Applying MNDO approximatlon, the heats of formation (LlHt) and structures of the navel compounds helvetane (1) and israelane
(2) have been calculated. The MNDO sn, for 1 and 2 are 336 and
719 kcal/mol, respectively, in agreement with the previous prediction
that 1 is more stable than 2. In addition, in view of the structures
calculated, the large positive LlHt values of 1 and 2 are most
likely the result of these malecules\u27 angular strain

See-Wing Chiu

Tien-Yau Luh

Wai-Kee Li

English

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CROATICA CHEMICA ACTA CCACAA 58 (1) 1-3 (1985)CCA-1551YU ISSN 0011-1643UDC 541.1NoteMNDO Study of Helvetane and IsraelaneWai-Kee Li*, Tien-Yau Luh, and See-Wing Chiu**Department of Chemistry, The Chinese University of Hong Kong, Shatin,New Territories (Hong Kong)Received December 12, 1983Applying MNDO approximatlon, the heats of formation (LlHt)and structures of the navel compounds helvetane (1) and israelane(2) have been calculated. The MNDO sn, for 1 and 2 are 336 and719 kcal/mol, respectively, in agreement with the previous predict-ion that 1 is more stable than 2. In addition, in view of the struct-ures calculated, the large positive LlHt values of 1 and 2 are mostlikely the result of these malecules' angular strain.In arecent note,' the synthetic strategy for two isomeric members 'of the(CH)24series, helvetane (1) and israelane (2), was discussed. In addition, eventhough these two compounds were not prepared, it was predicted that 2 wouldrearrange thermally to 1. Although the note was apparently written in jest,"the navel compounds 1 and 2 are undoubtedly of interest. Hence we havecarried out MND03 calculations on these two molecules in order to investigatetheir relative stability and their structures. Also, a cornparison between thesetwo compounds and related systems was made.For the present calculations, D4h and D6h symmetries were assumed for 1and 2, respectively. The MNDO structures of these two molecules are depictedin Figures 1 and 2. The MNDO heats of formatian (L/Hf) for 1 and 2 are 336 and719 kcal/mol, respectively.Examining Figures 1 and 2, it is worth noting that the two twelve-mem-Figure 1. MNDO structure of helvetane (1). Bond Iengths (A): a = o: = 1.60, b = b' == b" = 1.56 c = c' = 1.57, d = 1.60, e = 1.09, f = 1.10. Bond angles (0): a-b = 114.0,b-b" = 138.5, a-c = 90.0, a'-c' = 90.0, b-d = 89.5, b'-d = 90.5, a'-e = 115.4, b'-e == 118.5, c-e = 123.1, b-f = b"-f = 105.8, d-f = 128.3. Only two hydrogens areshown.* Author for correspondence.** Current address: Department of Chemistry, Marquette University, Milwaukee,WI 53233, U.S.A.w.-K. LI ET AL.Figure 2. MNDO structure of israelane (2). Bond lengths (A): a = a' = a" = a'"== 1.60, b = 1.56, c = 1.58, d = 1.09, e = 1.11. Bond angles (0): a-a' = 97.2, a"_a'" == 157.8, a-b = 90.4, a-c = 89.6, a-d = a'-d = 122.4, b-d = 124.9, a"-e = a"'-e == 99.1, c-e = 130.3. Only two hydrogens are shown.bered rings in both molecules have only very minor puckering and hence arenearly planar. When compared with the structure+ of bicyclo[2.2.0]hexane (3)[a= a' = 1.54 A, b = 1.56 A, c = 1.58 A, a-a' = 113.5°], significant lengtheningof all peripheral C-C distances (bond a) in 2 and eight »outer« C-C distances(bond a) in 1 is apparent. On the other hand, the bridging C-C lengths in 1(bonds c and d) and 2 (bonds b and c) are on the whole comparable with thatin 3. The nonbonding distances between the »inside- hydrogens in 2 are 1.55 Afor ortho, 2.69 A for meta, and 3.11 A for para hydrogens, whereas the separa-tions between the »inside« hydrogens in 1 are 1.68 A for vicinal and 2.37 Afor diagonal hydrogens. Furthermore, it is noted that the C-C distance d in 1,where two »inside« hydrogens are attached to the respective carbon atoms, isslightly longer than the bridging C-C bond jn 3.The relatively large positive L1Hf values of 1 and 2 are most likely theresult of these molecules' angular strain. Here, again, compound 3 may beused as a reference. The strain energy for 3 is 51 kcal/mol at 25 °C.5Additionally,the cyclobutane moiety in 3 is puckered (puckering angle is 11.5°). For both1 and 2, all cyclobutane units are planar. In 1, bond angle a-b is similar toa-a' in 3, but angle b-b" is significantly larger. Hence, it is expected thatthe strain energy for 1 would be somewhat higher than the sum of those forsix bicyclohexanes. Based on the classical mechanical model," the strain con-tributed by angles b-b" in 1 would be 10.9 kcal per angle, or 10.9 X 8 = 87kcal/mol. If it is assumed that the strain difference between 1 and the sumof six bicyclohexanes is mainly contributed by the b-b" angle strains, thenthe strain energy for 1 would be 6 X 51 + 87 = 393 kcallmol. Alternatively,MNDO STUDY OF HELVETANE AND ISRAELANE ;)applying Schleyer's group increment strain energy correction for CH groups",the strain energy for 1 based on the MNDO LlHf would be 387 kcal/mol, inexcellent agreement with the classical mechanical model result.Similar results can be obtained for 2. As shown in Figure 2, bond anglesa-a' and a" -a"' are severely distorted. The former is smaller than the anglea-a' in 3, wlrile the latter is considerably larger. In fact, an increase in anglea-a' wil occur at the expense of an increase in angle a" -a"'. rf it is assumedthat the difference in strain energy between 2 and the surn of six bicyclohexanesaris es from the strain" of angles a-a' (57 kcal/mol) and a" -a"' (344 kcal/mol),the strain energy for 2 would be 6 X 51 + 57 + 344 = 707 kcal/mol. On theother hand, applying Schleyer's methcd," the strain energy for 2 based on theMNDO LlHf would be 770 kcal/mol, in fair agreement with the classical me-chanical model result.To conclude, the present results are in accord with the prediction thathelvetane is thermodynamically more stable than israelane. In addition, thelarge positive LlHf values for both 1 and 2 are due to these molecules' severeangular strain. The strain per CH unit is approximately 16 'kcal/mol for 1and 32 kcal/mol for 2. It is interesting to note that the strain per CH unit for 1is still somewhat less than those for several known (CH)n compounds,? suchas cubane (20 kcal/mol) and prismane (23 kcal/mol).REFERENCE S1. G. D i n s b u r g, Nachr. Chem. Tech. Lab. 30 (1982) 289; Nouv. J. Chim. 6 (1982) 175.2. D. G i n s b u r g, private communication (1983).3. M. J. S. De war and W. T h i e 1, J. Amer. Chem. Soc. 99 (1977) 4899.4. B. And e r s o n and R. S r i n iva s a n, Acta Chem. Scand. 26 (1972) 3468.5. E. M. Eng 1e r, J. D. And o s e, and P. v. R. Sc h 1e y e r, J. Amer. Chem.Soc. 95 (1973) 8005.6. The force constant ko used is 35 cal/deg.", See F. H. Wes the ime r in M. S.New man, Steru: EfJects in Organic Chemistry, Wiley, New York (1956).7. A. G r e e n b e r g and J. F. Lie b man, Strained Organic Molecules, AcademicPress, New York (1978).SAŽETAKMNDO studij helvetana i izraelanaWai-Kee Li, Tien-Yau Luh i See-Wing Chiu!zračunani su strukturni podaci i topline stvaranja slobodnih molekula helve-tana (1) i izraelana (2), koje još do sada nisu sintetizirane. Pri tome je primijenjenasemiempirijska MNDO metoda. Pokazano je da je spoj 1 za oko 380 kcal/mol stabil-niji od 2. To je posljedica manje kutne napetosti.

MNDO Study of Helvetane and Israelane

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