Journal of Molecular Structure (Theochem), 206 (1990) 89-98 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

89

MILLS-NIXON EFFECT IN BENZOCYCLOBUTENES

M. ECKERT-MAKSIC and D. KOVACEK

Ruder BoSkovib Institute, Bijenicka 54, P.P. 1016,410Ol Zagreb (Yugoslavia)

M. HODOSCEK

Boris KidriE Institute, Hajdrihova 19,610OO Ljubljana (Yugoslavia)

D. MITIC and K. POLJANEC

Joief Stefan Institute, Jamova 39, P.P. 53, 61111 Ljubljana (Yugoslavia)

Z.B. MAKSIC

Ruder BoSkoviC Institute, BijeniEka 54, P.P. 1016,410Ol Zagreb (Yugoslavia) and Faculty of Natural Sciences and Mathematics, University of Zagreb, MaruliCev trg 19, 41000 Zagreb (Yugoslavia)

(Received 15 June 1989)

ABSTRACT

The structural features of benzocyclobutenes were studied using several semiempirical and ab initio techniques. Qualitative hybridization arguments and actual 6-31G Hartree-Fock calcula- tions show conclusively that benzocyclobutenes exhibit a typical Mills-Nixon effect which is most pronounced in benzo [ 1,2:3,4:5,6]tricyclobutene. It is concluded that the experimental X-ray structure of the perfluoro derivative of the latter compound is seriously in error.

INTRODUCTION

The concept of hybridization, introduced by Pauling as early as 1928 [ 11, has proved very useful in discussing the bonding features of molecules. It de- scribes the response of an atom embedded in the intramolecular potential of the nearest neighbours, thus being a genuine effect. The physical content of the hybridization model is involved in the ability of polarized hybrid orbitals to accommodate lower local symmetries taking place in molecular environ- ments. Hybridization parameters and bond-overlap integrals can be used to correlate a large number of molecular physico-chemical properties [ 2-51. Fur- thermore, hybridization is the underlying principle which interconnects sev- eral observables which are otherwise unrelated. It was suggested, therefore, that hybridization is a hidden observable par excellence. For many relevant references the reader should consult the recent special issue of the Journal of Molecular Structure (Theochem) [ 61.

0166-1280/90/$03.50 0 1990 Elsevier Science Publishers B.V.

90

The maximum overlap method, particularly in its iterative form [ 71, yields reasonable estimates of the shape and size of hydrocarbons. These simple cal- culations have a surprising predictive power and can serve as forerunners of more advanced theoretical treatments. For example, rehybridization at the carbon junction atom(s) in small ring compounds possessing exo-double bond(s) indicates a considerable shift of s character to the latter. Conse- quently, an exo double bond emanating from the small rings should be stronger and shorter. Ab initio calculations carried out at STO-3G, 3-21G and 4-21G levels of accuracy have confirmed this expectation [ 81.

In the present paper we address the question of structural variation in ben- zocyclobutenes, because the experimental data are inconsistent (vide infra) .

In anticipation of forthcoming results it can be said that simple hybridization arguments and large basis set ab initio computations convincingly show that there is a pronounced bond fixation in the benzene nucleus, which is very sim- ilar to the original Mills-Nixon proposition [ 91.

STATEMENT OF THE PROBLEM

Mills and Nixon [9] observed that electrophilic substitution in the benzo- cycloalkenes (n = 3,4) depicted in Fig. 1 (a) is favoured in the pposition. They interpreted this finding by a double bond localization which prefers the Kekule structure shown in Fig. 1 (b). The molecules in question were indan (n = 3) and tetralin (n = 4). Although the experimental data which led to the Mills- Nixon hypothesis were not unambiguous [lo], subsequent CNDO/B studies of benzocycloalkenes [ 111 gave a distribution of CC bond distances in the ben- zene ring which was in accordance with original postulate. In other words, the bridge bond between the benzene moiety and the alicyclic ring was longer than the adjacent CC bonds in the six-membered ring, indicating increased bond localization and decreased aromaticity. The effect attenuates as the number of CH, groups (n) increases, in agreement with chemical intuition. For this pur- pose Cheung et al. [ll] calibrated CNDO/B distances on smaller fragment molecules and used empirical correlations for the CC

d(CC),=d(CC)c+0.001263 nH/[1.563-d(CC)c] A (1)

(a) b)

Fig. 1. (a) Schematic representation of benzocycloalkenes; (b) the predominating Kekul6 struc- ture according to Mills and Nixon.

91

and CH bond distances

d(CH),=d(CH),-0.008 (5-n,) A (2)

where the subscripts e and C correspond to the experimental and CNDO/B distances, respectively. In eqns. (1) and (2), nn denotes the number of hydro- gen atoms attached to the C atom(s) in question. The problem is not settled, however, by this semiempirical study; the available theoretical and/or exper- imental data are contradictory. The early calculations of Longuet-Higgins and Coulson [ 121 indicated an anti-Mills-Nixon effect. On the other hand a va- lence-bond treatment of benzocyclopropene by Hiberty et al. [ 131 gave results consistent with the Mills-Nixon hypothesis. This molecule received wide at- tention in view of its high strain. Ab initio SCF calculations on benzocyclopro- pene were performed by Apeloig and Arad [ 141 using STO-3G, 3-21G and 3- 21G* basis sets. It was concluded that the concept of bond fixation did not provide much help in rationalizing either the geometry or the reactivity of this system. Indeed, both bridge CC bonds of the two annelated rings and the ad- jacent CC bonds are shorter than in the parent benzene molecule. This finding is in agreement with the experimentally determined geometries of some heav- ily substituted benzocyclopropenes [ 151. However, a simple interpretation of the geometrical distortions upon fusion of benzene and cyclopropane rings is lacking at present.

The experimental data for the benzocyclobutenes, considered in the present work, are also controversial. Recent X-ray measurements on benzocyclobu- tene and benzo [ 1,2:4,5]dibenzocyclobutene showed a mild Mills-Nixon effect [ 161. On the contrary, the X-ray analysis of perfluoro- benzo [ 1,2:3,4:5,6] tricyclobutene showed no evidence of any bond alternation in the benzenoid fragment of the molecule. In fact, the bond distances and angles of the central ring were essentially identical to those of benzene itself [ 171. This result of course contradicts the much debated Mills-Nixon effect. Hence the problem deserves close scrutiny,

CALCULATIONS, RESULTS AND DISCUSSION

In order to shed more light on the problem defined above, the hybridization in benzene, durene and some benzocyclobutenes was calculated employing maximum overlap criterion and the available experimental geometries. The results presented in Table 1 show that there is a substantial rehybridization at the carbon junction atoms belonging to both the annelated rings. In benzocy- clobutene a substantial increase in s character is seen in the adjacent C (l)- C (3) bond relative to the gauge molecules benzene and durene. The hybrid orbital placed at C (1) and pointing to C (3 ) has the highest s character (38.3% ). Its bonding partner at the C (3) site also has an increased value of 35.7%, be- cause hybrids describing the same bond tend to achieve the same composition.

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TABLE 1

Hybridization indices in benzene, durene and some benzocyclobutenes as calculated using the maximum overlap and MNDO methods

Molecule Bond Maximum overlap MNDO

(a)*- (s)n Hybriddeviation (s)*- (s)e EAB

(%o) angles ( ’ ) (%) (eV)

1 1

0 2

s #

0 1

2 2

1 1

s

B 0 3

4 4

2

fl

0 3 1 1

2 2

C(l)-C(l) 34.4-34.4 C(l)-H 31.0

C(l)-C(l) 33.8-33.8 C(l)-C(3) 35.1-34.7 C(l)-C(2) 31.2-24.0 C(2)-H 25.3 C(3)-H 30.5

C(l)-C(1) 30.5-30.5 C(l)-C(3) 38.3-35.7 C(3)-C(4) 33.3-33.3 C(4)-C(4) 35.8-35.8 C(l)-C(2) 31.2-24.9 C(2)-C(2) 21.1-21.2 C(2)-H 27.0 C(3)-H 31.1 C(4)-H 30.9

C(l)-C(1) 31.3-31.3

C(l)-C(3) 38.3-34.0

C(l)-C(2) 30.5-23.2 C(2)-C(2) 21.9-21.9 C(2)-H 27.5 C(3)-H 31.9

C(l)-C(1) 31.3-31.3

2 C(2)-C(2) 21.6-21.6 C(2)-H 27.4

C(l)-C(1’) 37.6-37.6 C(l)-C(2) 31.1-23.5

s 11 0.8

6 11 0.9 s 13 0.9

6 31 0.9

6,, -8.5

6 13 7.7 s 31 5.3 6 34 0.4 6 6;

0.9 -0.8

8,z 14.5 s,, 10.2 S,, 10.6

61, -8.8

6 13 6.9 6;; 6 14.4 4.5

s,, 11.3

6 22 9.0

611 -8.4 S,l, 10.1 &, 10.1 612 14.9 S,, 11.6

6 22 9.0

32.8-32.8 31.9

33.2-33.2 - 19.67 33.1-33.1 - 19.96 31.3-24.0 - 15.44 24.6 - 12.40 31.3 - 12.86

27.9-27.9 - 17.79 38.0-32.9 -21.18 32.2-32.3 - 19.14 33.5-33.5 - 20.77 31.1-22.3 - 14.67 21.6-21.6 - 13.59 26.9 - 12.52 32.6 - 12.92 31.6 - 12.90

28.8-28.8 - 18.53 37.5-32.4 - 20.32 30.7-22.3 - 14.66 21.5-21.5 - 13.57 26.9 - 12.51 33.4 - 12.94

27.0-27.0 - 16.45 38.5-38.5 -22.66 31.9-22.4 - 14.72 21.6-21.6 - 13.61 26.8 - 12.51

This is a consequence of the maximum-overlap criterion [ 201. The question arises why a redistribution of s character takes place in fused rings? The inter- pretation is given by the fact that small rings prefer higherp character in order

93

to reduce bending and, consequently, the angular strain. The hybrids describ- ing the C ( 1) -C ( 1) and C ( 1) -C ( 2 ) bonds and centred at carbon junction atom C (1) possess 30.5% and 31.2% s character, respectively. Since the hybrid x31 has a slightly higher s character, its geminal neighbour x34 has a diminished value (33.3% ), thus inducing a decrease in the s content of its bonding partner x43. Concomitantly, there is a small increase in s character in the C (4)-C (4) bond. Hence, there is an alternation in average s character within the benzene ring which indicates that the C (1 )-C (3) and C (4)-C (4) bonds should be shorter than those in benzene, whilst the opposite should be the case in bonds C (1 )-C ( 1) and C (3)-C (4). The indicated bond alternation would be in line with the Mills-Nixon hypothesis. It is tacitly assumed here that bond distances are determined by the composition of G hybrids, the effect of n electrons being a perturbation imposed on the rr framework. This picture is essentially correct as evidenced by numerous studies of the geometries of hydrocarbons [ 3-51. The same pattern is found in benzo [ 1,2:4,5] dicyclobutene and benzo [ 1,2:3,4:5,6] tricyclobutene, compatible with a general conclusion that hybrids are to a high degree transferable and that similar structural groupings have almost the same distribution of s and p character. Hence it is concluded that in benzo [ 1,2:4,5] dicyclobutene the C (1 )-C (3) bonds should be stronger and shorter than the bridge C (1 )-C (1) bonds. Particularly strong bond local- ization is predicted in benzo [ 1,2:3,4:5,6] tricyclobutene because both hybrids forming the C (1)-C (1’ ) bond have a high s-content of 37.6%. This molecule is in fact a crown case because the experimental geometry employed implies equal C ( 1) -C ( 1) and C ( 1) -C ( 1’ ) bond distances and yet the maximum-over- lap hybridization strongly indicates their pronounced difference. The exo bonds C (1 )-C (1’ ) should be considerably shorter in accordance with the Mills-Nixon prediction. Apparently, bond alternation in benzocyclobutenes is a conse- quence of structural features and is dictated by a tendency of relieving angular strain in the four-membered ring (s ) . This conjecture is supported by an anal- ysis of the deviation angles of the hybrids (Table 1). The bond bending in benzene and durene is found to be very small (ca 0.9 ’ ); this could be an artefact of using a crude maximum overlap method, but it should be borne in mind that bond bending is a general feature [ 211 and that the present result may well bear some resemblance to the real situation. The fusion of a four-membered ring induces substantial angular strain in the benzene moiety as evidenced by the deviation angles 6,, = 7.7”) S,, = 5.3” and 6,, = - 8.5’. The most strained part of, for example, the benzocyclobutene system is due to the C (1 )-C (2 ) and C (2)-C (2) bonds with the corresponding deviation angles of 6,, = 14.5’ and f&,-s 22 = 10”. Two points are worthy of mention. First, the deviation angles of hybrids forming the same bond tend to be the same as required by a general theorem [ 221 and the C (1 )-C (1) bond is bent inside the six-membered ring. There is experimental confirmation of this finding, provided by the recent X- ray measurements of Boese and Bliiser [ 161. Examination of the X-X defor-

94

mation isopycnic (isodensity ) maps reveals that parts of the electronic charge are shifted outside the four-membered ring. In other words, the maximum of the electron density along the C (1 )-C ( 1) bond is placed off the centre of the straight line connecting the nuclei and inside the benzene ring. The appear- ance of bent bonds is also detected in the C (1 )-C (3) bonds. The same holds for benzo [ 1,2:5,6] dicyclobutene. Obviously, structural features are governed by the angular strain of the four-mem~red cycle (s ) .

It is noteworthy that hybri~ation indices can be deduced from the first- order density matrix of the SCF wavefunctions. This has been discussed sev- eral times [ 3-51 and the details need not be repeated here. It is gratifying that the widely different MNDO method gives very similar values of the s character as the maximum-overlap procedure (Table 1). Importantly, the values have the same transferability property which makes possible classification of chem- ical bonds by hybridization parameters. One can say, for instance, that the C (2 )-C (2 ) bonds in ~nz~yclobu~nes are considerably weaker than the C ( 1) - C (2 ) bonds emanating from the benzene moiety. Furthermore, the C (1 )-C ( 1’ ) bonds in benzo [ 1,2:3,4:5,6] tricyclobutene should be much stronger than the bridge C ( 1 )-C ( 1) bonds. These conclusions are substantiated by the MNDO energy partitioning technique discussed earlier [ 231. Bond-energy terms (Em) indeed reveal that bridge bonds are significantly weaker than the adjacent ones (Table 1). It should be pointed out that two-centre EAB values must only be used as a quali~tive index of the bond strength because they depend on the molecular geometry which is not very accurately reproduced by the MNDO scheme.

Hence, qualitative arguments at the semiempirical level indicate that the Mills-Nixon effect might be operative in benzocyclobutenes and that the ex- perimental structure of the perfluoro derivative of benzo [ 1,2:3,4:5,6] - tricyclobutene [ 171 is in error. It is therefore desirable to perform ab initio calculations employing good basis set (s ) which offer more ~re~bility. For this purpose, the present STO-3G, 3-21G and 6-31G SCF computations were made on the parent hydrocarbons. The resulting bond distances are compared with the experimental data in Table 2. In addition, some current semiempirical methods (MIND0/3, MNDO and AM1 ) and the force-field procedure MMBPI were also applied in order to test their performance. Since the 6-31G basis set seems to be well suited to aromatic systems, the results of the Hartree-Fock calculations employing these basis functions are discussed first. The general agreement with the X-ray data for benzocyclobutene and benzo [ 1,2:4,5] dicyclobutene is good. The calculations predict shortening of the adjacent bonds relative to the bridge bond of 0.011 (0.006) A and 0.006 (0.005) A for the first and second molecules, respectively, in reasonable ac- cordance with the experimental results given in parentheses. The effect is more pronounced in benzo [ 1:2,314 ] dicyclobutene where the interbridge C ( 1 )-C ( 1) bond is shorter by 0.030 A (Table 2). The most dramatic effect is seen in

95

TABLE 2

Bond distances in some substituted and annelated benzenes as obtained by semiempirical, ab initio and experimental methods

Molecule Bond Bond length (A) Exp.

MIND0/3 MNDO AM1 MMPPI STO- 3-21G 6-31G 3G

3

2

F\

0 1

4

2

#

0 1

3

2n2 1 1

3 0 0 J

4 4

3

8

0 3

1 1

2 2

3 2

1 P 0 1

2 1

4 4

Cl-Cl 1.447 1.424 1.405 1.405 1.381 1.395 1.401 Cl-C2 1.426 1.417 1.401 1.400 1.390 1.390 1.394 C2-C3 1.402 1.403 1.392 1.396 1.381 1.381 1.385 c3-c3 1.404 1.404 1.395 1.405 1.395 1.383 1.386 Cl-C4 1.495 1.509 1.482 1.508 1.526 1.526 1.520 C2-H 1.108 1.092 1.101 1.103 1.073 1.073 1.074 C3-H 1.105 1.091 1.099 1.103 1.073 1.073 1.074 C4-H 1.111 1.110 1.118 1.114 1.083 1.083 1.082

Cl-Cl 1.444 1.423 1.406 1.402 1.399 1.401S Cl-C2 1.420 1.411 1.397 1.399 1.393 1.393 Cl-C3 1.494 1.512 1.481 1.508 1.525 1.511 C2-H 1.110 1.094 1.101 1.102 1.084 1.097 C3-H 1.112 1.110 1.118 1.114 1.090 1.030

Cl-Cl 1.461 1.439 1.437 1.388 1.388 1.386 1.387 1.391b Cl-C2 1.513 1.515 1.509 1.506 1.529 1.538 1.525 1.518 c2-c2 1.536 1.575 1.537 1.599 1.571 1.599 1.582 1.576 Cl-C3 1.395 1.380 1.369 1.382 1.374 1.370 1.376 1.385 c3-c4 1.420 1.427 1.414 1.406 1.399 1.397 1.399 1.400 c4-c4 1.401 1.399 1.387 1.407 1.387 1.387 1.392 1.399 C2-H 1.114 1.105 1.110 1.115 1.089 1.081 1.083 C3-H 1.105 1.088 1.097 1.102 1.083 1.072 1.073 C4-H 1.106 1.091 1.100 1.103 1.088 1.073 1.074

Cl-Cl 1.455 1.432 1.428 1.390 1.390 1.390 1.392 1.399b Cl-C2 1.514 1.516 1.510 1.509 1.537 1.538 1.525 1.521 c2-c2 1.536 1.574 1.577 1.594 1.597 1.597 1.580 1.575 Cl-C3 1.408 1.398 1.387 1.392 1.382 1.382 1.386 1.394 C2-H 1.114 1.104 1.110 1.115 1.081 1.081 1.083 C3-H 1.105 1.086 1.100 1.101 1.071 1.072 1.073

Cl-Cl 1.383 1.356 1.344 1.371 1.365 1.361 1.367 Cl-C2 1.478 1.458 1.456 1.384 1.399 1.397 1.397 C2-C3 1.389 1.376 1.363 1.393 1.375 1.372 1.378 c3-c3 1.433 1.443 1.432 1.415 1.409 1.408 1.408 Cl-C4 1.513 1.514 1.509 1.501 1.529 1.538 1.525 c4-c4 1.536 1.575 1.575 1.608 1.572 1.599 1.582 C3-H 1.106 1.089 1.098 1.102 1.083 1.072 1.074 C4-H 1.114 1.105 1.099 1.115 1.089 1.081 1.083

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TABLE 2 (continued)

Molecule Bond Bond length (A) Exp.

MINDO/S MNDO AM1 MM2PI STO- 3-21G 6-31G 3G

Cl-Cl 1.492 1.473 1.471 1.389 1.454 1.408 1.406 1.388’ Cl-Cl’ 1.379 1.355 1.341 1.382 1.388 1.361 1.368 1.388 Cl-C2 1.512 1.512 1.506 1.505 1.523 1.538 1.525 1.508 C2-C2 1.536 1.575 1.576 1.614 1.571 1.598 1.581 1.582 C2-H 1.114 1.105 1.110 1.115 1.085 1.081 1.083

“Ref. 18. ‘Ref. 16. ‘Ref. 17.

benzo [ 1,2:3,4:5,6] tricyclobutene where the C (1 )-C (1’ ) bond is shrunk rela- tive to the C (1)-C (1) bridge bond by 0.04 A. This is in harmony with earlier qualitative discussion. Since the 6-31G set cannot fail to this extent and the perfluoro effect cannot be so pronounced it can safely be concluded that the experimental value [ 171 is in error. It is interesting to observe that the exper- imentalvalueofd[C(1)-C(1)]=d[C(1)-C1’)]=1.388~isequaltotheav- erage value of these two distances estimated using the 6-31G SCF procedure. The STO-3G basis set performs surprisingly well in view of the simplicity of the elementary functions used. On the other hand, the 3-21G set is somewhat disappointing because it yields too long C ( 1 )-C (2 ) and C (2)-C (2) bond dis- tances. As far as the performances of the semiempirical MIND0/3, MNDO, AM1 and MMBPI schemes is concerned, they leave much to be desired. The first three approaches correctly predict that adjacent bonds are shorter than bridge ones, but the differences are grossly overestimated. The force field MMBPI procedure yields more subtle estimates but fails seriously in benzo [ 1,2:5,6] dicyclobutene. Finally, it should be mentioned that all the sem- iempirical methods fail to give realistic C-H bond distances. In contrast, the 6-31G procedure nicely distinguish between sp3 and sp’ C-H bonds yielding quantitative information that is in agreement with that of an accurate exper- imental technique.

The bond angles deserve some attention because they illustrate deformation in shape caused by annelation. The estimated 6-31G angles in benzocyclobu- teneare:C(l)C(l)C(3)=122.3” (122.3°),C(1)C(3)C(4)=l16.10 (116.0”), C(3)C(4)C(4)=121.4” (121.7”), C(l)C(l)C(2)=93.7” (93.5”) and C(l)C(2)C(2)=86.3” (86.5”). The agreement with the experimental data cited in parentheses is excel!ent. The increase in the C (1 )C (1 )C (3) angle relative to benzene and the concomitant decrease in the C (1) C (3) C (4) angle to the low value of 116” is obviously a consequence of a tendency of a more

97

even distribution of the angular strain over the C (3 ) C (1) C (3) fragment. More specifically, the hybrid ~3~ deviation angle approaches the al3 value as far as possible, since overlap is then optimum. At the same time, the S,, deviation angle should be as low as possible. Both requirements are met by the afore- mentioned angular deformations. The same holds for benzo [ 1,2:4,5]~~yclobu~ne, but the effect of angular distortion is enhanced, as expected. The 6-31G bond angles are in fine accordance with experiment (given in parentheses): C(l)C(l)C(3)=123.7” (124.0”), C(l)C(S)C(l) =112.7” (l12.1°),C(l)C(l)C(Z)=93.5* (93.4”) and~(l)~(2)C(2) =86.5” (86.6”).

In conclusion, it has been shown conclusively that the benzocyclobutenes exhibit Mills-Nixon bond fixation in the aromatic nucleus. Theoretical argu- ments and actual 6-31G calculations strongly indicate that the X-ray structure determination of the perfluoro derivative of benzo [ 1,2:3,4:5,6] tricyclobutene is in error.

ACKNOWLEDGEMENT

A part of this work has been done at the Organish Chemisches Institut der Universitat Heidelberg and two of us (M.E.M. and Z.B.M. ) would like to thank Alexander von Humboldt-Sti~ung for financial support and Professor R. Glei- ter for hospitality.

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