Double-bond geometry in norbornene, sesquinorbornenes, and

Richard Vaughan Williams, , Michael E. Colvin and, Ngoc Tran, , Ronald N. Warrener and, Davor Margetic. Exceptionally Pyramidalized Olefins: A Theoret...
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J. Phys. Chem. 1993,97, 10021-10027

10021

Double-Bond Geometry in Norbomene, Sesquinorbornenes, and Related Compounds. A High-Level Quantum Chemical Investigation Max C. Holthausen and Wolfram Koch' Institut j3r Organische Chemie, Technische UniversitcTt Berlin, Strasse des 17. Juni 135, D- 10623 Berlin, Germany Received: June 16, 1993.

Quantum chemical ab initio calculations on the equilibrium structures and harmonic frequencies of norbornene,

syn- and anti-sesquinorbornene, tetracyclo[6.2.1.1 3*6.02.7]dodeca-4,9-diene, and related compounds at HF/631G(d) and the correlated MP2/6-31G(d) (and for norbornene also at higher levels of theory) are reported. With the exception of anti-sesquinorbornene, all structures show a nonplanar double bond. The extent of the double-bond pyramidalization is found to be considerably larger than previously predicted by theory. The results are compared to experimental data, and the agreement is excellent. In particular, the out-of-plane angle of the olefinic hydrogens in norbornene is for the first time in almost perfect harmony with the recently published neutron diffraction results for a derivative of norbornene. Assuming the same accuracy of our calculations for the other molecules considered, the gas-phase equilibrium geometries reported for these species are most likely the most exact structure determinations, theoretical or experimental, available so far. The decisive influence of electron correlation as well as selected substituent effects is discussed in light of the controversy regarding the origin of the nonplanarity of the double bond.

Carbon-carbon double bonds are usually planar: The two carbon atoms, which have a formal sp2 hybridization, and the four atoms attached to them lie in a common plane. Notable exceptions areobservedfor doublebondsincorporatedintostrained cyclic systems, where considerable deviations from planarity of the double bond can O C C U ~ . ~ - Closely ~ related to this unusual geometric feature is the observation that in such alkenes, where the two faces of the double bond are no longer equivalent, a pronounced *-facial stereoselectivity in addition reactions is found.415 One of the prototype strained olefins with a nonplanar double bond is norbornene (1; bicyclo[2.2.l]hept-2-ene; all structures are displayed in Chart I). It is experimentally well established that the reactivity of the double bond in norbornene is characterized by a substantial preference for attack from the ex0 side (Le. same side as the methylene bridge),@ and theoretical studies predict that the double bond is not planar but that the hydrogens are bent in the endo direction.l@l* Various explanations for this hydrogen out-of-plane bending have been put forward in the literature, based on either steric or electronic interactions, which will be discussed in more detail below in connection with our results. However, the obvious basis for an understanding of the nonplanarity of the double bond and its potential consequences for the r-facial stereoselectivity, Le. an accurate knowledge of the degree of nonplanarity the double bond in norbornene assumes, was lacking for a long time. Experimentally, the standard tool for geometry determination, X-ray crystal structure analysis, is in principle unsuitable for the reliable location of hydrogen atoms in a crystal. On the theoretical side, all previous investigationsof 1 and derivatives thereof were limited to either empirical force field, semiempirical,or ab initio model calculations using small or at best moderate one-particle basis sets. The effects of electron correlation have not been considered so far at all. The experimental uncertainty was only lifted very recently, when Ermer et al. reported their accurate neutron diffraction measurement of the simple norbornene derivative 2 (exo,exo-2,3-norbom-5-enedicarboxylic anhydride).I9 The key result of that study was that the hydrogens of the double bond in 2 were bent out of planarity by 7.3(2) and 7.5(2)O, Abstract published in Aduonce ACS Absrracrs, September 1, 1993.

respectively (in the crystal, 2 loses its strict C, symmetry). This result is in contrast to all theoretical predictions of the out-ofplane angle which, as shown in Table I, is computed to be much smaller at all levels of approximation used so far, being in the range between 1.7 and 4.9O. As already alluded to by Ermer et U I . , ~the ~ question of the origin of this discrepancy now needs to be addressed. The influence of the substituent and/or crystal packing is one explanation; the obvious other one questions the reliability of the available theoretical predictions. An accurate knowledge of the extent of nonplanarity of the double bond is of interest in its own right; in addition, the degree of bending is thought to be one of the decisive factors determining *-facial stereoselectivity. Thus we decided to settle this problem quantitatively by performing high-level ab initio calculations using extensivebasis sets and accounting for electron correlation effects in the geometry determinations of 1 and 2. In addition to norbornene itself, the related molecules syn- and anti-sesquinorbomene (3and 4, respectively)as well as tetracyclo[6.2.1.13.6.02.7]dodeca-4,9-diene(S), which consists of two norbornene units sharing a single bond, were included in our study. syn-Sesquinorborneneis known to have a strongly pyramidalized double bond. X-ray studies on various isomers yield out-of-plane angles on the order of 15-18O with the bending in an endo,endo fasion (i.e. moving the two ethylene bridges toward each other).2@23 Houk et al. reported MM2 force field calculations on the parent compound which yield an angle of 14" and partial ab initio geometry determinations with the minimal STO-3G basis set which gave 9.7O .I3 Semiempiricalcalculations employing the MIND013 or MNDO schemes, on the other hand, predicted an almost planar double-bond geometry.22 In their elaborate experimental and theoretical study of syn- and anti-sesquinorbornenes, Ermer and BMecker24 reported that force field calculationson 3using the CFF parameters result in two different isomers, corresponding to bending in the exo,exo and endo,endo fashions, the former being more stable than the latter by 2.2 kcallmol with very large out-of-plane angles of 36.7 and 26.2O, respectively. Using X-ray techniques, the same authors found for a derivative of anti-sesquinorbornene(4) an out-of-plane angle of 13.2O,24 in distinct contrast to those in the crystal structures obtained by Watson et a1.20 and Paquette et aI.:3 who reported an essentially planar double bond for slightly different derivatives, respectively.

0022-365419312097-10021$04.00/0 Q 1993 American Chemical Society

Holthausen and Koch

10022 The Journal of Physical Chemistry, Vol. 97, No. 39, 1993

CHART I: Structures 1-8' 7

._.I

a

2

6

2, c s

1, c s

6

0

7

Ermer and BiMecker also performed CFF molecular mechanics calculations on the parent compound 4. A nonplanar molecule with a deviation from planarity as large as 35.6O resulted, while earlier and only partial STO-3G optimizations resulted in a planar double bond. Ermer and BBdecker attribute this apparent overestimation of the nonplanarity as well as the failure of their calculations to reproduce the experimentally observed endo,endosyn-sesquinorbornenesas the favored isomer of 3 to inadequacies of the force field to reproduce the local double-bond geometry in such systems. Nonplanar double bonds are also predicted by force field calculationsfortetracyclo[6.2,1.13~6.~~']d~~-4,9-diene (S), and the X-ray structure determination of a derivative supports this conclusion.15 Interestingly,the olefinic hydrogens are bent inside, i.e. toward each other. For this molecule, the force field calculations as compared to the X-ray data underestimate the degree of bending: 3.1O calculated for 5 vs 8.1 (2.1") measured for one of the double bonds in the derivative 6 (the other double bond is almost planar in the crystal). In the original publication,'S 5 was described as a very peculiar molecule due to the small distance of the two double bonds and consequences for the thermally forbidden dimerization of two ground-state ethylenes werediscussed. Thisinterpretation was, however, later questioned by the same authors.19 For all these molecules, we report high-level quantum chemical calculations which provide a much more accurate and detailed picture of the structural features. The discrepancies between the X-ray data and the theoretical predictions obtained so far are resolved. In particular, the degree of out-of-plane bending in these prototype molecules is for the first time predicted theoretically in a precise and consistent fashion. Theoretical Methods Using the Gaussian 92 all structures have been fully optimized in the specified point group symmetry.2' Basis sets employed for 1 ranged from polarized sets of 6-31G(d) and 6-311G(d) quality up to basis sets with f- and d-type polarization functions on C and H, respectively, such as 6-3 1lG(3df,3pd). All other structures have been treated using 6-31G(d). The effects of valence electron correlation have been estimated by secondorder M~ller/Plessetperturbation theory (MP2). In addition, for 1, a HOMO/LUMO two-configuration (TC) SCF/631G(d) geometry optimization was carried out.?* The harmonic vibrational frequencies have been obtained at the MP2/6-3 1G(d) or HF/6-3 1G(d) levelof theory. For detailson the theoretical procedures, the reader is referred to the excellent discussion by Hehre, Radom, Schleyer, and P ~ p l e . * ~

8, cs

Results and Discussion

2

1

6

9, c s

The numbering of the atoms is based on norbornene and thus with the exception of 1 does not follow IUPAC rules.

TABLE I: Out-of-PlaneAngles for Norbomene (1) Previouslr Predicted bv Theow theoretical level out-of-planeannle (den) MM2 force field 1.7 CFF force field 4.5 extended Hiickel 4.2 MNDO 0.3 STO-3G ab initio 4.9 3-21G ab initio

4.8

ref 12 15 14

this work 10 17

An essentially planar double bond was also found by Gajhede et al. for the unsubstituted anti-sesquinorbornene.Z~In their work,24

Norbornene (1) and exqex~2,3-Norborn-S-enedicarboxylic Anhydride (2). The norbornene derivative 2 is the only species in this context for which a reliable experimental structure is a~ailable.1~ As already pointed out above and shown in Table I, the experimentally measured degree of out-of-plane bending of the double bond in 2 exceeds the theoretically predicted data by roughly a factor of 2. In the discussion of this result, Ermer et al. conclude that it should be very unlikely that crystal packing or the substituent effectis responsible for this discrepancy between the neutron diffraction result for 2 and the theoretical estimates reported for l . I 9 Thus, it seems that the previous calculations were not performed at a level well suited for an adequate description of the double-bondgeometry. To quantitatively check this supposition, we optimized the geometry of norbornene (1) and of the derivative 2 using levels of theory much higher than those reported earlier. For 1, a series of geometry determinations with increasing sophistication of the theoretical level was carried out to investigate the convergence of the structural parameters

The Journal of Physical Chemistry, Vol. 97, No. 39, 1993 10023

A High-Level Investigation of Double-Bond Geometry

TABLE Ik Geometrical Data (Bond Lengths in A, Angles in deg) and Total Energies (hartrees) for 1 and 2 structure 2 (C,)

structure 1 (C,) HF/ 6-31G(d)

TCSCF/ 6-31G(d)

MP2/ 6-31G(d)

MP2/ 6-31G(d,p)

-270.861 84

-270.889 96

-271.768 98

-271.849 72

Cl-C2 C2-C3 C146 C546 C1-C7 Cl-H C2-H C6-&/C8 C 6 - k C7-hb C7-H" C7-0 10 c7-09

1.522 1.322 1.556 1.557 1.539 1.082 1.075 1.084 1.086 1.083 1.087

1.522 1.344 1.555 1.558 1.539 1.083 1.075 1.085 1.084 1.084 1.087

1.513 1.348 1.558 1.553 1.538 1.093 1.086 1.096 1.094 1.094 1.097

Cl-C2-C3 Cl-C7-C4 C 1-C2-H H-C7-H

107.6 93.5 124.8 109.5

107.2 93.7 124.9 109.4

107.3 93.8 125.1 110.0

5.8

8.2

7.9

MP2/ 6-311G(d)

HF/ 6-31G(d)

MP2/ 6-31G(d)

-271.866 22

-570.060 03

-571.735 07

1.515 1.351 1.561 1.555 1.540 1.093 1.086 1.095 1.093 1.094 1.097

1.523 1.322 1.562 1.540 1.540 1.080 1.074 1.513 1.081 1.081 1.086 1.175 1.359

1.514 1.349 1.567 1.535 1.540 1.093 1.086 1.512 1.093 1.093 1.097 1.206 1.400

1.519, 1.518 1.342 1.572, 1.573 1.541 1.544 1.094, 1.096 1.083, 1.084 1.501, 1.508 1.098, 1.099 1.096 1.100 1.193, 1.198 1.392, 1.384

107.7 93.7 124.6 108.7

107.4 94.0 124.9 109.3

107.3, 107.7 94.0 124.8, 124.6 109.0

4.7

6.8

7.3.7.5

exv

E L M

Bond Lengths 1.512 1.348 1.558 1.552 1.538 1.089 1.081 1.091 1.089 1.090 1.093

Selected Bond Angles 107.3 107.3 93.9 94.0 125.1 125.2 110.1 110.2 Out-of-PlaneAnnle 718 7.9 I

a Reference 18. "Cis" and "trans" with respect to the double bond. with increasing quality of the calculation. For the larger system 2, only HF/6-31G(d) and MP2/6-31G(d) optimizations were performed. The results obtained at these levels are compared to Ermer's neutron diffraction data for 2 in Table 11. Several conclusions become evident from the comparison. First of all, the overall agreement between the theoretical and experimental data for 2 is excellent. Even at the uncorrelated HF/6-31G(d) level of theory, most of the bond distances are computed within 0.01 A (rms error = 0.0042 A). Exceptions are the double-bond distance, which is predicted to be too short by 0.02 A, the C-H bond lengths, which are systematically underestimated by some 0.014-0.018 A, and the C-O single bond length, which is 0.025 or 0.033 A shorter than the corresponding experimental bond length. Bond angles are reproduced within less than a degree already at HF/6-31G(d). The most important deviation from the experimental geometry concerns the out-of-plane angle, which at HF/6-31G(d) is computed as 4.7 as compared to 7.5" (or 7.3"). Inclusion of electron correlation leads to a significant improvement; the theoretically predicted geometry is in almost quantitative agreement with the neutron diffraction results. The difference in the double-bond length has decreased to 0.007 A, and the computed C-H bond lengths almost quantitatively coincide with the experimental ones. The largest error occurs for the C-O single bond length, which is 0.008 or 0.016 A longer at MP2/6-3 1G(d) than in the experimentalstudy (it should be noted that for this bond the crystal structure shows the largest deviation from C, symmetry). The rms error for the bond lengths has decreased to 0.0017 A. Most notable is the effect on the outof-plane angle: The bending of the double bond is increased by more than 2O upon inclusion of electron correlation. The resulting angle of 6.8O is now only 0.5 or 0.7" smaller than that in the experiment. Thus, it is clear that crystal packing effects are indeed negligible for 2. That also the substituent has almost no effect on the geometry is evidenced by the comparison of the computed MP2/6-31G(d) data for the parent molecule 1 with those of 2 (Table 11). Only the C 1 4 6 and C 5 4 6 bonds in 1 are slightly shorter than the corresponding C-C single bonds in 2. This effect was already mentioned by Ermer et al.19 The second, more important, difference occurs again for the out-ofplane angle. It is computed as 7.9" in 1, thus 1.1" larger than that in 2. Further improvement of the theoretical level to MP2/

6-3 lG(d,p), i.e. addition of p-type polarization functions on hydrogen, and to MP2/6-311G(d), i.e. adding an additional sp shell to the basis set, does not significantly change the MP2/ 6-31G(d) results for 1. In particular, no effect on the out-ofplane angle is observed upon increasing the basis set. At the HF level, it is computed to be smaller by 2.1 ",closely resembling the situation observed for 2. The harmonic frequency describing the out-of-plane motion (a') of the olefinic hydrogens appears at HF/6-3 1G(d) at 813 cm-1, while inclusion of electron correlation lowers it to 733 cm-1. The corresponding out-of-plane bending frequency in ethylene is computed as 1095cm-l (HF/6-31G(d)) and 989 cm-' (MP2/6-31G(d)). Theenergetical consequenceof the pyramidalization of the double bond is, however, only marginal. The bending potential is rather flat, and optimizing 1 without allowing the double bond to become nonplanar results in a structure being merely 0.5 kcal/mol less stable than completely optimized norbornene.30 Since the nonplanarity of thedouble bond is the most important parameter in the current investigation, we further studied its variation with increasing size of the basis set at the Hartree/ Fock level. Improvement of the basis set by adding more and higher angular quantum number polarization functions and a third set of sp functions has only a marginal effect on this angle. Even using the very large 6-31 lG(3df,3pd) basis set, the angle is still computed to be very similar: 6.0". Thus, the inclusion of electron correlation is crucial for obtaining realistic out-of-plane angles while the 6-3 1G(d) basis set suffices to describe the oneparticle problem. sym (3) and m&Sesquinorbornene (4). The key structural parameters of 3 and 4 optimized at HF/6-31G(d) and MP2/ 6-3 1G(d) are summarized in Table 111. In contrast to the results of the force field calculations reported in ref 24, but in agreement and with the available crystal structures of derivatives of PZ3 the known preference of ex0 attack in thermal additions, only the C;, symmetric endo,endo-syn-sesquinorbornene is found as a minimum structure. All attempts to locate the corresponding exo,exo isomer, even without the C, symmetry constraint, failed. Thedouble bond is nonplanar, and the out-of-planeangle assumes a value of 16.4O at MP2/6-31G(d), in very satisfying agreement with the X-ray structures in which this angle is between 15.4 and 18.0°, depending on the substituent. At the HF/6-31G(d) level,

Holthausen and Koch

10024 The Journal of Physical Chemistry, Vol. 97, No. 39, 1993

TABLE III: Geometicd m t a ( ~ o n dLength in A, Angles in deg) and Total Energies (hnrtrees) for 3 and 4 structure 4 (Cu) structure 3 (Cb) HF/ 6-31G(d)

MP2/ 6-31G(d)

HF/ 6-31G(d)

MP2/ 6-31G(d)

-463.680 89 -465.250 91 -463.677 27 -465.245 35

Bond Lengths 1.516 1.324 1.560 1.558 1.546 1.083 1.083 1.086 1.083 1.087

1.505 1.361 1.562 1.553 1.546 1.094 1.093 1.096 1.094 1.098

1.517 1.320 1.559 1.560 1.547 1.082 1.083 1.086 1.084 1.088

107.7 94.8 107.4

108.2 94.5 109.3

P

4 2.0 2

1.507 1.354 1.561 1.556 1.548 1.094 1.094 1.096 1.095 1.099

1.0

-

0.0

0

16.4

0.0

107.9 94.8 107.7

40

50

MP2/6-31G(d)

Total Energies -462.477 49

-464.039 75

Bond Lengths

0.0 C1-C2 C2-C3 C146 (25x6 C1-C7 C1-H C2-H C6-H c7-H&a C7-H””

I

1.520 1.320 1.562 1.564 1.548 1.083 1.075 1.086 1.084 1.086

1.510 1.348 1.563 1.562 1 S47 1.094 1.086 1.098 1.095 1.098

Selected Bond Angles

30.0 .

3

30 Dialonion p]

HF/6-31G(d)

a “Cis” and “tran with respect to the double - md.

’O.O

20

TABLE IV Geometries (Bond Lengths in A, Angles in deg) and Total Energies (hartrees) for 5

Out-of-Plane Angle 13.0

10

Figure 2. Out-of-plane bending potential (HF/6-31G(d)) for antisequinorbornene (4).

Selected Bond Angles Cl-C2-C3 108.2 Cl-C7-C4 94.5 H-C7-H 109.5

{ 3.0 d

Total Energies C1-C2 C2-C3 C1-C6 C546 C1X7 Cl-H C6&@ C6-Hma C7-G’ C7-H”’

5’01 4.0

c

Cl-C2-C3 Cl-C7-C4 H47-H Cl-CZ-H

20.0

I

107.9 93.5 109.4 124.9

107.6 93.8 110.0 125.3

Out-of-PlaneAngle

0.0

5.7

Dirlonion p]

Figure 1. Out-of-plane bending potential (HF/6-31G(d)) for sesquinorbomene (3).

syn-

the out-of-plane angle is computed as 13.0°, too small by 3.4‘, following the trend already found for 1and 2. The out-of-plane bending potential in Ck has been investigated by scanning the out-of-plane angle between +40 and -60’ (positive angle corresponds to endo,endo bending) at the HF/6-31G(d) level. All remaining geometrical parameters have been optimized at each point of the scan. The resulting, very flat potential curve is displayed in Figure 1 and reveals that there is indeed no minimum for the exo,exo isomer. As expected for such a flat bending potential, the computed HF/6-3 1G(d) harmonic frequency for the out-of-plane bending mode (al) has a very low frequency of 135 cm-1. That this frequency is much lower for 3 (and 4; see below) than for 1 is of course also partially due to the different masses involved. anti-Sesquinorbornene (4), which at MP2/6-3 1G(d) is computed to be less stable than the syn isomer by 3.5 kcal/mol, was predicted by Ermer et al. to be nonplanar, on the basis of force field calculations and an X-ray structure determination of a derivative.24 This conclusion is not supported by our theoretical results, which unambiguously show that at least the parent compound has a planar, C2h symmetric equilibrium structure in the gas phase. This result is in qualitative agreement with the early low-level and only partial ab initio STO-3G structure determinations of Houk et aL13 and the crystal structures for different derivatives obtained by Watson et al.20 and Paquette et al.23and for the parent compound itself.25 As can be seen from

7.3

a “Cis” and “trans” with respect to the double bond. the bending potential for anti-sesquinorbornene determined at HF/6-31G(d) and shown in Figure 2, the out-of-plane bending in anti-sesquinorbomene is extremely facile. This is corroborated by the calculation of the harmonic vibrational frequencies of 4 at HF/6-3 lG(d). The vibration describing the out-of-plane bending is very low, amounting to merely 81 cm-*. Thus, it is not surprisingthat, depending on the actual substituent,derivatives of 4 may assume a planar double-bond geometry in the crystal or a nonplanar one. T e t r a c y c 1 ~ 6 . 2 . 1 . 1 ~ ~ . ~ ~ ~ - 4 , (5). 9 - d The i e n final e compound included in our study is the Ca symmetric species 5. The geometrical parameters predicted theoretically at HF/6-31G(d) and MP2/6-3 1G(d) are collected in Table IV. Also, 5 shows the typical effect of endo bending of the olefinic hydrogens characteristic of norbornene derivatives. Interestingly,the hydrogens are bent inward, Le. toward each other. The computed out-ofplane angle is 5.7 and 7 . 3 O at HF/6-31G(d) and MP2/63lG(d), respectively. These values are only marginally smaller than the results obtained for the parent compound 1 (5.8 and 7.99. Thus, the hydrogens of the two double bonds are still sufficiently far apart (MP2/6-31G(d), 2.785 A) that steric repulsion does not significantly counteract the inward bending. The double-bond distance in 5 is computed as 3.019 and 2.922 A at HF/6-31G(d) and MP2/6-31G(d), respectively. The optimized parameters of 5 are in general very similar to those of 1. Thus, fusing a second norbornene unit across the C 5 4 6 single bond does not substantially alter the structure of the individual norbornene skeletons. Even though the two double bonds are

A High-Level Investigation of Double-Bond Geometry

The Journal of Physical Chemistry, Vol. 97, NO. 39, I993

relatively close to each other, this hardly seems to have any particular effect on the out-of-plane bending of the olefinic hydrogens. The only significant changes between the geometries of 1 and 5 occur for the C5-C6 and the Cl-C7 bonds, which are both stretched by 0.009 A upon fusion, while, for example, the double-bond distance is computed to be the same (1348 A) in both molecules. The analysis of the HF/6-31G(d) harmonic vibrational spectra supports the similarity of norbornene and 5. Most importantly, the two ("out-of-phase" (al) and 'in-phase" (bz)) out-of-plane bending modes for the olefinic hydrogens of 5 appear at 603 and 820 cm-1, in the same region as the corresponding a' frequency in 1 (813 cm-'; see above). Early force field calculations of 5 by Ermer3I led to a surprisingly low double-bond distance of 2.756 A. The same calculation gave an out-of-plane angle for the double bonds of only 3.1'. A subsequent X-ray structural determination of the derivative 6 by Ermer, B&lecker, and Preut15revealed, however, that the force field underestimates the double-bond distance as well as the out-of-plane angle significantly. In the crystal, the two double bonds are separated by 2.921 A, while the out-ofplane angle for the double bond at the unsubstituted side is 8. 1' (2.1'). The other double bond is virtually planar (0.8' (1.8')). Keeping in mind that the errors connected with the localization of the positions of the hydrogens in the X-ray structure determination are much larger than those typical of the neutron diffraction data available for the norbornene derivative 2, the experimental results are in excellent agreement with our best theoretical estimate for the parent compound 5. The rather large discrepancy between the force field calculation and the X-ray data was initially attributed to the situation particular for 5: strong through-space repulsion between the u orbitals of the close double bonds, which is only insufficiently accounted for in the force field parameters. However, as discussed above, the computed structural data, and in particular the nonplanarities of the double bond, are very similar for 1 and 5. Hence, it is safe to assume that, in contrast to this assumption, there are no additional interactions present in the latter compound responsible for the out-of-plane bending of the olefinic hydrogens.32 The largest difference between our theoretically obtained structure of 5 and the crystal structure of 6 is the almost planar double bond of the substituted norbornene unit. To investigate this difference, we performed a geometry optimization on 6 also. Due to the large size of this molecule and the loss of symmetry, we were, however, limited to the HF/6-31G(d) level of theory. In addition, most of the geometrical degrees of freedom of the phthalic acid substituent were frozen in the optimization to the HF/6-31G(d) values for isolated phthalicacid. Our calculations for 6 support the conclusion that the substituent leads to asymmetric bending of the two double bonds, but to a smaller extent than found experimentally: 4.6' for the unsubstituted norbornene unit and 3.0' for the substituted one. Electron correlation will probably increase the out-of-plane bending by 1.5-2'. That introduction of an electron-attracting substituent leads to a decrease of the out-of-plane bending in norbornene has been observed earlier by, e.g., Rondan et a/.11and Wipff and Morokuma.10 In fact, replacing the phthalic acid substituent in 6 with other electron-attracting groups such as -F, -OH, -0CH3, and -OC(O)CH3 gives the following out-of-plane angles for the double bonds at the unsubstituted and substituted norbornene units, respectively (at HF/6-31G(d)): -F, 5.7 and 4.7'; -OH, 5.9 and 4.6';-OCH3, 5.9 and 4.7';-OC(0)CH3,5.6 and 5.2'. Also, this substituent effect is not particular for 5; e.g., fluorine substitution at C7 syn to the double bond in norbornene itself produces exactly the same out-of-plane bending of 4.7' at HF/ 6-31G(d). Interpretation. The origin of the nonplanarity of the double bond in norbornene and related systems has been the subject of vivid discussion, and there are a large number of papers dealing

10025

SCHEME I: Torsional Interaction in Norborene (1) Shown by a Newman Projection along the C2-Cl and C 3 4 4 Single Bonds 7

6

S

SCHEME Ik Hyperconjugative Interaction in Norbornene (1) Shown by a Newman Projection along the C2-C1 and C3C4 Single Bonds 7

s

u[Cl-C6]

with this subject. Roughly speaking, there are two main lines of argumentation. The first group of investigationsemploy torsional interactions (which in electronic terms correspondto the exchange repulsion of electrons in u orbitals), as introduced in this context by Schleyer some 25 years ago.6 An example is the recent discussion of 1 and 2 by Ermer et al., according to which the driving force for the endo bending is to be sought in the decrease of the torsional strain around the C 1 4 2 single bonds.19 Endo pyramidalization leads to a more staggered, thus more favored, orientation, as shown in Scheme I. Almost the same point of view has been adopted by Burkert in his analysis.l* Houk and co-workers come to a similar conclusion,1l913 making torsional repulsions responsible for the pyramidalization. Gleiter and Spanget-Lar~en,l~.~3 on the other hand, attribute the observed nonplanarity to hyperconjugative interactions between the u orbital and cyclopentane ribbon orbitals. Also, Vogel and coworked6 and Castro et a1.l' conclude that u / r interactions are the dominant factor influencing the nonplanarity of the double bond. Veryrecently, Rastelliet using their model to analyze intramolecular interaction^,'^ stated that the nonplanarity of the double bond occurs in the direction of increasing stabilizing interactions between the u orbital and the u allylic orbitals. Even though our study is mainly aimed at providing accurate equilibrium geometries, our results contribute some new aspects to this discussion. An important observation is the decisive role of electron correlation in obtaining correct out-of-plane angles in the molecules at hand. The MP2 results, however, do not allow an unambiguous distinction between hyperconjugationand torsional interactionas the origin of this effect. Due to theordering of the orbital energies, the most pronounced hyperconjugative interaction in 1 will be between the u orbitals describing the C 1 4 6 bond and the antibonding u* orbital of the double bond (Scheme 11). To investigatethis further, we performed a TCSCF optimization of 1 involving the 16a' HOMO and 11V' LUMO. These orbitals mainly describe the bonding and antibonding C2C3 u orbitals, respectively, with small contributions to the C1C6 u orbitals but virtually no contribution to the allylicor olefinic CH bonds. Hence, if torsional effects are responsible for the correlation effect of the pyramidalization of the double bond, the TCSCF calculation cannot account for this, while hyperconjugative effects are partially covered by this wave function. AS shown in Table II, the TCSCF/6-31G(d) optimization leads not only to the expected lengthening of the u bond, due to the occupationofthe** orbital byO.O9electron, but also toanincrease

Holthausen and Koch

10026 The Journal of Physical Chemistry, Vol. 97, No. 39, 1993

TABLE V

Geometrical Data (Bond Lengths in A, Angles in deg) and Total Energies (hprtrees) for 7-9 structure 9 (C,), X = N structure 8 (CJ,X = C* structure 7 (CJ,X = b HF/6-31G(d)

MP2/6-31G(d)

HF/6-31G(d) EtOl

-243.286 17

-244.085 92

-269.577 05"

Xl-C2 C2-C3 X146 C5-C6 Xl-C7 C2-H CGHezo C 6 H d C7-Hd C7-HWb

1.567 1.353 1.598 1.635 1.593 1.078 1.084 1.083 1.080 1.083

1.550 1.387 1.592 1.637 1.587 1.090 1.093 1.093 1.088 1.092

1SO4 1.331 1.534 1.586 1.534 1.074 1.084 1.083 1.08 1 1.085

Xl-C2-C3 Xl-C7-X4 H-C7-H

100.6 74.5 113.0

99.5 73.5 141.1

16.7

20.5

MP2/6-31G(d)

HF/6-31G(d)

MP2/6-31G(d)

-270.430 05"

-302.807 11

-303.779 49

1.489 1.363 1.532 1.593 1.532 1.087 1.094 1.093 1.092 1.095

1.454 1.319 1.489 1.565 1.489 1.071 1.083 1.081 1.079 1.083

1.462 1.345 1.509 1.564 1.509 1.084 1.094 1.091 1.091 1.095

105.6 89.8 111.0

108.5 99.5 110.4

108.8 100.8 111.3

11.2

3.3

5.0

Bond Lengths

Selected Bond Angles 106.1 89.8 110.4

Out-of-PlaneAngle 7.6

* (9) = 2.018. b'Cis" and "trans" with respect to the double bond. of the out-of-plane angle to 8.2" compared to the HF/6-31G(d) data. This is a clear indication of the importance of hyperconjugation in these compounds. As a geometrical consequence of the hyperconjugation in 1, the C 1 4 6 bond, from which electrons are donated into the T* orbital, should be longer than that in norbornane, where such interactions is not possible. In fact, the C 1 4 6 bond is elongated by 0.02 A when going from norbornane to norbornene (MP2/6-3 lG(d)). Similar results were found for many carbocationic systems, where inclusion of electron correlation leads to a much more pronounced preference for nonclassical, bridged structures, which for these species are due to C-C or C-H hyperconjugati~n.~~~* In the discussion of torsional effects,oneof the main interactions was ascribed to the repulsion of the olefinic C-H bonds and the C-H bonds at the bridgeheadcarbons(Scheme II).12*1g Molecules without such bonds at bridgehead centers 1 and 4 should thus exhibit a much less pronoun4 pyramidalization of the double bond if torsional effects aredominant. TOcheck this, wecomputed data for 1,Cdiazanorbornene (7), the triplet 1,4-norbornene diradical(8), and 1,Cdiboronorbomene (9) (Table v). One must, of course, keep in mind that these species differ from in many respects, particularly due to the additional strain introduced by the trivalent bridgehead atoms. Nevertheless, the comparison of 7-9 with norbornene allows for an interesting discussion of eventualconsequencesof torsionalvs hyperconjugativeinteraction. In 7, where a 4-electron destabilizing interaction is still possible between the olefinic C-H bonds and the nitrogen lone electron pair, the is bond is nonplanar, but the out-of-plane only diminished to 5.0'. In the diradical 8, this 4-electron interaction reduces to a 3-electron interaction and a further decrease of the pyramidalization is expected if torsional effects are dominant. However, the MP2/6-3 1G(d) optimization leads to an increased angle of 11.2'. No such interaction is possible in the boron compound 9, and an even smaller pyramidalization is expected. The opposite takes place: a huge out-of-planebending of the olefinic hydrogens of 20.5O is computed for 9. That pyramidalization is smaller in 7 than in 1, while it is larger in 9 is, however, in line with hyperconjugative interactions: Replacing C-H by N (B)will lead to a decrease (increase) in the energy of the respective donor ,, C-N (B) orbitals. Compared to that in 1, hyperconjugation will be less favorable in 7, while it will be more pronounced in 9. Following this argumentation, an increase of hyperconjugationis also expected upon decreasing the orbital energy of the aoceptor T * orbital. Indeed, replacing both olefinic hydrogens by fluorine, yielding 2,3-difluoronor-

bornene, leads to an increased out-of-plane angle of 10.8O (at MP2/6-31G(d)). ~

~

~

~

l

~

In this study we presented ab initio quantum chemical calculations on the structures of norbornene, syn- and antisesquinorbornene, and some related compounds at a considerably higher level than previously reported. The focus of our work is mainly the degree of pyramidalization of the double bond. The following conclusions emerge: (i) Electron correlation is crucial for obtaining accurate results for the out-of-plane angle. Even using very large basis sets, the Hartree/Fock approximation yields out-of-planeangles Some 20 smaller than those at thecorrelated level. Force fieldcalculations, which have been frequently u s 4 in previous studies, do not seem to be adequate for quantitatively determining such structures, due to shortcomings in their parametrization. (ii) Our MP2/6-31G(d)-optimized equilibrium geometry for the norbornene derivative2 is in virtually quantitative agreement with the neutron diffraction structure of 2. The substituent has only marginal influence on the structure of parent norbornene (1). The most notable difference is the even slightly larger nonplanarity of the double bond in 1, which assumes a value of 7-90.

(iii) syn-Sesquinorbornene (3) has a nonplanar double bond of 16.40. Bending occurs solely in endo,endo fashion, antiSesquinorbornene (4) has a planar double bond in the gas phase, The out-of-plane bending potential is extremely flat, explaining the observation of planar and nonplanar double bonds in crystal structures, depending on the substituent. (iv) The fusion of a second norbornene unit across the ( 2 x 6 single bond, yielding tetracyclo[6.2.1.13~6.0*.7]dodeca-4,9-diene (5)s has hardly any effect on the geometry of the individual norbornene units* (v) The important role of electron correlation in obtaining reliable out-of-plane angles of the double bond as well as the observed substituent effects Pints to the importance of hyperconjugation in addition to torsional effects in determining the extent of the nonplanarity of the double bond in these systems. Acknowledgment. We owe many thanks to Prof. 0. Ermer (Kbln) for pointing out this problem to us and for interesting and helpful discussions and comments. Financial support by the Fonds

i

A High-Level Investigation of Double-Bond Geometry

der Chemischen Industrie and the Gesellschaft von Freunden der Technischen Universitiit Berlin is gratefully acknowledged. References and Notes ( 1) Greenberg, A.; Liebman, J. F. Strained OrganicMolecules;Academic Press: New York, 1978. (2) Wagner, H. U.;Szeimies, G.; Chandrasekhar, J.; Schleyer, P. v. R.; Pople, J. A,; Binkley, J. S.J . Am. Chem. Soc. 1978, 100, 1210. (3) Bordon, W. T. Chem. Rev. 1989, 89, 1095. (4) Mazzocchi, P. H.; Stahly, B.; Dodd, J.; Rondan, N. G.; Domelsmith, L. N.; Rozeboom, M. D.; Caramella, P.; Houk, K. N. J . Am. Chem. Soc. 1980,102,6482. (5) Burdisso, M.;Gamba, A.;Gandolfi,R.;Toma,L.; Rastelli,A.;Schiatti, E. J . Org. Chem. 1990,55, 3311. (6) Schleyer, P. v. R. J . Am. Chem. Soc. 1967,89, 701. (7) Fahey, R. C. Top. Stereochem. 1968,3,237. ( 8 ) Huisgen, R.; Ooms, P. H. J.; Mingin, M. N.; Allinger, N. L. J. Am. Chem. Soc. 1980, 102, 3951. (9) Huisgen, R. Pure Appl. Chem. 1981,53, 171. (10) Wipff, G.; Morokuma, K. Tetrahedron Lett. 1980, 21,4445. (1 1) Rondan, N. G.; Paddon-Row, M. N.; Caramella, P.; Houk, K. N. J . Am. Chem. Soc. 1981, 103, 2436. (12) Burkett, U. Angew. Chem. 1981, 93,602. W.L.;Madura, (13) Houk,K.N.;Rondan,N.G.;Brown,F.K.;Jorgensen, J. D.; Spellmeyer, D. C. J . Am. Chem. Soc. 1983, 105, 5980. (14) Spanget-Larsen. J.; Gleiter, R. Tetrahedron 1983, 39, 3345. BWecker, C. D.; Preut, H. Angew. Chem. 1984,96, 57. (15) Ermer, 0.; (16) Carrupt, P.-A,; Vogel, P. THEOCHEM 1985, 124, 9. (17) Castro, C. R.; Dutler, R.; Rauk, A.; Wieser, H. THEOCHEM 1987, 152, 241. (18) Rastelli, A.; Cocchi; M.; Schiatti, E.; Gandolfi, R.; Burdisso, M. J . Chem. SOC.,Faraday Trans. 1990,86,783. (19) Ermer, 0.;Bell, P.; Mason, S.A. Angew. Chem. 1989, 101, 1298. (20) Watson, W. H.; Galloy, J.; Bartlett, P. D.; Roof, A. A. M. J. Am. Chem. Soc. 1981, 103,2022. (21) Ermer, 0. Tetrahedron 1974,30, 3103. (22) Hagenbuch, J.-P.; Vogel, P.; Pinkerton, A. A.; Schwarzenbach, D. Helv. Chim. Acta 1981, 64, 1818. (23) Paquette, L. A.; Kravetz, T. M.; Hsu, L.-Y. J . Am. Chem. Soc. 1985, 107,6598. (24) Ermer. 0.;BWecker, C. D. Helv. Chim. Acta 1983, 66, 943.

The Journal of Physical Chemistry, Vol. 97, No. 39, 1993 10027 (25) Gajhede, M.; Jsrgensen, F. S.;Kopecky, K. R.; Watson, W. H.; Kashyap, R. P. J. Org. Chem. 1985, 50,4395. (26) Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M. W.; Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M. A.; Replogle, E. S.;Gomperts, R.; Andres, J. L.; Raghavacbari, K.; Binkley, J. S.;Gonzalez, C.; Martin, R. L.; Fox, D. J.; DeFrces, D. J.; Baker, J.; Stewart, J. J. P.;Pople, J. A. Gaussian 92, Revision A,; Gaussian Inc.: Pittsburgh, PA, 1992. (27) Using standard thresholds in the optimization. Employing tighter thresholds did not lead to any noticeable changes in the equilibrium geometry of 1. (28) The TCSCF calculation has been performed employing GAMESS: Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Jensen, J. H.; Koseki, S.; Gordon, M. S.;Nguyen, K. A.; Windus, T. L.; Elbert, S . T. QCPEBull. 1990, 10, 52. (29) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; Wiley Interscience: New York, 1986. (30) One of the reviewers suggested that vibrational averaging over the bending vibrational mode might be responsible for the large experimental out-of-planeangle. Since the stepwisecomputed bending potential (at 6-3 1G(d)) is fairly symmetric, this is very unlikely. (31) Ermer, A. Aspekte von Kraflfeldrechnungen; W. Baur Verlag: Miinchen, Germany, 1981. (32) Of course, there is an interaction of the two r orbitals of the double bonds leading to a r +and r- combination. The computed splitting (6-31G(d)) of 1.51 eV is in good agreement with photoelectron spectroscopy results of 1.26 eV: (a) Martin, H.-D.; Schwesinger, R. Chem. Ber. 1974,107,3143. (b) Prinzbach, H.; Sedelmayer, G.; Martin, H.-D. Angew. Chem. 1977,89, 111. (33) Gleiter, R.; Spanget-Larsen, J. Tetrahedron Lett. 1982, 23, 927. (34) Rastelli, A.; Cocchi, M.; Schiatti, E. J . Chem. Soc., Faraday Trans. 1990, 86, 777. (35) Koch,W.;Liu,B.;DeFrees,D.J.J.Am.Chem.Soc.1989,111,1527. (36) (a) Sieber, S.;Buzek, P.; Schleyer, P. v. R.; Koch, W.; Cameiro, J. W. d. M. J. Am. Chem. Soc. 1993, 115, 259. (b) Cameiro, J. W. d. M.; Schleyer, P. v. R.; Koch, W.; Raghavachari, K. J. Am. Chem. Soc. 1990,112, 4066. (37) Schleyer, P. v. R.; Carneiro, J. W. d. M.; Koch, W.; Raghavachari, K. J. Am. Chem. Soc. 1989, 111, 5475. (38) (a) Koch, W.; Schleyer, P. v. R.; Buzek, B.; Liu, B. Croar. Chem. Acta 1992,65,655. (b) Schleyer, P. v. R.; Koch, W.; Liu, B.; Fleischer, U. J. Chem. SOC.,Chem. Commun. 1991,1098.