Diasteromeric Effect on the Homolysis of the C–on Bond in Alkoxyamines: a Dft Investigation of 1,3-diphenylbutyl-tempo

The rate constants k d of the homolysis of the C–ON bond in styryl dyads TEMPO-based alkoxyamines have recently been published (Li et al. Macromolecules 2006, 39, 9201). The diastereoisomers exhibited different values which were higher than for the unimer TEMPO-styryl alkoxyamine 1. At a first glance, the localization of the steric strain was not obvious. To decipher this problem, diastereoisomer models 2 (RR/SS) and 3 (RS/SR), as well as the released alkyl radicals, were calculated at the \B3LYP/6-31G(d) level. It was revealed that the increase in k d from 1 to 3 was due to the compression (buttressing effect) of the reactive center by the second styryl moiety. The difference in k d for the diastereoisomer was clearly an activation entropy effect S ≠ because the alkyl fragment of the RS/SR diastereoismer exhibited the same conformation as the released radical whereas the conformation for the RR/SS diastereoisomer was quite different and thus required the rotation of several bonds to reach the correct TS, which cost S ≠ , and thus lowers k d .


Introduction
Since the pioneering work of Rizzardo in 1985 [1], research progress in Nitroxide Mediated Polymerization (NMP) has undergone exponential growth in the areas of materials preparation [2], kinetic investigations [3][4][5], and in the design of new initiators/controllers [6,7].It has been shown that each stage-initiation, propagation, and termination-of the polymerization is important for the fate of NMP [8,9].Over the last two decades, a tremendous amount of work has focused on analyzing the effects ruling the homolysis of the C-ON bond of the initiator/controller.The accumulation of data has shown that understanding the effects occurring during the C-ON bond homolysis is crucial for the design of new initiators.During the last decade, the effect of the penultimate unit on the C-ON bond was poorly investigated, and seemingly contradictory results were published concerning polystyryl-TEMPO alkoxyamines.Until recently, it has been shown [10] that the penultimate unit may exert a dramatic effect on the C-ON bond homolysis and, consequently, on the fate of NMP [11,12].Georges and colleagues [13] measured the C-ON bond homolysis in the diastereoisomers of styryl dyads of TEMPO-based alkoxyamines 7 (Figure 1).They reported that the (S,S) diastereoisomer [14] was cleaving two-folds as slowly as the (R,S) diasteroisomers.However, no ambiguous discussions were provided on the origin of this effect.At a first glance, although this led to apparently contradictory measurements [10,15,16], such small differences in k d may look unimportant, but nevertheless, we have recently shown that the fate of NMP [11,12,17] and the occurrence of side-reactions [18] depends on such small differences.
A few years ago, we showed that the two-fold difference between the two diastereoisomers of 1-alkoxycarbonylethyl based-SG1 6 was due to the hyperconjugative effect (n OCO →* C-ON interaction) between the carbonyloxyl group and the C-ON bond (Figure 1) [19].Then, for the homolysis 1-5 (Figure 1), we show hereafter that hyperconjugative interactions play a minor role, in sharp contrast with the remote steric effect.

Computational Method
In recent articles [19,20], we investigated the hyperconjugation effect as well as the steric strain [21] using Density Functional Theory (DFT) calculations at the B3LYP/6-31G(d) level of theory.All calculations were performed using the Gaussian 03 molecular orbital package [22].Geometry optimizations were carried out without constraints (Figure 2) [23,24].Vibrational frequencies were calculated at the B3LYP/6-31G(d) level to determine the nature of the located stationary points.Frequency calculations were performed to confirm that the geometry was a minimum (zero imaginary frequency).The single point energies were then calculated at the B3P86/6-311++G(d,p) level of theory for molecules 1-5 [25].Radical Stabilization Energies (RSE) of 4 and 5 were calculated at G3B3MP2 (compound method).For 1-3, Natural Bond Orbital (NBO) analysis [19,26] was performed with the NBO 3.1 program in the Gaussian 03 package.For NBO analysis on 4 and 5, more details are provided as Supplementary information.

Results and Discussion
Georges and colleagues [13] reported different homolysis rate constants k d at 120 °C for the RR/SS (k d = 9.7 × 10 −4 s −1 ) and RS/SR (k d = 19.6 × 10 −4 s −1 ) diastereoisomers of 7 (Figure 1) as well as for the unimeric species 1 (k d = 5.5 × 10 −4 s −1 ).It is known [19,27,28] that the steric effect ruling the C-ON bond homolysis is related to the geometrical parameters-bond length l, interatomic distance d, valence angle , and torsion angle -of the alkoxyamines.However, as the diastereoisomers of 7 are large molecules (71 atoms) implying time consuming calculations, it was assumed that the benzyloxy group exhibited neither significant polar effect nor important steric effect and that the second styryl group did not exhibit significant polar effect [10].Hence, DFT calculations were performed on smaller (58 atoms) molecule models 1-4 (Figure 2 and Table 1) to investigate the effect of the penultimate units of 2-4 as well as the effect of their configurations and conformations.Interestingly  and 3.This means that no peculiar steric strains were observed except that the phenyl ring was tilted (<O 5 C 4 C 13 C 14 >) from 4° to 6° closer from 90° from unimolecular alkoxyamine 1 to dimeric alkoxyamines 2 and 3, involving possible →* O5-C4 interaction (Figure 3d).Thus, all the molecules exhibited the same conformation around the reactive center, that is, the alkyl group and H 12 almost eclipsed the nitrogen lone pair, and the C 4 -C 13 bond was almost perpendicular to the N-O bond (Figure 3a-c).
As no differences in the geometrical parameters were observed at the reaction center N-O-C, the RSE of the released 4 and 5 radicals were calculated using the isodesmic reaction (1).
Thus, RSE were estimated to be 56.0 kJ/mol and 61.0 kJ/mol for 4 and 5, respectively, implying that 5 was 5.0 kJ/mol more stabilized than 4, despite the  ,C18 →* ,C2-C3 / ,C2-C3 →-LUMO and  -SOMO→* ,C2-C3 / ,C2-C3 →* ,C18 interactions (Table 1).Indeed, 4 and 5 exhibited strong -SOMO→* ,C13 interactions, as highlighted by the ca.0.1 Å shortening of the C 4 -C 13 bonds, and weak -SOMO→* ,C3-C4 and -SOMO→* ,C-H interactions for 4 and 5, respectively, as highlighted by the ca.0.05 Å shortening of the corresponding bonds as well as the shortening of the C 2 •••C 4 distance.Interestingly, weak but significant  ,C18 →* ,C2-C3 and  ,C2-C3 →* ,C18 interactions favored the anti conformation around the C 1 -C 3 bond (<C 1 C 2 C 3 C 4 > = 60°, Figure 4d) and the perpendicular arrangement between the C 13 -aromatic ring and the C 2 -C 3 bond (<C 2 C 3 C 4 C 13 > = 86.5°, Figure 4d).The weakness of these interactions was partly due to the tilted position (<C 19 C 18 C 2 C 3 > = 23°, Figure 4a) of the aromatic ring relative to the C 2 -C 3 bond (Table 1, Figure 4).It is noteworthy that the relief of the steric strain is more important from 2/3 to 4 (d C13• • • C2 = 0.36 Å) than from 1 to 5 (d C13•••H = 0.23 Å).However, 4 was still more constrained than 5, as highlighted by the smaller variation of d C13•••C3 for 5 than for 4 (0.05 Å and 0.08 Å, respectively) which means that 4 was less stabilized than 5.The stabilization and the interactions discussed above cannot account for the reported reactivity, i.e., k d for 3 and 4 larger than k d for 1.As the homolysis is an endothermic reaction, the structure of TS was expected to resemble the structure of the products, that is, radicals 4 and 5, and TEMPO.As TEMPO was always released, any changes observed were due to the structure/configuration/conformation of the alkyl fragments and radicals.As mentioned above, some d values pointed to a relief of steric strain in 3 and 4, leading to an increase in the freedom of motion at TS, and thus in S ≠ , and also in k d of 3 and 4.This was highlighted by the 0.3 Å-0.5 Å increase in the distances H      As mentioned above, the homolysis of 1-3 was an endothermic reaction, which means that their TS resembled the products (TEMPO and the alkyl radicals) [29].For the alkyl radicals, it is noteworthy to mention that the odd electron was delocalized on the aromatic ring by conjugation of the SOMO and the  cloud, which implied a 90° angle between the aromatic ring and the SOMO (-SOMO→ * ,C13 ), and consequently, at TS, aiming to favor this interaction, it is expected that the cleaving O-C bond, i.e., the nascent SOMO, exhibited an angle <O 5 C 4 C 13 C 14 > as close as possible from 90°.Hence, this remote internal strain implied a 4°-6° opening of the torsion angle <O 5 C 4 C 13 C 14 > for 2 and 3 in comparison to 1, forcing the aromatic ring to stand in a better position and reducing entropic cost at TS, as well as slightly improving (3 kJ/mol more) the hyperconjugative →* C-O interactions (Table 1).Thus, the difference between 1 and 2-3 was due to the remote steric strain in the starting materials, which implied both the destabilization of the starting materials (enthalpic effect, i.e., decrease in E a ) and a better conformation of the aromatic ring at the reactive center (reduction in activation entropic cost), and the relief of this remote steric strain at TS which involved more freedom for the motions at TS (activation entropic effect, i.e., S ≠ > 0) for 2 and 3 than for 1.This takes into account the two-fold increase in k d from 1 to 2 but not the two-fold increase from 2 to 3.
As the homolysis of 2 and 3 afforded either the same radicals or its enantiomer, the difference in k d was not due to the stabilization of the products.Amazingly, calculations showed that the faster isomer 3 was more stable than 2 by 3.0 kJ/mol, as highlighted by the d H12•••C10' .Consequently, the difference was due to the destabilization of TS.As highlighted by the 0.02 Å shorter C 18 ••• H 12 distance in 2 than the C 1 • ••H 12 distance in 3, the phenyl ring induced larger steric strain than the methyl group [30], which in turn indirectly constrained the reaction center, as mentioned above (smaller d H12•••C10' for 2 and 3 than for 1).Thus, the anti conformation for the aromatic rings in 3 was more stable than the gauche conformation for the aromatic rings in 2 (Figure 5).As mentioned above, diastereoisomers 2 and 3 afforded a pair of enantiomeric radicals, and as their TS were product-like, the same interactions as those observed in the radicals and consequently their conformations should be observed in their respective TS [29].As molecules were large and afford many conformations, and as energy changes were small, only the conformation [31] and the subsequent hyperconjugative interactions in starting materials were investigated by calculations.The weak 2 electron-2 orbital interactions mentioned above for 4 combined to the steric strain led to a preferred conformation exhibiting a W arrangement for the C 18 C 2 C 3 C 4 SOMO bond/orbital sequence (<C 1 C 2 C 3 C 4 > ≈ 61° in Table 1 and Figure 4b) and, thus, such conformation was expected to occur at TS. Interestingly, the faster diastereoisomer 3 exhibited this W arrangement (<C 1 C 2 C 3 C 4 > ≈ 63°, Figures 3g and h) whereas diasteroisomer 2 (<C 1 C 2 C 3 C 4 > ≈ 173°, Figures 2e and f) did not.It should be mentioned that the weak n ,O → * C3-C4 / C3-C4 →* C18 interactions (Table 1) supported that the W conformation for 3 was mainly due to the steric strain of the phenyl and methyl groups although the less tilted phenyl group (<C 19 C 18 C 2 C 3 > = 67°) afforded a slightly better interaction for 3 than for 2. Consequently, as the alkyl fragment of 3 and the alkyl radical exhibited the same conformationexcept at the C 4 center whose hybridization changed from sp3 to sp2-no entropic cost was associated with reaching TS from 3. On the other hand, the alkyl fragment of 2 exhibited a conformation quite different from that of 5, and consequently, reaching the expected conformation or a close one at TS required at least one C 2 -C 3 bond rotation, leading to a highly sterically strained conformer, and more likely several bond rotations, leading to high entropic cost.Thus, although 3 was more stabilized than 2, the lower entropic cost associated with reaching TS from 3 than from 2 afforded a faster cleavage for 3 than for 2 (G ≠ (3) < G ≠ (2)), as depicted in Figure 6.Gibbs enthalpy The Arrhenius parameters reported for the diastereoisomers of 7 (A = 3.1 × 10 15 s −1 and E a = 139.2kJ/mol for the RR/SS isomer, and A = 5.5 × 10 14 s −1 and E a = 131.2kJ/mol for the RS/SR isomer) deserve some comments assuming that the size, the conformation, and the polarity of the PhCOO group have very minor effects on the latter [34].Internal strains in 2/3 (and, hence, in 7) are larger than in 1, implying the destabilization of 2/3 (and 7).However, as the alkyl radical released by 2/3 (and 7) is less stabilized than the one from 1, TS for 2/3 (and 7) is slightly higher in energy, which balances the energetic gain due to the destabilization of the starting material.Consequently, E a for the isomers of 7 should be very close to E a of 1 as observed for the RS/SR isomer.Thus, the change of k d should be mainly observed by a change of A values.TS for 2 is more hindered that TS for 3, thus, it costs activation entropy to be reached.Consequently, a higher A value is expected for the RS/SR isomer of 7 than for its SS/RR isomer, in sharp contrast to the reported values, although the A value for the RS/SR isomer is in the expected range.In fact, this clear difference observed between expectations from calculations and the experimental values is only due the compensation entropy-activation energy [7].

Conclusion
As a conclusion, the increase in k d in the series 1 < 2 < 3 was due to a remote steric effect which induced enthalpic (destabilization of the starting materials and relief of steric strain at TS) and entropic (increase in freedom of motion and reduction in entropic costs both at TS) effects.Interestingly, this remote polar effect did not change the typical geometric parameters at the C-ON bond moiety.Importantly, the conclusions drawn here cannot be straightforwardly extended to alkoxyamines carrying a chiral nitroxide fragment such as TIPNO and SG1 because chirality close to the C-O-N moiety is expected to modify more or less strikingly the conformation, leading to an unexpected effect on k d , as already reported [35].
X-ray of 1 and structures of 1-5 are provided as Cif, pdb, and mol2 files in supplementary materials.

Figure 3 .
Figure3.Newman projections given by the torsion angles  gathered in Table1.
H Table 1.Geometrical parameters (bond length l, interatomic distance d, valence angle  and torsion angle ), interaction energy, and formation enthalpy H f calculated by DFT at the B3LYP/6-31G(d) level of theory.a l (Å) 1 (X-ray) 1(R) 2(R 4 R 2 ) 3(R 4 S is for "not determined"; b <C 4 O 5 N 6  N6 > = <C 4 O 5 N 6 C 10/10' > -120°; c The donation was from the bonding spin-orbital  C-H to the -LUMO.The conformation implied the donation from a second H atom of the methyl group; d The donation was from the -SOMO to the antibonding spin-orbital  C-H of the methyl group.The conformation implied the donation from a second H atom; e No n ,O → * C3-C4 interaction was observed for 5. 12 •••C 18/1 , C 13 • ••C 2 , C 13 •••H 17 , and H 12