Fragmentation of β-Silyl Radicals. A Computational Study

May 11, 2010 - β-Fragmentation of β-silyl radical species can be considered as a potent source of silyl radical species that should find useful appl...
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Organometallics 2010, 29, 2406–2412 DOI: 10.1021/om900940n

Fragmentation of β-Silyl Radicals. A Computational Study Rapha€el Mereau, Philippe d’Antuono, Frederic Castet,* Guy Rouquet, Frederic Robert, and Yannick Landais* Institut des Sciences Mol eculaires, UMR-CNRS 5255, Universit e de Bordeaux, 351, Cours de la Lib eration, 33405 Talence, France Received October 26, 2009

β-Fragmentation of β-silyl radical species can be considered as a potent source of silyl radical species that should find useful applications in tin-free radical processes. A computational study on the evaluation of the substituents effects both at silicon and on the R- and β-carbons of β-silyl radical species on the rate of the β-fragmentation step is presented. Density functional theory was used to determine the activation and reaction energies of β-fragmentation of the radical precursors. Singlepoint computations at the B3LYP/6-311þþG(d,p)//B3LYP/6-31G(d) and ROMP2/6-31G(d)// B3LYP/6-31G(d) level were further performed to obtain more precise energy predictions. The obtained results allow establishing structure-properties relationships linking the activation barrier of the β-fragmentation process to the nature of the substituents, which should help in predicting the structure of the most efficient β-silyl radical precursors.

1. Introduction Free radicals are nowadays of paramount importance in organic chemistry, and many syntheses of complex natural products incorporate one or several steps involving such reactive species.1 Free-radical reactions using Bu3SnH or (Bu3Sn)2 in reduction processes and formation of C-C bonds are the most useful tools in the armory of organic chemists.2 Tin derivatives constitute an important class of *Corresponding authors. E-mail: [email protected]; [email protected]. (1) Radicals in Organic Synthesis; Renaud, P.; Sibi, M. P., Eds.; WileyVCH: Weinheim, 2001; Vols. 1-2. (2) (a) Pereyre, M.; Quintard, J. P.; Rahm, A. Tin in Organic Synthesis; Butterworths: London, 1987. (b) Giese, B. Radicals in Organic Synthesis: Formation of Carbon-Carbon Bonds; Pergamon Press: New York, 1986; Vol. 5. (3) (a) Baguley, P. A.; Walton, J. C. Angew. Chem., Int. Ed. 1998, 37, 3072. (b) Studer, A.; Amrein, S. Synthesis 2002, 835. (c) Walton, J. C.; Studer, A. Acc. Chem. Res. 2005, 38, 794. (4) (a) Batley, G. The distribution and fate of tributyltin in the marine environment. In Tributyltin: Case Study of an Environmental Contaminant; de Mora, S. J., Ed.; Cambridge University Press: U.K., 1996; pp 139-166. (b) Clark, E. A.; Sterritt, R. M.; Lester, J. N. Environ. Sci. Technol. 1988, 22, 600–604. (c) Laughlin, R. B., Jr. Bioaccumulation of tributyltin by aquatic organisms. In Organotin: Environmental Fate and Effects; Champ, M. A., Seligman, P. F., Eds.; Chapman and Hall: London, 1996; pp 331-335. (d) Leroy, M. J. F.; Quevauviller, P.; Donard, O. F. X.; Astruc, M. Pure Appl. Chem. 1998, 70, 2051–2064. (e) Maguire, R. J. Water Qual. Res. J. Can. 2000, 35, 633–679. (f) Viglino, L.; Pelletier, E.; St-Louis, R. Environ. Toxicol. Chem. 2004, 23, 2673–2681. (5) For recent reports concerning the reduction of the amount of tin residues in radical reactions, see: (a) Dumartin, G.; Pourcel, M.; Delmond, B.; Donard, O.; Pereyre, M. Tetrahedron Lett. 1998, 39, 4663, and references therein. (b) Hayashi, K.; Iyoda, J.; Shiihara, I. J. Organomet. Chem. 1967, 10, 81. (c) Corey, E. J.; Suggs, J. W. J. Org. Chem. 1975, 40, 2554. (d) Gerlach, M.; Jordens, F.; Kuhn, H.; Neumann, W. P.; Peterseim, M. J. Org. Chem. 1991, 56, 5971. (e) Thibaud, S.; Moine, L.; Degueil, M.; Maillard, B. Eur. Polym. J. 2006, 42, 1273. (f) Curran, D. P.; Halida, S. J. Am. Chem. Soc. 1996, 118, 2531. (g) Light, J.; Breslow, R. Tetrahedron Lett. 1990, 31, 2957. (h) Clive, D. L. J.; Wang, J. J. Org. Chem. 2002, 67, 1192. pubs.acs.org/Organometallics

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radical initiators, so that any radical chemistry practitioner will find it very difficult to get away from Bu3Sn and other tin reagents to sustain a radical chain.3 Tributyltin however suffers from several drawbacks including perceived toxicity4 and often leads to tedious purifications and contamination of final products.5 Several elegant solutions have thus been proposed recently to initiate and propagate radical chain processes without tin.6 Silicon, tin, and germanium belong to the group 14 elements, and therefore share some chemical properties. Silicon may thus be viewed a priori as one of the best candidates able to replace tin. Silyl radicals are, similarly to tin, very reactive toward alkyl and aryl halides, forming very strong Si-X bonds. Unfortunately, trialkylsilyl radicals have remained much less exploited than trialkyltin radicals,7 due to the relatively high bond dissociation energy (BDE) of Si-H and Si-Si bonds as compared with their Sn-H and (6) (a) Quiclet-Sire, B.; Zard, S. Z. In Top. Curr. Chem. Gans€auer, A., Ed.; Springer: Berlin, 2006; Vol. 264, p 201. (b) Ollivier, C.; Renaud, P. Chem. Rev. 2001, 101, 3415. (c) Yorimitsu, H.; Oshima, K. In Renaud, P.; Sibi, M. P., Eds.; Radical in Organic Synthesis; Wiley: Weinheim, 2001; Vol. 1, p 11. (d) Darmency, V.; Renaud, P. In Topics in Current Chemistry; Gans€auer, A., Ed.; Springer: Berlin, 2006; Vol. 263, p 71. (7) For some reports on the generation of silyl radicals, see: (a) Sakurai, H.; Hosomi, A. J. Am. Chem. Soc. 1971, 93, 1709. (b) Chatgilialoglu, C.; Ingold, K. U.; Scaiano, J. C. J. Am. Chem. Soc. 1983, 105, 3292. (c) Curran, D. P.; Xu, J.; Lazzarini, E. J. Am. Chem. Soc. 1995, 117, 6603. (d) Schiesser, C. H.; Wild, L. M. Tetrahedron 1996, 52, 13265. (e) Studer, A.; Steen, H. Chem. Eur. J. 1999, 5, 759. (f) Amrein, S.; Bossart, M.; Vasella, T.; Studer, A. J. Org. Chem. 2000, 65, 4281. (g) Matsumoto, A.; Ito, Y. J. Org. Chem. 2000, 65, 5705. (h) Horvat, S. M.; Schiesser, C. H.; Wild, L. M. Organometallics 2000, 19, 1239. (i) Studer, A.; Amrein, S. Angew. Chem., Int. Ed. 2000, 39, 3080. (j) Matsubara, H.; Schiesser, C. H. J. Org. Chem. 2003, 68, 9299. (k) Studer, A.; Amrein, S.; Matsubara, H.; Schiesser, C. H.; Doi, T.; Kawamura, T.; Fukuyama, T.; Ryu, I. Chem. Commun. 2003, 1190. (l) Zhu, Z.; Wang, C.; Xiang, X.; Pi, C.; Zhou, X. Chem. Commun. 2006, 2066. (m) Vaillard, S. E.; M€uck-Lichtenfeld, C.; Grimme, S.; Studer, A. Angew. Chem., Int. Ed. 2007, 46, 6533. (n) Sibi, M. P.; Yang, Y.-H.; Lee, S. Org. Lett. 2008, 23, 5349. (8) (a) Chatgilialoglu, K. Acc. Chem. Res. 1992, 25, 188. (b) Chatgilialoglu, K. Chem. Rev. 1995, 95, 1229. r 2010 American Chemical Society

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Figure 1. β-Fragmentation of β-silyl radicals as a source of silyl radicals.

Sn-Sn analogues. Consequently, silanes such as (Me3Si)3SiH,8 having weaker Si-H bonds, were later introduced as efficient surrogates of Bu3SnH. Similarly, allyltristrimethylsilylsilane (AllylSi(SiMe3)3)9 was reported to be a useful allylation reagent of alkyl halides and thus a good substitute for allyltin reagents. Allylation through AllylSi(SiMe3)3 proceeds through the formation, as a key step, of a β-silyl radical intermediate, which β-fragments to provide the allylated product, regenerating the silyl radical, which propagates the chain, through abstraction of the halogen from the alkyl halide. Such a β-fragmentation constitutes an easy way to generate highly reactive silyl radicals, providing that the β-elimination is fast enough to propagate the radical chain. Apart from the studies on the fragmentation of the (Me3Si)3Si group,10 very little is known about the effects that might favor or slow down such a β-fragmentation process.11 In order to estimate the potential use of β-fragmentation as a source of silyl radical species, we thus initiated a theoretical study at the density functional theory (DFT) level, aiming at evaluating the effect of substituents both at silicon and on the carbon framework (R- and β-carbon) on the rate of the β-fragmentation of β-silyl radicals 3 (Figure 1). We report here a full account on these investigations, which should help in designing the best β-silyl radical precursors for potential use in tin-free radical processes.

2. Computational Section Geometry optimizations were carried out under vacuum using DFT with the three-parameter hybrid B3LYP exchangecorrelation functional12 and the 6-31G(d) basis set with a tight convergence threshold on the residual forces. To determine unambiguously the most stable structures of reactant species, preliminary conformational studies have been carried out systematically at the B3LYP/6-31G(d) level by varying step by step the dihedral angles characterizing the spatial orientation of the substituents. Every transition state (TS) was characterized by one single vibrational normal mode, associated with an imaginary frequency, corresponding to the relative motion of the Si and C1 atoms related to the breaking of the covalent bond during the (9) (a) Chatgilialoglu, K.; Ferreri, C.; Ballestri, M.; Curran, D. P. Tetrahedron Lett. 1996, 37, 6387. (b) Chatgilialoglu, K.; Ballestri, M.; Vecchi, D.; Curran, D. P. Tetrahedron Lett. 1996, 37, 6383. (c) Miura, K.; Saito, H.; Nakagawa, T.; Hondo, T.; Tateiwa, J.; Sonoda, M.; Hosomi, A. J. Org. Chem. 1998, 63, 5740. (d) Kosugi, M.; Kurata, H.; Kawata, K.; Migita, T. Chem. Lett. 1991, 1327. (10) Such an allylation is not possible using the corresponding allyltrimethylsilane, as the corresponding β-silyl radical does not fragment. For instance, no reaction was observed during reaction of thiyl radicals with allyltrimethylsilanes, indicating that while addition of thiyl radical on the olefin is a fast process, β-elimination of a S-centered radical is faster than that of a silyl radical: Light, J. P., II; Ridenour, M.; Beard, L.; Hershberger, J. W. J. Organomet. Chem. 1987, 326, 17. (11) In comparison, kinetic and stereochemistry of β-fragmentation of analogous β-sulfur radical species have been examined more thoroughly; see: (a) Wagner, P. J.; Sedon, J. H.; Lindstrom, M. J. J. Am. Chem. Soc. 1978, 100, 2579. (b) Boothe, T. E.; Greene, J. L., Jr.; Shevlin, P. B. J. Org. Chem. 1980, 45, 794. (c) Timokhin, V. I.; Gastaldi, S.; Bertrand, M.; Chatgilialoglu, C. J. Org. Chem. 2003, 68, 3532. (12) (a) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (b) Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1988, 37, 785.

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β-fragmentation process. The average spin expectation values ÆS2æ for the TS structures are lower than 0.78, which suggests no significant error due to spin contamination. Thermal corrections were calculated from the unscaled harmonic vibrational frequencies using standard temperature and pressure conditions. Although the reliability of conventional DFT approaches has recently been under question to study the thermodynamics of radical reactions,13 the good performance of the B3LYP/6-31G(d) level of theory was demonstrated in previous investigations on analogous systems, such as the free-radical-mediated 5-exo-trig cyclizations of hepta-1,6-dienes incorporating allylsilanes14 or the reactivity of silyl radicals toward the addition onto alkenes (i.e., the reverse process of the β-fragmentation studied here).15 Moreover, it is important to notice that the aim of this work is not to obtain a quantitative description of the thermodynamics of radical β-fragmentation reactions, but rather to establish structure-property relationships, providing insight into the effects of substitution in these chemical processes. Nevertheless, to obtain more precise wave functions and energies, single-point calculations on the B3LYP/6-31G(d) geometries were also performed at the B3LYP level, using the larger 6-311þþG(d,p) basis set, as well as at the restricted open shell second-order Møller-Plesset (ROMP2) level16 with the 6-31G(d) basis set. Indeed, the combination of ROMP2 single-point energies with B3LYP geometries was shown to be a good compromise when predicting radical stabilization energies.17 These procedures are referred to as B3LYP/6-311þþG(d,p)//B3LYP/6-31G(d) and ROMP2/6-31G(d)//B3LYP/6-31G(d) and abbreviated in the tables as B3LYP//B3LYP and ROMP2//B3LYP, respectively. Moreover, since previous studies reported that transition states calculated at the B3LYP level for radicals might, in some cases, be too early with underestimated associated energy barriers, we also performed calculations using the BHandHLYP functional, which has been shown to be well suited for calculating barrier heights in radical processes.18 The DFT geometries were also validated against structures optimized at the ROMP2 level for small systems (see the Supporting Information, SI). Finally, Mulliken atomic charge distributions and natural bond orbital (NBO) analyses19 were further carried out to obtain additional details on the electronic structure of reactive species and TSs. All calculations were performed with Gaussian03.20 (13) Izgorodina, E. I.; Brittain, D. R. B.; Hodgson, J. L.; Krenske, E. H.; Lin, C. Y.; Namazian, M.; Coote, M. L. J. Phys. Chem. A 2007, 111, 10754. (14) d’Antuono, P.; Fritsch, A.; Ducasse, L.; Castet, F.; James, P.; Landais, Y. J. Phys. Chem. A 2006, 110, 3714. (15) Lalevee, J.; Allonas, X.; Fouassier, J.-P. J. Org. Chem. 2007, 72, 6434. (16) Møller, C.; Plesset, M. S. J. Chem. Phys. 1934, 46, 618. (17) (a) Parkinson, C. J.; Mayer, P. M.; Radom, L. Theor. Chem. Acc. 1999, 102, 92. (b) Parkinson, C. J.; Mayer, P. M.; Radom, L. J. Chem. Soc., Perkin Trans. 2 1999, 11, 2305. (18) Wang, Y.; Grimme, S.; Zipse, H. J. Phys. Chem. A 2004, 108, 2324. (19) Foster, J. P.; Weinhold, F. J. Am. Chem. Soc. 1980, 102, 7211. (20) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, Revision C.02; Gaussian, Inc.: Wallingford, CT, 2004.

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Figure 2. Reactants leading to Z- and E-alkenes as fragmentation products (Si stands for Si(SiMe3)3).

3. Results and Discussion 3.1. Impact of Alkyl Substituents at the r- and β-Carbons of β-Silyl Radicals 1 (Figure 1). The impact of chemical substitutions on the thermodynamics of the fragmentation process schematized in Figure 1 has been first investigated by considering functional alkyl groups with increasing size (Me, Et, i-Pr, t-Bu) in the R1 and R2 positions. In fact, two reactive processes have been considered, leading respectively to Zand E-alkenes as fragmentation products. Indeed, Z-reactants bearing methyl or ethyl groups at R1 and R2 are quasi isoenergetic to their E-analogues, as indicated by the Gibbs free energy differences reported in Table S1 (SI). The most striking geometrical characteristic of E- and Z-reactants is that they all display eclipsing interactions between the σC1-Si bond and the radical SOMO (single occupied molecular orbital), as characterized by δ angle values smaller than 30 in all compounds, except those with R2 =t-Bu (see Figure 2 and Table S2, SI). Such eclipsed conformations are known to maximize the stabilizing hyperconjugation interactions between the electron-rich σC1-Si bond and the halffilled hybrid orbital at the radical center,21 as observed in a wide range of silyl radicals by means of electron spin resonance (ESR) and other spectroscopic measurements.22 They are also consistent with our recent investigations on intramolecular radical cyclizations14 and carboazidation of chiral allylsilanes.23 The magnitude of the stabilizing σC1-Si f SOMO* interactions, evaluated from NBO analysis on the B3LYP/6-31G(d) wave functions, is ∼9 kcal/mol for E-reactants with R2 = H and progressively decreases when increasing the size of the R2 substituent (Table S3, SI). Note that destabilizing effects due to the loss of the strict σC1-Si/SOMO alignment when using bulky substituents can be partly compensated by the more pronounced (stabilizing) delocalization of the radical electron, as indicated by the atomic spin density values (defined as the difference of the Mulliken charges of spin-up and spin-down electrons) at the radical center (Table S4, SI). This effect remains, however, small for alkyl substituents. The magnitude of the hyperconjugation effect was also evaluated at the B3LYP/6-31G(d) level by calculating the rotational barrier around the C1-C2 bond in compound 1 with R1=Me and R2=Me (see Figure S1, SI). The value of the rotational barrier is consistent with (21) (a) Sugawara, M.; Yoshida, J. I. J. Org. Chem. 2000, 65, 3135. (b) Lambert, J. B. Tetrahedron 1990, 46, 2677, and references therein. (c) Lambert, J. B.; Zhao, Y.; Emblide, R. W.; Salvador, L. A.; Liu, X.; So, J.-H.; Chelius, E. C. Acc. Chem. Res. 1999, 32, 183. (d) Zhang, S.; Borwell, F. G. J. Org. Chem. 1996, 61, 51. (22) (a) Kawamura, T.; Kochi, J. K. J. Am. Chem. Soc. 1972, 94, 648. (b) Griller, D.; Ingold, K. U. J. Am. Chem. Soc. 1974, 96, 6715. (c) Jackson, R. A.; Ingold, K. U.; Griller, D.; Nazran, A. S. J. Am. Chem. Soc. 1985, 107, 208. (d) Auner, N.; Walsh, R.; Westrup, J. J. Chem. Soc., Chem. Commun. 1986, 207. (23) Chabaud, L.; Landais, Y.; Renaud, P.; Robert, F.; Castet, F.; Lucarini, M.; Schenk, K. Chem.;Eur. J. 2008, 14, 2744.

M ereau et al.

the stabilization energy deduced from NBO analyses, as well as with previous experimental and ab initio determinations on similar compounds.24 In Z-reactants, the alignment between the σC1-Si bond and the radical SOMO is even better than in the corresponding E-structures, implying larger stabilizing effects. As an example, for R1=R2=Me, the δ value is reduced from 28 to 10 when going from the E- to the Z-conformer (Table S2), while the σC1-Si f SOMO* interaction increases from 4.89 to 8.15 kcal/mol. These stabilizing electronic effects roughly compensate the larger steric interactions, leading therefore to similar energies for the Z- and E-configurations in the case of small alkyl substituents. Finally, the degree of pyramidalization of the carbon radical center is found to depend strongly on the nature of the R1 and R2 groups. Indeed, for E-reactants, the C1-C2-R2-Hβ dihedral angle calculated at the B3LYP/6-31G(d) level varies from 0 (no pyramidalization) when R1=R2=Et, to 19 when R1=H or Me and R2=t-Bu (Table S5, SI). Z-Reactants display radical pyramidalization similar to or slightly smaller than their E-analogues. Compared to reactant species, transition structures are stabilized further by the lowering of the δ angles (except for R2 =H, see Table S6, SI), which maximizes the interactions between the σC1-Si and the half-filled hybrid orbital. The calculated activation barriers and reaction energies of radical β-fragmentation processes leading to E-alkenes and;when relevant;to Z-alkenes are reported in Table 1 for all combinations of R1 and R2. Reaction energies have been calculated by taking the difference between the Gibbs energy of the TSs and the sum of the Gibbs energies of the two isolated fragmentation products. At the B3LYP/6-31G(d) level, when increasing the size of the alkyl group at R1 while keeping R2 constant, ΔGq globally evolves linearly with ΔGR. Thus, within the same series of compounds (i.e., R2 constant), the lowest fragmentation barriers are predicted to be associated with the most exothermic processes. In addition, it is noteworthy that the reaction energies ΔGR progressively decrease (i.e., the reaction exothermicity increases) while the size of R1 increases. Combining these two observations leads to the conclusion that the smallest fragmentation barriers should be obtained by grafting bulky alkyl substituents at R1 or both R1 and R2. As a representative example, the transition structure of the compound with R1=t-Bu and R2=Me is schematized in Figure 3. The same conclusions can be drawn when refining the wave function at the B3LYP/6-311þþG(d,p)//B3LYP/631G(d) and ROMP2/6-31G(d)//B3LYP/6-31G(d) levels (Table 1). For comparison purposes, the barrier heights were also calculated at the BHandHLYP/6-31G(d) for representative compounds (see Table S7). Due to larger Si-C1 distances, the barriers calculated with B3LYP are systematically smaller than those computed using BHandHLYP. However, both levels of calculations follow the same trends regarding the impact of the substituents on the fragmentation process. The structure-property relationship linking the fragmentation ability of β-silyl radicals to the size of the alkyl substituents at the R- and β-carbon centers provides a first guideline for increasing the efficiency of the radical precursors. However, the (24) See for instance: (a) Wilt, J. W.; Lusztyk, J.; Peeran, M.; Ingold, K. U. J. Am. Chem. Soc. 1988, 110, 281. (b) Bertrand, M. P.; De Riggi, I.; Lesueur, C.; Gastaldi, S.; Nouguier, R.; Jaime, C.; Virgili, A. J. Org. Chem. 1995, 60, 6040.

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Table 1. Activation, ΔGq, and Reaction, ΔGR, Energies (in kcal/mol) of Radical β-Fragmentation Processes Leading to E-Alkenes (Z-alkenes in parentheses) as a Function of the Nature of Alkyl Substituents R1 and R2 (Figure 1), As Calculated Using Various Computational Levels (see Computational Section) substituents

B3LYP//B3LYPa

B3LYP/6-31G(d)

ROMP2//B3LYPb

R1

R2

ΔGq

ΔGR

ΔGq

ΔGR

ΔGq

ΔGR

H Me Et i-Pr t-Bu H Me Et i-Pr t-Bu SiMe3 H Me Et i-Pr t-Bu H Me Et i-Pr t-Bu H Me Et i-Pr t-Bu

H H H H H Me Me Me Me Me Me Et Et Et Et Et i-Pr i-Pr i-Pr i-Pr i-Pr t-Bu t-Bu t-Bu t-Bu t-Bu

11.74 8.95 9.47 6.52 7.27 9.53 9.03 (7.40) 9.03 (8.31) 8.05 6.55 10.70 9.59 8.98 (8.53) 9.95 8.81 9.02 10.96 10.97 (8.55) 7.63 7.47 7.46 11.88 11.32 8.85 8.77 6.89

-5.43 -14.36 -14.08 -19.25 -24.30 -8.42 -16.35 (-16.20) -15.96 (-16.64) -20.73 -27.15 -19.60 -8.02 -16.58 (-16.05) -15.86 -21.23 -26.50 -9.31 -17.15 (-16.96) -19.71 -23.65 -29.57 -9.81 -19.22 -21.47 -26.94 -34.59

11.04 8.30 8.83 5.95 6.70 8.98 8.50 (6.89) 8.58 (7.80) 7.64 6.25 10.62 9.04 8.42 (8.02) 9.40 8.50 8.72 10.42 10.30 (7.76) 7.16 6.55 6.99 11.53 10.71 8.32 8.21 6.56

-7.72 -16.63 -16.54 -21.79 -27.21 -10.73 -18.63 (-18.40) -18.27 (-18.94) -23.25 -29.92 -21.48 -10.32 -18.84 (-18.65) -18.40 -23.83 -29.42 -11.78 -19.67 (-19.50) -22.31 -26.47 -31.27 -12.34 -21.97 -24.42 -30.09 -38.13

14.17 11.65 12.22 8.99 9.14 11.30 10.64 (9.22) 10.69 (10.27) 9.01 9.87 12.81 11.02 10.18 (10.73) 11.42 10.09 10.06 12.07 12.24 (9.81) 8.76 7.97 10.81 12.65 11.34 8.67 12.10 10.85

-1.04 -6.31 -5.08 -9.06 -12.29 -3.44 -7.66 (-7.27) -6.18 (-7.09) -9.55 -13.92 -6.25 -3.01 -7.92 (-7.03) -5.94 -9.46 -12.56 -3.97 -7.67 (-7.59) -9.23 -11.36 -15.06 -3.71 -9.26 -10.43 -14.26 -19.75

a

B3LYP/6-311þþG(d,p)//B3LYP/6-31G(d). b ROMP2/6-31G(d)//B3LYP/6-31G(d).

Figure 3. Transition state associated with the fragmentation of the precursor with R1 = t-Bu and R2 = Me.

synthesis of compounds with bulky substituents at R1 might not be easy to carry out due to the vicinity of the tris(trimethylsilyl)silyl group. A way to circumvent this difficulty is to replace sterically demanding alkyl substituents by functional groups introducing favorable electronic effects. Additional calculations were then performed by replacing the alkyl group at R1 by a second silyl substituent, with the subjacent idea to affect electronically the stabilization due to hyperconjugation and to reduce the importance of the alignment of the SOMO with the σC1-Si orbital. Indeed, the δ angle obtained for the compound with R1=SiMe3 and R2=Me is larger than the one calculated for the compound bearing a t-Bu group at R1 (29.1 vs 22.4, see Table S2), leading to smaller σC1-Si f SOMO* interactions (3.83 vs 5.82 kcal/mol, see Table S3).

However, the calculated fragmentation barriers (Table 1) are larger than those obtained with alkyl groups at R1, indicating that grafting a silyl group on the R-carbon center does not improve the efficiency of the β-fragmentation process. The reason lies in the fact that the C1-Si distance is larger in the compound with R1 = t-Bu (1.996 vs 1.973 A˚), leading to a smaller bond dissociation. Moreover, the spin density distributions (Table S4, SI) show that the delocalization of free electron over the R1 substituent is larger with R1 = SiMe3 than with R1 = t-Bu, inducing a larger stabilization of the reactant species. On the contrary, as indicated by the larger amount of the free electrons on the β-silicon atom, as well as by the larger C1-Si distance [2.585 vs 2.552 A˚], the TS occurs later with R1 = SiMe3 than with R1 = t-Bu, which has the consequence of increasing the reaction barrier. We then envisaged two other ways to lower the fragmentation barriers while avoiding the use of bulky substituents. The first one consists in using aromatic instead of alkyl groups, in order to lower the fragmentation energy by introducing stabilizing delocalization effects in the TSs. The second consists in localizing the radical center on a ring, in order to mimic the favorable geometrical conformations obtained with bulky alkyl groups, playing with restricted ring conformations, while avoiding the difficulties associated with the synthesis of such precursors. The corresponding chemical processes are investigated in the next two sections. 3.2. Impact of a Phenyl Substituent on the r- and/or β-Carbon of β-Silyl Radicals 1 (Figure 1). As above, the relative energies of the Z- and E-configurations of radical precursors (Figure 2) have been calculated for precursors bearing a phenyl group at the R- or β-carbon centers. Considering compounds with a phenyl group at R1, all theoretical levels predict that several reactive species having a Z-configuration may exist at room temperature, with Gibbs energy

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Table 2. Activation, ΔGq, and Reaction, ΔGR, Energies (in kcal/mol) of Radical β-Fragmentation Processes Leading to E-Alkenes (Z-alkenes in parentheses) for Compounds Bearing a Phenyl Group at R1 or R2 (see Figure 1), As Calculated Using Various Computational Levels (see Computational Section) substituents

B3LYP//B3LYPa

B3LYP/6-31G(d)

ROMP2//B3LYPb

R1

R2

ΔGq

ΔGR

ΔGq

ΔGR

ΔGq

ΔGR

Ph Ph Ph Ph Ph H Me Et i-Pr t-Bu Ph

H Me Et i-Pr t-Bu Ph Ph Ph Ph Ph Ph

6.58 7.57 (7.93) 10.48 9.75 11.96 15.38 14.81 14.00 13.29 11.94 11.93

-18.26 -20.33 (-17.66) -19.25 -20.17 -22.67 0.00 -8.73 -9.13 -14.68 -19.67 -12.71

6.15 7.20 (7.79) 10.25 9.25 11.32 14.71 14.40 13.62 12.80 11.74 11.75

-20.48 -22.67 (-19.92) -21.61 -22.87 -25.71 -2.45 -11.07 -11.54 -17.36 -22.63 -15.08

9.78 10.92 (9.80) 10.86 10.75 17.37 16.29 15.92 15.59 14.41 13.83 12.88

-4.81 -6.05 (-4.14) -4.5 -4.58 -6.25 5.36 0.69 1.55 -2.51 -4.79 2.37

a

B3LYP/6-311++G(d,p)//B3LYP/6-31G(d). b ROMP2/6-31G(d)//B3LYP/6-31G(d).

differences on the order of or smaller than 1 kcal/mol (Table S8). Relative energies are much higher when the phenyl group is located at R2, giving rise to a negligible statistical weight for the Z-compound. Contrary to their alkylated analogues, the E-reactants bearing a phenyl group at R1 or R2 are characterized by large values of the δ angle (Table S2). Indeed, while compounds with R1 =alkyl and R2 =H show a perfect eclipsed conformation, the δ angle is found equal to 13 when a phenyl group is substituted at R1. When R2 is an alkyl group, the δ values range between 34 and 55. As a consequence of the loss of the alignment of the σC1-Si and the half-filled orbital, the stabilizing σC1-Si f SOMO* interactions are strongly reduced (from 1.50 and 3.89 kcal/mol, see Table S3). In addition, one notices that compounds with R1 =Ph and R2=alkyl exhibit a significant degree of pyramidalization of the radical center (15-18). In contrast, when R2 = Ph, almost no pyramidalization is observed, as a consequence of the radical delocalization on the phenyl ring. Radical delocalization in the reactant species and transition states also has a direct impact on the activation barriers and reaction energies of the fragmentation processes, as reported in Table 2. In particular, it is noteworthy that the activation energies of compounds with R2 =Ph are systematically higher than those obtained for compounds bearing an alkyl group at R2 (while keeping the same substituent at R1). In the reactive species with R2=Ph, the free electron at C2 is significantly delocalized on the phenyl group with total spin density values of ∼0.7 on Ph and of ∼0.3 on C2 (Table S4, SI). Such electron delocalization strongly stabilizes the reactive species and raises the fragmentation barrier. Besides, the analysis of the spin density distribution in the TSs with R2=Ph indicates that the amount of the free electron on the β-silicon atom is larger than in analogous compounds bearing an alkyl group at R2 (Table S4, SI). As a consequence, the geometrical structures of the transition species are closer to the structure of the fragmentation products, inducing a lowering of reaction exothermicity. The fragmentation process is even predicted to be endothermic at the ROMP2/6-31G(d)//B3LYP/6-31G(d) level for compounds with R1 =H, Me, or Et. The reverse conclusions hold when considering compounds with a phenyl group at R1, whose β-fragmentation is made easier by electronic effects. In this case, the spin density at the radical center C2 is close to 1 in the reactants, indicating the absence of stabilizing effects due to radical delocalization, while the distribution of the spin

Figure 4. Transition state associated with the fragmentation of the precursor with R1 = Ph and R2 = H.

density between C2 and the β-silicon atom in the TSs is quite symmetrical. Note also that, for such compounds, the fragmentation barrier increases when increasing the size of the alkyl group at R2, so that good candidates for silyl radical generation from β-fragmentation should be obtained by grafting a phenyl group at R1 without substitution at R2 (the corresponding transition structure is schematized in Figure 4). The fragmentation barrier obtained in this case is predicted to be on the same order of magnitude (even slightly lower) as that obtained using bulky t-Bu groups at both R1 and R2. 3.3. β-Fragmentation of Cyclic Radical Precursors 4 and 6 (Figure 5). In this section, five- and six-membered cyclic radical precursors 4 and 6 are investigated with the aim of evaluating the impact of constraining the geometry of the carbon framework (Figure 5). The six-membered ring in 6 presents two stable geometries, according to the chair- and boat-like conformations. However, the boat-like structure is found to be higher in energy by 3.62 kcal/mol (at the B3LYP/ 6-31G(d) level) and will not be discussed further. The calculated activation barriers and reaction energies of β-fragmentation processes for these cyclic radicals are reported in Table 3. The β-fragmentation barriers of the five-membered and six-membered (chair-like) cyclic radical precursors (25) A-values of 4.9 and 4.89 have been reported respectively for t-Bu and Si(SiMe3)3. See: Eliel, E. L.; Wilen, S. H. Stereochemistry of Organic Compounds; Wiley: New York, 1993; p 686. For Si(SiMe3)3: Frey, J.; Schottland, E.; Rappoport, Z.; Bravo-Zhivotovskii, D.; Nakash, M.; Botoshansky, M.; Kaftory, M.; Apeloig, Y. J. Chem. Soc., Perkin Trans. 2 1994, 2555. In agreement with MM2-force-field calculations above, B3LYP/6-31G(d) calculations give A-values of 6 kcal/mol for both t-Bu and Si(SiMe3)3. As a comparison, an A-value of 2.5 was reported for SiMe3.

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Figure 6. β-Fragmentation of substituted (chair-like) six-membered cyclic radical precursors 8a-d. Figure 5. β-Fragmentation of five- and six-membered cyclic radical precursors. Table 3. Activation, ΔGq, and Reaction, ΔGR, Energies (in kcal/mol) of Radical β-Fragmentation Processes for Cyclic Compounds (see Figures 4, 5), As Calculated Using Various Computational Levels (see Computational Section)a B3LYP/6-31G(d) preentry cursor 1 2 3 4 5 6

4 6d 8ad 8bd 8cd 8dd

B3LYP//B3LYPb

ΔGq

ΔGR

ΔGq

10.74 9.92 6.95 (2.57) 7.77 (5.20) 5.56 (7.53) 9.81 (0.00)

-12.65 -16.37 -18.67 -17.41 -19.73 -16.08

10.23 9.28 6.60 (2.41) 6.91 (5.31) 5.13 (7.49) 9.29 (0.00)

ΔGR

ROMP2//B3LYPc ΔGq

ΔGR

-14.88 11.81 -4.36 -18.83 10.80 -7.01 -20.96 7.77 (2.08) -8.51 -19.91 9.27 (4.85) -8.02 -22.10 6.08 (6.68) -9.86 -18.53 10.09 (0.00) -6.42

Figure 7. Transition state associated with the fragmentation of the 8a precursor.

a

The relative Gibbs energies of the reactant species 8a-d are given in parentheses. b B3LYP/6-311++G(d,p)//B3LYP/6-31G(d). c ROMP2/ 6-31G(d)//B3LYP/6-31G(d). d Chair-like structures.

amount to 10-11 kcal/mol (entries 1 and 2, Table 3), which is higher than that obtained for the best candidates, implying a bulky alkyl substituent or a phenyl group on the R-carbon. As a possible way to lower the β-fragmentation barrier, we have then addressed the impact of adding a tert-butyl group at C4 of the six-membered cyclic radical precursor to lock chair conformations (i.e., 8a-d, Figure 6). Considering the similar Winstein-Holness A-values for the silyl and t-Bu substituents,25 four different chair-like structures have been considered. Two structures are obtained by adding the t-Bu group cis to the resident (Me3Si)3Si substituent: 8a, in which the silyl group is axial and the t-Bu equatorial (entry 3, Table 3), the other one, 8b, with the reverse position of the two substituents (entry 4). In the corresponding trans structures, both the silyl and t-Bu groups point either in the axial or in the equatorial direction (8c and 8d, respectively, entries 5 and 6). The β-fragmentation barrier of the most stable substituted precursor (8d) amounts to 9-10 kcal/mol (entry 6), which is similar to that obtained for the unsubstituted compound 6. The three other substituted precursors (entries 3-5) present significantly smaller fragmentation barriers; however, this lowering mainly originates from the fact that reactant species have a much higher energy. cis-8a appears as the best compromise with relatively low activation energy and reasonable ground-state energy. As shown in the corresponding TS (issued from 8a) depicted in Figure 7, the Si(SiMe3)3 group is pseudoaxial and the C-Si bond is thus nearly aligned with the radical orbital, which ensures a good overlapping, favoring the β-elimination, as this conformation does not require any costly conformational rearrangement

to generate olefin 9. The pseudoaxial arrangement of the Si (SiMe3)3 group, β to the radical center, is thus crucial for the β-elimination rate, which is further confirmed by the low activation energy calculated for the trans-isomer 8c, where both substituents are axial. Unfortunately, the ground-state conformation of this isomer is much higher in energy (>7 kcal/mol) due to severe 1,3-diaxial interactions between the bulky substituents and axial hydrogens. 3.4. Impact of Substitution at Silicon. Finally, for comparison purposes, we have investigated the impact of replacing the tris(trimethylsilyl)silyl group by a trimethylsilyl substituent in the best precursors designed in the previous sections (i.e., 1 with [t-Bu, Me], [t-Bu, t-Bu], and [Ph, Me] at [R1, R2], and 8e having a t-Bu and a SiMe3 in equatorial and axial position, respectively). The thermodynamic data are gathered in Table 4. All theoretical levels of calculation predict much larger barrier heights for the trimethylsilylated compounds 8e, showing unambiguously the advantage of using tris(trimethylsilyl)silyl substituents in the generation of radical precursors through β-fragmentation.9 Note also that the high increase of the β-fragmentation barriers when replacing the tris(trimethylsilyl)silyl by a trimethylsilyl group is accompanied by a significant reduction of the reaction energy, the fragmentation process being in some cases (especially for the cyclic precursor) slightly endothermic.

4. Conclusion In order to estimate the potential use of β-fragmentation as a source of silyl radical species, we have performed a computational study at the DFT and ROMP2 levels, aiming at evaluating the effect of substituents both at silicon and on the carbon framework (R- and β-carbon) on the rate of the

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Table 4. Activation, ΔGq, and Reaction, ΔGR, Energies (in kcal/mol) of Radical β-Fragmentation Processes for Various Compounds Implying a Trimethylsilyl Group, As Calculated Using Various Computational Levels (see Computational Section) B3LYP/6-31G(d)

B3LYP//B3LYPa

ROMP2//B3LYPb

precursor

ΔGq

ΔGR

ΔGq

ΔGR

ΔGq

ΔGR

1, R1 = t-Bu, R2 = Me 1, R1 = t-Bu, R2 = t-Bu 1, R1 = Ph, R2 = Me 8e

17.92 17.50 17.56 18.20

-1.95 -5.79 0.45 2.18

17.08 16.60 17.00 17.64

-4.06 -8.56 -0.74 1.36

28.48 28.16 32.65 27.92

4.16 1.04 7.77 6.73

a

B3LYP/6-311++G(d,p)//B3LYP/6-31G(d). b ROMP2/6-31G(d)//B3LYP/6-31G(d).

β-fragmentation of β-silyl radicals. Structure-properties relationships linking the activation barrier of the β-fragmentation process to the nature of the substituents can be deduced from these theoretical investigations, which should help in designing efficient β-silyl radical precursors for a potential use in tin-free radical processes. In particular, β-silyl radical precursors with low fragmentation barriers should be obtained by (1) grafting bulky alkyl substituents at the R-carbon or at both the R- and β-carbons; (2) grafting a phenyl substituent at the R-carbon without substituting the β-carbon; and (3) including the radical center in a sixmembered ring, while substituting C4 with a bulky alkyl group. Efforts are now directed at applying these predictions to radical chain transfer processes. Synthesis of β-silyl radical precursors and their use in free-radical-mediated addition processes is actively pursued in our laboratories and will be reported in due course.

Acknowledgment. This work has benefited from the financial support of the French “Agence Nationale de la Recherche (ANR)” (project 07-BLAN-0176-02 - SILABOR). The calculations have been performed on the intensive calculation pole “M3PEC-MESOCENTRE” of the University Bordeaux financed by the Conseil Regional d’Aquitaine and the French Ministry of Research and Technology, as well as at the Inter-University Scientific Computing Facility (ISCF) installed at the Facultes Universitaires Notre-Dame de la Paix (FUNDP). Supporting Information Available: Representative geometrical features of reactants and TS, atomic electron and spin densities, magnitude of the σC1-Si f SOMO* interactions in reactants, and geometrical structures of transition states optimized at the B3LYP/6-31G(d) level. This material is available free of charge via the Internet at http://pubs.acs.org.