Interactions of Tetrahedrane and Tetrasilatetrahedrane with CH2

Part of the Dietmar Seyferth Festschrift. This paper acknowledges the long and pleasant relationship between the author and Professor Dietmar Seyferth...
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Organometallics 2010, 29, 4975–4982 DOI: 10.1021/om100193f

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Interactions of Tetrahedrane and Tetrasilatetrahedrane with CH2 and SiH2: A Computational Study† Robert Damrauer*,‡ Chemistry Department, Denver Campus, University of Colorado Denver, Box 194, P.O. Box 173364, Denver, Colorado 80217-3364. ‡ E-mail: [email protected] Received March 11, 2010

Ab initio exploration of the interactions of triplet and singlet methylene (CH2) and singlet silylene (SiH2) with both tetrahedrane and tetrasilatetrahedrane has yielded a number of stable optimized species. Structures 5-7 have been found on the triplet C4H4 plus CH2 potential energy surface (PES), structures 8-13 on the singlet C4H4 plus CH2 PES, structures 14-20 on the triplet Si4H4 plus CH2 PES, structures 21-30 on the singlet Si4H4 plus CH2 PES, structures 31-35 on the singlet C4H4 plus SiH2 PES, and structures 36-44 on the singlet Si4H4 plus SiH2 PES. These structures display a wide variety of geometrical features that in some cases are unusual. Characterization of the transition states connecting several of these species leads to a partial understanding of the various potential energy surfaces. The computational results suggest that some aspects of this chemistry might be profitably explored experimentally, particularly for substituted derivatives.

Introduction Chemists always have been fascinated by molecules of high symmetry. Wide-ranging structural studies have uncovered symmetrical species ranging from ones where a central atom bonds symmetrically to various atoms/ligands (e.g., carbon in methane (Td), nickel in Ni(CO)4 (Td), mercury at the center of an I3 equilateral triangle in HgI3; (D3h), and sulfur and cobalt in octahedral arrays such as SF6 and Co(NH3)63þ (Oh)) to structures with no central atom but other highsymmetry elements (e.g., white phosphorus (P4; Td), cubane (C8H8; Oh), and dodecahedrane (C20H20; Ih)).1-7 Tetrahedrane (C4H4; Td) particularly has been sought after by organic chemists yet never prepared.7,8 Computational estimates of the strain energy of tetrahedrane have ranged widely but cluster around 140 kcal/mol.9,10 Substituted

tetrahedranes (R4C4), on the other hand, have been synthesized with considerable effort and determination. Maier and co-workers have spearheaded such work, which culminated in the synthesis of (t-Bu)4C4.7,8,11-13 Various other R4C4 derivatives have been prepared as well.14-18 Tetrasilatetrahedrane (Si4H4; Td) also has never been reported,19 although various computational studies of it and related polyhedral clusters have.10,20-25 Computational estimates of the strain energy of tetrasilatetrahedrane are not very different from that of tetrahedrane. Its strain energy is ∼140 kcal/mol, with substitution on the framework silicon lowering the strain energy, particularly when silicon-atom

† Part of the Dietmar Seyferth Festschrift. This paper acknowledges the long and pleasant relationship between the author and Professor Dietmar Seyferth, whose impact on the field of organometallic chemistry has been beyond measure, not only in his research contributions but also in his editorial ones. He has been a good and caring friend. (1) Cotton, F. A.; Wilkinson, G.; Murillo, C. A.; Bochmann, M. Advanced Inorganic Chemistry, 6th ed.; Wiley-Interscience: New York, 1999. (2) Greenwood, N. N.; Earnshaw, A. Chemistry of the Elements, 2nd ed.; Pergamon Press: Oxford, 1997. (3) Eaton, P. E.; Cole, T. W., Jr. J. Am. Chem. Soc. 1964, 86, 3157– 3158. (4) Eaton, P. E.; Cole, T. W., Jr. J. Am. Chem. Soc. 1964, 86, 962–964. (5) Ternansky, R. J.; Balough, D. W.; Paquette, L. A. J. Am. Chem. Soc. 1982, 104, 4503–4504. (6) Paquette, L. A.; Ternansky, R. J.; Balough, D. W.; Kentgen, G. J. Am. Chem. Soc. 1983, 105, 5446–5450. (7) Hopf, H. Classics in Hydrocarbon Chemistry; Wiley-VCH: Weinheim, New York, Chichester, Brisbane, Singapore, Toronto, 2000. (8) Maier, G.; Pfriem, S.; Sch€afer, U.; Matusch, R. Angew. Chem., Int. Ed. 1978, 17, 520–521. (9) Baric, D.; Maksic, Z. B. Theor. Chem. Acc. 2005, 114, 222–228. (10) Earley, C. W. J. Phys. Chem. A 2000, 104, 6622–6627.

(11) Maier, G.; Pfriem, S. Angew. Chem., Int. Ed. 1978, 17, 519–520. (12) Maier, G.; Pfriem, S.; Sch€afer, U.; Malsch, K.-D.; Matusch, R. Chem. Ber 1981, 114, 3965–3987. (13) Maier, G. Angew. Chem., Int. Ed. 1988, 27, 309–332. (14) Maier, G.; Neudert, J.; Wolf, O.; Pappusch, D.; Sekiguchi, A.; Tanaka, M.; Matsuo, T. J. Am. Chem. Soc. 2002, 124, 13819–13826. (15) Sekiguchi, A.; Tanaka, M. J. Am. Chem. Soc. 2003, 125, 12684– 12685. (16) Maier, G.; Born, D.; Bauer, I.; Wolf, R.; Boese, R.; Cremer, D. Chem. Ber. 1994, 127, 173–189. (17) Maier, G.; Wolf, R.; Kalinowski, H. O. Chem. Ber 1994, 127, 201–204. (18) Nakamoto, M.; Inagaki, Y.; Nishina, M.; Sekiguchi, A. J. Am. Chem. Soc. 2009, 131, 3172–3173. (19) Sekiguchi, A.; Nagase, S. In The Chemistry of Organic Silicon Compounds in The Chemistry of Functional Groups Series; Rappoport, Z., Apeloig, Y., Eds.; Wiley: New York, 1998; Vol. 2, pp 119-152. (20) Li, C.; Yang, J.; Bai, X. J. Mol. Struct. (THEOCHEM) 2005, 755, 65–74. (21) Srinivas, G. N.; Jemmis, E. D. J. Am. Chem. Soc. 1997, 119, 12968–12973. (22) Nagase, S.; Nakano, M. Angew. Chem., Int. Ed. 1988, 27, 1081– 1083. (23) Nagase, S.; Kobayashi, K.; Nagashima, M. Chem. Commun. 1992, 1992, 1302–1304. (24) Yates, B. F.; Schaefer, H. F. I. Chem. Phys. Lett. 1989, 155, 563–71. (25) Sax, A. F.; Kalcher, J. J. Comput. Chem. 1989, 10, 309–328.

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substitution occurs (e.g., (R3Si)4Si4).10,22,23,26 The first substituted derivatives (R4Si4) were prepared by Wiberg and coworkers ((tBu3Si)4Si4).27-30 Later Sekiguchi and co-workers reported other R4Si4 derivatives, where R= Si(CH3)(CH(SiMe3))2,31 (CH3)3Si (with Maier and co-workers),14 R3R0 Si4, where R = (CH3)3Si and R0 =Li,15 and R3R0 Si4, where R = Si(CH3)(CH(SiMe3))2 and R0 = K.31 The Wiberg compound ((tBu3Si)4Si4) has recently been prepared in a one-pot synthesis.32 Tetrahedranes and tetrasilatetrahedranes raise interesting questions. (1) Would the parent compounds be thermodynamically stable? (2) Are large substituent groups required for such stability? (3) Do substituents confer only kinetic stability or do other phenomena explain the isolation of stable R4C4 and R4Si4 species with large R groups? For tetrahedrane some of these questions have been addressed in a recent computational study by Schreiner and co-workers, where several C4H4 isomers, including tetrahedrane, are reported to be thermodynamically and kinetically stable.33 Of the eight stable C4H4 isomers studied, however, only 1 is of higher energy than tetrahedrane. On the other hand, unsubstituted tetrahedrane would have to surmount at least a 30 kcal/mol barrier to rearrange either to cyclobutadiene or vinylacetylene (the lowest energy isomers connected to tetrahedrane on this potential energy surface). Other computational studies have addressed related issues of thermodynamic and kinetic stability as well as strain energy.24,25,9 Studies of parent Si4H4 indicate that it is unlikely to be isolable, since low barrier isomerization is predicted.19,22,34

Despite the considerable experimental and computational attention to tetrahedranes,15 tetrasilatetrahedranes,35,36 and their derivatives over the years, relatively little is known about their intrinsic reactivity. Extensive studies of the chemistry of P4 (Td) are an exception to the paucity of reactivity information on the tetrahedral species of carbon and silicon. These P4 studies are driven by attempts to prepare new and interesting phosphorus species as well as the inherent reactivity (26) Sekiguchi, A.; Sakurai, H. Adv. Organomet. Chem. 1995, 37, 1– 38. (27) Wiberg, N.; Finger, C. M. M.; Polborn, K. Angew. Chem., Int. Ed. 1993, 32, 1054–1056. (28) Wiberg, N.; Finger, C. M. M.; Auer, H.; Polborn, K. J. Organomet. Chem. 1996, 521, 377–386. (29) Wiberg, N. In Organonsilicon Chemistry II: From Molecules to Materials; Auner, N., Weis, J., Eds.; VCH: Weinheim, New York, 1996; pp 367-387. (30) Wiberg, N. Coord. Chem. Rev. 1997, 163, 217–252. (31) Ichinohe, M.; Toyoshima, M.; Kinjo, R.; Sekiguchi, A. J. Am. Chem. Soc. 2003, 125, 13328–13329. (32) Meyer-Wegner, F.; Scholz, S.; S€anger, I.; Sch€ odel, F.; Bolte, M.; Wagner, M.; Lerner, H.-W. Organometallics 2009, 28, 6835–6837. (33) Nemirowski, A.; Reisenauer, H. P.; Schreiner, P. R. Chem. Eur. J. 2006, 12, 7411–7420. (34) Karni, M.; Kapp, J.; Schleyer, P. v. R.; Apeloig, Y. In The Chemistry of Organic Silicon Compounds in The Chemistry of Functional Groups; Rappoport, Z., Apeloig, Y., Eds.; Wiley: Chichester, U.K., 2001; Vol. 3, pp 1-163. (35) Ichinohe, M.; Takahashi, N.; Sekiguchi, A. Chem. Lett. 1999, 1999, 553–554. (36) Wiberg, N.; Auer, H.; N€ oth, H.; Knizek, J.; Polborn, K. Angew. Chem., Int. Ed. 1998, 37, 2869–2872. (37) Back, O.; Kuchenbeiser, G.; Donnadieu, B.; Bertrand, G. Angew. Chem., Int. Ed. 2009, 48, 5530–5533. (38) Cossairt, B. M.; Cummins, C. C. Angew. Chem., Int. Ed. 2008, 47, 8863–8866.

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of P4 under many conditions.37-45 Studies by Bertrand46,47 and Driess48 and their respective co-workers of reactions of P4 with nucleophilic, stabilized carbenes 2 and 3 and the stable silylene 4 (see the structures below) are of particular relevance to this report. These experimental studies combined with the inherent fascination that chemists have with high molecular symmetry suggested that computational investigations of (1) singlet and triplet CH2 with tetrahedrane (C4H4; Td) and tetrasilatetrahedrane (Si4H4; Td) and (2) singlet SiH2 with tetrahedrane (C4H4) and tetrasilatetrahedrane (Si4H4) would be fruitful in uncovering some fundamental interactions of such species. What follows are the results of such studies, where the major findings deal more with widely surveying the structural features of these interactions and less with locating transition states that interconvert various species.

Computational Methods Geometry optimizations based on previously described protocols49,50 were carried out without symmetry constraints (C1) using density functional theory (DFT) with the B3LYP exchange-correlation functional50-54 and the 6-311þþG(3df,3p)55-59 basis. These optimizations located several structures that were clearly of higher symmetry. Some of these were studied at high molecular symmetry, with the results indicated in the body of the paper. Two structures were shown to be singlet diradicals using two-configuration self-consistent field (TCSCF) methods (see Results and Discussion).60 Triplet species have been studied using restricted open-shell Hartree-Fock methods (ROHF).61 Zero-point energy corrections have been applied to all reported structures. Energies relative to the lowest energy (39) Scherer, O. J.; Swarowsky, M.; Wolmershaeuser, G. Organometallics 1989, 8, 841–842. (40) Uhl, W.; Benter, M. Chem. Commun. 1999, 1999, 771–772. (41) Power, M. B.; Barron, A. R. Angew. Chem., Int. Ed. 1991, 30, 1353–1354. (42) Scherer, O. J.; Swarowsky, M.; Swarowsky, H.; Wolmershaeuser, G. Angew. Chem., Int. Ed. 1988, 27, 694–695. (43) Lerner, H.-W.; Bolte, M.; Karaghiosoff, K.; Wagner, M. Organometallics 2004, 23, 6073–6076. (44) Fox, A. R.; Wright, R. J.; Rivard, E.; Power, P. P. Angew. Chem., Int. Ed. 2005, 44, 7729–7733. (45) Peng, Y.; Fan, H.; Zhu, H.; Roesky, H. W.; Magull, J.; Hughes, C. E. Angew. Chem., Int. Ed. 2004, 43, 3443–3445. (46) Masuda, J. D.; Schoeller, W. W.; Donnadieu, B.; Bertrand, G. Angew. Chem., Int. Ed. 2007, 46, 7052–7055. (47) Masuda, J. D.; Schoeller, W. W.; Donnadieu, B.; Bertrand, G. J. Am. Chem. Soc. 2007, 129, 14180–14181. (48) Xiong, Y.; Yao, S.; Brym, M.; Driess, M. Angew. Chem., Int. Ed. 2007, 46, 4511–4513. (49) Damrauer, R.; Pusede, S. E. Organometallics 2009, 28, 1289– 1294. (50) Damrauer, R.; Pusede, S. E.; Staton, G. M. Organometallics 2008, 27, 3399–3402. (51) Chan, W. T. K.; Garcia, F.; Hopkins, A. D.; Martin, L. C.; McPartlin, M.; Wright, D. S. Angew. Chem., Int. Ed. 2007, 46, 3084– 3086. (52) Becke, A. D. J. Chem. Phys. 1993, 98, 5648–52. (53) Hertwig, R. H.; Koch, W. Chem. Phys. Lett. 1997, 268, 345–351. (54) Stephens, P. J.; Devlin, F. J.; Chablowski, C. F.; Frisch, M. J. J. Phys. Chem. 1994, 98, 11623–11627. (55) Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. J. Chem. Phys. 1980, 72, 650–654. (56) Takahashi, M.; Kawazoe, Y. Organometallics 2005, 24, 2433– 2440. (57) Bauschlicher, C. W., Jr.; Partridge, H. Chem. Phys. Lett. 1995, 240, 533–540. (58) Martin, J. M. L. J. Chem. Phys. 1998, 108, 2791–2800. (59) Damrauer, R.; Noble, A. L. Organometallics 2008, 27, 1707– 1715. (60) Jensen, F. Introduction to Computational Chemistry, 2nd ed.; Wiley: Chichester, U.K., 2007. (61) Cramer, C. J. Essentials of Computational Chemistry: Theories and Models; Wiley: Chichester, U.K., 2002.

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species in each series of compounds studied are reported in the paper. Explicit energies, as well as structural representations and optimized Cartesian coordinates of all the reported structures, can be found in the Supporting Information. Frequency calculations were carried out using standard techniques on the optimized structures.61 All reported species are local minima (no “imaginary” frequency) or transition states as indicated. Various selected transition states were connected with their corresponding stable species using intrinsic reaction coordinate (IRC) methodology.60 Computations were carried out using the GAMESS (24 Mar 2007 version)62 suite of programs with MacMolPlot63 visualization of the molecular structures. Because of the bonding characteristics of some species, particularly those with bridging hydrogen atoms, the convergence tolerance in GAMESS was increased 10-fold beyond the default (to OPTTOL = 10-5) for all the reported species.

Results and Discussion Recent studies of the chemistry of carbenes 2 and 3 and silylene 4 with P4 demonstrate various reactivity patterns.46-48 Of particular concern to this report are studies by Bertrand46,47 and Driess and their respective co-workers48 of reactions of P4 with the nucleophilic, stabilized carbenes 2 and 3 and the stable silylene 4. For both the carbenes and silylene, interesting products result, depending on conditions. On the basis of their predominantly experimental studies, we reported related computational studies by considering whether the simple unsubstituted carbene and silylene, namely CH2 and SiH2, would “react” in ways similar to those of the aforementioned stabilized carbenes and silylene.49,50

Studies of such simple species require a clear accounting of their singlet-triplet splittings to realistically assess reactivity. Ground-state CH2 is the triplet species by ∼9 kcal/ mol,64 while singlet SiH2 is more stable by a greater margin, ∼21 kcal/mol.65 Thus, triplet SiH2 is inaccessible under ordinary conditions, but both triplet and singlet CH2 are accessible, although singlet CH2 clearly is minimally populated. Our recent computational studies49,50 of P4 take note of these practical concerns.46-48 The stabilized nucleophilic carbenes 2 and 3 react with P4 in complex ways.46,47 Mechanistic studies indicate that 1 equiv of 2 reacting with 1/2 equiv of P4 produces an intermediate species whose structure is 2dP-PdP-Pd2, this being along the way to an isolable P12 cluster.47 Trapping experiments with 2,3-dimethylbuta-1,3-diene validate this conclusion. The reaction of 3 with 1/2 equiv of P4 leads to (62) Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Elbert, S. T.; Gordon, M. S.; Jensen, J. H.; Koseki, S.; Matsunaga, N.; Nguyen, K. A.; et al. J. Comput. Chem. 1993, 14, 1347–63. (63) Bode, B. M.; Gordon, M. S. J. Mol. Graphics Mod. 1998, 16, 133– 138. (64) Leopold, D. G.; Murray, K. K.; Miller, A. E. S.; Lineberger, W. C. J. Chem. Phys. 1985, 83, 4849–4865. (65) Tokitoh, N.; Ando, W. In Reactive Intermediate Chemistry; Moss, R. A., Platz, M. S., Jones, M., Jr., Eds.; Wiley-Interscience: Hoboken, NJ, 2004; pp 651-715.

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the E and Z isomers of 3dP-PdP-Pd3.46 Both studies report reaction path computational studies on simplified versions of the stabilized nucleophilic carbenes 2 and 3 (with the large substituents replaced by hydrogen atoms) (carried out at the B3LYP/6-311G(d,p) level). Our computational studies of singlet and triplet CH2 gave quite different results, with a P-P insertion structure being the lowest energy species by ∼24 kcal/mol in the singlet manifold.50 Exploration of triplet CH2 interactions with P4 showed little in the way of bond formation, with one exception, where a structure was found having an energy some ∼19 kcal/mol higher than the insertion product. Driess and co-workers have shown that stable silylene 4 reacts with P4 to give a single and double insertion into P4 molecule.48 Our computational studies of singlet SiH2 interacting with P4 report a number of one-to-one adducts, but the single insertion product is the most stable one by more than 20 kcal/mol.49 Structural, Energetic, and Transition State Considerations. Computations with singlet and triplet CH2 and singlet SiH2 have been carried out with both tetrahedrane and tetrasilatetrahedrane at the 6-311þþG(3df,3p)55-59 basis level. Geometry optimizations from a variety of initial orientations of the divalent group 14 species (CH2 or SiH2) juxtaposed with respect to tetrahedrane and tetrasilatetrahedrane (apex, face, edge) yielded many structures of varying energies and molecular detail. These increased in complexity and number in interactions with tetrasilatetrahedrane versus tetrahedrane, presumably because silicon bonds in more complex patterns than does carbon.21,34,66 An arbitrary 12 kcal/mol (∼0.5 eV) relative energy limit above the most stable species in each study series has been used in what follows to limit the amount of discussion to the more stable structures that have been found, no matter how unusual the structural features may be of the less stable structures. Thus, those structures higher in energy (less stable) than the comparison molecule by more than 12 kcal/mol will not be discussed, although their structural representations will be shown. The optimized Cartesian coordinates given in the Supporting Information will allow the reader to determine the detailed features for the species not discussed. On the basis of the number and complexity of the structures found with Si4H4, it was decided to study only those transition-state species found from interactions of Si4H4 with triplet and singlet CH2 and with singlet SiH2. A limited number of transition state species were found unfortunately, despite considerable expended effort. These results are discussed immediately following each of the corresponding sections that present structural and energetic results. Triplet CH 2 Studies-Interactions with Tetrahedrane (C4H4): Structures and Energies. Exploring the interaction of triplet CH2 and tetrahedrane proved more difficult than expected, yielding only three stable species using restricted openshell Hartree-Fock methods (ROHF) methods. This is surprising in view of the high strain energy of tetrahedrane and contrasts with several experimental studies by Lee, Kaiser, and co-workers, where various triplet C5H6 species have been reported.67-69 In these experimental studies designed (66) Apeloig, Y.; Karni, M. In The Chemistry of Organic Silicon Compounds; Rappoport, Z., Apeloig, Y., Eds.; Wiley: New York, 1998; The Chemistry of Functional Groups Series Vol. 2, pp 1-101. (67) Hahndorf, I.; Lee, H. Y.; Mebel, A. M.; Lee, Y. T.; Kaiser, R. I. J. Chem. Phys. 2000, 113, 9622–9636. (68) Huang, L. C. L.; Lee, H. Y.; Mebel, A. M.; Lin, S. H.; Lee, Y. T.; Kaiser, R. I. J. Chem. Phys. 2000, 113, 9637–9648.

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to uncover routes to polycyclic aromatic hydrocarbon (PAH)like species in the interstellar medium, ground-state atomic carbon (3Pj)70 has been reacted with a variety of C4H6 isomers.67-69 The C5H6 species formed have been characterized both experimentally in single-collision, cross molecular beam experiments and computationally using B3LYP/6-311G(d,p) techniques. Their importance in the molecular beam studies is based on the presumed loss of a hydrogen atom to give C5H5 species that are believed to be precursors to PAH-like molecules. The computational results of Lee, Kaiser, and co-workers are extensive,67-69 focusing on the interactions of 3Pj carbon with three C4H6 isomers, buta-1,3-diene, buta-1,2-diene, and dimethylacetylene.67,69 Their lowest energy computed species is the cyclic C5 structure 5 (discussed below).67,69 While the computational studies reported here sought to examine the C5H6 PES in detail, various attempts to locate more than the three stable C5H6 species resulted in triplet CH2 drifting away from tetrahedrane instead of interacting. The three species found are the cyclic C5H6 structure 5 (relative energy 0 kcal/mol; ∼56 kcal/mol relative to singlet cyclopenta-1,3-diene 8), 6 (∼13 kcal/mol relative to 5), and 7 (∼61 kcal/mol). Despite its connectivity, the cyclic C5 triplet species 5 is dramatically different from singlet cyclopenta1,3-diene. The triplet species has 1-2, 2-3, and 3-4 C-C bond distances of 1.51, 1.46, and 1.36 A˚, while those of cyclopenta-1,3-diene are 1.50, 1.34, and 1.47 A˚. The unpaired spin population in 5, analyzed by both L€ owdin and Mulliken techniques,61,71 localizes the unpaired electrons (∼1.8 and ∼1.9 by L€ owdin and Mulliken, respectively) on the five carbons in 5 with most of the spin population (between ∼1.6 and ∼1.8) on the four CH carbons.

The energies of 6 and 7 fall beyond the arbitrary limit for discussion, but their structures are shown. Singlet CH2 Studies-Interactions with Tetrahedrane (C4H4): Structures and Energies. Several common and some less common species are found computationally on the singlet C5H6 PES, where cyclopenta-1,3-diene 8 is the lowest in energy species by far: cyclopenta-1,3-diene 8 (relative energy 0 kcal/mol), bicyclo[2.1.0]pentane 9 (∼49 kcal/mol relative to 8), vinylcylopropene 10 (∼50 kcal/mol), the C-C insertion product 11 (∼66 kcal/mol), the cyclic carbene 12 (∼68 kcal/mol), and the C-H insertion product 13 (∼87 kcal/ mol). Singlet 12 has the same connectivity as triplet 6, although structural comparison reveals some important differences. The carbon framework of the singlet carbene 12 is distinctly nonplanar, but its triplet counterpart 6 is (69) Kaiser, R. I.; Lee, H. Y.; Mebel, A. M.; Lee, Y. T. Astrophys. J. 2001, 548, 852–860. (70) The 3Pj term symbol is cited by the authors in refs 67-69. It presumably is meant to describe a mixture of the three lowest energy carbon triplet spin-orbit states 3P0, 3P1, and 3P2 (0.0-43.4 cm-1). No specific information on this or the calculations carried out was found in these references or in a broad literature search. However, one of the authors, Ralf Kaiser, when contacted, confirmed the presumption. (71) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; Wiley: New York, 1986.

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planar (sum of the internal angles 539.9°). The highest occupied molecular orbital minus one (HOMO-1) of 12 stretches over the three low-valent silicon atoms. This orbital looks very much like the highest doubly occupied orbital in triplet 6. There is a close similarity in the bond distances in 6 and 12 with greater differences in the C-C-C angles. All of the singlet species found are very much more stable than their triplet counterparts, despite the lower energy of triplet CH2 (∼9 kcal/mol) relative to singlet CH2.64

Triplet CH2 Studies-Interactions with Tetrasilatetrahedrane (Si4H4): Structures and Energies. Although the triplet CSi4H6 PES has been unexplored experimentally or computationally, the studies reported here have found seven optimized structures (14-20) in a fairly narrow relative energy range (∼31 kcal/mol). These all are ring-opened species that relieve strain in the tetrasilatetrahedrane core. Only 14-17 fall within the arbitrary 12 kcal/mol limit for discussion, but structures 14-20 nevertheless reveal a dizzying array of unusual features, including three-membered silicon-containing rings, four-membered silicon-containing rings, divalent and trivalent silicon, and divalent carbon. The two lower energy structures 14 (relative energy 0 kcal/mol; ∼20 kcal/mol relative to 21) (21 is the lowest energy structure found for singlet CH2 plus tetrasilatetrahedrane species) and 15 (relative energy ∼4 kcal/mol; ∼24 kcal/mol relative to 21) are the only structures where CH2 becomes part of a ring. Surprisingly, the bicyclo[2.1.0] structure 14 is somewhat lower in energy than that of the five-membered-ring system 15 (both have a divalent silicon). There are other noteworthy structural features in 14 and 15. The bridgehead Si-Si bond in 14 is ∼2.5 A˚, somewhat longer than the typical Si-Si bond distance of ∼2.3 A˚. There is no obvious perturbing structural effect introduced by a divalent silicon, since in 14 the Si-Si bonds adjacent to the divalent silicon are both ∼2.3 A˚. In 15 the Si-Si bonds adjacent to the divalent silicon atom are ∼2.3 and ∼2.4 A˚ and the more distal Si-Si bond length is ∼2.4 A˚. Most of the bond angles in 14 and 15 are unremarkable, with the exception of the Si-Sidivalent-Si angle, which is ∼64° in 14, larger than the other three-membered-ring angles in 14 (both ∼58°). The Si-Sidivalent-Si angle in 15 is ∼85°, suggesting high p character of the divalent silicon. Of the two closely related triplet CSi4H6 structures 16 and 17 (relative energies ∼10 and ∼12 kcal/mol), interactions between nearby hydrogen atoms and those of hydrogen atoms in the CH3 group might be thought to slightly destabilize 17, but that seems unlikely, given that the hydrogen atoms in question are beyond the combined van der Waals radii of the hydrogen atoms (rvdW for hydrogen ∼1.1 A˚).72 The closest ring hydrogen to the “topmost” methyl hydrogen atom in 16 is (72) Carroll, F. A. Perspectives in Structure and Mechanism in Organic Chemistry; Brooks/Cole: Pacific Grove, CA, 1998.

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∼3.8 A˚, while the closest distance between the “topmost” methyl hydrogen and two ring hydrogen atoms in 17 is ∼3.9 A˚. In the first case, four atoms intervene between the hydrogen atoms; in 17, three atoms intervene. The cis-1,3-atom distance in 16 is ∼4.0 A˚; in 17, it is ∼3.4 A˚. It seems more likely that subtle features of the ring systems in isomers 16 and 17 lead to the slightly higher energy for 17. Isomers 1820, in which the carbon atoms are divalent, are shown as well.

Figure 1. Reaction coordinate connecting triplet species 14 and 15 (energies in kcal/mol, relative to 21; zero point energy corrected; not drawn to scale).

Singlet CH2 Studies-Interactions with Tetrasilatetrahedrane (Si4H4): Structures and Energies. Ten structures (21-30) with a 44 kcal/mol energy spread have been located on the singlet tetrasilatetrahedrane plus CH2 potential energy surface. Six of these are within the 12 kcal/mol arbitrary limit for discussion. The lowest energy structure is the C2v species 21 (relative energy 0 kcal/mol), in which CH2 has inserted into a Si-Si bond and a distal Si-Si bond has been broken. The resulting structure has two trivalent silicon atoms with Si-Si bonds of ∼2.31 A˚. The “broken Si-Si non-bond” between the two trivalent silicon atoms at ∼2.9 A˚ is about 0.5 A˚ longer than the normal single Si-Si bond distance.34,73 The possibility that structure 21 is a singlet diradical was examined using two-configuration self-consistent field methodology (TCSCF).74 The results of such an analysis (using a 6-31G(d) basis) suggest that 21 has ∼21% diradical character (see structure 21-H, the highest occupied molecular orbital of 21).

Transition States in Triplet CH2 Studies-Interactions with Tetrasilatetrahedrane (Si4H4). A transition state linking triplet structures 14 and 15 was found (Figure 1). Structure 14 must overcome a modest ∼6 kcal/mol barrier (TS14/15) to convert to 15, a rearrangement that involves the scission of the bridgehead Si-Si bond and a hydrogen-atom transfer. The overall 14 f 15 reaction is uphill by ∼4 kcal/mol. Although the Si-Si scission in 14 would appear to require electron spin density to localize at the silicon atoms that were bonded, there is no evidence for this as 14 moves through TS14/15 to 15. Spin populations hardly vary when the three silicon atoms forming the three-membered ring in 14 are followed through TS14/15 to 15. The localized unpaired spin density of these three silicon atoms is between ∼1.9 and ∼1.8 throughout (by L€ owdin and Mulliken population analyses, respectively).61,71 One other transition state has been located, namely that between methyl rotamers in 16, where the barrier is ∼0.03 kcal/mol; all other attempts to find transitions linking the CH2/Si4H4 structures have been unsuccessful.

Structures 22 (∼7 kcal/mol), 23 (∼9 kcal/mol), and 24 (∼9 kcal/mol) display additional structural features of interest. Two silicon atoms are pentacoordinate, and two are divalent in 22. The two hydrogen atoms bound to the pentacoordinate silicon atoms have very different bond lengths (∼1.5 and 1.7 A˚), not unlike the bond length differences in the apical (∼1.6 A˚) and equatorial (∼1.5 A˚) positions of SiH5 (D3h).34 The tendency of silicon hydrides to have a hydrogen atom bridge bond has been found in computational studies of (73) Corey, J. Y. In The Chemistry of Functional Groups; Patai, S., Rappoport, Z., Eds.; Wiley: New York, 1989; pp 1-56. (74) The possibility of structure 21 being a singlet diradical was raised by a reviewer and pursued accordingly. I am grateful for this suggestion.

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Si4H4.21,34,66 Similar results are revealed in structures 23 and 24, which are only subtly different. In 23 the pentacoordinate silicon also has very different Si-H bond lengths (∼1.5 and ∼1.7 A˚), but the longer bond to hydrogen is part of an extended bonding system involving another silicon atom, also with long bonds to hydrogen (both ∼1.7 A˚). Interestingly, this silicon atom is trivalent. In 24 the hydrogen atom bridge bond spans tetra- and divalent silicon atoms, each having long bonds to the bridging hydrogen atom (∼1.7 A˚).

Figure 2. Transition state studies connecting singlet species 22, 25, and 26 (energies in kcal/mol, relative to 21; not drawn to scale).

Compound 25 (∼10 kcal/mol) and the insertion product 26 (∼12 kcal/mol) have structural similarities with 21. In contrast with our study in which the lowest energy product results from singlet CH2 insertion into P4,50 interactions between singlet CH2 and Si4H4 are far more varied. Here the insertion product 26 is only the sixth most stable species found. Structures 25 and 26 differ only in the opening of one Si-Si bond and the transfer of a hydrogen atom to a silicon atom attached to carbon. The two hydrogen atoms on this silicon in 25 have different lengths (∼1.5 and ∼1.7 A˚), with the longer Si-H bond pointed toward the divalent silicon atom. The distance between that divalent silicon atom and the “long-bonded” hydrogen atom is ∼1.74 A˚, just beyond the distance set for bonding in MacMolPlot. Indeed, this interaction could easily be considered a bridging situation, not differing dramatically from that in 24. Structures 27-30, all having relative energies greater than the 12 kcal/mol limit relative to 21, are shown as well. Transition States in Singlet CH2 Studies-Interactions with Tetrasilatetrahedrane (Si4H4). Efforts to link the singlet CH2/Si4H4 structures have yielded three transition states. The unusual divalent silicon product 25 connects with 22 over an ∼11 kcal/mol barrier that requires Si-Si bond breaking and remaking at a different silicon atom as well as a hydrogen atom migration (overall downhill ∼2 kcal/mol to 22) (Figure 2). Product 25 also connects with insertion product 26 over a ∼6 kcal/mol barrier (overall uphill

∼2 kcal/mol to 26) (Figure 2). The route to 26 requires both Si-Si bond formation and hydrogen atom rearrangement. The energetically very similar structures 23 and 24 are connected over a small ∼2 kcal/mol barrier that involves a simple hydrogen atom shift from a trivalent to a divalent silicon atom. The energy difference between 23 and 24 is vanishingly small (∼0.1 kcal/mol). Singlet SiH2 Studies-Interactions with Tetrahedrane (C4H4): Structures and Energies. Of the five structures found when singlet SiH2 interacts with tetrahedrane, only one meets the low-energy criterion established: that is, 1-sila2,4-cyclopentadiene 31 (relative energy 0 kcal/mol), in which the Si-C bond lengths are 1.87 A˚, the C-C bonds proximate to the silicon atom are 1.34 A˚, and the distal C-C bond is 1.48 A˚. The proximate C-C bond distances are consistent with a carbon-carbon double bond length; the distal carboncarbon bond has a length closer to that of a single than that of a double bond, and the silicon-carbon bonds are typical of single bonds.34,73 The four other structures shown (32-35) have relative energies ranging from ∼46 to ∼82 kcal/mol higher than 31. Note that 34 (∼53 kcal/mol relative to 31) is the insertion product, which again in contrast to the P4 studies is not the most stable structure found.

Singlet SiH2 Studies-Interactions with Tetrasilatetrahedrane (Si4H4): Structures and Energies. Four low-energy

Article

(relative energy range 0.0 to ∼10 kcal/mol; 36-39) and five higher energy (∼14 to ∼37 kcal/mol; 40-44) optimized structures have been found. The large number of relatively low energy structures again is a reflection of the facility of silicon to bond in a variety of different ways.21,34,66 Three structures have virtually identical energies: the hydrogenbridged species 36, the Si-Si insertion product 37, and isomer 38 (all ∼0 kcal/mol). The low energy of the hydrogen-bridged species 36 reflects both the relief of strain associated with breaking an Si-Si bond in tetrasilatetrahedrane and the propensity of silicon for unusual, particularly hydrogen-bridge, bonding. Group 14 elements are often involved in such hydrogen bridging, as revealed in various computational studies.21,34,75 Bridging becomes more favorable as one descends group 14, although the ethane-like structure for M2H6 is more favored for carbon, silicon, germanium, and lead than the hydrogen-bridged structure.34,75 On the other hand, hydrogen-bridged structures become more stable than tetrahedrane-like structures for M4H4 with silicon, germanium, and lead, with bridging being more favored by the heavier metals.21,34 Isomers 38 and 36 are closely related. Structure 38 has a hydrogen atom very close to its divalent silicon (1.74 A˚); in 36 “that same hydrogen” is actually bridged (1.70 A˚). In 38 the hydrogen that is so close to the divalent silicon is bonded to a tetravalent silicon atom (1.66 A˚), while in 36 the hydrogen that is bridged also bonds to the tetravalent silicon atom (1.68 A˚). Structure 39 (∼10 kcal/mol) derives from SiH2 insertion into an Si-H bond with concomitant Si-Si bond scission. Because the “opposed” trivalent silicon atoms (1,3) in structure 39 are somewhat reminiscent of the singlet diradical 21, TCSCF calculations were conducted to examine the divalent radical character of 39. These led to an estimate of ∼27% diradical character localized on the opposed silicon atoms (see structure 39-H, the highest occupied molecular orbital of 39).

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Figure 3. Reaction coordinate connecting singlet species 36-38 (energies in kcal/mol, relative to 21; not drawn to scale).

A wide variety of additional bonding patterns are illustrated in structures 40-44 (∼14-37 kcal/mol).

Transition States in Singlet SiH2 Studies-Interactions with Tetrasilatetrahedrane (Si4H4). Structure 25 (a CH2Si4H4 structure) differs from 38 (a SiH2Si4H4 structure) only in the replacement of its carbon atom by silicon. The relationships to various transition states of structure 38 are somewhat similar to the case for 25 as well. It is connected to the insertion product 37 over a ∼5 kcal/mol barrier (downhill to 37 by only ∼0.3 kcal/ml) and to 36 over a very small ∼0.3 kcal/ mol barrier (downhill to 36 by only ∼0.3 kcal/ml) (Figure 3). The route to the insertion product 37 involves both Si-Si bond formation and hydrogen atom migration. That to 36 involves the formation of a hydrogen-atom bridge bond and Si-Si bond scission. Structures 41 and 42 are connected over a ∼6 kcal/mol barrier that involves a hydrogen atom shift (their energies differ by ∼0.3 kcal/mol) (Figure 4).

Final Remarks

(75) Trinquier, G. J. Chem. Soc., Faraday Trans. 1993, 89, 775–782.

A large number of optimized structures that meet the criterion established for discussion have been located on the following potential energy surfaces: (1) triplet C4H4 plus CH2 (structure 5), (2) singlet C4H4 plus CH2 (structure 8),

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Figure 4. Reaction coordinate connecting snglet species 41 and 42 (energies in kcal/mol, relative to 36 and 37; zero point energy corrected; not drawn to scale).

(3) triplet Si4H4 plus CH2 (structures 14-17), (4) singlet Si4H4 plus CH2 (structures 21-26), (5) singlet C4H4 plus SiH2 (structure 31), and (6) singlet Si4 H4 plus SiH2 (structures 36-39). Many complex structural features have been observed in these optimized species, in keeping with the diversity of bonding schemes expected in silicon compounds. Those structures obtained in studies bringing tetrasilatetrahedrane (Si4H4) in proximity (a) with triplet CH2, (b) with singlet CH2, and (c) with singlet SiH2 were the most varied. (a) In triplet interactions between Si4H4 and CH2 (see 14-17), two of the structures found have CH2 incorporated as part of a ring while two others have Si4 rings with appended methyl groups. All four have two- or three-coordinate silicon atoms (both in the case of 15). Given that triplet species are often quite reactive, it might have been

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expected that triplet CH2 would be more reactive than singlet CH2; that is not the case in these studies. (b) The singlet interactions between Si4H4 and CH2 lead to six criterion-meeting structures (see 21-26), all of which have CH2 incorporated into Si4 rings. The formation of 21 involves CH2 insertion into and distal scission of Si-Si bonds leading to a singlet diradical (21H is a representation of its highest occupied molecular orbital) with ∼21% diradical character. The other species found display a dizzying array of unusual structural features: two- or three-coordinate silicon atoms, hydrogen atom bridging, and three-memberedring arrangements. (c) The singlet interactions between Si4H4 and SiH2 leading to four criterion-meeting structures (see 36-39) similarly reveal unusual structural features, including two- or three-coordinate silicon atoms, hydrogen atom bridging, and threemembered-ring structures. Another singlet diradical species (39) has been identified with ∼27% diradical character. While surveying the structural diversity of the optimized species obtained has been the major emphasis of this study, probing various pathways leading to transition-state structures that connect such species has been fruitful as well. Among the transition states found are those linking structures (1) 14 and 15, (2) 25 with both 22 and 26, (3) 38 with both 36 and 37, and (4) 41 and 42. These links reveal quite complex interconversion processes.

Acknowledgment. I thank Professor Michael W. Schmidt for providing invaluable advice concerning the two-configuration SCF calculations and Professor John F. Stanton for help regarding coupled cluster methods. Supporting Information Available: Tables giving corrected energies and relative energies and tables and figures giving final Cartesian coordinates and visuals of important structures. This material is available free of charge via the Internet at http:// pubs.acs.org.