A Computational Study of the Mechanism of Addition of Singlet

Sep 10, 2009 - B3LYP, MPW1K, and CCSD(T) electronic structure calculations were employed to investigate the mechanisms for the addition of singlet car...
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Organometallics 2009, 28, 5612–5622 DOI: 10.1021/om900369e

A Computational Study of the Mechanism of Addition of Singlet Carbene Analogues to 1,3-Butadiene to Form 1,1-Dimethylmetallacyclopent-3enes [MMe2C4H6, M = Si, Ge, Sn] and Their Reverse Retro-addition Reactions Mrinmoy Nag and Peter P. Gaspar* Department of Chemistry, Washington University, St. Louis, Missouri 63130-4899 Received May 8, 2009

B3LYP, MPW1K, and CCSD(T) electronic structure calculations were employed to investigate the mechanisms for the addition of singlet carbene analogues dimethylsilylene, Me2Si:, dimethylgermylene, Me2Ge:, and dimethylstannylene, Me2Sn:, to 1,3-butadiene to form 1,1-dimethylmetallacyclopent-3-enes and their reverse retro-addition reactions. The calculations suggest that silylenes and germylenes add to 1,3-butadiene to form the 1,2-adduct, vinylmetalliranes, and the 1,4-adduct, metallacyclopent-3-enes, via 1,2-addition and concerted 1,4-addition processes, respectively, while stannylenes add exclusively to form the 1,4-adduct. Our calculations also predict that direct rearrangements of vinylmetalliranes make minimal contribution to the formation of the 1,4-adducts since the retro-addition reactions of the metallylenes followed by 1,4-addition are much faster than the rearrangement reactions of vinylmetalliranes to form metallacyclopent-3-enes. Introduction Much attention was devoted in the second half of the last century to the study of heavier carbene analogues, metallylenes (R2M:): silylenes (R2Si:),1 germylenes (R2Ge:),2,3 and *Corresponding author. E-mail: [email protected]. (1) (a) Becerra, R.; Walsh, R. Phys. Chem. Chem. Phys. 2007, 9, 2817. (b) Tokitoh, N.; Ando, W. In Reactive Intermediate Chemistry; Moss, R. A.; Platz, M. S.; Jones, M., Jr., Eds.; Wiley-Interscience: New York, 2004; pp 651-715. (c) Gaspar, P. P.; West, R. In The Chemistry of Organic Silicon Compounds; Rappoport, Z.; Apeloig, Y., Eds.; John Wiley and Sons: New York, 1998; Vol. 2, pp 2463-2568. (d) Becerra, R.; Walsh, R. Res. Chem. Kinet. 1995, 3, 263–326. (e) Weidenbruch, M. Coord. Chem. Rev. 1994, 130, 275. (f) Gaspar, P. P. In Reactive Intermediates; Jones, M., Jr.; Moss, R. A., Eds.; John Wiley and Sons: New York, 1985; Vol. 3, pp 333-427. (g) Gaspar, P. P. In Reactive Intermediates, Jones, M., Jr.; Moss, R. A., Eds.; John Wiley and Sons: New York, 1981; Vol. 2, pp 335-385. (h) Gaspar, P. P. In Reactive Intermediates; Jones, M., Jr.; Moss, R. A., Eds.; John Wiley and Sons: New York, 1978; Vol. 1, pp 229-277. (2) (a) Boganov, S. E.; Egorov, M. P.; Faustov, V. I.; Krylova, I. V.; Nefedov, O. M.; Becerra, R.; Walsh, R. Russ. Chem. Bull., Int. Ed. 2005, 54, 483. (b) Neumann, W. P. Chem. Rev. 1991, 91, 311. (c) Becerra, R.; Boganov, S. E.; Egorov, M. P.; Lee, V. Y.; Nefedov, O. M.; Walsh, R. Chem. Phys. Lett. 1996, 250 (1), 111. (d) Schriewer, M.; Neumann, W. P. Angew. Chem., Int. Ed. Engl. 1981, 20, 1019. (e) Schriewer, M.; Neumann, W. P. J. Am. Chem. Soc. 1983, 105, 897. (f) Neumann, W. P.; Michels, E.; Koecher, J. Tetrahedron Lett. 1987, 28, 3783. (g) Lei, D.; Gaspar, P. P. Polyhedron 1991, 10, 1221. (h) Bobbitt, K. L.; Maloney, V. M.; Gaspar, P. P. Organometallics 1991, 10, 2772. (i) Bobbitt, K. L.; Lei, D.; Maloney, V. M.; Parker, S. C.; Raible, J. M.; Gaspar P. P. In Frontiers of Organogermanium, -Tin and -Lead Chemistry; Lukevics, E.; Ignatovich, L., Eds.; Latvian Institute of Organic Synthesis: Riga, 1993. (3) (a) Leigh, W. J.; Harrington, C. R.; Vargas-Baca, I. J. Am. Chem. Soc. 2004, 126 (49), 16105. (b) Harrington, C. R.; Leigh, W. J.; Chan, B. K.; Gaspar, P. P.; Zhou, D. Can. J. Chem. 2005, 83, 1324. (c) Leigh, W. J.; Lollmahomed, F.; Harrington, C. R. Organometallics 2006, 25, 2055. (d) Leigh, W. J.; Lollmahomed, F.; Harrington, C. R.; McDonald, J. M. Organometallics 2006, 25 (22), 5424. (e) Huck, L. A.; Leigh, W. J. Organometallics 2007, 26, 1339. (f) Lollmahomed, F.; Huck, L. A.; Harrington, C. A.; Chitnis, S. S.; Leigh, W. J. Organometallics 2009, 28, 1484. (4) Davidson, P. J.; Harris, D. H.; Lappert, M. F. J. Chem. Soc., Dalton Trans. 1976, 21, 2268. pubs.acs.org/Organometallics

Published on Web 09/10/2009

stannylenes (R2Sn:).1b,2a,b,4,5 Addition reactions of carbenes to multiple bonds are well documented,6-8 and the cyclopropane products of their addition to olefins are abundant. While silicon analogues of these products, siliranes, are well known,1b,h,9-11 and there are two examples12,13 of stable germiranes and considerable evidence for their intermediacy,1b,2b the existence of stanniranes remains to be established. Carbenes add to 1,3-butadiene to form their 1,2addition products vinylcyclopropanes (Scheme 1).14,15 Although there are reports that silylenes bearing bulky substituents add to 1,3-dienes to form vinylsiliranes,16-18 the products most often found from addition of heavier carbene (5) Becerra, R.; Gaspar, P. P.; Harrington, C. R.; Leigh, W. J.; Vargas-Baca, I.; Walsh, R.; Zhou, D. J. Am. Chem. Soc. 2005, 127, 17469. (6) Jones, M., Jr.; Moss, R. A. In Reactive Intermediate Chemistry; Moss, R. A., Platz, M. S., Jones, M., Jr., Eds.; Wiley-Interscience: Hoboken, NJ, 2004; pp 273-328. (7) Tomioka, H. In Reactive Intermediate Chemistry; Moss, R. A., Platz, M. S., Jones, M., Jr., Eds.; Wiley-Interscience: Hoboken, NJ, 2004; pp 375-461. (8) Doyle, M. P. In Reactive Intermediate Chemistry; Moss, R. A., Platz, M. S., Jones, M., Jr., Eds.; Wiley-Interscience: Hoboken, NJ, 2004; pp 561-592. (9) Ishikawa, M.; Kumada, M. J. Organomet. Chem. 1974, 81, C3. (10) Gaspar, P. P.; Xiao, M.; Pae, D. H.; Berger, D. J.; Haile, T.; Chen, T.; Lei, D.; Winchester, W. R.; Jiang, P. J. Organomet. Chem. 2002, 646, 68. (11) Hwang, R.-J.; Conlin, R. T.; Gaspar, P. P. J. Organomet. Chem. 1975, 94, C38. (12) Ando, W.; Ohgaki, H.; Kabe, Y. Angew. Chem., Int. Ed. Engl. 1994, 33, 659. (13) Kabe, Y.; Ohgaki, H.; Yamagaki, T.; Nakanishi, H.; Ando, W. J. Organomet. Chem. 2001, 636, 82. (14) Frey, H. M. Trans. Faraday Soc. 1962, 58, 516. (15) Fujimoto, H.; Hoffmann, R. J. Phys. Chem. 1974, 78, 1167. (16) Zhang, S.; Conlin, R. T. J. Am. Chem. Soc. 1991, 113, 4272. (17) Moiseev, A. G.; Leigh, W. J. Organometallics 2007, 26, 6277. (18) Takeda, N.; Tokitoh, N.; Okazaki, R. Chem. Lett. 2000, 29, 622. r 2009 American Chemical Society

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Scheme 5

Scheme 2

Scheme 6

Scheme 3

Scheme 4

analogues to 1,3-butadienes are their 1,4-adducts, metallacyclopent-3-enes1b,2b,1h (Scheme 2). Two different mechanisms have been proposed for the formation of these 1,4-adducts from metallylenes and 1,3dienes and for the corresponding retro-addition processes. The first mechanism is a single-step 1,4-addition, and the second involves a 1,2-addition step followed by rearrangement via a 1,3-sigmatropic shift (Scheme 3). In 1968 Atwell and Weyenberg first reported that thermally generated silylenes reacted with 1,3-butadiene to give silacyclopent-3-enes.19 They suggested a stepwise mechanism for the formation of the silacyclopentenes. Since then, many reports have been published favoring this mechanism.1b,c,h Some of the experimental results implicating vinylsilirane intermediates will be discussed later in this paper. The first thermally induced addition of a germylene to butadiene was reported by Neumann et al. in 1981 (Scheme 4).2d The authors suggested a concerted 1,4-addition for this reaction and provided stereochemical evidence in support of this mechanism in their subsequent publications on similar reactions.2b,e,f In 1982 Gaspar et al. reported the stereoselective addition of germylenes to 1,3-dienes in the gas phase.20 However, strong experimental evidence has been presented in favor of a stepwise mechanism by several groups.1b,2b,3b Reaction of a germylene with 2 equiv of butadiene produced a 3,4-divinyl1-germacyclopentane, which could arise by insertion of a butadiene molecule into a vinyl germirane2b,c,h (Scheme 5). In the past decade many reports of germylene-butadiene addition and retro-addtion reactions have favored the (19) Atwell, W. H.; Weyenberg, D. H. J. Am. Chem. Soc. 1968, 90, 3438. (20) Ma, E. C.-L.; Kobayashi, K.; Barzilai, M. W.; Gaspar, P. P. J. Organomet. Chem. 1982, 224, C13. (21) Leigh, W. J.; Toltl, N. P.; Apodaca, P.; Castruita, M.; Pannell, K. H. Organometallics 2000, 19, 3232.

stepwise mechanism of Scheme 3, but those reactions were performed under photochemical conditions.3,21 Reactions involving stannylenes and 1,3-dienes have been less thoroughly explored.2b Recently stannacyclopent-3-enes have been shown to be good thermal and photochemical precursors for stannylenes.5,22,23 The first stannylene-diene reaction was published by Lappert et al., who reported a 1-stannacyclopent-3-ene from the addition of [(Me3Si)2CH]2Sn: to 2,3-dimethylbutadiene in 1976 (Scheme 6, X = H, Y = Me).24 Later Neumann et al. reported the addition of this stannylene to other substituted dienes (Scheme 6, X = CO2Me, Y=H) in 198425 (Scheme 6). Neumann et al. suggested a concerted 1,4-addition mechanism for this reaction. Several theoretical calculations on reactions of higher carbene analogues with olefins and alkynes have been presented.26-31 Gordon and co-workers suggested a barrierless addition for SiH2 and olefins,27 while Su suggested involvement of a precursor complex and a barrier for the addition of heavier carbene analogues to ethylene.30 There is a computational study by Dewar on the reaction of a stannylene (Br2Sn:) and butadiene in which the authors predicted a concerted synchronous 1,4-addition mechanism.32 However, the latter results were based on a semiempirical (MNDO) method. No other calculations have been reported so far involving addition of silylenes and germylenes to butadiene, to the best of our knowledge. Our hope in beginning this study was that the relative importance of stepwise versus concerted 1,4-addition mechanisms could be assessed for the singlet carbene analogues of heavier group XIV elements and that these assessments could be related to variations in the properties of the (22) Zhou, D.; Reiche, C.; Nag, M.; Soderquist, J. A.; Gaspar, P. P. Organometallics 2009, 28, 2595. (23) Zhou, D. Doctoral Dissertation, Washington University, 2004. (24) Cotton, J. D.; Davidson, P. J.; Lappert, M. F. J. Chem. Soc., Dalton Trans. 1976, 2275. (25) Marx, R.; Neumann, W. P.; Hillner, K. Tetrahedron Lett. 1984, 25, 625. (26) Karni, M.; Kapp, J.; Schleyer, P. v. R.; Apeloig, Y. In The Chemistry of Organic Silicon Compounds; Rappoport, Z., Apeloig, Y., Eds.; John Wiley and Sons: Chichester, 2001; Vol. 3, pp 1-164. (27) Gordon, M. S.; Nelson, W. Organometallics 1995, 14, 1067. (28) Sakai, S. Int. J. Quantum Chem. 1997, 70, 291. (29) Su, M.-D.; Chu, S.-Y. J. Am. Chem. Soc. 1999, 121, 11478. (30) Su, M.-D. Chem.;Eur. J. 2004, 10, 6073. (31) Chung, G.; Gordon, M. S. Organometallics 1999, 18 4881. (32) Dewar, M. J. S.; Friedheim, J. E.; Grady, G. L. Organometallics 1985, 4, 1784.

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individual elements. A computational study using DFT methods and post Hartree-Fock calculations to elucidate the mechanisms of the addition and retro-addition reactions mentioned in Scheme 3 is reported here, as well as kinetic simulations employing rate constants predicted from the results of the electronic structure calculations. Only singlet state reactions of metallylenes are considered here.

Nag and Gaspar Scheme 7

Computational Methods To find the lowest energy conformations of the starting materials, products, intermediates, and transition states, geometry optimizations were performed using PM3 semiempirical or HF methods in Windows Spartan ’04.33 These optimized structures were used as the initial geometries for subsequent calculations. All other calculations were performed using density functional theory (DFT) and coupled-cluster (CCSD(T))34 methods as implemented in the Gaussian ’03 series of programs.35 Geometries and vibrational frequencies of the stationary points were calculated using the B3LYP36,37 level of theory with a 6-31G(d, p) basis set for C, H, and Si, 6-311G(d,p) for Ge, and the LANL2DZ38-40 ECP basis set for Sn. The zero-point energies were not scaled. Single-point energies at these optimized geometries were calculated at CCSD(T, frozen)/cc-pVTZ41,42 for all atoms except tin. The ECP basis set cc-pVTZ-PP43,44 was used for the Sn atoms. Some of the organosilicon compounds were also geometryoptimized using MPW1K, a new hybrid-GGA DFT functional pioneered by Truhlar45,46 employing the 6-31þG(d,p) basis set. The zero-point energies were scaled by a factor of 0.9515.47,48 Single-point energies of those optimized geometries were further calculated at CCSD(T, frozen)/MG3. The MG3 basis set was obtained from the University of Minnesota’s computational chemistry Web site and is equivalent to 6-311þG(3d2f,2df,2p) for H through Si atoms.48 Throughout the Results and Discussion sections, if not otherwise defined, “energy” and “barrier” will signify zero-point(33) Hehre, W. J.; Kong, J. Spartan ’04 Windows; Wavefunction Inc.: Irvine, CA, 2004. (34) Raghavachari, K.; Trucks, G. W.; Pople, J. A.; Head-Gordon, M. Chem. Phys. Lett. 1989, 157, 479. (35) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, M.; Cossi, M.; Scalmani, G.; Rega, N.; Peterssom, G. A.; Nakatsuji, M.; Hoda, 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-E.01; Gaussian Inc.: Wallingford, CT 2004. (36) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (37) Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M. J. J. Phys. Chem. 1994, 98, 11623. (38) Hay, P. J.; Wadt, W., R. J. Chem. Phys. 1985, 82, 270. (39) Hay, P. J.; Wadt, W., R. J. Chem. Phys. 1985, 82, 284. (40) Hay, P. J.; Wadt, W., R. Chem. Phys. Lett. 1985, 82, 299. (41) Dunning, T. H., Jr. J. Chem. Phys. 1989, 90, 1007. (42) Woon, T. E.; Dunning, T. H., Jr. J. Chem. Phys. 1993, 98, 1358. (43) Peterson, K., A. J. Chem. Phys. 2003, 119, 11099. (44) Peterson, K., A. J. Chem. Phys. 2003, 119, 11113. (45) Lynch, B. J.; Fast, P. L.; Harris, M.; Truhlar, D. G. J. Phys. Chem. A 2000, 104, 4811. (46) Lynch, B. J.; Truhlar, D. G. J. Phys. Chem. A 2001, 105, 2936. (47) http://comp.chem.umn.edu/database/freq_scale.htm. (48) http://comp.chem.umn.edu/basissets/basis.cgi.

corrected computed electronic energy and zero-point-corrected computed electronic energy barrier (at 0 K), respectively.

Kinetic Simulation Kinetic simulation was used to estimate rates and relative abundance of products formed in some selected reactions using the energies predicted from our computational studies. These data were compared with the experimental results to test the validity of our calculations and the applicability of the predictions. Predicted free energies of activation for the selected reactions (see Scheme 7) were used to obtain rate constants using the Eyring equation:

k ¼ ðk B T =hÞ expð -ΔG=RTÞ where kB is Boltzmann’s constant, h is Planck’s constant, ΔG‡ is free energy of activation, R is the gas constant, and T is temperature in Kelvin. The change in concentration for each stationary point with respect to time for a given reaction scheme was represented by a differential rate equation, and initial concentrations of those species, along with the reaction conditions, were employed as inputs. From these inputs the concentrations of those species as functions of time were obtained by numerical integration of the rate equations. Variation of the concentrations of those species with time was plotted, and their ratios after a certain period of time were determined. The Mathcad program was employed for these kinetic simulations.

Results and Discussion General Overview of the Results. Our computational studies predict that 1,2-addition of dimethylsilylene and dimethylgermylene to 1,3-butadiene is faster than the corresponding 1,4-addition (Figures 1 and 2). However, the rearrangements of the vinylmetalliranes Si-GS2 or GeGS2 to the most stable products Si-GS1 or Ge-GS1, the corresponding metallacyclopent-3-enes, have higher barriers than the reverse extrusion reactions to re-form free 1,3-dienes and metallylenes Me2Si: and Me2Ge:, respectively. The 1,4-addition reactions have moderate free energy barriers, thus making them favorable pathways

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Figure 3. Free energy profile for the addition of dimethylstannylene to butadiene and the retro-addition at 298 K. The free energies are calculated at CCSD(T)/cc-pVTZ/cc-pVTZ-PP for Sn //B3LYP/6-31G(d,p)/LANL2DZ for Sn and (B3LYP/6-31G(d,p)/LANL2DZ for Sn in parentheses). Figure 1. Free energy profile for the addition of dimethylsilylene to butadiene and the retro-addition at 298 K. The free energies are calculated at CCSD(T)/cc-pVTZ//B3LYP/631G(d,p) and (B3LYP/6-31G(d,p) in parentheses).

Figure 4. Geometries (A˚, deg) of stationary points in Figure 1 optimized at B3LYP/6-31G(d,p).

Figure 2. Free energy profile for the addition of dimethylgermylene to butadiene and the retro-addition at 298 K. The free energies are calculated at CCSD(T)/cc-pVTZ//B3LYP/631G(d,p)/6-311G(d,p) for Ge and (B3LYP/6-31G(d,p)/6-311G(d,p) for Ge in parentheses).

for the formation of the metallacyclopent-3-ene products. In the case of the corresponding tin analogues the free energy barrier for the 1,4-addition is slightly higher than for the 1,2-addition process (Figure 3). However, formation of the vinylstannirane, Sn-GS2, is endothermic and has a very small free energy barrier for the reverse extrusion reaction, making its formation highly improbable and explaining the lack of experimental evidence for the existence of such species. These results reinforce previous conclusions from experimental studies that vinylsiliranes1 and vinylgermiranes1,9 are formed by 1,2-addition during the reactions of corresponding matallylenes and 1,3-dienes, but it is suggested that the corresponding matallacyclopent-3-enes are preferentially formed from the direct 1,4addition of matallylenes to 1,3-dienes, with only a minor contribution from the rearrangement of vinylmetallirane intermediates. Addition of Dimethylsilylene to 1,3-Butadiene, Forming 1,1Dimethylsilacyclopent-3-ene, and Its Reverse Retro-Addition Reaction. The reaction between dimethylsilylene and 1,3butadiene to form the 1,4-addition product 1,1-dimethylsilacyclopent-3-ene and the corresponding retro-addition

reaction were investigated computationally (Scheme 3, M = Si). The structures and geometries of the stationary points on the potential energy surface are shown in Figure 4. The MeSiMe bond angle in the free silylene is predicted to be 97.9°, which changes to 110.1° and 115.6° in the silacyclopentene Si-GS1 and vinylsilirane Si-GS2, respectively. Previous theoretical calculations at the MP2/6-31G(d,p) level by Apeloig et al.49 predicted the MeSiMe bond angle in dimethylsilylene to be 97.1°, and a previous DFT calculation by Su et al.50 predicted the angle to be 97.7°, which are in accord with our calculation. A MeSiMe bond angle of 102.2° is predicted in the transition structure for 1,4-addition, SiTS2, which suggests partial silylene character. The changes in bond lengths observed in the optimized structures of both transition structures Si-TS1 and Si-TS2 are also in accord with that interpretation. Si-TS2 is a transition structure for a concerted asynchronous addition, and partial CdC doublebond character in the butadiene moiety is clearly indicated. The calculated energies of the stationary points shown in Figure 2 are given in Table 1. Previous computational studies by Gordon et al. as well as by Sakai suggested that the addition of SiH2 to ethylene was a barrierless reaction.27,28 For the reaction involving SiMe2 and ethylene, however, Su has found a transition structure with a zero-point-corrected energy of 2.0 kcal/mol below the reactants and with a barrier of 1.7 kcal/mol from a precursor complex, 3.7 kcal/mol lower (49) Apeloig, Y.; Sklenak, S. Can. J. Chem. 2000, 78, 1496. (50) Su, M.-D.; Chu, S.-Y. J. Phys. Chem. A 1999, 103, 11011.

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Table 1. Relative Energies, Zero-Point-Corrected Energies, Enthalpies, and Free Energies of Stationary Points (Figure 4) for the Addition of Me2Si: to 1,3-Butadiene and the Retro-addition Calculated at CCSD(T)/cc-pVTZ//B3LYP/6-31G(d,p) and at B3LYP/6-31G(d,p) (within parentheses)

in energy than the reactants at the CCSD(T)/LANL2DZdp// B3LYP/LANL2DZ level of theory.30 However, in our study, neither a transition structure nor a complex along the reaction coordinate could be found computationally for the 1,2-adddition reaction between dimethylsilylene and butadiene to form vinylsilirane SiGS2, and the addition was predicted to be exothermic by 42.2 kcal/mol (37.2 kcal/mol at the B3LYP level). The computed free energies of activation for the rearrangement interconverting silacyclopentene, Si-GS1, and vinylsilirane, Si-GS2, at 298 K were 41.4 (41.6 at the B3LYP level) and 73.7 (72.8 at the B3LYP level) kcal/mol, starting from Si-GS2 and Si-GS1, respectively. The free energy barrier for the concerted asynchronous addition of dimethylsilylene to butadiene was predicted to be 1.4 kcal/mol (5.6 kcal/mol at the B3LYP level) at the same temperature, which is much lower than the predicted free energy barrier for the stepwise mechanism (Figure 1). Our calculations suggest the 1,2-addition to be kinetically favored over the 1,4-addition reaction. Experimentally, however, it is the 1,4-addition product that has been isolated in most cases. To explain this apparent paradox, one should consider the conditions under which these reactions were executed. Most reactions were carried out at temperatures higher than 400 °C and at pressures much lower than one atmosphere, and under those conditions the Si-GS2 intermediate could easily rearrange to Si-GS1. There are at least two possible ways by which this transformation can take place: via direct rearrangement and via retro-1,2-addition to the free silylene and butadiene followed by the 1,4-addition. While the rate of direct rearrangement depends only on the free energy barrier for that reaction (and the temperature), the second pathway also depends on the concentration of butadiene in the reaction mixture. In order to determine whether our predictions are in accord with the experimental results and to gauge the contributions of vinylsilirane rearrangement, vinylsilirane dissociation, and direct 1,4-addition to the formation of the silacyclopent-3-ene product, kinetic modeling of the reaction system has been carried out for realistic reaction conditions. The results are presented in a separate section. Addition of Dimethylgermylene to 1,3-Butadiene, Forming 1,1-Dimethylgermacyclopent-3-ene, and Its Reverse Retroaddition Reaction. The reaction between dimethylgermylene and 1,3-butadiene to form the 1,4-addition product 1,1dimethylgermacyclopent-3-ene and the corresponding retro-addition reaction were investigated computationally (Scheme 3, M=Ge). The structures and geometries of the stationary points located on the potential energy surface of the above reactions (Figure 2) are shown in Figure 5. The

Figure 5. Geometries (A˚, deg) of stationary points in Figure 2 optimized at B3LYP using a 6-31G(d,p) basis set for C and H and 6-311G(d,p) for Ge.

MeGeMe bond angle in free germylene is predicted to be 95.8°, which changes to 110.4° and 118.2° in the germacyclopentene, Ge-GS1, and vinylgermirane, Ge-GS2, respectively. The C-Ge bond length in the free germylene is predicted to be 2.01 A˚. A previous HF calculation on dimethylgermylene using a double-ζ plus polarization basis set predicts the MeGeMe bond angle to be 98° and the C-Ge bond length to be 2.02 A˚,51 and a previous DFT calculation predicted the CGeC bond angle to be 95.5° and the C-Ge bond length to be 2.02 A˚.50 MeGeMe bond angles of 114.9° and 99.9° are predicted in the transition structures for 1,2-addition, GeTS2, and 1,4-addition, Ge-TS3, respectively, which suggest partial germylene character. The changes in bond lengths observed in the optimized structures of both transition structures Ge-TS2 and Ge-TS3 are also in accord with that interpretation. Ge-TS3 is a transition structure for a concerted asynchronous addition, and partial CdC double-bond character in the butadiene moiety is clearly indicated. The transition structures for the 1,2-addition (GeTS2) and the direct 1,4-addition (Ge-TS3) reaction of dimethylgermylene to 1,3-butadiene as well as the transition structure (GeTS1) for the rearrangement of vinylgermirane (Ge-GS2) to germacyclopent-3-ene (Ge-GS1) were found. The 1,2-addition of germylene to 1,3-butadiene is predicted to take place via a stabilized precursor complex (Ge-Comp1) followed by a barrier of 2.4 kcal/mol at the B3LYP level, which is consistent with the germylene addition to ethylene observed by Sakai and Su.28,29 However, this barrier disappears at the CCSD(T) level. The 1,4-addition is also predicted to occur via a precursor complex (Ge-Comp2) followed by a concerted asynchronous cyclic transition structure Ge-TS3. The calculated energies of the stationary points shown in (51) Barthelat, J.-C.; Roch, B. S.; Trinquier, G.; Satge, J. J. Am. Chem. Soc. 1980, 102, 4080.

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Table 2. Relative Energies, Zero-Point-Corrected Energies, Enthalpies, and Free Energies of Stationary Points for the Addition of Me2Ge: to 1,3-Butadiene and the Retro-addition (Figure 5) Calculated at CCSD(T)/cc-pVTZ//B3LYP/6-31G(d,p) for C, H and 6-311G(d,p) for Ge and at B3LYP/6-31G(d,p) for C, H and 6-311G(d,p) for Ge (within parentheses)

Figure 5 are given in Table 2. The transition structure for the 1,2-addition to s-cis-1,3-butadiene could not be located despite several attempts. However, we cannot rule out the existence of such a species. The s-cis,s-trans rotational free energy barrier for the butadiene is predicted to be about 5.7 kcal/mol starting from the s-trans conformer (experimental value 5.0 kcal/mol),52 whereas the rotational free energy barrier (Ge-Rot) for Ge-GS3 was calculated to be 4.6 kcal/mol higher than for the more stable Ge-GS2. Photochemically generated dimethylgermylene has been shown to react with 2,3-dimethylbutadiene both in the gas phase and in solution.2c,h,3 In none of those cases were vinylgermirane intermediates (Ge-GS2 or Ge-GS3) detected, but a vinylgermirane was proposed to be an intermediate along the reaction path for the formation of germacyclopent3-ene, Ge-GS1. However, similar to our previous prediction for dimethylsilylene addition to butadiene, we also predict a direct 1,4-addition to be the preferred mechanism for the formation of Ge-GS1. While a negative free energy barrier is predicted for the 1,2-addition of dimethylgermylene to butadiene at 298 K at the CCSD(T) level, making it a very fast reaction, the subsequent rearrangement barrier is predicted to be 38.3 kcal/mol, making it a much slower reaction. On the contrary the free energy barrier for the reverse extrusion of dimethylgermylene from the vinylgermirane is predicted to be only 8.4 kcal/mol, and the free energy barrier for the direct 1,4-addition is predicted to be only 5 kcal/mol both at the CCSD(T) level. These results indicate a concerted mechanism for the formation of germacyclopent-3-ene, Ge-GS1. Addition of Dimethylstannylene to 1,3-Butadiene, Forming 1,1-Dimethylstannacyclopent-3-ene, and Its Reverse Retroaddition Reaction. The reaction between dimethylstannylene and 1,3-butadiene to form the 1,4-addition product 1,1-dimethylstannacyclopent-3-ene and the corresponding retro-addition reaction were investigated computationally (Scheme 3, M=Sn). The structures and geometries of the stationary points located on the potential energy surface of (52) Aston, J. G.; Szasz, H. W.; W, W. H.; Brickwedde, F. G. J. Chem. Phys. 1946, 14, 67.

Figure 6. Geometries (A˚, deg) of stationary points in Figure 3 optimized at the B3LYP level using a 6-31G(d,p) basis set for C and H and LANL2DZ for Sn.

Figure 7. Electronic energy profile for the addition of dimethylsilylene to butadiene and the retro-addition. The zero-pointcorrected energies are calculated at CCSD(T)/MG3//MPW1K/ 6-31þG(d,p) and DFT(MPW1K/6-31þG(d,p) in parentheses).

the above reactions (Figure 3) are shown in Figure 7. The MeSnMe bond angle is predicted to be 93.0°, and the Sn-C bond length is predicted to be 2.20 A˚ for dimethylstannylene. Our calculated geometries agree well with previous DFT studies in which Su reported the MeSnMe bond angle to be 93.6° and the C-Sn bond length to be 2.20 A˚.50 MeSnMe bond angles of 116.3° and 97.8° are predicted in the transition structures for 1,2-addition, Sn-TS2, and 1,4-addition, Sn-TS3, respectively, whereas the corresponding bond angles are predicted to be 109.9° and 119.5° for stannacyclopentene, Sn-GS1, and vinylstannirane, Sn-GS2, respectively. The similarities in MeSnMe bond angle in Sn-TS2 and Sn-GS2 indicate an early transition state for the stannylene extrusion from Sn-GS2 and thus a late transition state for 1,2-addition, which is also evident from the free energy profile (Figure 3). On the other hand the similarities in MeSnMe bond angles in free stannylene and Sn-TS3 indicate an early transition state for the direct 1,4-addition. The changes in bond lengths observed in the optimized

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Table 3. Relative Energies, Zero-Point-Corrected Energies, Enthalpies, and Free Energies of Stationary Points for Addition of Me2Sn: to 1,3-Butadiene and the Retro-addition (Figure 6) Calculated at CCSD(T)/cc-pVTZ (cc-pVTZ-PP for Sn)//B3LYP/ 6-31G(d,p) (LanL2DZ for Sn) and at B3LYP/6-31G(d,p) (LanL2DZ for Sn) (within parentheses)

structures of both transition structures Sn-TS2 and Sn-TS3 are also in accord with those interpretations. Sn-TS3 is a transition structure for a concerted asynchronous 1,4-addition, and partial CdC double-bond character in the butadiene moiety is clearly indicated. Transition structures for 1,2-addition, Sn-TS2, and direct 1,4-addition, Sn-TS3, were found. Similar to the germanium case, the energies of these transition structures were lower than the starting butadiene and free stannylene (at 0 K). However, stabilized precursor complexes Sn-Comp1 and SnComp2 were also located. The energies of these complexes are lower than the starting butadiene-stannylene by 10.1 and 9.4 kcal/mol (4.7 kcal/mol for both at the B3LYP level). However, unlike the germanium case at 298 K the free energies of these species are slightly higher that the starting butadiene and free stannylene. Similar phenomena were also observed by Sakai, who suggested that these precursor complexes might not exist at higher temperature.28 In the case of dimethylstannylene the barrier for the 1,4addition (Sn-TS3) is slightly higher (by 1.2 kcal/mol at the CCSD(T) level) than that for the 1,2-addition (Sn-TS2) at 298 K (Table 3). Although vinylstannirane, Sn-GS2, can be formed by a 1,2-addition reaction, its kinetic instability is evident from the negligible energy barrier of 0.9 kcal/mol (2.6 kcal/mol at the B3LYP level) for the reverse extrusion reaction. If one compares the computational results obtained for the silicon and germanium reactions with those for the tin reactions, a marked difference can be found. In all three cases vinylmetallirane formation is predicted to be kinetically favored over the 1,4-addition reaction. However, in the case of silicon and germanium, vinylmetallirane formation is exothermic by about 42 and 22 kcal/mol, respectively, compared with the starting matallylenes and butadiene, while in the case of tin the reaction is exothermic by only 6.4 kcal/mol at CCSD(T) and actually endothermic by 3.1 kcal/mol at the B3LYP level (Table 3, see EþZPE). These observations make vinylstannirane an unlikely candidate for detection by kinetic spectroscopy and thus make the 1,4-addition reaction path the sole choice for the formation of stannacyclopent-3-ene, Sn-GS1. Recently we have reported the results of thermal decomposition of several stannacyclopent-3-enes and their kinetic behavior in solution.22 The experimentally obtained enthalpy and entropy of activation for the unimolecular decomposition of Sn-GS1 were reported to be 29.4 ( 0.3 kcal/mol and -1.6 ( 0.8 eu, respectively, in a temperature range of 87.4-126.0 °C in cyclohexane-d12. Our calculations predict

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the enthalpy and entropy of activation for the same reaction in the gas phase at 106 °C to be 31.8 kcal/mol and -1.1 eu, respectively, at the B3LYP level and an activation enthalpy of 35.8 kcal/mol at the CCSD(T) level. Thus our computational results are in decent agreement with the experimental results. Kinetic Simulation of Dimethylsilylene Addition to 1,3Butadiene. There have been several studies reported for reactions involving dimethylsilylene and a variety of 1,3dienes, with the corresponding silacyclopent-3-enes as the major products.53-55 The product yields varied from 10 to 80%, and in many cases the results were complicated due to the presence of several minor products. In order to model our computational predictions for comparison with the experimental results, we have chosen the gas-phase experimental conditions of Lei and Gaspar53 (see Scheme 7), under which the total product yield was reasonably high (>85%) and the major products were only two: silacyclopent-3-ene (Si-GS1-d2) and silacyclopent-2-ene (Si-GS3-d2), when 1,4-dideutero-1,3-butadiene was reacted with thermally generated dimethylsilylene. The intermediacy of the vinylsilirane (Si-GS2-d2) in the Lei, Gaspar experiments was established by use of deuterium labeling. At 2 Torr pressure, 0.01 s residence time, and at temperatures of 500, 610, and 650 °C, the ratio of silacyclopent-3-ene SiGS1-d2, to silacyclopent-2-ene Si-GS3-d2 varied from 4.7:1 to 4.4:1 to 3.9:1. It was reasoned that the silacyclopent-2-ene Si-GS3-d2 can be formed only via the vinylsilirane intermediate (Si-GS2-d2), since no product was observed from a 1,3-H-shift of the 1,4-adduct Si-GS1-d2. To check whether our computational results are consistent with such a trend, we calculated free energies of activation for each of the elementary steps at three temperatures and used them as inputs in kinetic simulations. We have employed two different computational methods for obtaining the free energy values for kinetic simulation. The first uses B3LYP structures and CCSD(T) single-point energies, and the second uses MPW1K structures and CCSD(T) singlepoint energies (vide supra). Truhlar and co-workers have shown that MPW1K, a hybrid-GGA DFT functional, predicts better geometries and barrier heights than B3LYP for several reactions,45,46 and single-point energy calculations using CCSD(T)/MG3 at those MPW1K-optimized geometries provide an excellent performance to cost ratio.46 The CCSD(T)/MPW1K values provided a closer match to the experimentally measured product ratios, and those results are shown in Figure 7. The CCSD(T)/B3LYP results can be found in the Supporting Information. Relative zero-point-corrected energies and free energies at three temperatures are shown in Table 4. Similarly to the CCSD(T)/B3LYP calculations, CCSD(T)/MPW1K calculations also predict the 1,4-addition process to be the lowest energy pathway for the formation of silacyclopent-3-ene, Si-GS1. We found that the zero-point-corrected electronic energy for the transition state Si-TS2 is lower than the free silylene and butadiene from our calculations (Table 1). However, at various experimental temperatures the free energy barrier for (53) Lei, D.; Gaspar, P. P. Res. Chem. Intermed. 1989, 12, 103. (54) Lei, D.; Gaspar, P. P. Organometallics 1985, 4, 1471. (55) Lei, D.; Hwang, R. J.; Gaspar, P. P. J. Organomet. Chem. 1984, 271, 1.

Article Table 4. Relative Zero-Point-Corrected Energies (0 K) and Free Energies (at 2 Torr pressure) of Stationary Points for Addition of Me2Si: to 1,3-Butadiene-1,4-d2 (Figure 7) Calculated at CCSD(T)/MG3//MPW1K/6-31þG(d,p) and at MPW1K/6-31þG(d,p) (within parentheses)

the 1,4-addition becomes positive due to the entropy factor56 (as seen from the values in Table 4). From Table 4 it is clear that variations of the temperature have a subtle effect on the relative free energies of the several Si-GS and Si-TS species. As the temperature changes, the free energies of free Me2Si: and butadiene change drastically compared with other stationary points due to the -TΔS‡ term. At lower temperature (298 K) the free energy of activation for the 1,4-concerted addition is very low (1.4 kcal/mol at 298 K, see Table 1). This value jumps to 31.9 kcal/mol at 773 K and further to 38.2 and 40.5 kcal/mol at 883 and 923 K, respectively. However, the free energy barrier for the reverse reaction involving 1,4-retroaddition remains almost the same over this broad range of temperatures (67.7-68.4 kcal/mol). For the kinetic simulation we decided to employ a hypothetical transition state for the 1,2-addition and retroaddition reaction, having been unable to locate a transition structure or a precursor complex for 1,2-addition. Since we found that the reverse free energy barrier for the 1,4-addition does not change dramatically with respect to temperature, we decided to assign a constant free energy barrier for the transformation of vinylsilacyclopropane to free silylene and butadiene (ΔG‡ chosen to be 31.5 kcal/mol). This barrier was calculated from the Walsh et al.’s experimental rate constant for the 1,2-addition of dimethylsilylene to 1,3-butadiene.57 The authors reported a rate constant of 7.45  10-11 cm3 molecule-1 s-1, which corresponds to a 2.9 kcal/mol free energy barrier for the addition reaction at 298 K. The predicted difference in free energies between s-trans-butadiene-dimethylsilylene and trans-Si-GS2 is about 28.6 kcal/ mol at 298 K (at CCSD(T)/MPW1K). By combining these numbers we obtained the assigned value of 31.5 kcal/mol for the free energy barrier of the reverse reaction. As the temperature increases from 773 to 923 K, the sum of the free energies of the Me2Si: and butadiene decreases due to the entropy factor. Both 1,2- and 1,4-addition processes are slowed relative to the unimolecular processes in the reaction scheme. However, the 1,2-addition process remains the faster reaction among the two. From Table 4 we can see that the barrier for the rearrangement of Si-GS2 to Si-GS3 is about 1.7 (CCSD(T)/MPW1K) kcal lower than for the rearrangement to Si-GS1. At a higher (56) Houk, K. N.; Rondan, N. G.; Mareda, J. Tetrahedron 1985, 41, 1555. (57) Baggott, J. E.; Blitz, M. A.; Frey, H. M.; Lightfoot, P. D.; Walsh, R. J. Chem. Soc., Faraday Trans. 2 1988, 84, 515.

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temperature, while the rate of the fastest transformation of Si-GS2, that to free silylene and butadiene, remains moderate, the two rates of rearrangement of Si-GS2 increase significantly (more than a 10-fold increase). The free energy barrier for the forward 1,2-reaction was, however, variable and was predicted by adding 31.5 kcal/mol to the free energy difference between Si-GS2 and free silylene plus butadiene at various temperatures. For the kinetic simulation we have also taken the presence of s-trans-butadiene and trans-vinylsilirane and their rearrangements into account (see Supporting Information). The ratio of s-trans to s-cis butadiene varies at different temperatures, with s-trans being the major component. We have included the energy data for s-cis/ s-trans interconversions of butadienes and vinylsiliranes, and the values of rate constants employed are included in the kinetic simulations in the Supporting Information. A representative kinetic simulation plot is shown in Figure 8. The trend of forming Si-GS3 in higher relative yield at higher temperature is evident from both the experimental and the theoretical data. When the CCSD(T)/ MPW1K method was used, the kinetic simulation shows that the product ratio of Si-GS1 to Si-GS3 changes from 55 to 15 to 12 at 773, 883, and 923 K, respectively. These are about an order of magnitude greater than the experimental ratios of 4.7, 4.4, and 3.9, respectively. When the CCSD(T)/ B3LYP method was used, the kinetic simulation predicted that the product ratio of Si-GS1 to Si-GS3 changes from 90 to 66 to 51 at 773, 883, and 923 K, respectively. However, considering the approximations we have made by not including a possible intermediate complex for the 1,2-addition, possible experimental error, and computational limitations, these results are encouraging. The jump in the computationally predicted product ratio at 773 to 883 K and its absence in the experimental ratio could be due to the decomposition of the compounds at higher temperature under the experimental conditions. In fact, when the overall conversion of the silylene source increased from 65% at 773 K to 87% at 883 K to 100% at 923 K, the overall combined product yield (of SiGS1 and Si-GS3) did not increase significantly when temperature increased from 773 to 883 K and actually decreased at 923 K (see Scheme 7).53 The contribution of the vinylsilirane, Si-GS2, to the formation of Si-GS1 by rearrangement increases from 0.18% at 773 K to 0.37% at 883 K to 0.48% at 923 K for the CCSD(T)/ B3LYP calculations, which changes to 0.29% at 773 K, 1.13% at 883 K, and 1.34% at 923 K for CCSD(T)/MPW1K calculations (see the Supporting Information Pc/Pt value). While the contribution of the rearrangement increases with the rising temperature, it is still very low compared with the contribution from the direct 1,4-addition. Hence, one may conclude that while Si-GS3 is formed solely from the rearrangement of Si-GS2, the major product Si-GS1 is mainly formed by the concerted addition of butadiene and silylene. As a result, the contribution of the intermediate vinylsilirane, Si-GS2, should be reflected in the yield of Si-GS3 rather than Si-GS1. The experimental results also support this conclusion. The overall yield of Si-GS1 actually decreased slightly as the temperature rose from 773 to 923 K (Scheme 7), while the yield of Si-GS3 remained essentially constant. This can be attributed to the increased free energy barrier for 1,4-addition due to the entropy factor (vide infra) and is also revealed by the predicted decrease in the absolute rate for the 1,4-addition process in

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Figure 8. Kinetic simulation plot for Me2Si: addition to 1,3-butadiene-1,4-d2 at 773 K, 2 Torr, using free energy data calculated at CCSD(T)/MG3//MPW1K/6-31þG(d,p). In this plot A represents s-cis-1,3-butadiene-1,4-d2, T represents its s-trans conformer (not shown), B represents Me2Si:, C represents Si-GS2-d2, P represents Si-GS1-d2, and Q represents Si-GS3-d2 (Inset: simulation plot after a millisecond). Scheme 8

the kinetic simulations (Supporting Information rate k7 and absolute value of Pab). Addition of Diphenylsilylene to 2,3-Dimethylbutadiene. Recently Moiseev and Leigh reported condensed-phase addition of photochemically generated dimethylsilylene and diphenylsilylene to 2,3-dimethylbutadiene.17,58 In the latter system the authors detected a vinylsilirane intermediate, Si-DPGS2, as the major product along with the corresponding silacyclopent-3-ene, Si-DPGS1 (Scheme 8). Si-DPGS2 was reported to rearrange to Si-DPGS1 in the dark over two days. Previous studies by Zhang and Conlin showed that dimesitylsilylene reacted with several 1,3-dienes to form corresponding vinylsiliranes that were stable for days.16 Moiseev and Leigh suggested that the Si-DPGS1 is mainly formed by the rearrangement of Si-DPGS2 rather than the corresponding direct 1,4-addition reaction, and this was consistent with earlier conclusions.1,59 We chose to test this suggestion by computationally investigating the reaction of diphenylsilylene and 2,3-dimethylbutadiene (Scheme 8). The computational resources available prevented us from examining this reaction beyond the B3LYP/6-31G(d) level. No transition structure could be located for the 1,2-addition reaction of diphenylsilylene to 2,3-dimethylbutadiene, (58) Moiseev, A. G.; Leigh, W. J. Organometallics 2007, 26, 6268. (59) Bobbitt, K. L.; Gaspar, P. P. J. Organomet. Chem. 1995, 499, 17.

Figure 9. Free energy profile for the addition of diphenylsilylene to 2,3-dimethylbutadiene and the retroaddition at 298 K. The free energies are calculated at B3LYP/6-31G(d,p).

but transition structure Si-DPTS1, for the rearrangement of Si-DPGS2 to Si-DPGS1, and transition structure Si-DPTS2, for the direct 1,4-addition, were located. The gas-phase free energies of the stationary points calculated at 298 K using B3LYP/6-31G(d,p) are shown in Figure 9. The free energy barrier for the rearrangement of SiDPGS2 to Si-DPGS1 is predicted to be about 35 kcal/mol, which is rather high for a room-temperature reaction. However, the free energy barrier for the direct 1,4-addition is only 10 kcal/mol, making it a preferred choice for the Si-DPGS1 formation. Given our experience with Me2Si: þ butadiene (see Figure 1 and Table 1), higher level calculations are expected to lower the free energy barrier for 1,4-addition of Ph2Si: to dimethylbutadiene but leave the rearrangement barrier essentially unchanged. Moiseev and Leigh also observed that the formation of Si-DPGS1 showed good

Article

linearity over the 0-30% conversion range of the diphenylsilylene source, and that led them to question the conventional wisdom of it being formed solely via the rearrangement of Si-DPGS2. Our results predict that the alternate mechanism, the direct 1,4-addition, is the preferred pathway for the observed reaction. However, our predictions are based on gas-phase reactions, and the experiments were done in solution. Involvement of a secondary photoreaction cannot be ruled out for the rearrangement of Si-DPGS2 to Si-DPGS1. Compound Si-DPGS2 when kept under dark for 48 h decomposed to form Si-DPGS1. We decided to probe this result to test our suggested mechanism by employing our calculated barrier heights in a kinetic simulation. Since we could not locate a transition structure for the 1,2-addition reaction, we assigned a free energy barrier of 3.6 kcal/mol for the addition of diphenylsilylene to 2,3-dimethylbutadiene to form Si-DPGS2 (from the experimental absolute rate constant value of 14.5  109 M-1 s-1 obtained for diphenyl silylene and 2,3-dimethylbutadiene).17 We have also considered the presence of s-cis and s-trans conformers of 2,3-dimethylbutadiene and their 1,2-addition products with the silylene, cis and trans conformers of vinylsiliranes. The initial concentrations of the conformers were calculated from their free energy differences at 298 K. A detailed reaction scheme with the rate processes included in the kinetic simulation can be found in the Supporting Information. Our kinetic simulation predicts that within 4 h the SiDPGS2 decomposes by >80% to form Si-DPGS1, and within a day there is >99% conversion, which is in good agreement with the experimental results.17 The simulation also predicts that there is virtually no product formed by the direct rearrangement of Si-DPGS2. Si-DPGS2 decomposes more rapidly to form the free silylene and diene, which irreversibly add to form the Si-DPGS1. The kinetic simulation plot and the rate constants employed in this simulation are given in the Supporting Information. Addition of Diphenylgermylene to Isoprene. In 2005 Leigh and Harrington reported time-resolved laser-spectroscopic studies of diphenylgermylene Ph2Ge: in the presence of isoprene.60 Reversible germylene addition to isoprene forming a vinylgermirane, irreversible dimerization to tetraphenyldigermene, and the disappearance of the vinylgermirane leading to the formation of 3-methyl-1,1-diphenyl-1-germacyclopent-3-ene were observed, as shown in the mechanism below.

Leigh and Harrington reported a rate constant of (5.5 ( 1.2)  109 M-1 s-1 for k1 at 23 °C in hexane solution, which corresponds to a free energy barrier of 3.8 kcal/mol. A value for the equilibrium constant k1/k-1 of 6000 ( 2500 M-1 was estimated from the initial and residual transient absorption values for the germylene as a function of the isoprene concentration, and this corresponds to a free energy difference (60) Leigh, W. J.; Harrington, C. R. J. Am. Chem. Soc. 2005, 127, 5084.

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of -5.1 kcal/mol. These data can be combined to predict a free energy barrier for extrusion of Ph2Ge: from the vinylgermirane of 8.9 kcal/mol. At a 50 mM concentration of isoprene, the transient absorption with λmax = 285 nm attributed to the vinylgermirane underwent clean first-order decay with a half-life of 500 μs, corresponding to a rate constant of (2.0 ( 0.1)  103 s-1, which implies a free energy barrier of 13 kcal/mol. The question remains whether the disappearance of the vinylgermirane can be attributed to the rearrangement of the vinylgermirane formed by 1,2-addition of Ph2Ge: to the less substituted π-bond of isoprene to the observed final product, the 3-methyl-1,1-diphenylgermacyclopent-3-ene. We believe that the answer is no, because we estimate the rearrangement free energy barrier to be greater than 30 kcal/mol (see Supporting Information). As shown in Figure 2, the free energy barrier for 1,4addition of dimethylgermylene Me2Ge: to butadiene is low (8.1 kcal/mol predicted at CCSD(T) for 298 K). Since the free energy barrier for extrusion of diphenylgermylene from the vinylgermirane formed from addition of Ph2Ge: to isoprene is estimated above to be 8.9 kcal/mol from the experiments of Leigh and Harrington,60 a free energy barrier for 1,4-addition of Ph2Ge: to isoprene of 4 kcal/mol would give an overall free energy barrier for formation of germacyclopent-3-ene in good agreement with the free energy barrier for loss of that vinylgermirane, if the mechanism for germacyclopent-3-ene formation is germylene extrusion from the vinylgermirane followed by 1,4-addition to isoprene. This 1,4-addition serves to siphon off the equilibrating mixture of germylene, isoprene, and vinylgermirane formed by 1,2addition. One last question is whether there is any other reaction that can account for the irreversible loss of Ph2Ge: in addition to 1,4-addition to isoprene. The only other process that could in principle lead to irreversible loss of Ph2Ge: is dimerization to tetraphenyldigermene. Dimerization is very rapid, occurring at nearly a diffusion-controlled rate (k3 = 1.1  1010 M-1 s-1 given by Leigh and Harrington),60 but the equilibrium concentration of Ph2Ge: in the presence of 50 mM isoprene can be estimated as being ca. 1.7  10-9 M, so the rate of dimerization can be estimated as 3.1  10-8 M s-1, which is very slow compared to the estimated rate of 1,4-addition by germylene to isoprene, 4.6  10-1 M s-1. It thus appears that loss of rapidly formed vinylgermirane can lead to the formation of the germacyclopentene product by 1,4-addition to isoprene of diphenylgermylene, whose immediate source is largely re-extrusion from the vinylgermirane rather than by unimolecular rearrangement of the vinylgermirane directly to the germacyclopentene product. We lack the computational resources at this time to model the addition of Ph2Ge: to isoprene at the CCSD(T) level of theory expected to provide reliable results. Our modeling of this reaction at the DFT B3LYP level predicts high free energy barriers for both 1,2- (15.4 kcal/mol) and 1,4-addition (19.0 kcal/mol, see Supporting Information). These high barriers are due to an underestimate of the free energy of Ph2Ge: þ isoprene relative to other stationary points on the free energy profile. But it should be remembered that a similar situation was encountered in our modeling of the addition of Me2Ge: to butadiene (see Figure 2). At the B3LYP level the free energy barriers for 1,2- (8.7 kcal/mol) and 1,4-addition (16.3 kcal/ mol) decreased to -2.7 and 8.1 kcal/mol, respectively, at the

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CCSD(T) level. This difference is due largely to the increase in the estimated free energy of Me2Ge: þ butadiene at CCSD(T) compared with B3LYP. The predicted free energy barrier for concerted rearrangement of 1,1-dimethyl-2-vinylgermirane to 1,1-dimethylgermacyclopent-3-ene underwent only a small change, from 36.9 to 38.3 kcal/mol from B3LYP to CCSD(T) (see Figure 2). Our B3LYP calculations on the addition of Ph2Ge: to isoprene predict free energy barriers of 15.4 and 19.0 kcal/ mol, respectively, for the free energy barriers for 1,2- and 1,4addition. These free energy barriers are higher than those predicted for the analogous additions of Me2Ge: to butadiene (see Figure 2), but the difference between them is smaller. The predicted free energy barrier at B3LYP for direct rearrangement of the vinylgermirane from addition of Ph2Ge: to isoprene to the corresponding germacyclopent3-ene, 34.5 kcal/mol, is quite similar to that for the corresponding rearrangement to a germacyclopent-3-ene of the vinylgermirane formed from addition of Me2Ge: to butadiene, 36.9 kcal/mol. Thus we anticipate that modeling of the Ph2Ge: þ isoprene addition at a level higher than DFT B3LYP will lead to predicted free energy barriers for 1,2and 1,4-addition in accord with the experimental rate constants of Leigh and Harrington.

Conclusions The calculations described here predict that dimethylmetallylene addition to butadiene can be a stepwise or a concerted process. It was found that in general 1,4-retroaddition of 1-metallacyclopent-3-enes is much more rapid than their rearrangement to the vinylmetalliranes. The principle of detailed balance thus ensures that formation of the 1-metallacyclopent-3-ene from addition of metallylene Me2M: (M = Si, Ge, Sn) takes place almost entirely by direct 1,4-addition. There is a significant difference between the Si and Ge cases on one hand and the Sn case on the other. For Si and Ge, formation of a vinylmetallirane is exothermic, and there is a barrier for extrusion of the metallylene from the vinylmetallirane. The barrier for rearrangement of the vinylmetallirane to the metallacyclopent-3-ene is much higher than that for the retro-addition that regenerates the metallylene and butadiene. In the tin case formation of the vinylstannirane is endothermic from Me2Sn: and butadiene, and there is

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a negligible enthalpy barrier for extrusion of Me2Sn: from vinylstannirane. Thus for Me2Si: and Me2Ge:, the 1,2-adduct to butadiene is the kinetic product, siphoned off by the retro-adddition, leading to the formation of the thermodynamic product, the 1,4-adduct, by the kinetically slower 1,4-addition process. Upon generation of Me2Si: and Me2Ge: at room temperature, i.e., photochemically, one can expect significant formation of vinylmetalliranes, but their disappearance is predicted to occur by retro-addition, rather than the previously suggested rearrangement. For Me2Sn: the predicted rates of 1,2- and 1,4-addition are within an order of magnitude of each other, but the lifetime of the vinylstannirane is vanishingly short even at room temperature. So while vinylstannirane may be formed, it is bound to return immediately to Me2Sn: and butadiene and thus plays a negligible role and is not expected to be detectable even by nanosecond kinetic spectroscopy. Kinetic simulations performed with the free energy data obtained from our calculations for some selected silylene-butadiene reactions suggest that our mechanistic model is in accord with experimental results. This is the first computational study, to the best of our knowledge, that unequivocally predicts that metallacyclopent3-enes of heavier carbon analogues (except Pb, yet unexamined) are preferentially formed or decomposed via a concerted 1,4-addition or retro-addition of metallylenes and diene.

Acknowledgment. We are grateful for financial support from the National Science Foundation under grant CHE-0316124. This research was supported in part by the NSF through TeraGrid resources provided by NCSA under grant TG-CHE070050N. This work made use of the Washington University Computational Chemistry Facility, supported by NSF grant CHE-0443501. We also thank Dr. Lee Sobotka for helping us understand the kinetic simulation technique as implemented with the Mathcad software program and Dr. William J. Leigh for helpful discussion. Supporting Information Available: Cartesian coordinates and absolute energies for all stationary points predicted by electronic structure calculations, kinetic simulation plots, and predicted rate constants employed in the kinetic simulation are available free of charge via the Internet at http://pubs.acs.org.