Journal of Molecular Structure (Theochem), 285 (1993) 187- 194 0166-1280/93/$06.00 0 1993 - Elsevier Science Publishers B.V. All rights reserved

187

The Mills-Nixon effect in trindan and some related tris-annelated benzeneP

M. Eckert-Maksik”, Z.B. MaksiC*>“, M. HodoSEekb, K. PoljanecC

“Ruzer BosXoviC Institute, 41001 Zagreb, Croatia bDepartment of Health and Human Services, National Institute of Health, Bethesda, MD 20892, USA “Joief Stefan Institute, Jamova 39, 61111 Ljubljana, Slovenia

(Received 12 February 1993; revision accepted 2 March 1993)

Abstract

Structural features of trindan and some related tris-annelated benzenes are examined by the SCF 3-21G procedure. It turns out that the central fragment exhibits characteristic albeit rather weak Mills-Nixon (MN) type of distortion in all studied systems. This finding is in agreement with some available accurate X-ray data. In trindan, however, X-ray measurements are less precise thus yielding less conclusive evidence. Nevertheless, if upper and lower levels of the experimental errors are taken into account, the MN effect just might be operative in this molecule too. Both theoretical and experimental geometries are interpreted in terms of the rehybridization concept caused by fusion and redistribution of the a-density arising due to hyperconjugation with CH, groups of annelated carbocycles. Both mechanisms act sinergistically in the same direction leading to MN deformations.

Introduction

The effect of small-ring fusion on the geometry of benzene and its physico-chemical properties has attracted considerable attention in the past since it embodies an interplay of the two opposing effects: angular strain destabilization and aromatic stabili- zation [l]. In particular, c-strain imposed by the five-membered cycloalkene in indan should lead to different reactivity toward electrophilic substitu- tion reactions at a and p positions as put forward by Mills and Nixon [2]. Recent ab initio studies have conclusively shown that the original Mills- Nixon (MN) hypothesis was correct [3]. However, interest in strained fused aromatic compounds has not been continuous or constant but has exhibited

*Corresponding author - also at the Faculty of Science and Mathematics, The University of Zagreb, Marulicev trg 19, 41000 Zagreb, Croatia. aDedicated to the memory of Professor T. Skerlak who was shot dead in Sarajevo in May 1992.

low and peak periods. For example, Boyko and Vaughan stated in the sixties that: “For a number of reasons, most modem workers in the field con- sider MN original explanation (hypothesis) to be obsolete” [4]. Later work, mostly theoretical, has lead to a renewed scrutiny of the MN systems being in harmony with the authentic conjecture [5-71. More recently, however, a number of NMR measurements and interpretation thereof have again cast some doubts on the existence of the MN effect [8]. This scepticism is supported by some X-ray data in several fused benzene rings [4,9,10]. In this situation we felt it worthwhile to undertake a rather systematic theoretical study of annelated strained organic aromatic compounds both substituted [11,12] and unsubstituted [13- 151. Most of the theoretical results have been dis- cussed in a review article [ 161, hence, we shall only briefly mention that the MN effect occurs in a number of fused systems although there are some exceptions. In particular, MN deformations of the

188 M. Eckert-Maksid et al./.J. Mol. Struct. (Theochem) 285 (1993) 187-194

aromatic nuclei can be tuned by judicious choice of substituents placed at particular molecular sites. Further, anti-MN distortions seem to take place in benzoborirene, benzocyclopropenyl cation [ 171 and in some perfluoro compounds [12]. As a part of this large project we examine here the MN effect in trindan, dicyclopentenobenzocyclobutene and some related molecules. They are depicted in Fig. 1 which also shows the numbering of the atoms. These molecules are of some interest since X-ray measurements could not find any significant alternation of bond lengths in the benzene ring [4,10], at least not within the experimental errors. The aim of the present calculations is to test whether the MN distortion is indeed absent in these systems or not and to provide interpretation of the predicted structural features in terms of bond indices.

2

Methodology

If the question of fine differences in bond lengths within the benzene ring in an annelated system is examined, the theoretical method has to be selected rather carefully even if closely related molecules are considered. The method of choice has to be eco- nomical enough to be feasible in a large system and yet it has to reproduce faithfully the main struc- tural features. Our extensive calculations have shown that the 3-21G basis set performs rather well in parent hydrocarbons [13,15] yielding results which are close to those obtained by larger 6-31G and 6-31G* basis sets. Their quality in the quantitative sense can be further improved by the scaling procedure [18]. It appears that the 3-21G procedure gives essentially correct answers although the extent of the MN effect is overesti- mated. Some care has to be exercized, however,

7

a

9

6 1 _ . &=j:o $A&+-& 11

Fig. 1. Schematic representation of the studied compounds and numbering of atoms.

h4. Eckert-MaksiC et al./J. Mol. Struct. (Theochem) 285 (1993) 187-194 189

when systems involving heteroatoms possessing lone pairs are explored. Then calculations at the 6-31G* level seem to be “conditio sine qua non”

WI. In this work only pure hydrocarbons are exam-

ined and consequently the 3-21G basis set is adopted in the SCF calculations for practical rea- sons. We shall see later that the results obtained offer a consistent picture. All structures have been fully optimized within the given point group sym- metry.

Results and discussion

Structural Features

The estimated 3-21G structural parameters for trindan and some related tris-annelated benzenes are given in Table 1 (the monoannelated benzocy- clobutene (1) and benzocyclopentene (2) are pre- sented for comparison). The geometries of 1 and 2 are taken from earlier papers [13,14] and their predicted geometries are compared with the avail- able X-ray data. It should be mentioned that the measured values for 2 correspond to average struc- tural parameters for a number of benzocyclopen- tenes where substituents at position 8 are restricted to C, N and 0 atoms [20]. Carbon skeletons of all molecules can be considered planar except for the outermost C atom of the five-membered rings. This finding is in accordance with experimental results. Perusal of the presented results shows that the calculated bond angles are in very good agreement with the experimental values (see Table 1). More specifically, annelation of the four- and five-mem- bered rings in 1 and 2 leads to squeezing of the central benzene C( l)-C(2)-C(3) angles whereas C(2)-C( 1)-C(6) and C(2)-C(3)-C(4) angles are correspondingly enlarged. They give an insight into distribution of the angular strain over the benzene fragment imposed by fusion of a smaller ring. It should be noted in passing that all benzene angles are equal (120”) in systems exhibiting Dsh symmetry, for example, compounds 5 and 6 (see Fig. 1). In spite of that one can distinguish two

different C-C bonds (vide infra). We shall focus now on the bond lengths in 1 and 2. Both theore- tical and experimental results reveal a slight aniso- tropy in C-C bond lengths, the annelated bonds being somewhat longer than exo ones. This is con- sistent with the MN-type of deformation. Aniso- tropy of these bonds can be measured e.g. by the difference in the bond lengths A = 0.016 (0.006) A and A = 0.008 (0.011) a for 1 and 2, respectively, experimental results are given in parentheses. Both structures reveal bond alternation compatible with the KekulC schemes depicted in Fig 1. It should be noted however, that the variation in bond lengths is rather weak. A more pronounced diversity is expected in tris-annelated compounds. This is indeed the case as evidenced by the anisotropies in bond lengths for the compounds 3-6 which assume A values between 0.02 and 0.05 A. It is illustrative that annelated bonds belonging to five-membered rings are somewhat shorter than those joining four-membered carbocycles with a benzene fragment (see compounds 5 and 6). This is compatible with higher amount of strain in the latter small rings. The same underlying mechanism apparently leads to shorter exo bonds bridging two four-membered rings than those between either four- and five-membered carbocycles or two anne- lated cyclopentenes. For example, the bond lengths of C(5)-C(6) and C(l)-C(2) in 3 and C(3)-C(4) in 4 are 1.362, 1.370 and 1.383 A, respectively, exhi- biting an expected increase along the series. Simi- larly, the exo bonds in 5 and 6 assume values of 1.361 and 1.375 A, respectively. The experimental X-ray data for 4 and 6 have unfortunately large errors. Hence, it is impossible to draw a convinc- ing conclusion about C-C bond length variations in the benzene moieties. They are possible but uni- form distribution of bond lengths in 4 and 6 cannot be excluded. It is gratifying that there is an accurate experimental determination of the structure of 5 by Boese et al. [19] which shows obvious bond alter- nation in the MN sense. The difference in A values between exo- and fused-bond distance is 0.023 A which is significant. By extrapolating this finding to compounds 3 and 4 one is inclined to conclude that

190

Table 1

M. Eckert-MaksiC et al./J. Mol. Struct. (Theochem) 285 (1993) 187-194

Structural parameters in (poly)annelated benzenes involving four- and five-membered rings as calculated by the 3-21G basis set. The hybridization s-characters and n-bond orders are obtained by the MNDO method by using 3-21G geometries

Molecule Bond 3-21G basis set

s-Character

W)

T-Bond order

1

Bond length (2)

Bond angle (deg)

2 Bond length (A)

Bond angle (deg)

3 Bond length (A)

Bond angle (deg)

W )-C(6) 1.386 (l.391)a 29.4-29.4 0.61

C(l)-C(2) 1.370 (1.385) 37.2-32.4 0.70

C(2)-C(3) 1.397 (1.400) 32.6-32.8 0.63

C(3)-C(4) 1.387 (1.399) 33.1-33.1 0.70

C(l)-C(8) 1.538 (1.518) 30.3-21.5 0.14

C(7)-C(8) 1.599 (1.576) 21.3-21.3 0.18 C(2)-C( 1)-C(6) 122.3 (122.3) C( 1)-C(2)-C(3) 116.3 (116.0) C(6)-C( 1)-C(8) 93.9 (93.5) C(2)-C(3)-C(4) 121.6 (121.7)

‘71)-C(6) C(l)-C(2) C(2)-C(3) C(3)-C(4) C(1 )-C(9) C(8)-C(9) C(2)-C( 1)-C(6) C( 1)-C(2)-C(3) C(6)-C( 1)-C(9) C( 1)-C(9)-C(8) C(7)-C(8)-C(9) C(2)-C(3)-C(4)

C(~)-CVJ) 1.397 30.3-30.0 0.59

C(l)-C(2) 1.370 37.6-35.4 0.72

C(2)-C(3) 1.405 32.0-32.0 0.59

C(5)-C(6) 1.362 37.4-37.4 0.72

C(l)-C(8) 1.539 29.6-21.5 0.13

C(7)-C(8) 1.599 20.5-20.5 0.07

C(2)-C(9) 1.516 30.6-23.1 0.14 C(9)-C( 10) 1.568 22.7-22.6 0.08

C(6)-C(7) 1.537 30.6-21.4 0.13 C(l)-C(2)-C(3) 118.2 C(2)-C(3)-C(4) 118.2 C(3)-C(4)-C(5) 123.1 C(4)-C(5)-C(6) 118.6 C(2)-C(3)-C( 11) 111.7 C(2)-C(9)-C( 10) 104.7 c(9)-c(lo)-c(ll) 107.2 C(l)-C(6)-C(7) 93.7 C(6)-C(7)-C(8) 86.2 C(7)-C(S)-C( 1) 86.3 C(6)-C( 1)-C(8) 93.9

1.388 (1 .393(4))b ’ 32.2-32.2 0.64 1.380 (1.382(3)) 35.5-32.9 0.67 1.388 (1.391(3)) 33.1-32.9 0.66 1.385 (1.381(3)) 33.1-33.1 0.68 1.521 30.1-22.9 0.14 1.559 22.5-22.4 0.08

120.5 (120.8(2)) 119.2 (118.2(2)) 110.9 (108.0(5)) 102.8 105.0 120.4 (120.9(2))

M. Eckert-MaksiC et al./J. Mol. Strut. (Theochem) 285 (1993) 187-194 191

Table 1 (continued)

Molecule Bond 3-21G basis set

s-Character

(“/)

T-Bond order

4

Bond length (A)

Bond angle (deg)

5 Bond length (A)

Bond angle (deg)

6 Bond Iength (A)

Bond angle (deg)

C(l)-C(6) 1.387 (1.39 f 0.01)’

C(l)-C(2) 1.370 (1.39 f 0.01)

C(2)-C(3) 1.396 (1.40f0.01)

C(3)-C(4) 1.383 (1.38 f 0.01)

C(l)-C(8) 1.538 (1.53 +O.Ol)

C(7)-C(8) 1.600(1.57&0.01)

C(2)-C(9) 1.517 (1.51 f 0.01) C(9)-C( 10) 1.567 (1.54f0.01) C(2)-C( 1)-C(6) 121.7 (122.0 zt 0.3) C( l)-C(2)-C(3) 117.2 (116.4 xk 0.3) C(2)-C(3)-C(4) 121.1 (121.6f0.3) C( l)-C(6)-C(7) 94.0 (93.3 f 0.1) C(3)-C(2)-C(9) 111.8 (111.6f0.3) C(2)-C(3)-C( 11) 111.8 (110.5 k0.3) C(9)-C( lO)-C( 11) 107.1 (108.5 f 0.4)

C(l)-C(6) 1.408 (1.413)d

C(l)-C(2) 1.361 (1.390)

C(l)-C(8) 1.538 (1.525)

C(7)-C(8) 1.598 (1.579) C(6)-C( 1)-C(2) 120 (120) C(l)-C(6)-C(7) 93.6

C(lF-36) 1.393 (1.395 f 0.011y

C(l)-C(2) 1.375 (1.387f0.010)

C(l)-C(9) 1.521 (1.544kO.014)

C(8)-C(9) 1.561 (1.568 kO.018) C(6)-C( 1)-C(2) 120.0 (120) C(l)-C(6)-C(7) 111.0 (112.5 kO.8) C(6)-C(7)-C(8) 103.2 (101.5 f 0.6) C(7)-C(8)-C(9) 105.3 (110.5 f 2.0)

30.3-30.3 0.61 37.4-35.2 0.69 32.0-32.6 0.62 35.2-35.2 0.69 29.8-21.5 0.13 20.4-20.4 0.07 30.7-23.1 0.14 22.7-22.6 0.08

29.5-29.5 0.56 37.7-37.7 0.74 30.4-30.4 0.13 20.5-20.5 0.08

32.3-32.3 0.62 35.4-35.4 0.69 30.1-22.9 0.14 23.1-22.2 0.08

a Ref 19. b Ref. 20. ‘Ref. 10. d Ref. 21. e Ref. 4.

a similar shortening is expected in the former mole- small when differences between similar bonds are cule. A weak anisotropy is anticipated in the latter considered. This finding is in agreement with compound and in 6 in view of the larger number of general notion that variation in bond lengths five-membered rings. This conclusion is corrobo- within a molecule or within a set of closely related rated by the 3-21G calculations although the varia- molecules is much better reproduced by theoretical tion in C-C distances is exaggerated as observed methods than the absolute values themselves [22]. earlier. It is easy to see that the scaled 3-21G SCF It should be pointed out again that the experimen- procedure [18] yields differences in bond lengths tal data for 4 and 6 are not inconsistent with a small which are given by :A;‘, = 0.896 A:!210, where MN-type of distortion if upper and lower limits of the superscript denotes the two carbons of the the measured values are taken into account. Hence, double bond. Hence, the empirical correction is we are tempted to state that the MN effect is

192 M. Eckert-Maksif et al/J. Mol. Struct. (Theochem) 285 (1993) 187-194

operative in these systems too in spite of the opposite interpretation in the original papers [4,10]. Finally, we note that peripheral carbon atoms of the cyclopentene rings in 6 are not co- planar and that two of them are up whilst the third is below the plane of the molecule in the most stable conformation making a dihedral angle of 169”. The X-ray thermal ellipsoids show that the non-benzylic methylene groups move perpendicularly through the plane of the molecule

[41.

Interpretation

Structural parameters of hydrocarbons can be conveniently discussed in terms of hybridization indices and Coulson’s r-bond orders. Influence of the local atomic density redistribution (polariza- tion) described by hybrid orbitals on the molecular geometry is well established by now [23]. There is a number of procedures for calculating hybrid s-characters, each of them defining its own scale of the intra-atomic orbital mixing. We have found that the MNDO s-characters extracted from the first-order density matrix is very close to the original hybridization concept put forward by Pauling [24]. Consequently, the MNDO hybridiza- tion indices are adopted and estimated in this paper by using 3-21G geometries. For that purpose a proposal of Trindle and Sinanoglu [25(a)] is followed where the s-character WkB of a hybrid placed at atom A being directed toward atom B is given by:

AB w2s = WS(AB)/(~/~) WAB (1)

Here Ws(AB) is a portion of the 2sA orbital involved in A-B bonding

W s(AB) = c p2sAv

and WAB is the total bond order of the A-B bond in question

(3)

P cLv are conventional bond orders defined by

2C~i~~i~. Hence, W2tB represents a part of the 2sA mixed density in the A-B intra-bond region normalized to the total A-B bond density which in turn is generally held responsible for covalent bonding. It is customary to multiply WtB by 100 to obtain s-characters as a percentage.

The s-characters presented in Table 1 show rehybridization at the carbon junction atoms. The s-content of hybrids placed at the C(1) and C(6) atoms is shifted from annelated C(l)-C(6) and carbocyclic C(6)-C(7) bonds to exo-C( 1)-C(2) and C(5)-C(6) bonds. The latter has an s-charac- ter higher than 33.3% which characterizes the ideal sp2 hybridization. This is intuitively clear because C(l)-C(6)-C(7) angles are smaller than 120”. The redistribution of the s-character is naturally more pronounced in fused four-membered carbocycles whereas in cyclopentenes it is rather small. The highest s-content is found in exo bonds in 5 as expected (37.7-37.7%). This is in accordance with the corresponding bond distances since higher s-contributions mean stronger and shorter bonds. Relationship between C-C bond lengths and hybridization is illustrated by s-characters for fused, exo-cyclic and carbocyclic bonds given in Table 1.

Another useful index in delocalized n-systems is provided by Coulson’s bond orders of the mobile r-electrons [25(b)]. Their variation caused by hyperconjugation with methylene groups is also compatible with the observed and computed bond lengths (Table 1). The MNDO bond orders show that the Kekule structures given in Fig. 1 are slightly prefered over the opposite coupling scheme. The largest difference between annelated and fused bonds is found again in 5. It appears that in all systems studied here rehybridization and n-bond orders act sinergistically in a sense of the original MN effect. Both contributions are tiny in systems involving five-membered carbocycles being more pronounced when the four-membered rings appear. It is difficult to delineate c and 7r effects. Streitwieser et al. [26] believe that the influence of hyperconjugation is more decisive.

M. Eckert-MaksiC et al./J. Mol. Struct. (Theochem) 285 (1993) 187-194 193

Conclusion References

Theoretical calculations at the SCF 3-21G level of complexity (simplicity) show that the MN effect is operative in fused systems l-6 although to varying extents. The most pronounced bond fixation and consequently bond alternation is found in 5. Fusion of five-membered carbocycles leads to much smaller perturbation of the benzene moiety and to rather weak structural deformation, whereas a somewhat more pronounced bond fixation is induced by annelation of four-mem- bered ring(s). These findings are in harmony with accurate X-ray data for systems 1, 2 and 5. The experimental structure determinations for 4 and 6 are less precise and do not reveal any variation in the central benzene C-C bond length. However, if upper and lower levels of the experimental errors are taken into account the measured values are compatible in principle with a small MN effect. The structural features are rationalized in terms of the local atomic rehybridization caused by anne- lation and r-electron redistribution caused by hyperconjugative perturbation arising from CH2 groups of the fused carbocycles. Both O- and 7r-electrons act in the same direction resulting in the moderate MN distorsions.

1

2 3

4

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6

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9

10 Recent calculations of Baldridge and Siegel [271 on

tricyclopentabenzene (6) gave bond lengths of 1.386 and 1.381 A for endo- and exo-C-C bonds, respec- tively, using the 3-21G basis set [271, thus yielding very small bond anisotropy in the MN sense. Since these results were at variance with our bond length estimates of 1.393 a and 1.375 A for the correspond- ing C-C bonds, we have repeated calculations and found out that Baldridge and Siegel [27] geometry corresponds to a planar carbon skeleton. It turns out that out of plane bending of the terminal CH2 groups increases the MN deformation of the central benzene ring.

11

12

13

14

Acknowledgment 15

16 We thank Professor Boese for sending us X-ray

data prior to publication.

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17 Z.B. Maksic, M. Eckert-MaksiC and K.H. Pfeifer, J. Mol. Struct. (Theochem), submitted for publication.

18 Z.B. MaksiC, M. Eckert-MaksiC D. Kovafek, M. HodoHEek, K. Poljanec and J. Kudnig, J. Mol. Struct. (Theochem), 234 (1991) 201.

19 R. Boese and D. Bllser, Angew. Chem., 100 (1988) 293. 20 F.H. Allen, Acta Cryst., Sect. B, 37 (1981) 900. 21 R. Boese, private communication. 22 J.E. Boggs, in Z.B. MaksiC (Ed.), Theoretical Models of

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23 See for example: Z.B. MaksiC, in Z.B. Maksic (Ed.), Theoretical Models of Covalent Bonding, Vol. 2, Springer, Berlin, 1990, p. 137.

24 L. Pauling, J. Am. Chem. Sot., 53 (1931) 1367. 25 (a) C. Trindle and 0. Sinanoglu, J. Am. Chem. Sot., 91

(1969) 853. (b) R. McWeeny, Coulson’s Valence, 3rd Edn., Oxford University Press, 1979.

26 R. Faust, E.D. Glendening, A. Streitwieser and K.P.C. Vollhardt, J. Am. Chem. Sot., 114 (1992) 8263.

27 K.K. Baldridge and J.S. Siegel, J. Am. Chem. Sot., 114 (1992) 9583.