It is found that path (i), which is concerted and stereospecific, is
favored both thermodynamically and kinetically, in agreement
with exp~\u27rimental results. In addition, paths (ii) and (iii) are found
to be competitive with each other and both are highly energetic
due to steric effects, with activation energy being about 50 kcal/mo!

See-Wing Chiu

Wai-Kee Li

English

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CROATICA CHEMICA ACTA CCACAA 54 (2) 183-191 (1981) CCA-1273 YU ISSN 0011-1643 UDC 547.62 OriginaL Scientific Paper MIND0/3 Study of the 'Thermal Rearrangements of Bicyclobutanylidene See-Wing Chiu and Wai-Kee Li* Department of Chemistry, The Chinese University of Hong Kong Shatin, N. T., Hong Kong Received June 23, 1980 The following three rearrangements of bicyclobutanylidene have been studied using the MIND0/3 method: (i) (ii) (iii) 11\ HC=C-CH=CHz ~: A=-~-~ A. ~ (via a biradical--like inter-mediate) (direct C-H insertion) It is found that path (i), which is concerted and stereospecific, is favored both thermodynamically and kinetically, in agreement with exp~'rimental results. In addition, paths (ii) and (iii) are found to be competitive with each other and both are highly energetic due to steric effects, with activation energy being about 50 kcal/mo!. INTRODUCTION Recently, there has been considerable interest in carbene rearrangements as routes to high-energy species.1 The work presented here consists of theoretical investigations on some of the possible rearrangements of the bicyclic carbene, bicyclobutanylidene, 1, which has been generated by addition of atomic carbon2 or carbon suboxide3•4, O=C=C:, to cyclopropenes. There appear to be three possible rearrangement paths for 1: * Address correspondence to this author. 184 SEE-WING CHIU AND WAI-KEE LI II I -l m A further rearrangement fs) Bond breaking with electron rearrangement (path I) gives vinylacetylene (2) , which has been observed as the major product by Shevlin and Wolf4. Path II leads, via a C-H insertion, to tetrahedrane, 3, which has been postulated as an intermediate in the gas phase photolysis of carbon suboxide in the presence of cyclopropene4 • Finally, path III leads to bicyclo[l.1.0]butene, 4, via a 1,2-hydrogen migration. Species 4 has not been investigated theoretically, but it may be as energetic as bicyclo[l.1.0]but-1,3-ene, which has been studied by Hehre and Pople5 using ab initio MO methods, and will probably rearrange further under the condition of its formation. In this work, only paths I and II have been studied. METHOD · OF CALCULATION The semi-empirical molecular orbital model used in this study is the well-tested MIND0/3 method6• The calculations were performed on the IBM 3031 computing system at the Chinese University of Hong Kong. ---------r---:::: f3 \ ... -----------2 H-7 -Figure 1. Structural parameters for the rearrangements of bicyclobutanylidene. The structural parameters for the rearrangement paths I and II are defined in Figure 1. For the rearrangement 1 ~ 2, i. e., path I, r 1 (1.4 A-3.0 A) and r2 (1.5 A-- 3.0 A) were chosen as reaction coordinates for the potential energy surface. All other geometrical parameters were optimized. The potential energy surface of 1 ~ 3, i.e., path II, was obtained from the energy curves E(/J) for each given value of e, ranging from 60° to 180°, with Cs symmetry assumed throughout and a minimum 2 X 2 configuration interaction treatment included. REARRANGEMENTS OF BICYCLOBUTANYLIDENE 185 RESULTS AND DISCUSSION Calculated structural parameters of 1 are shown in Figure 2; the MIND0/3 results of bicyclobutane7 are also presented for comparison. In addition, the MIND0/3 charges on C1 to C4 are 0.103, -0.179, 0.103, and 0.046, respectively. Judging from the optimized geometry and the charge distributiion, the electronic H H Blcyclobutane Bicyclobutanylidene nHf = 100.S kcal/mol H5~c1 -c3 -c2 = 107 H nlif = 49.8 kcal/mol (51.9 kcal/mol) 131.5 1.098 (128.4) (l.071) H 2 H H Figure 2. Calculated geometries of 1 and bicyclobutane (observed values' for the latter are given in brackets). Bond lengths are in A and angles in degrees. 186 SEE-WING CHIU AND WAI-KEE LI structure of 1 may be more properly described as 5, in agreement with the ~ 5 ab initio results of Hehre and Pople0• Another interesting result that is relevant to the present work is the calculci.tion of cycloheptatrienacarbene of Dewar and Landman.8• The potential energy surface of 1 ~ 2 presented in Figure 3 indicates that the rearrangement proceeds with two distinguishable stages: initial breaking of the C1-C4 (or C3-C4 ) bond, i.e., lengthening of r 1 , followed by the bond breaking of C1-9.3 (lengthening of r 2). Obviously, concomitant breaking of these two bonds is very unlikely. From Figure 3 it is seen that 1.5 2.0 2.5 3.0. r, (A' ) Figure 3. Energy contour map for the rearrangem ent 1->2. Contours are labelled in kcal/mol. The asterisk denotes the transition state, the geometry of which is show n in Figure 4. the C1-C3 bond remains intact until the C1~C4 bond is almost completely broken. Detailed examination of the results suggests that the lengthening of the C1-C4 bond leads to an increase in the bonding interaction between C1 and C2, and the same is true for C3 and C4 • At the same time, the bonding interaction between C2 and C3 decreases. The overall effect is an increase in potential energy, i. e., the rearrangement proceeds via a transition state. The appearance of the plateau in the region 2.5A<1\ < 2.9 A and 1.5 A< r 2 < 1.8 A may be due to the fact that MIND0/3 overestimates the stability of small ring systems7•9• Figure 4. shows the predicted geometry of the transition state; the curved arrow indicates the direction the methylene group rotates. The calculated energy barrier and heat of reaction for 1 ~ 2 are 22 and -39 kcal/rnol, respectively. In summary, the rearrangement is concerted and ste-reospecific as depicted in Figure 5. REARRANGEMENTS OF BICYCLOBUTANYLIDENE 5 bHr = 123 kcal/nol C4-C3-C1 = 90 c5-erc2 = 193 c5-e1-c3 = 131 C5-C3-c2 = 114 C5-C3-c1·= 131 c7-c4-c3 = 126 C8-C4-C3 = 125 C4-C3-c1-c2 = 144 2.0 \ \ \ \ \ \ \ 1.30 2 1.54 187 Figure 4. Geometry of the transition state for the rearrangement 1~2. Bond lengths are in A and angles in degrees. H ... Transition State Figure 5. Depiction for the stereospecificity of the rearrangement 1~2. It is interesting to note that the transition state geometry for 1 ~ 2 and that for cyclobutenylidene ~ -21° are quite similar and, hence, have comparable 11 Hf values. For easy comparison, the geometry of the transition state for the latter process is shown in Figure 6. Thus it may be concluded that the post-transition-state paths for these two rearrangements are quite similar to each other. Attention is now turned to the second rearrangement studied in this work : 1~3; the energy contour map for the process is shown in Figure 7. The results indicate that the optimum path does not proceed via a direct C-H insertion. Instead, a biradical-like intermediate, 6, which has an electronic structure (such as HOMO and LUMO symmetries) similar to that of 3, is formed. The optimized geometry of 6 is shown in Figure 8. 188 SEE-WING CHIU AND WAI-KEE LI ,i 1.47 / ; ~--.&::""\; 1.77 / "2.1 ~Hf = 121 kcal /mol Figure 6. Geometry of the transition state for the rearrangement cyclobuteny!iden e ->2". Only the bond lengths (in A) are shown. ( 0) 8 50 100 f3 (°) Figure 7. Energy contour map for the rearrangement 1->3. Contours are labelled in kcal/mol. The asterisk denotes the transition state, the geometry of which is chown in Figure 9. REARRANGEMENTS OF BICYCLOBUTANYLIDENE 189 1.099 Fogure 8. Geometry of the biradical-like intermediate, 6, found in the rearrangement 1->3. The optimized structure has C2v symmetry. Bond lengths are in A and angles in degrees. H 6Hf = 150 kcal/m:il H5-Cl -C3-C2 = 142 1.11 Fegure 9. Geometry of the transition state for the rearrangement 1->3. Bond lengths are in A and angles in degrees. 190 SEE-WING CHIU AND WAI-KEE LI The formation of 6 can be interpreted as follows . At an early stage of the reaction, a decrease in e and an increase in fJ result in a decrease in C2-H1 distance (Figure 1). The structure of the transition state presented in Figure 9 indicates the formation of a three-center bond. It is obvious that the strain energy involved in such a structure is high and a further decrease in e (leading to the formation of 3) causes still more strain such that the stabilization energy gained by the formation of the three-center bond canno l compensate for it. As a result, an increase in 6 with a concomitant increase in fJ, i. e., formation of 6, release the strain after the transition state is reached. In other words, the MIND0/3 potential anergy surface predicts that the rearrangement 1--:> 3 is accomplished via a two-step (abstraction-recombination) path: 1--:> 6--:> 3. As can be seen from Figure 7, it costs littl ein energy to move away from the aforementioned optimum path so that the formation of 3 from 1 via a direction C-H insertion is possible. According to the study of Hoffmann et al.11 for the insertion of singlet methylene into a C-H bond, the transition state has a nearly linear configuration for C-H .. . (carbene)C. Since such a configuration cannot be obtained in the present intramolecular case, it is not surprising that the direct insertion or the two-step path requires a high activation energy of about 50 kcal/mol. In addition, 1 is predicted to be a polyene-like carbene (5) and the carbenic center is hence nucleophilic rather than electrophilic. The conclusion that 1--:> 3 m ay or may not involve inter -mediate 6 is in agreement with Kollmar's study12 of the insertion reaction of singlet cyclopropenylidene, which, like 1, has a nucleophilic carbenic center. Kollmar has found that a non-concerted path with a radical intermediate may compete with the concerted process, with the latter also requiring a high activation energy, 41 kcal/mol. Whatever the reaction mechanism (concerted or two-step) for 1--:> 3, the calculated heat of reaction and activation energy are 26 and 50 kcal/mol, r espectively. Thus MIND0/3 predicts that both heat of reaction and energy of activation favor the rearrangement 1--:> 2 over 1--:> 3, as found experi-mentally3•4. Finally, it should be mentioned that a minimum, 7, which cor responds to a distorted cyclobutadiene m olecule, appears on the upper right-hand corner of Figure 7. According to previous studies13•14 , the conversion of 3 into 7, assuming C2v symmetry, is thermally forbidden and does not involve 6. In the present study, it is found that 6 and 7 are lumomers15 and they are separated by an energy ridge as shown in Figure 7. The existence of such a ridge suggests16 that the rearrangement 3 --:> 7 is accomplished without going through 6, as results13•14 of other workers indicate. CONCLUSION MIND0/3 calculations appear to be able to rationalize the observed for-mation of vinylacetylenes as the major products in the rearrangements of 14• In addition, it is found that the process 1--:> 2 is concerted and stereospecific. On the other hand, for the r earrangement of 1--:> 3, there is competition between the concerted and non-concerted (involving a biradical-like inter-mediate) paths, with the latter being slightly favored. Also , due to steric effects both paths are highly energetic, with activation energy being about 50 kcal/mol. REARRANGEMENTS OF BICYCLOBUTANYLIDENE 191 REFERENCES 1. M. Jones, Jr., Accounts Chem. Res 7 (1974) 415 ; C. W e nt r up, Top. Curr. Chem. 62 (1976) 173; W. M. Jones and U . H . Brinker in A. P. Marchand and R. E . Lehr (Eds.) , Pericyclic Reactions, Vol. 1, Academic Press, New York, 1977. 2. R. F. Peterson, Jr., R. T. K. Baker, and R. L. W o 1 f gang, Tetrahedron Lett. (1969) 4749. 3. H. W. Ch an g, A. Lautz en he is er, and A. P. W o 1 f, Tetrahedron Lett. (1966) 6295. 4. P. B. She v 1 in and A . P. W o 1 f, J. Amer. Chem. Soc. 92 (1970) 406. 5. W. J. Hehr e and J. A. Pop 1 e, J. Amer. Chem. Soc. 97 (1975) 6941. 6. R. C. B in g ham, M. J . S. D e war, and D. H. L o, J. Amer. Chem. Soc. 97 (1975) 1285 and accompanying papers. 7. R. C. Bingham, M. J. S. Dewar, and D. H. Lo, J. Amer. Chem. Soc. 97 (1975) 1294. 8. M. J. S. Dewar and D. Landman, J. Amer. Chem. Soc. 99 (1977) 6179. 9. M. S. Gordo n, P. M. S o at z a, and R. D. Koo b, Chem. Phys. Lett. 37 (1976) 217; E. P. Kyba, J. Amer. Chem. Soc. 99 (1977) 8330. 10. S. F. Dyer, S. Kamm u 1 a, and P. B . She v 1 in, J. Amer. Chem. Soc. 99 (1977) 8104. 11. R. C. Dobson, D. M. Hayes, and R. Hoffmann, J. Amer. Chem. Soc, 93 (1971) 6188. 12. H. Ko 11 mar, J. Amer. Chem. Soc. 100 (1978) 2660. 13. M. C. B ti h m and R. G 1 e it er, Tetrahedron Lett. (1978) 1179. 14. A. Sch we i g and W. Thie 1, J. Amer. Chem. Soc. 101 (1979) 4742. 15. M. J. S . Dewar, S. Kirschner, and H. Ko 11 mar, J . Amer. Chem. Soc. 96 (1974) 5240. 16. M. J . S . Dewar and S. Kirschner, J. Amer. Chem. Soc. 93 (1971) 4291; ibid. 93 (1971) 4292. SAZETAK MIND0/3 istrazivanje termiCkog pregrailivanja biciklobutanilidena See-Wing Chiu i Wai-Kee Li Tri su mehanizma pregradivanja biciklobutanilidena studirana pomocu MIND0/3 metode. To su slijedeci: (1) HC =c-CH=CHz (2) (3) Teorijski racun daje prednost mehanizmu (1), koji je uskladen i stereospecifican, prema mehanizmima (2) i (3). Taj je rezultat u slaganju s eksperimentalnim opafa-njima. Mehanizmi (2) i (3) zahtjevaju veliku aktivacijsku energiju (oko 50 kcal/mol) zbog nepovoljnih sterickih efekata. ODJEL ZA KEMIJU KINESKOG SVEUCILISTA U HONG KONGU HONG KONG Prispjelo 23. lipnja 1980. 

MIND0/3 Study of the \u27Thermal Rearrangements of Bicyclobutanylidene

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