Geometric structure and energetics of small strained hydrocarbons

Armin de Meijere , Malte von Seebach , Sergei I. Kozhushkov , Roland Boese , Dieter Bläser , Stefano Cicchi , Tula Dimoulas , Alberto Brandi. Europea...
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2786

J . Phys. Chem. 1987, 91, 2186-2190

currently under investigation by this lab.

other, providing nearly conclusive evidence that trans-stilbene is also planar.

Summary

Acknowledgment. The authors thank Prof. George Leroi for the loan of the monochromator used in these studies. T.S.Z. and R.V.Z. thank the National Science Foundation Research in Undergraduate Institutions Program (CHE 8408048), the Research Corporation, and the donors of the Petroleum Research Fund, administered by the American Chemical Society, for the support of this research. L.H.S. thanks the Department of Energy for support via a Los Alamos National Laboratory Directors Funded Postdoctoral appointment. Registry No. trans-Stilbene, 103-30-0;p-methyl-trans-stilbene,

We have assigned all transitions of less than 400 cm-I and having intensity greater than 1% of the origin intensity in the fluorescence excitation spectrum of trans-stilbene. We have also assigned most of the low frequency transitions in the dispersed spectra from Oo, 36I37I, and 372. Only even quanta transitions of u36 and u j 7 are seen indicating the molecule has inversion symmetry. In addition, the fluorescence excitation and dispersed emission spectra of p-methyl-trans-stilbene also show only even quanta of u3,, proving that this molecule is planar. The transstilbene spectrum and that of its derivative closely resemble each

1860-11-9.

Geometric Structure and Energetics of Small Strained Hydrocarbons Involving an Exo Double Bond. A Combined Semlempirical and ab Initio Study M. Eckert-MaksiL.,*+Z. B. Maksie,: A. Skancke,s and P. N. Skancke*l Department of Organic Chemistry and Biochemistry, and Theoretical Chemistry Group, Institute “Ruder BoSkovic‘”. 41 001 Zagreb, Yugoslavia, Faculty of Natural Sciences and Mathematics, Physical Chemistry Department, The University of Zagreb, Marulic‘ev trg 19, 41000 Zagreb, Yugoslavia, and Department of Chemistry. University of Tromsa N- 9001 Tromser. Norway (Received: January 5, 1987)

Structural properties of small bicyclic hydrocarbons bridged by a cOmmon double bond are studied by the semiempirical IMO, MIND0/3, and MNDO procedures supplemented by ab initio calculations employing several basis sets. It is found that central double bonds in bicyclobutylidene (6),cyclopropylidenecyclobutane(7), and bicyclopropylidene (8) are significantly shorter than in the reference compounds ethylene (I), isobutene (2), and tetramethylethylene (5). Concomitantly, shortening of adjacent and lengthening of distal C-C single bonds are observed. These effects are most pronounced in bicyclopropylidene. Angular distortions caused by fusion of small rings are small. Structural features of the examined molecules can be qualitatively rationalized by the hybridization concept. Energetics and angular strain destabilizationswere estimated by a series of homodesmic reactions by using Wiberg’s group equivalent adjustments for the 4-31G set in calculating the heats of formation. It appears that strain energies roughly follow the additivity rule which states that the total strain of a molecule is a sum of strain energies of the constituent fragments.

Introduction

In spite of some conceptual difficulties,’ the idea of a definite geometric structure of molecules is one of the fundamental tenets of chemistry. Hence, understanding and interpreting the structural features of molecules is a basic chemical undertaking and the primary task of theories of chemical bonding. A wealth of useful chemical information is stored in bond distances and bond angles2 which, if retrieved properly, shed light on the fine details of the electronic charge distribution in m o l e c ~ l e s . Modern ~ ~ ~ quantum chemistry has now reached a stage of development which allows a reliable prediction of the trends in the structural properties of organic molecules. As a matter of fact, ab initio calculations based on split valence basis sets are capable of uncovering subtle differences in geometric parameters, which are not always well resolved by various experimental techniques. Thus ab initio methods are used nowadays as a complementary tool to microwave spectroscopy (MW) and electron diffraction (ED) methods particularly in examining systems where discrimination between alternative molecular structures is out of range of experimental methods a10ne.~“ In addition to ab initio procedures, simple models like variable hybridization coupled with the iterative maximum overlap (IMO) approximation’ have proved useful in ‘Department of Organic Chemistry and Biochemistry, Institute “Ruder BoSkoviE*. ‘Theoretical Chemistry Group, Institute “Ruder BoSkoviE” and Faculty of Natural Sciences, The University of Zagreb f Faculty of Natural Sciences, The University of Zagreb. Department of Chemistry, University of Tromso.

rationalizing the shape and size of molec~les.~,~ Interestingly, this simple model has a remarkable predictive power. For instance, IMO calculations predicted that double bonds emanating from small strained rings should be considerably shortened relative to unstrained systems due to rehybridization of the carbon junction atom.* This finding is in contradiction with the results of earlier calculations on methylenecyclopropane performed by a minimum basis set involving partial geometry optimi~ation.~It was concluded that the ex0 double bond in methylenecyclopropane should be unchanged if not longer than the one in i s o b ~ t e n e .In ~ order to elucidate this problem, we have studied a series of hydrocarbons possessing carbon-carbon double bonds fused to one or two threeor four-membered rings. Ethylene, isobutene, and tetramethylethylene were used as gauge molecules which define angularly unstrained double bond moieties. The employed methods en(1) Woolley, R. G.; J. Am. Chem. SOC.1978, 100, 1073. (2) MaksiE, 2. B.; Eckert-MaksiE, M.; Rupnik, K. Croar. Chem. Acta 1984,57, 1295. (3) Allen, F. H.Acfa Crysfallogr.,Sect. 8 1980, 836, 81, 1981, 837, 890, 1981, 837, 900, 1984, 840, 64, Tetrahedron 1982, 38, 2843, Allen, F. H.; Kennard, 0.; Taylor, R. Acc. Chem. Res. 1983, 16, 146. (4) SchBfer, L.J. Mol. Struct. 1983, 100, 51. (5) Boggs, J. E. J . Mol. Struct. 1983, 97, 1 , 1985, 130, 31. (6) (a) van Alsenoy, C.; Scarsdale, J. N.; Schafer, L. J . Comp. Chem. 1982,3, 53. (b) Schiifer, L.;van Alsenoy, C.; Scarsdale, J. N. J. Mol. Strucr. 1982, 86, 349. (7) (a) KovaEeviE, K.; MaksiC, 2.B. J. Org. Chem. 1974, 39, 539. (8) (a) Eckert-MaksiE, M.; MaksiE, Z. B. J . Mol. Struct. 1982, 86, 325, (b) MaksiE, Z. B.; Eckert-MaksiE, M. Ibid. 1983, 91, 295. (9) Deakyne, C. A.; Allen, L. C.; Laurie, V. W. J. Am. Chem. SOC.1977, 99, 1343.

0022-365418712091-2786$01.50/0 0 1987 American Chemical Society

Exo Double-Bonded Hydrocarbons

The Journal of Physical Chemistry, Vol. 91, No. 11, 1987 2787

compass semiempirical IMO, MIND0/3, and MNDO procedures and ab initio methods with STO-3G, 3-21G, and 4-21G basis sets. All computations were executed with full relaxation of nuclear coordinates except for some constraints on the methyl groups in (2) and (5) (vide infra). The results displayed in the following sections conclusively show that the double bond is substantially shortened when joined to small strained ring@). A property closely related to molecular geometries is strain energy which is an important indicator of chemical reactivity. It is considered here by making use of the idea of homcdesmotic reactions. The estimated strain energies assume appreciable values as expected on the basis of large angular distortions of the studied compounds.

Discussion of the Applied Methods Experimentally determined and theoretically predicted bond distances differ in general for two main reasons. The first source of discrepancy is that measured values in some cases give vibrationally averaged structures while the computed distances refer to the equilibrium distribution of the nuclei. Furthermore, there are inaccuracies inherent in both experimental and theoretical approaches. The electron diffraction (ED) technique is unable to distinguish between closely similar bonds whereas microwave spectroscopy (MW) suffers from ambiguities introduced by isotope substitution^.^ Shortcomings of the theoretically determined geometries can be traced to incompletness of basis sets and to unsatisfactory, if any, treatment of correlation effects. These effects are difficult to take into account to a significant extent in complex molecules. It is gratifying however, that the variation of the length of a given type of a bond in different chemical environments is well reproduced with moderate basis sets.1° It has been found that a good compromise between accuracy and efficiency is obtained by the 4-21G basis Theory at this level of sophistication is capable of predicting shifts in bond distances relative to a predetermined reference value. Therefore, we have employed the 4-21G set and the slightly smaller 3-21G which has a very similar performance. Standard minimum basis set (STO-3G) calculations were also performed for the purpose of comparison. All a b initio geometry optimizations were carried out by using the program package GAUSSIAN 82.13 The semiempirical I M 0 , 7 MIND0/3,14 and MNDOIS schemes were applied in their original forms. Their merits and drawbacks are well doc~mented.~~~~~~~ Results and Discussion Geometries. The molecules studied in this work, methylenecyclobutane (3), methylenecyclopropane (4), bicyclobutylidene (6),cyclopropylidenecyclobutane(7), and bicyclopropylidene (S), and the reference molecules ethylene (1) and tetramethylethylene (5) are shown in Figure 1 where also the numbering of atoms are included. The calculated bond distances are compared with available experimental data in Table I. In order to reduce the number of structural parameters to be varied, the methyl groups in (2) and ( 5 ) were assumed to have threefold symmetry. In (5) conformations having symmetries D2, DZh,C2*, and C2, were optimized. The lowest energy conformation was found to have D2 symmetry, and the optimized geometry parameters given in Table I are for this form. Perusal of the displayed experimental C=C bond distances do not exhibit a monotonic variation along the series 2-4 possessing the (C)2C=CH2 structural unit. On the contrary, one could conclude that C=C distances are ap(10) Skancke, P. N. Int. J . Quantum Chem. 1984,26, 729, and the references given therein. (11) Ditchfield, R.; Hehre, W. J.; Pople, J. A. J . Chem. Phys. 1971, 54, 724. (12) Pulay, P.; Fogarasi, G.; Pang, F.; Boggs, J. E. J . Am. Chem. Soc. 1979, 101, 2550. (1 3) GAUSSIAN 82, Release A. Binkley, J. S.; Frisch, M.; Raghavachari, K.; DeFres, D.; Schlegel, H. B.; Whiteside, R.; Fluder, E.; Seeger, R.; Pople, J. A. Carnegie-Mellon University, 1985. (14) Bingham, R. C.; Dewar, M. J. S.; Lo, D.H. J . Am. Chem. Soc. 1975, 97, 1285, 1975, 97, 1294, Bischof, P. J. Am. Chem. SOC.1976, 98, 6844, Croat. Chem. Acta 1980, 53, 51. (15) Dewar, M. J. S.;Thiel, W. J . Am. Chem. SOC.1977, 99,4899,4907, Bischof, P.; Friedrich, G.J. Comp. Chem. 1982, 3, 486.

1

2

3

4

5

6

5

I

2

2

0

Figure 1.

proximately constant if experimental errors are taken into account. This conjecture would be in harmony with qualitative theoretical arguments put forward by Allen et aL9 However, all theoretical methods (ab initio as well as semiempirical) applied in this work indicate a smooth decrease of the carbon-carbon double bond distance. The same holds for the series 5-8 involving a central (C),C=C(C), moiety. In the course of the calculations two independent experimental investigations of the geometry of 8 were performed. These results lend some credibility to our theoretical finding^.'^,'^ The first study involves X-ray and ED measurements of Traetteberg et a1.I6 Both experimental techniques reveal a shortening of the double bond (Table I). However, other CC bond distances offered by these two methods exhibit significant discrepancies which widely exceed the limits of experimental errors. This example shows once again that experimental data are not sacrosanct and that they should be constantly tested against the results of other experimental techniques and theoretical methods. In case of 8 the question arises which of two sets of (X-ray and ED) data is more reliable. Is the adjacent bond shortened and the distal bond stretched relative to the reference value found in cyclopropane? In this connection it is useful to invoke the X-ray data of Schenk” which for C(l)=C(l), C(l)-C(2), and C(2)-C(2) read 1.305, 1.467, and 1.539 A, respectively. They are in good agreement with the results of the IMO, MNDO, 3-21G, and 4-21G procedures and the ED data.16 Hence, it seems that the X-ray data of the ref 16 are in error. Further, it is beyond reasonable doubt that the C=C bond in 8 undergoes considerable compression although the value of the I M O bond distance is probably too low, because intramolecular repulsions are not explicitly included in the treatment. It should be kept in mind when comparing the 4-21G results with the measured values that the empirical “offset” corrections for the C=C and C-C (in cyclopropane) bonds are estimated to be 0.025 and -0.004 A, respectively.18 These empirical adjustments were obtained by using the experimental rg data as a reference. It appears therefore that the ab initio approach underestimates the central double bond too. Another striking feature of the ring containing molecules is that C-C bonds adjacent to a double bond are significantly shorter than distal bonds. This is borne out both by experiment and by theoretical methods except the MINDOJ3 method, which is particularly unsatisfactory for four-membered rings.I4 It should be pointed out that the MINDO/3 scheme gives too low a value for the C=€ bond distance in ethylene even within a scale defined by its own framework. On the whole, one can say that the (16) Traetteberg, M.; Simon, A,; de Meijere, A. J . Mol. Struct. 1984, 128, 333. (17) Schenk, H. Presented at the XI11 Congress of the International Union of Crystallography, Hamburg 1984.

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Eckert-Maksic et al.

TABLE I: Theoretical and Experimental Estimates of Bond Distances (in A) in Strained Small Ring Hydrocarbons Involving an Exo Double Bond“ compd bond IMO MNDO (MIND0/3) STO-3G 3-21 G 4-21 G exptl 1

c=c

1.338 1.085

1.335 1.084

( 1.314) ( 1.090)

1.306 1.073

1.316 1.079

1.313 1.082

1.337 (2)* 1.086

1.336 1.508 1.082 1.100

1.348 1.508 1.089 1.1 I O

(1.339) (1.498) (1.101) (1.112)

1.312 1.530 1.080 1.086

1.318 1.520 1.074 1.084

1.317 1.516 1.073 1.085

1.330 (3)‘ 1.508 1.072 1.095

1.321 1.522 1.556 1.08 1 1.094 1.094

1.333 1.520 1.553 1.089 1.105 1.105

(1.330) (1.522) (1.524) ( I . 100) (1.1 15) (1.113)

1.306 1.531 1.556 1.088 1.086 1.08 1

1.309 1.537 1.557 1.089 1.086 1.080

1.309 1.536 1.573 1.074 1.081 1.079

1.316 1.475 1.522 1.08 1 1.089

1.319 1.492 1.536 1.090 1.097

(1.31 8) (1.495) (1.486) ( 1.100) ( I . 107)

1.298 1.474 1.521 1.083 1.083

1.301 1.472 1.545 1.074 1.073

1.300 1.476 1.546 1.073 1.073

1.332f 1.457 1.542 1.088 1.090

1.330 1.512 1.100

1.368 1.51 1 1.110

(1 ,381)

(1.500) (1.112)

1.321 1.531 1.086

1.324 1.523 1.084

1.325 1.522 1.086

1.3519 1.51 1 1.110

1.311 1.521 1.556 1.093 1.093

1.330 1.520 1.553 1.105 1.105

(1.349) (1 S 2 3 ) (1.524) (1.114) (1.114)

1.306 1.531 1.557 1.089 1.087

1.303 1.535 1.575 1.082 1.080

1.304 1.536 1.574 1.081 1.079

1.338 (8)d 1.518 (7) 1.571 (8) 1.106 (8) 1.106 (8)

1.305 1.472 1.525 1.519 1.556 1.094 1.094 1.089

1.316 1.521 1.553 1.491 1.538 1.105 1.105 1.097

(1.335) (1.523) (1.524) ( I ,486) (1.495) (1.114) (1.114) (1,107)

1.297 1.533 1.556 1.474 1.520 1.089 1.087 1.083

1.293 1.537 1.557 1.475 1.546 1.089 1.082 1.082

1.298 1.524 1.560 1.467 1.533 1.082 1.080 1.074

1.298 1.475 1.522 1.089

1.302 1.496 1.538 1.097

(1.322) (1.485) (1.496) (1.107)

1.287 1.476 1.521 1.083

1.284 1.475 1.545 1.080

1.286 1.478 1.544 1.073

1.34d

1.527 1.556 1.12 1.09 1.09

1.304 (8)‘ 1.442 (6) 1.504 (7)

1.331 (3)‘ 1.517 (5) 1.565 (4) 1.104 1.104 1.104

1.314 ( I ) 1.468 (1) 1.554 (2) 1.099 (2)

Ethylene, isobutylene, and tetramethylene serve as etalons. Experimental errors are given in parentheses. Callomon, J. H.; Hirota, E.; Kichitsu, K.; Lafferty, W. J.; Maki, A. G.; Pote, C. S . In Landolt-Bomstein, Vol. 7, Hellwege, K. H.; Hellwege, A. M., Eds.; Springer-Verlag: Berlin, 1976. ‘Sharpen, L. H.; Laurie, V. W. J . Chem. Phys. 1963,39, 1732. dMalloy, Jr., T. B.; Fisher, T.; Hedges, R. M. J . Chem. Phys. 1970,52, 5325. This is an assumed structure obtained by guesses based on the structural data for cyclobutanone and isobutylene. eAllinger, N. L.; Mastryukov, V. S . Z h . Struct. Khim. 1983, 24, 172. flaurie, V. W.; Stigliani, W. H. J . A m . Chem. SOC.1970, 92, 1485. BCarlos, J. L.; Bauer, S. H. J . Chem. Soc., Faraday Trans. 2 1974, 70, 171. *Mastryukov,V. S . ; Tarasenko, N. A.; Vilkov, L. V.; Finkelshtein, E. Sh.; Jonvik, T.; Andersen, B.; Aanensen, E. Zh. Strukt. Khim. 1981, 22, No. 5, 57. ’X-ray geometry of Traetteberg, M.; Simon, A,; Peters, E. M.; DeMeijere, A. J . Mol. Struct. 1984, 118, 333. Electron diffraction geometry given in the preceding reference.

J

M I N D 0 / 3 method gives structural parameters which are less consistent than the more recent M N D O scheme. The IMO procedure predicts a shortening of the central bond in 5 (by 0.008 A) relative to ethylene contrary to the experimental finding and the other theoretical results. This may be a consequence of neglecting nonbonded repulsions in this approach. Nevertheless, the predicted I M O bond distance of 1.330 A is a useful piece of information, because it provides a rough estimate of the C==C bond lengthening (0.015 A) due to repulsions of the methyl groups in this molecule. It is a well-known fact that the C-H bond distances are usually not very well resolved by experimental X-ray and ED techniques. Consequently, theoretically predicted distances are of interest. It is apparent that C-H bond distances in methylene and the methyl groups differ, the latter being longer as revealed by all the calculation procedures, notably the IMO method where the elongation is found to be around 0.015 A. This is corroborated by careful analyses of “isolated” CH stretching frequencies and their linear relation to CH bond distances.Is It should be mentioned that predicted bond angles are in accordance with the observed values.

Numbers produced either by experiment or by theory usually have a message which should be decoded by physical models. It is gratifying that the trend in properties within the families of molecules 2-4 and 5-8 is easily interpreted in terms of the hybridization concept. For this purpose we computed hybridization indices from M I N D 0 / 3 and M N D O wave functions via the corresponding density matrices.lg They are compared with the IMO values in Table 11. One observes that the u part of the C=C bond in ethylene requires more s character than prescribed by the canonical sp2 value. Furthermore, the average s character of the C==€ bond emanating from a small ring is substantially increased due to rehybridization of the carbon junction atom. This is a consequence of the drift of s content from the adjacent C-C bond to the exo bond. Let us consider the IMO results for 4 which represents a typical case. Canonical sp2 hybridization would lead to considerable ring bond bending as evidenced by a deviation angle 6 = 29’ (the C(C=)C angle is 62’). The deviation angle can be diminished only by larger p-orbital participation in the ring, the IMO calculation predicting 6 = 25’ and an s character of the ring hybrid of 27.8%. This is significantly lower than 33.3%.

(18) McKean, D. C . ;Boggs, J. E.;Schafer, L. J . Mol. Srrucr. 1984, 116, 313.

(19) Trindle, C.; Sinanoglu, 0. J . Am. Chem. SOC.1969, 9 / , 853, MaksiE, 2. B.; RandiE, M. Ibid. 1973, 95, 6522.

The Journal of Physical Chemistry, Vol. 91, No. 11, 1987

Exo Double-Bonded Hydrocarbons TABLE 11: Hybridization Indices As Obtained by Semiempirical IMO, MINDO/3, and MNDO Methods

compd

bond

IMO - SB 36.8-36.8 31.5-31.5

MIND0/3 40.3-40.3 27.8

MNDO - sB 35.6-35.6 30.5

36.8-37.9 31.1-23.7 31.5 25.4

40.2-36.2 31.2-30.7 27.5 27.2

36.0-35.3 30.5-24.5 30.7 24.6

37.3-41.7 29.2-23.3 22.3-22.7 31.3 27.2 27.3

39.6-39.6 29.0-26.3 26.7-26.4 27.8 22.2 22.3

35.2-38.5 28.3-23.9 22.1-22.1 30.9 26.5 26.3

31.3-44.2 27.8-22.1 20.8-20.8 31.3 28.6

38.6-45.8 26.8-23.1 23.7-23.7 28.7 26.7

34.9-44.5 26.2-20.0 19.4-1 9.4 31.2 29.5

38.2-38.2 3 1 .O-24.0 25.3

36.4-36.4 30.6-30.7 22.2

36.1-36.1 30.5-24.6 24.5

4 1.5-4 1.5 29.2-23.2 22.3-22.7 27.2 27.3

39.0-39.0 29.0-26.3 26.8-26.3 22.2 22.3

39.4-39.4 27.9-21.8 22.4-22.0 26.5 26.4

44.1-41.7 29.2-23.7 22.3-22.8 27.9-22.5 20.5-20.5 27.0 27.2 28.5

45.2-38.2 29.7-26.2 26.6-26.2 26.8-23.1 23.7-23.7 22.2 22.3 26.7

44.1-39.1 29.1-22.4 22.1-22.1 27.0-20.0 19.3-19.3 26.5 26.4 29.5

44.2-44.2 27.9-22.1 20.8-20.8 28.5

44.1-44.1 27.6-23.1 23.8-23.8 26.7

43.7-43.7 27.3-1 9.9 19.4-19.4 29.5

SA

SA

- sB

Another reason for the increased p character is a tendency of hybrids, which form a bond, to achieve similar deviation angles20 and s/p composition.* We note in passing that the latter is equivalent to electronegativity equalization. Hence the resulting hybridization in the C(2)-C(3) bond is 27.8%-22.1% with the corresponding deviation angles 823 = 25' and 832 = 24'. These values should be compared with the 21.3%-21.3% hybridization in the cyclopropane ring and the corresponding deviation angle 6 = 23'. It should be recalled that bond bending of this magnitude causes considerable bond shortening (viz. cyclopropane) because this is the only way to increase overlapping even at the expence of somewhat increased repulsion of the nuclei. Since the C(2)-C(3) bond has both larger bending and s content than a C - C bond in cyclopropane, a substantial shortening occurs. Arguments along the same line show that the distal bond should be longer than in cyclopropane. This has also been pointed out by Traetteberg et al. in the case of Analogous rehybridization takes place in 3, but to a lesser extent as shown in Table 11. It is of interest to consider the average s characters of the C=C bonds in the series 2, 3, and 4. The s content monotonically increases assuming values 37.4, 39.5, and 40.8%, respectively. In a simple bonding picture increased s character means better overlapping and stronger and shorter C=C bonds. This finding is supported by the energy partitioning technique introduced first by Pople et al?I for the semiempirical schemes employing the ZDO approximation. KollmarZ2has shown that this type of energy (20) MaksiE, Z. B.; KovaEeviE, K.; Mogu'S, A. J . Mol. Struct. 1981, 85, 9.

(21) Pople, J. A.; Santry, D. P.; Segal, G. A. J . Chem. Phys. 1965, 43, 129.

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partitioning is chemically meaningful by numerous applications. The MNDO two-center C=C terms in the series 2-4 are -24.0, -24.5, and -25.0 eV, in accord with the increase in s characters. Similarly, bicentric E(C=C) terms in the series 5-8 are -23.5, -24.5, -25.0, and -25.5 eV, respectively, in agreement with the corresponding s character values of 38.2, 41.5, 42.9, and 44.2%. Hence, the highest s character and the strongest C=C bond is found in 8 as expected. Another point of interest is the difference between adjacent and distal bonds relative to the fusion center. It appears that the latter are weaker than the former in accordance with the bond distance variation. For example, E(C-C) terms for peripheral and adjacent bonds in 4 are -12.8 and -13.6 eV, respectively. The corresponding values in 3 are -13.9 and -14.6 eV. Importantly, these energy terms are transferable as they assume practically the same values in 6, 7, and 8: this is a chemically relevant finding. The same holds for hybridization indices characterizing the same type of a bond in different chemical environments. They are transferable to a high degree, being almost invariant (Table 11). Thus one can say that hybridization is an important determinant of the covalent bonds. One should also point out that hybridization parameters extracted from the MNDO wave functions are closer to the IMO estimates than the M I N D 0 / 3 indices. However, each method defines its own hybridization scale giving a fairly consistent picture within the adopted theoretical framework. Regarding the distal distance in 4 we may invoke the orbital interaction model for its interpretation. There is a hyperconjugative interaction between the occupied p u orbital and the highest, vacant Walsh orbital23of the ring. This orbital is antibonding in the region of the distal bond, thus reducing the electron density and weakening the bond. The net effect of such an electron transfer would add to the effect of the rehybridization thus enhancing the effect. As for the impact on the carbon-carbon double bond, the electron transfer through orbital interaction would induce a lengthening also of this bond. This effect is clearly overshadowed by the shortening induced by the rehybridization. It is, however, noteworthy that the predicted shrinkage of the double bond on going from 2 to 4 is comparatively small. Strain Energies. Strain energies are intimately related to chemical reactivity and are therefore of wide interest and importance. Strictly speaking, strain cannot be rigorously and unequivocally defined because ideal strain-free reference molecules do not exist. Nevertheless, there are reasonable ways of determining strain destabilization in molecules. The best are perhaps provided by hypothetical i ~ o d e s m i cand ~ ~homodesmic25chemical reactions. The homodesmotic reactions seem to be particularly convenient for this purpose, because the correlation effects cancel out to a large extent. Additionally, the influence of the zero-point energy should be practically zero because it is a linear function of the sort and number of atoms only.26 Applying this concept to the investigated compounds, one obtains two systems of gedanken homodesmotic reactions, which can be formally written as [c-(CH2),-,]C=CH2 + n(CH3CH3) (CH3)2C=CH2 + ( n - 1)(CH3CH2CH3)(1)

-

-

[C-(CH~),-~]C=C[C-(CH~),-,] + ( n + m)(CH,CH,) (CH3)2C=C(CH3)2 + ( n + m - 2)(CH3CH2CH3)(2) where both n and m assume values of 3 and 4. One observes that (22) Fischer, H.; Kollmar, H . Theor. Chim. Acta 1970, 16, 163. (23) The term Walsh orbital is used here in a loose way. The orbital in question has only symmetry and a number of nodes in common with the original Walsh orbital. The matter of truth is that the corresponding orbital composed of bent hybrid orbitals is much more realistic. The interested reader can find a comprehensive discussion of this topic in: Honegger, E.; Heilbronner, E.; Schmelzer, A. Nouu. J . Chem. 1982, 6, 519-526. Eckert-MaksiE, M.; MaksiE, 2.B.; Gleiter, R. Theor. Chim. Acta 1984, 66, 193. (24) Hehre, W. J.; Ditchfield, R.; Radom, L.; Pople, J. A. J . Am. Chem. SOC.1970, 92, 4796. (25) George, P.; Trachtman, M.;Bock, C. W.; Brett, A. M. Tetrahedron 1916, 32, 317. (26) Schulman, J. M.; Disch, R. L. Chem Phys. Lett. 1985, 113, 291.

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TABLE 111: Total SCF Energies, Heats of Formation, and Estimated Strain Energies As Obtained by the 4-31G Setn molecule E, AHI E, &(add) -79.1 15 93 -118.09345 -155.884 14 -233.84082 -193.659 71 -154.659 28 -309.397 33 -270.396 34 -231.39537

-20.1 -25.1 -5.7 -22.1 25.0 44.4 36.0 55.7 75.5

25.6 40.0 47.9 62.6 77.4

51.2 65.6 80.0

“Total energies in au; heats of formation and strain energies in kcal/mol

the number of primary, secondary, and quaternary carbon atoms is preserved in reactants and products. There is also an equal number of C C bonds classified according to the coordination numbers of the participating carbons. The main difference is the strain content inherent in the CC bonds of cyclic compounds. Hence, strain energy is by definition a negative change in enthalpy for reactions 1 and 2. If the heats of formation of compounds involved in reactions 1 and 2 are known, the corresponding strain energies of the cyclic molecules are readily obtained. One should keep in mind, however, that a system of homodesmotic reactions defines a particular scale for the measuring strain energy. It was recently shown by Wiberg% that the total molecular S C F energies can be converted to heats of formation by using empirical adjustments based on the idea of characteristic group equivalents. The corresponding values for the 4-21G basis set used here in treating energetic features are -39.54195, -38.96948, -38.97225, and -37.81888 au for CH3, CH2(alif), CH2(olef), and C(o1ef) moieties, respectively.26 Total energies and strain destabilizations are presented in Table 111. It is interesting to compare the estimated 4-3 1G strain energies for methylenecyclobutane (3) and methylenecyclopropane (4) with the available experimental values obtained by the same homodesmotic reactions.* Theoretical values for 3 and 4 are 25.6 and 40.0 kcal mol-], respectively, in good accord with the experimental data of 27.9 and 41.7 kcal mol-]. This is of importance because Wiberg’s estimate of the C(olef) group equivalent leans heavily on the single molecule (isobutene).26 Hence, it appears that the strain energy is well reproduced in 3 and 4 by the modest 4-3 1G basis, thus lending credence to results obtained for the remaining molecules of the set as well. It is worth mentioning that strain energies in 3 and 4 are higher than in the parent compounds cyclobutane and cyclopropane, respectively. This finding is in qualitative agreement with the increased bending of the hybrids describing ring C-C bonds. The effect is most pronounced a t the C-junction atom. An obvious mechanism of strain relief is the increase of the C-C(’j)-C angle where the carbon junction atom is denoted by CG). This is, however, accompanied by a decrease of other angles in the ring which increases the angular strain around the respective centers. Hence, enlargement of the C-C(j)-C angle in 3 and 4 is very small (2’). Another point of interest is additivity of the strain energy in polycyclic compounds which is intuitively appealing. Inspection of the results presented in Table 111 reveals that the strain in polycyclic compounds is indeed given approximately by a sum of strain energies of fragment molecules. More precisely, 4-31G strain energies in 6, 7,and 8 are consistently lower by -3 kcal mol-’ than the values suggested by the additivity, which can be ascribed to the energetic difference between =CH2 and ==C(CH3)2 moieties appearing in reactions 1 and 2.

Final Remarks Static description of molecules by atoms in their equilibrium

Eckert-Maksic et al. positions has its limitations. Nevertheless, it is one of the most important pilars of the phenomenological chemistry. Knowledge of molecular geometry offers information on the plethora of physicochemical properties of chemical compounds, both qualitative and semiquantitative in nature. Recent results of the promolecule model conclusively support this c o n j e c t ~ r e . ~In *~~>~~ this paper we considered structural features of small strained rings possessing an exo double bond. Our calculations conclusively show that a double bond attached to a strained ring is shorter than the corresponding double bond in the reference molecules provided by ethylene, isobutene, and tetramethylethylene. This effect is particularly pronounced in small bicyclic molecules joined by a common double bond, achieving its maximum in bicyclopropylidene. Fusion of small rings via a double bond causes simultaneously shortening of adjacent and lenghtening of distal C-C bonds. Angular distortions of rings are small. Although the basis sets employed in this work did not include polarization functions, we believe that more sophisticated calculations based on extended basis sets with polarization functions and involving a large portion of correlation energies will not alter our main conclusions. Theoretical results presented in this paper are of some importance because the experimental data are inconclusive for series 1-4 and incomplete for the molecules 5-8. In addition, the X-ray data of Traetteberg et for compound 8 are probably in error. We hope that the present study will stimulate experimental investigations of these intriguing molecules. Generally speaking, the need and importance of consistent sets of structural data for characteristic molecules obtained within a particular experimental technique backed by high-quality theoretical results cannot be overestimated. Structural features of the molecules in question can be interpreted at the qualitative level by the hybridization concept introduced by Pauling as early as 1928,30 which in turn proved very useful in rationalizing a large body of local and global molecular properties exhibiting characteristic bond a d d i t i ~ i t i e s . ~ - ~Rehybridization ’-~~ at the carbon junction atom shifts the s character to the double bond which should have interesting chemical consequences. For example, one can predict a substantial increase in the double bond energy, ’J(C=C) spin-spin coupling constants, stretching f r e q ~ e n c i e s etc. , ~ ~ in molecules 6-8. Experimental data are unfortunately nonexistent. Finally, the estimated strain energies seem to be reasonable. Some care has to be excercized because a detailed electron charge distribution in highly strained molecules is obtained only by large basis sets involving polarization functions. Nevertheless, we feel that the strain energies provided by 4-31G basis set are correct within a couple of kcal mol-]

Acknowledgment. This research has been supported by Norsk Hydros Fond and by the Self-Managing Authority for Scientific Research of the S R of Croatia. A part of this work was done at the Organisch-chemisches Institut der Universitat Heidelberg and M. E. M. and Z. B. M. thank Professor R. Gleiter for his hospitality and the Alexander von Humboldt-Stiftung for financial support. (27) Wiberg, K. B. J. Comp. Chem. 1984, 5, 197. (28) Spackman, M. A.; Maslen, E. N. J. Phys. Chem. 1986, 90, 2020. (29) MaksiE, Z.B.; KovaEek, D.; VidiE, B. Chem. Phys. Lett. 1986, 129, 619. J. Mol. Struct. 1987, 150, 71. (30) Pauling, L. Proc. Natl. Acad. Sci. U.S.A.1928, 14, 359. Pauling, L. J. Am. Chem. SOC.1931, 53, 1367. (31) Pauling, L. The Nature of the Chemical Bond, 3rd ed; Cornell University: New York, 1960. (32) Bent, H. A. Chem. Reu: 1961, 61, 275. (33) MaksiE, 2.B. Pure Appl. Chem. 1983, 55, 307-314. (34) Skancke, A.; Skancke, P. N.; Eckert-MaksiE, M.; MaksiE, 2. B. J. Mol. Srrucr., in press.