYP/631G(d) level: 0.991 for all the compounds, 0.969 for CX bonds, and 0.945 for XY bonds with a systematic underestimation of the BDEs. Herein, the geometry optimization and the calculation of vibrational frequencies were performed at the B3LYP/6-31G(d) level and a single point at the B3P86/6-311 + + G(d,p) level was used to calculate the energy. All minima were confirmed by a calculation of vibrational frequencies. For thermodynamic calculations, as recommended by Wong,[14] a scale factor of 0.9804 was applied to vibrational frequencies. Bond dissociation enthalpies were calculated by Equation (5): Computational Section Semiempirical calculations were performed with the PM3[7] method of the AMPAC software.[8] In addition to its low computational cost, ChemPhysChem 2006, 7, 430 – 438 BDE ¼ DHr o ð298 KÞ ¼ De þ DZPE þ DHtrans þ DHrot þ DHvib þ RT : 2006 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim ð5Þ www.chemphyschem.org 431 D. Siri et al. where De is the classical electronic bond dissociation energy; DZPE is the difference in zero-point energy between products and the N-alkoxyamine; DHtrans , DHrot , DHvib are the contributions from translational, rotational, and vibrational degrees of freedom. An NBO analysis was performed at the B3P86/6-31 + G(d) level, using the NBO 3.1 program[15] included in the Gaussian 03 package. Results and Discussion Table 1. Comparison between experimental and calculated BDE (OR) for various hydroxylamines and N-alkoxyamines with an alkyl leaving group at 298 K. N-alkoxyamine or hydroxylamine BDEPM3 [kJ mol1] Signed error[b] [kJ mol1] BDEDFT[c] [kJ mol1] Signed error[b] [kJ mol1] BDEexp [kJ mol1] 1 IIH 2 IH 3 IMe 4 ICH2Ph 5 Istyryl 6 Icumyl 7 IIICH2Ph 8 IIIstyryl[a] mean signed error 295 296 178 161 130 105 157 118 10 5 19 16 1 5 31 1 5 275 279 185 121 110 89[d] – – 10 12 12 24 19 21 – – 16 285[16b] 291[16a] 197[3a] 145[5a] 129[5a] 110[3d] 126[5a] 117[5a] [a] Mean value for the SR/RS and RR/SS diastereomers. [b] Signed errors in calculated BDE (OR). [c] Ref. [5a] with B3P86/6-31G(d)//HF/6-31G(d) method. [d] T was set to 358 K. Experimental and Calculated BDE (NOC) Only few experimental BDEs of N-alkoxyamines or hydroxylamines have been reported in the literature.[3a–d, 5a, 16] When these scarce experimental data were compared to calculated BDEs (Table 1), we first noted that, in most cases, PM3 calculations slightly overestimated the BDE values (mean error value of 5 kJ mol1), while B3P86/6-31G(d)// HF/6-31G(d) calculations underestimated them (mean error value of 16 kJ mol1). BDEs calculated at the DFT level offered a better correlation (Figure 1 a) with experimental data (r2 = 0.999), but PM3 results were also satisfactory (r2 = 0.962). Steric effects were well-described with a decrease in BDE (NOC) from a primary (CH2Ph, Table 1, entry 4) to a secondary ( styryl, Table 1, entry 5), and a tertiary (cumyl, Table 1, entry 6) leaving group (Scheme 3 shows the structures of the leaving groups used in this study). Moreover, with a given leaving group, the BDE (NOC) of N-alkoxyamines derived from III were always lower than those of N-alkoxyamines derived from I. These results for alkyl leaving groups are in very good agreement with experimental data. However, at the PM3 level of calculation, some BDEs were overestimated, while others were underestimated (Table 1): then, individual absolute values must be considered carefully. Consequently, the PM3 method appears to be a valuable tool for estimating relative BDEs of a series of N-alkoxyamines with alkyl leaving groups within reasonable calculation times, while a higher-level method is recommended for calculating accurate BDEs. In order to also validate the PM3 method for N-alkoxyamines with electron-withdrawing groups, we compared PM3 results with those obtained at the B3P86/6-311 + + G(d,p)//B3LYP/6-31G(d) level (Table 2, Figure 1 b). PM3 predicts BDEs in good agreement with B3P86 results (r2 = 0.995). In most cases, PM3 BDEs were slightly underestimated; the particular case of N-alkoxyamine 40 will be discussed below. Figure 1. a) Correlation between experimental and theoretical BDEs for the NOC homolytic cleavage of various N-alkoxyamines with an alkyl or a p-delocalized alkyl leaving group. (&) PM3 calculations. (^) B3P86/6-31G(d)//HF/631G(d) calculations. b) Comparison between BDEs calculated with PM3 and BDEs calculated at the B3P86/6-311 + + G(d,p)//B3LYP/6-31G(d) level for the NOC homolytic cleavage of various N-alkoxyamines with an electron-withdrawing leaving group. Correlations Between Experimental Data and Calculated BDE (NOC) The N-alkoxyamine Tc values were determined by experimental chemists in our laboratory.[3m] As expected, they were strongly 432 www.chemphyschem.org Scheme 3. Chemical structures of leaving groups. : 2006 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim ChemPhysChem 2006, 7, 430 – 438 Homolysis of N-alkoxyamines Table 2. Comparison between the PM3 method and the B3P86/6-311 + + G(d,p)//B3 LYP/6-31G(d) level at 298 K for various N-alkoxyamines with an electron-withdrawing leaving group. Table 3. Comparison between Tc determined by ESR, kd measured by ESR (393 K), and BDE (NOC) calculated by PM3 at 298 K. N-alkoxyamine N-alkoxyamine 22 26 34 36 40 43 26 ICH2C(O)OMe IMA IMMA IIMMA IXMMA ICMe2CN VICMe2CN BDEPM3 (OR) [kJ mol1] BDEDFT (OR) [kJ mol1] Signed error[a] [kJ mol1] 149 118 86 77 94 89 88 146 121 92 83 140 92 96 3 3 6 6 46 3 8 [a] BDEPM3 (OR)BDEDFT (OR). dependent on the structure of the leaving radical (Table 3). From a qualitative point of view: 9 10 11 12 13 4 14 7 5 15 8 16 17 18 19 a 19 b * * Tc decreased when the substitution at the radical center of the leaving radical increased (see for example, N-alkoxyamines entries 9, 11 and 10, 12) for a given released radical, N-alkoxyamines derived from III exhibited a lower Tc than those derived from I (see for example, N-alkoxyamines entries 10, 11 or 12, 13). These results are in agreement with the BDE values of the NOC bond calculated with the PM3 method. However, no direct correlation between Tc and BDE (NOC) was found for the whole series of N-alkoxyamines, because the polar effects of the nitroxide moiety and the leaving radical must be also considered. Hence, we first defined three sets of N-alkoxyamines according to the nature of the radical released during the dissociation: an alkyl radical, a p-delocalized alkyl radical, and a radical bearing an electron-withdrawing group. Interesting correlations were obtained within the three sets of N-alkoxyamines (Figure 2 and Figure 3). Slightly better correlations were obtained between logkd and BDE (NOC) than between Tc and BDE (NOC). The same slope was obtained for the correlations corresponding to leaving groups expected to exert similar polar effects, such as alkyl groups and p-delocalized alkyl groups. We noted a slightly larger slope for leaving groups bearing an electron-withdrawing substituent, such as  CN or C(O)OR. The combination of both steric and electronwithdrawing effects for the released radical (e.g., methylmethacrylate MMA) led to a significant increase in the dissociation rate. In addition to experimental Tc and kd values, calculated Tc and kd values are reported in Table 3 (italic). These values were calculated with the correlations of Figures 4 and 6, and Figures 5 and 7, respectively. The predicted kd value for entry 20 (1.99 s1 at 1208C) is in agreement with the value estimated by Marque and co-workers[3m] (1.7 s1 at 1208C). The whole series of N-alkoxyamines studied in this work can be represented by the three general formula shown in Scheme 4. If the transition state of the NOC bond homolysis is stabilized by polar contributions, the homolysis of N-alkoxyamines B (Scheme 4) is expected to be favored, while no signifiChemPhysChem 2006, 7, 430 – 438 8 20 21 22 23 24 25 26 27 28 29 29 a 29 b 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 III(CH2)5CH3 IcyHex IIIcyHex It-Bu IIIt-Bu ICH2Ph IICH2Ph IIICH2Ph Istyryl IIstyryl IIIstyryl[a] VIstyryl[a] VIIIstyryl XIstyryl XIIstyryl (SR/RS) XIIstyryl (SS/RR) Icumyl IIIcumyl ICH2C(O)Ot-Bu ICH2C(O)OMe IIICH2C(O)OMe IIICH2C(O)OH IIICH2CN IMA IBuA IIBuA IIIMA[a] IIIMA (RS/SR) IIIMA (RR/SS) IIIAA IVMA[a] V-MA IIICH(Me)CN[a] IMMA IMBuA IIMMA IIMBuA IIIMMA VIIIMMA IXMMA XMMA IIIMMA ICMe2CN IIICMe2CN VICMe2CN VIICMe2CN Tc[b] [8C] BDEPM3 [kJ mol1] kd[e] [s1] logkd 160[3m] 170[3m] 140[3m] 110[3m] 95[3m] 115[3m] 121[c] 80[3m] 95[3m] 84[c] 60[3m] 65[3m] 100[17] 35[17] 49[c] 148 129 122 94 77 161 162 157 131 131 118 116 123 97 113 8.00E09[3m] < 2.80E08[3m] 6.40E08[3m] 1.00E05[3m] 6.50E05[3m] 1.10E05[3m] 1.90E04[3l] 3.30E04[3m] 5.20E04[3m] 1.40E02[3l] 5.50E03[3m] 3.30E03[3m] – 1.80E01[f] 4.60E02[3l] 8.10 > 7.55 7.19 5.00 4.19 4.96 3.72 3.48 3.28 1.89 2.26 2.48 – 0.74 1.34 46[c] 109 7.50E02[3l] 1.12 45[3m]  15[3m] 145[3m] 145[18] 100[3m] 100[d] 90[i] 115[18] 115[3m] 96[d] 75[3m] – – 64[d] 90[3m] 85[i] 70[17] 50[18] 50[3m] 15[19] 39[d]  15[3m] 60[19] 165[19] 90[19] 18[d] 46[d] 20[i] 46[d] 35[d] 105 74 156 149 145 146 148 118 122 119 112 113 110 111 120 121 116 86 94 77 84 66 67 94 121 66 89 72 88 81 8.50E02[3m] 1.99[f] 8.10E08[3m] 8.10E08[18] 3.60E06[3m] 2.30E06[h] 2.00E04[h] 3.40E05[18] 3.40E05[3m] 1.10E03[3l] – 3.00E03[3m] 1.00E03[3m] 5.30E04[h] 4.50E04[3m] 5.10E04[g] 2.80E03[i] 2.20E02[18] 2.20E02[3m] 4.80E01[g] 3.10E01[3l] 8.00[i] – – 6.50E05[g] 2.80E01[h] 1.30E01[3l] 1.31[h] 1.90E02[3l] 1.60E01[3l] 1.07 0.30 7.09 7.09 5.44 5.64 3.70 4.47 4.47 2.96 – 2.52 3.00 3.28 3.35 3.29 2.55 1.66 1.66 0.32 0.51 0.90 – – 4.19 0.55 0.89 0.12 1.72 0.80 [a] Tc or kd measured for the racemic and mean value of BDE calculated for the two diastereomers. [b] The error in Tc measurements is  5 8C. [c] Estimated Tc values obtained from the correlation of Fig. 4. [d] Estimated Tc values obtained from the correlation of Figure 6. [e] The error in kd measurements is  10 %. [f] Estimated kd values obtained from the correlation of Figure 5. [g] Estimated kd values obtained from the correlation of Figure 7. [h] S. Marque, D. Gigmes, personal communication. [i] To be published. cant influence of polar contributions is expected for N-alkoxyamines A and C. In Figure 4, only p-delocalized alkyl leaving groups of similar electronegativities were considered, and two satisfactory corre- : 2006 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim www.chemphyschem.org 433 D. Siri et al. lations were obtained according to the presence or the absence of an electron-withdrawing substituent on the nitroxide moiety. A better correlation, and a significantly smaller slope, was obtained for monophosphonylated nitroxides (III, XI, XII) than for dialkyl ones (I, IV). The polar contribution represented by B is expected to be more stabilizing than that represented by A and, as observed, a smaller slope was expected for the correlation involving the N-alkoxyamines based on monophosphonylated nitroxides (III, XI, XII). The diphosphonylated cyclic N-alkoxyamine 17 (VIII-styryl) did not corFigure 2. Correlations between BDE (NOC) calculated with the PM3 method and available experimental Tc conrelate to any linear fit. As already sidering three series of leaving groups: alkyl, p-delocalized alkyl, and electron-withdrawing moieties. pointed out by Moad and Rizzardo,[3f] a decrease in the q(CNC) valence angle leads to a higher BDE (NOC) and then, an increase in Tc. However, more experimental data from a series of cyclic and acyclic diphosphonylated nitroxides should be analyzed in order to draw any conclusions on the effect of the two phosphonyl substituents. In Figure 5, a slightly larger slope was also obtained for dialkyl nitroxides (I, II, IV) than for the monophosphonylated ones (III, XI, XII). The N-alkoxyamines considered in Figures 6 and 7 are A Figure 3. Correlations between BDE (NOC) calculated with the PM3 method and available experimental kd values and C types. Good correlations considering three series of leaving groups: alkyl (&), p-delocalized alkyl (^), and electron-withdrawing (~) moietwere obtained. Note again the ies. synergy of the polar and steric effects of the leaving group with a larger slope in the case of dialkyl nitroxides (I, II, IV, VI, VII). The lower slope for N-alkoxyamines based on III and V is due to the larger steric hindrance of the nitroxide moiety (Figure 6). N-alkoxyamines 39 and 40 were considered (BDE (NOC) = 67 kJ mol1, Tc = 608C and BDE (NOC) = 94 kJ mol1, Tc = 1658C,[19] respectively), but neither correlated with a linear fit. For N-alkoxyamine 17, we note significant differences in the valence angle q(CNC) for 39 and 40, compared to 34 and 36 (Table 4), and an increase in the BDE (NOC) and in the cleavage temperature was again observed. In conclusion, satisfactory correlations were obtained between calculated BDE (NOC) with the PM3 method and experimental Tc or logkd. In order to test new nitroxides in NMP, Figure 4. Correlations between BDE (NOC) calculated with the PM3 correlations found in this section might help organic chemists, method and experimental Tc considering alkyl p-delocalized leaving groups and dialkyl or monophosphonylated nitroxides. it they first estimate Tc or kd values for new model N-alkoxy- 434 www.chemphyschem.org : 2006 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim ChemPhysChem 2006, 7, 430 – 438 Homolysis of N-alkoxyamines Table 4. Comparison of structural parameters of acyclic (36), cyclic (34, 39), and bicyclic (40) N-alkoxyamines according to PM3 calculations. The w(CCON) dihedral angle measures the pyramidalization angle of the N atom. N-alkoxyamine 34 36 39 40 q(CNC) [deg] [a] 119(118) 121 110 110(110)[a] d(NOC) [O] [a] 1.436(1.433) 1.434 1.438 1.420(1.442)[a] w(CCON) [deg] 29(32)[a] 28 35 35(38)[a] [a] Experimental X-ray data values are given in italics. Figure 6. Correlations between BDE (NOC) calculated with the PM3 method and experimental Tc considering electron-withdrawing leaving groups and dialkyl or monophosphonylated nitroxides. amines before their experimental determination, which requires many kinetic runs. NOC versus NOC Bond Cleavage Figure 5. Correlations between BDE (NOC) calculated with the PM3 method and experimental kd values considering alkyl leaving radicals and dialkyl or monophosphonylated nitroxides. The cleavage temperature of N-alkoxyamines releasing a primary alkyl radical is very high (e.g., 9). Then, NMP of ethylenic monomers should be conducted at very high temperature and pressure. The NOC bond in N-alkoxyamines is usually considered as the most labile but, at high temperatures, the competitive NOC homolytic bond cleavage must be also considered. This pathway is not reversible and leads to two reactive radicals: an aminyl radical and an alkoxyl radical (Scheme 5), which are both able to initiate radical reactions. Hereafter, we present our computations on the BDE of the NOC and NOC bonds for a series of N-alkoxyamines. Scheme 5. Competition between homolytic NOC and NOC bond cleavage in N-alkoxyamines. Figure 7. Correlations between BDE (NOC) calculated with the PM3 method and experimental kd values considering electron-withdrawing leaving radicals and dialkyl or monophosphonylated nitroxides. Scheme 4. General formula of the N-alkoxyamines studied. ChemPhysChem 2006, 7, 430 – 438 At first, some representative N-alkoxyamines were chosen to test the ability of the PM3 method to give BDE (NOC) values in agreement with experimental observations (Table 5). In agreement with experimental results for N-alkoxyamines releasing primary or secondary alkyl radicals, semiempirical BDE (NOC) were very high (130–155 kJ mol1). However, BDE (NOC) of I-n-hexyl and III-n-hexyl were significantly lower than BDE (NOC). This result was not in agreement with the experimental determination of BDE (NOC) of I-Me,[3a] which indicates that BDE (NOC) < BDE (NOC) for I-n-alkyl. N-alkoxyamines releasing tertiary radicals (cumyl and MMA) showed highly labile NOC bonds, in agreement with experimental data. However, spurious results were obtained for primary and secondary p-delocalized radicals. In order to determine if these : 2006 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim www.chemphyschem.org 435 D. Siri et al. Table 5. Comparison of BDE (NOC) and BDE (NOC) at 298 K calculated with the PM3 method and at the B3P86/6-311 + + G(d,p)//B3LYP/6-31G(d) level for a series of N-alkoxyamines. N-alkoxyamine BDEPM3 (NOC) [kJ mol1] BDEPM3 (NOC) [kJ mol1] BDEDFT (NOC) [kJ mol1] BDEDFT (NOC) [kJ mol1] 6 5 4 26 34 47 9 48 49 a 49 b 105 130 161 118 86 151 148 142 135 129 130 112 107 – 117 104 77 107 75 69 87 108 119 121 – 176[a] – 179 – – – 174 – 180 – 189[a] – 176 – – I-cumyl I-styryl I-CH2Ph I-MA I-MMA I-(CH2)5CH3 III-(CH2)5CH3 I-VA III-VA (SR)[b] III-VA (SS)[b] ysis was carried out where the hyperconjugation in I-VA and IMA was compared. The hyperconjugation in III-VA was also studied. Starting from the crystal structure of III-VA, the geometry optimization of III’-VA was performed at the B3P86/631G(d) level of calculation, and a diffuse function on the nitrogen and oxygen atoms was added to deal with the lone pairs properly. Nitroxide III’ differs from III because the ethoxyl moieties attached to the phosphorus atom are substituted by methoxyl groups, in order to reduce the calculation time. Optimized geometries of I-VA and I-MA are reported in Figures 8 and 9. Some structural variations can be noted in favor [a] The n-hexyl moiety was replaced by a methyl group. [b] The configuration of the nitroxyl chiral center is given first. discrepancies were due to the use of a semiempirical method, BDE (NOC) and BDE (NOC) were calculated with the B3P86/ 6-311 + + G(d,p)//B3LYP/6-31G(d) method. Results are reported in Table 5. In order to model the polyethylene chain, the methyl group was taken to reduce calculation times. Table 5 shows that BDEs calculated with the DFT method were in better agreement with experimental data. Only I-MA and Istyryl have a labile NOC bond (110–120 kJ mol1). In contrast to the PM3 results, all the N-alkoxyamines had strong NOC bonds (175-190 kJ mol1) and BDE (NOC) of I-Me was then lower than BDE (NOC). For I-VA, BDE (NOC) and BDE (NOC) were similar and very high. These values were in agreement with the absence of experimental cleavage temperature for IIIVA to 1408C.[20] This study showed that a comparison of BDE (NOC) and BDE (NOC) calculated with the PM3 method did not give reliable relative values. This result can be explained considering the characteristics of the two bonds: a NOC bond with only one heteroatom and experimental data used in the parametrization of PM3 versus a NOC bond between two heteroatoms. Moreover, it is known that lone-pair–lone-pair repulsions are not always well represented by semiempirical methods.[21] Hyperconjugation in N-alkoxyamines: Structural and NBO Analysis The special cases of the N-alkoxyamines I-VA and III-VA is particularly interesting. The steric hindrance in I-VA and I-MA is similar, but their Tc are very different, showing a dramatic strengthening of the NOC bond in I-VA. Ciriano et al.[3a] have published a study of TEMPO N-alkoxyamines derived from tetrahydrofuran and triethylamine. Stronger BDE (NOC) were attributed to the presence of the heteroatom in the a-position of the NO group. The N-alkoxyamine is stabilized by an anomeric interaction[22] between the lone pairs of the heteroatom and the s*(NO) bond. The NOC bond is then strengthened while the NOC bond is weakened. In order to understand the unusual strength of the NOC bond in I-VA better, a NBO anal- 436 www.chemphyschem.org Figure 8. Structural parameters of I-VA optimized at the B3P86/6-31 + G(d) level. Bond lengths in angstrçms, angles in degrees. Figure 9. Structural parameters of I-MA optimized at the B3P86/6-31 + G(d) level. Bond lengths in angstrçms, angles in degrees. of an anomeric interaction in the (N)O9C10O11C moiety of IVA. At first, the (N)O9C10 bond of I-VA was significantly shortened (3 P 102 O) while the NOC bond length did not change. On the other hand, the C10O11 bond was significantly lengthened (3 P 102 O). Moreover, the w(NOCO) dihedral angle was close to 908 (89.48) and the q(O9C10O11) angle was significantly more acute, compared to the equivalent q(O9C10C11) angle in I-MA. All these facts support a hyperconjugation between a lone pair of the nitroxyl oxygen O9 and the adjacent antibonding s* (C10O11) orbital.[3a, 23] In order to confirm this hypothesis, we carried out a NBO analysis[6] of I-VA and I-MA. Table 6 shows a strong stabilizing interaction (17.9 kcal mol1) between a p lone pair of O9 and the polar antibonding : 2006 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim ChemPhysChem 2006, 7, 430 – 438 Homolysis of N-alkoxyamines Table 6. Main hyperconjugative interactions in I-VA. Interaction Stabilization [kcal mol1] n(N)!s* (C1Caxial) 7.7 n(N)!s* (C5Caxial) 7.8 n(O9)!s*(C10O11) Lone-pair delocalization 96.1 % 0.7 % 0.6 % 96.1 % 0.7 % 0.6 % 95.2 % 2.3 % 0.9 % 17.9 sp3(N) p(C1) sp3(Caxial) sp3(N) p(C5) sp3(Caxial) p(O9) p(C10) sp(O11) s*(C10O11) orbital. A similar interaction is also noted in I-MA, but the stabilizing energy is much weaker and close to that resulting from the delocalization of the N lone-pair in the nonpolar axial s*(CMe) orbitals (Table 7, Figure 10). Some structural Figure 11. Structural parameters of III’-VA optimized at the B3P86/631 + G(d) level with an additional diffuse function for the N and O atoms. Bond lengths in angstrçms, angles in degrees. For clarity, hydrogen atoms have not been drawn. Table 8. Main hyperconjugative interactions in III’-VA. Interaction Stabilization [kcal mol1] Lone-pair delocalization n(N)!s* (C1Cb) 6.9 n(N)!s*(C5P) 4.7 n(O9)!s*(C10O11) 15.6 96.2 % 0.6 % 0.5 % 96.2 % 0.7 % 0.5 % 95.3 % 2.1 % 0.8 % Table 7. Main hyperconjugative interactions in I-MA. Interaction Stabilization [kcal mol1] Lone-pair delocalization n(N)!s* (C1Caxial) 7.8 96.0 % 0.7 % 0.6 % 96.1 % 0.7 % 0.6 % 96.6 % 0.9 % 0.8 % n(N)!s*(C5Caxial) 7.8 n(O9)!s*(C10C11) 8.8 sp3(N) p(C1) sp3(Caxial) sp3(N) p(C5) sp3(Caxial) p(O9) p(C10) sp(O11) sp3(N) p(C1) sp3(Cb) sp3(N) p(C5) s(P) p(O9) p(C10) sp(O11) usual lower BDE (NOC) of III-based N-alkoxyamines compared to I-based N-alkoxyamines. In Table 9 are reported the natural charges of the NOCO and NOCC moieties of I-VA, I-MA, and III’-VA. Natural charges are preferred to Mulliken population analysis, because of instabili- Table 9. Comparison of natural charges in I-MA, I-VA, and III’-VA. Natural charge N O9 C10 C11 or O11 I-MA I-VA III’-VA (SS)[a] 0.230 0.227 0.208 0.458 0.463 0.461 0.009 0.370 0.393 0.797 0.581 0.582 [a] The configuration of the nitroxyl chiral center is given first. Figure 10. a) Hyperconjugation in I-VA between the O9 lone pair and the antibonding s* (C10O11) orbital. b) Hyperconjugation in I-MA between the O9 lone pair and the antibonding s* (C10C11) orbital. variations could also be noted in favor of an anomeric interaction in the (N)O9C10O11C moiety of III’-VA (Figure 11). The (N)O9C10 bond of III’-VA is shortened (1.403 O), while the N OC and C10O11 bonds are lengthened, showing a hyperconjugation between a lone pair of the nitroxyl oxygen O9 and the adjacent antibonding s*(C10O11) orbital. Table 8 shows a strong stabilizing interaction (15.6 kcal mol1) between a p lone pair of O9 and the polar antibonding s*(C10O11) orbital. This interaction is similar to the anomeric interaction noted in I-VA, but it is less stabilizing. This is in agreement with the ChemPhysChem 2006, 7, 430 – 438 ties with respect to basis expansion and underestimation of ionic character in bonds between atoms with large electronegativity differences.[6d] The charge of either the nitrogen atom or the oxygen atom of the nitroxide moiety is not affected by the nature of the leaving group. On the other hand, the charge of the C10 carbon atom is dramatically modified by the presence of O11 in I-VA and III’-VA, leading to a highly polarized O9C10 bond. This charge separation again does not favor the homolytic cleavage of the N-alkoxyamine NOC bond. The NBO analysis showed that the NOC bond cleavage in N-alkoxyamines releasing a VA radical is not favored, because of an anomeric stabilization and a more polar NOC bond. : 2006 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim www.chemphyschem.org 437 D. Siri et al. Conclusions Herein, we reported a semiempirical study of the homolysis of N-alkoxyamines. The PM3 method is a valuable tool for estimating relative BDE (NOC) within a series of N-alkoxyamines, and correlations between calculated BDE (NOC) and the experimental Tc or kd may be useful for finding new nitroxide controllers for NMP of acrylic or styrenic monomers. These correlations showed the strong influence of steric effects in the NOC bond cleavage, but polar substituents in the nitroxide are important too, as they modify the polar contributions in the transition state of the homolysis. PM3 failed to give reliable relative values of BDE (NOC) and BDE (NOC). A higher level of theory was necessary to compare the homolytic cleavage of these two bonds. DFT calculations herein were in good agreement with experimental data. Furthermore, the NBO analysis of two N-alkoxyamines releasing a VA radical clearly showed that the control of the polymerization of VA derivatives with nitroxides is unlikely. 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