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Aromaticity on the edge of chaos: An ab initio study of the bimodal

balance between aromatic and non-aromatic structures for

10p-dihetero[8]annulenesyz

Henry S. Rzepa* and Nikola Sanderson

Department of Chemistry, Imperial College London, UK SW7 2AY

Received14th October 2003, Accepted 3rd November 2003

F|rstpublished as an AdvanceArticle on the web20th November 2003

The computed geometries of a class of 10p-annulenes containing two heteroatoms, which exhibit an acutelysensitive balance between p and s influences upon ring planarity, reveal that the recent KMLYP hybridisationof the exchange functional in the DFT method is qualitatively superior to the more commonly used B3LYPhybrid for modelling the aromaticity of such systems.

Introduction

Aromaticity as a concept has been dominated for most of itshistory by the study of benzenoid systems containing singleor fused six-membered rings, and the recognition in the1920s that this motif was associated both with ring planarityand with an aromatic sextet of electrons.1 Dewar in 1945was the first to recognise unambiguous aromatic character ina larger (seven-membered) ring,2 although the potential foraromaticity in the eight-membered ring cyclooctatetraene (1)had been considered much earlier, most revealingly by Penney3

in 1934 and Lennard-Jones in 1937.4 The latter was apparentlythe first to conclude from Huckel-like calculations that this 8psystem would exhibit strong bond alternation and relativelylittle stabilisation as a planar species. Penney appears to have

been the first to consider planar and buckled conformations,and his analysis of angular strain in the (CH2)n rings in parti-cular is remarkably prescient of the theories of conformationalanalysis developed some 15 years later by Barton.5 By 1945 ina review of non-benzenoid aromatic hydrocarbons, Baker6 feltable to conclude that it is doubtful if the instability ofcyclooctatetraene can be explained on grounds of angularstrain alone, although it was not until 1965 that Breslow7 for-malised this apparent instability with the term 4n anti-aro-matic, invoking what had by then become known as theHuckel 4n +2/4n rule8 of aromaticity. We use term apparentinstability because it has recently9 been argued in fact that such4n anti-aromatic species are not destabilized electronicallyto any significant extent.

Angular ring strain is avoided in larger monocyclic ringswhich also follow the 4n + 2 rule such as [14] or [18] annulene210 by including transoid motifs to retain planarity or methanobridges11 to avoid close non-bonded contacts. The [9]annulenemonoanion 3 with D9h symmetry appears to be the largest 10pannulene ring which is both planar and can accommodateall-cisoid motives.12 Somewhat surprisingly however, given therather controversial origins surrounding the aromatic/non-aromatic/anti-aromatic character of the 4n 1, less attentionhas been given to eight-membered rings involving instead 10(and hence 4n + 2) rather than 8p electrons. Whilst the angular

strain may be considered similar to that of 1, the presumptionis that significantly more aromatic stabilisation will be present,hence tipping the balance towards planarity. The heterocyclic10p 1,4-heteroannulenes 4 are one such a class for which anumber of crystal structures have been reported. Remarkably,these exhibit wide variation in ring planarity and degree ofbond alternation, in synchrony with the diatropic/non-diatro-pic NMR character of the molecules. This suggests that thebalance between planarising aromaticity and non-planarisingangular strain in these systems is a fine one. They may indeedbe good examples of bimodal molecules where small changesto the substituents can invoke disproportionately large changesin their structure; a phenomenon which could be described asaromaticity on the edge of chaos. We considered that such

bimodal molecules should serve as highly sensitive tests ofmodern quantitative electronic theories, since an accurate bal-ance between ring strain, s/p conjugation, bond delocalisationand associated electron correlation effects can often be a verydifficult one to achieve in such theories. Here we report a con-sistent set of calculations on such systems at two levels of the-ory, the standard B3LYP/6-31G(d) ab initio density functionalprocedure, and a newly reported13 rehybridisation known asKMLYP, in order to evaluate how sensitive the computedmolecular geometries of such molecules are to variations inthe computational method employed.

Computational procedureCalculations were performed using Gaussian 98 (Rev A11)14

using standard optimization methods on all the known exam-ples of ring system 46 for which crystal structures have beenreported. To invoke the KMLYP functional, the followingGaussian route commands were used:13

#iop5=45 10000557 iop5=46 00000443

#iop5=47 04481000

For reference, some calculations were also performed at the(computationally very much more expensive) MP2 correlatedlevel. All final energies and geometries are available as electro-nic supplementary information (ESI).y Diatropic character

was estimated using the NICS procedure as described bySchleyer and coworkers.15

y Electronic supplementary information (ESI) available: Geometricinformation and 3D coordinates. See http://www.rsc.org/suppdata/cp/b3/b312724a/z Presented at the ESF Exploratory Workshop: New Perspectives onAromaticity, Exeter, UK, July 59, 2003.

PCCP

www.rsc.org/pccp

R E S E A R C H P A P E R

310 P h y s . C h e m . C h e m . P h y s . , 2 0 0 4 , 6 , 3 1 0 3 1 3 T h i s j o u r n a l i s Q T h e O w n e r S o c i e t i e s 2 0 0 4

DOI:1

0.1

039/b312724a

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Results and discussion

Schleyer and Wannere16 have recently suggested that thedegree of bond length alternation in both [14] and [18] annu-lene (2) may be significantly greater than inferred from thehitherto accepted (1995) analysis of the X-ray structure.10

Noting that the commonly used B3LYP/6-31G(d) ab initiodensity functional procedure associated little bond alternationwith a poor prediction of the 1H NMR shifts6 of2, they foundthat use of Kang and Musgraves (KMLYP) rehybridisation13

of the density functional exchange terms predicted greater

bond alternation but significantly also a much superior matchbetween the computed 1H NMR shifts at this geometry andexperiment. Following this suggestion, we considered it appro-priate to also evaluate these two computational proceduresfor the bimodal series 4 to see if it represents an improvedprocedure for use when modelling molecules with aromaticproperties.

The crystal structure of 1,4-dioxocine 4, X=Y=O, R=6-(pyran-4-on-2-yl)17 exhibits a non planar geometry, with an81 dihedral angle for C3O4C5C6 and an approximateC2 axis passing through the mid points of C2C3 and C6C7. At the B3LYP/6-31G(d) level only one minimum corres-ponding to an almost planar structure could be located(Table 1);y clearly this predicted geometry is qualitatively dif-ferent from the crystal structure, and although crystal packingforces (no hydrogen bonding is possible) might explain thedifference, there is little precedent for such large variationcaused by this effect.

In contrast, two minima were located at the KMLYP/6-31G(d) level; an essentially planar aromatic-like geometryequivalent to the B3LYP structure, and an apparent valencebond isomer (lower than the former by DG 1.4 kcal mol1

following zero-point and entropy corrections) which matchesthe twisted crystal structure with a predicted C3O4C5C6angle of 78. Similar results were obtained at the larger 6-311+G(3d,p) basis set level, indicating this result is not highlybasis set dependent. The differing electronic nature of thesetwo isomers is also reflected in the diatropic NMR character,as quantified using NICS values15 (Table 1); the planar

B3LYP and KMLYP forms indicating moderate diatropicity,the twisted KMYLP form indicating a non-diatropic systemcomprising almost orthogonal p

p-p

poverlap at e.g. O4C5.

Two valence bond isomers are also located at the MP2correlated level, the non-planar being lower by 0.8 kcal mol1.

When the pyranonyl substituent is replaced by the modestlymore electronegative chloroacetyl group, both B3LYP andKMLYP now concur, predicting the ring to be exactly planar17

(at both the 6-31(d) and 6-311+G(3d,p) basis set levels) and inessential agreement with the crystal structure; the small experi-mental non-planarity (Table 1) may indeed now be due to crys-tal packing effects. No non-planar valence bond forms couldbe located at either level, although this does not preclude theirexistence as very shallow stationary points. Also of interest isthe parent ring system (4, X=Y=O, R=H).17b Only a single

planar minimum is predicted at B3LYP and KMLYP levels,with the NICS values indicating modest diatropicity. MP2

optimisation results in location of two minima, the planarone being 2.6 kcal mol1 lower than the non-planar form.Experimentally,17b this system is reported as being planar insolution (from the 2,3JHH coupling constants), with

1H NMRshifts in a region (5.17.6 ppm) normally associated with dia-tropicity, but having a high olefin-like reactivity. It is possiblethat both planar and non-planar valence isomers are present asan equilibrium mixture in solution, thus imparting dual char-acteristics to this molecule. We therefore highlight this ringsystem as being close to a bimodal system on the edge ofaromatic chaos, with relatively small changes to substituents

apparently capable of invoking large changes in the geometryand aromaticity.

Exact planarity from both (solid-state) experiment and cal-culation is a feature of the parent 1,4-dihydro-1,4-diazocine(4, X=Y=NH) and the 1,4-bis(trimethylsilyl) derivative,18

but not so when the N-substituent is an electron withdrawingester group.19 Here again a significant difference betweenB3LYP and KMLYP is predicted, the latter appearing to bethe more correct in terms of the computed bond lengths (nodihedral angles being reported for this system). The N-dimethylamide group is predicted as intermediate in planaritybetween N-alkyl and N-ester, although the X-ray structure19 isquoted as being planar. This molecule may be particularlyfinely balanced between planar aromaticity and non-planarnon-aromaticity and may again be a good example of a bipolararomatic molecule. 4, X=Y=N-mesyl at the KMLYP levelalso shows subtle behaviour; a non-planar stationary pointappears as a near inflexion point during geometry optimiza-tion, but the final geometry is almost planar; at the MP2 levelthe non planar form is a genuine minimum. Replacing afurther ring carbon with a nitrogen heteroatom (5, X=Y=NCO2Me), Table 1) induces non-planarity which is moreunambiguously predicted.

For the mixed heteroatom series, planarity is both observedand computed for X=O, Y=N-3,4,5-trimethoxyphenyl. WithY=N-Ts however, the crystal structure is described as havingconsiderable torsion .20 Both MP2 and KMLYP optimiza-tions result in location of such isomer (C3O4C5C6 ffi93

and ffi82.5 respectively), although only with the former is

the more stable the non-planar form (vis the similar KMLYPbehaviour for 4, X=Y=N-Mesyl). The 1,4-dithiocine series (4,X=Y=S)21,22 are all non-planar and equally well predictedwith B3LYP and KMLYP, as is the oxathiocine (4, X=O,Y=S).23 The series 4, X=CH are all predicted planar andare known25 to be diatropic (Table 1). The (as yet unknown)parent system for 4, X=O, Y=S, R=H however shows anotheramplified difference between B3LYP and KMLYP. Valencebond isomers were located at both levels; for the former, theplanar aromatic form was 3.0 kcal mol1 lower, with KMLYPthe non-aromatic form was 0.7 kcal mol1 more stable. Theexistence of a locatable transition state between the twovalence forms suggests these minima may not simply be arti-facts of the single reference KMLYP (and MP2) procedures,but genuine (aromatic and non-aromatic) isomers straddling

a Mobius-type26 transition state (C3O4C5C6 ffi38/KMLYP) which represents the least stable configuration for

T h i s j o u r n a l i s Q T h e O w n e r S o c i e t i e s 2 0 0 4 P h y s . C h e m . C h e m . P h y s . , 2 0 0 4 , 6 , 3 1 0 3 1 3 311

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the 4n + 2 p electrons present. The analogy would be to planar1 being the least stable 4n electronic configuration between twonon-planar non-aromatic minima and hence a transition stateconnecting them.

The seven-ring analogue 6 (X=Y=Z=NH) is predicted bothslightly non-planar and diatropic; the only two known crystalstructures of this 10p ring system (X=Y=Z=NR27 andX=Y=Z=Se28) likewise reveal non-planarity. Finally, we notethat only known example of a 6p four membered ring system(7, R=Cl, R0=2,4,6-tri-t-butylphenyl) is also non-planar,29

but the origins of this are unlikely to be angular strain andare more likely associated either with poor p

ppp

overlaps ora high degree of electron repulsion in a small ring.

Conclusions

We argue here that molecules such as 46 are good examples ofbipolar systems on the chaotic edge of aromaticity, wheresmall changes of substitution on either the ring or the hetero-atom can induce large (but predictable) changes to both thedegree of delocalisation of the double bonds, reflected in thecorresponding planarity and hence aromaticity of the system.As such, they serve to provide challenging tests of modernquantitative electronic structure theories. Of these, we suggestthat the KMLYP/6-31(d) method appears capable of predict-ing this sensitivity more reliably than the older B3LYPtreatment. We propose that synthesis and accurate structure

determination of a more comprehensive set of substitutedheteroaromatics such as 4 or 6 could serve as a novel type of

reference library which could serve as the basis for developingeven better hybridisations of density functional and othermethods.

References

1 J. J. Thomson, Phil. Mag., 1921, 41, 510; E. C. Crocker, J. Am.Chem. Soc., 1922, 44, 1618.

2 M. J. S. Dewar, Nature, 1945, 155, 50.3 W. G. Penney, Proc. R. Soc. London, Ser. A, 1934, 146, 223.4 J. E. Lennard-Jones and J. Turkevitch, Proc. R. Soc. London, Ser.

A, 1937,

158, 297305.5 D. H. R. Barton and R. C. Cookson, Q. Rev. Chem. Soc., 1956,

10, 4482.6 W. Baker, J. Chem. Soc., 1945, 258267.7 R. Breslow, Chem. Eng. News, 1965, 43(26), 909.8 E. Huckel, Z. Physik, 1936, 70, 204; A. Streitweiser, Molecular

Orbital Theory for Organic Chemists, John Wiley and Sons,New York, 1961.

9 C. S. Wannere, D. Moran, N. L. Allinger, B. Andes Hess, Jr., L. J.Schaad and P. von R. Schleyer, Org. Lett., 2003, 5, 29832986.

10 S. Gorter, E. Rutten-Keulemans, M. Krever, C. Romers andD. W. J. Cruickshank, Acta Crystallogr., Sect. B: Struct. Sci.,1995, 51, 1036.

11 R. Bianchi, T. Pilati and M. Simonetta, Acta Crystallogr., Sect. B:Struct. Crystallogr. Cryst. Chem., 1980, 36, 3146.

12 R. A. King, T. D. Crawford, J. F. Stanton and H. F. Schaefer, III,J. Am. Chem. Soc., 1999, 121, 1078810793; V. G. Boche, H.Weber, D. Martens and A. Bieberbach, Chem. Ber., 1978, 111,24802496. We note here that optimisation at the KMLYP/6-31(d) level retains planarity.

Table 1 Geometries, energies and NICS values for 46

X, Y, R, Cambridge refcode

B3LYP/KMLYP 6-31G(d)Energy/Hartree [NICS(0),

B3LYP/KMLYP/ppm]

C3Y4C5C6 dihedral crystal

structure [B3LYP/KMLYP]/

4, X=Y=O, R=H 382.59901/381.82874a [8.2/7.3] Planar17b [0.0/0.0]

4, X=Y=O, R=6-

(pyran-4-on-2-yl) CUWWEW,17a724.75782/723.29019b [7.5/0.1] 80.8 [10.5/78.1c ]

4, X=Y=O, R=6-carboxylic acid

chloride CUWWIA,17a

955.53210/954.11459 [7.7/7.0] 1.2 [0.3/0.3]

4, X=Y=NH DHDZOC,18 342.89994/342.21433 [12.9/12.5] Planar [0.0/0.0]

4, X=Y=N-Trimethylsilyl MSIHDZ,18 1160.27700/1158.59120 [11.3/10.8] Planar [0.0/0.0]

4, X=Y=N-CONMe2 MCBHDZ,19 837.52547/835.89800 [8.5/6.0] Diatropic, Practically planar [19.4/30.5]

4, X=Y=NCO2Me MXCHAZ,19 798.64839/797.07613 [6.0/1.3] Non diatropic, strongly C2

twisted [17.9/58.5]

4, X=Y=NSO2Me MSHDAZ,18 1518.65134/1516.49681d [9.6/7.4] Twisted [13.5/23.6e ]

5, X=Y=N-Acetyl CAXZBT,24 1715.32163/1712.39694 [0.8/0.6] 90.1 [90.5/91.4]

4, X=O, Y=N-3,4,5-Trimethoxybenzyl,R0=(3,4,5-trimethoxybenzyl) COGPIX,20

976.66132/974.75355 [9.9/9.2] Planar [0.4/2.5]

4, X=O, Y=N-Tosyl COGPET,20 1181.67739/1179.74661f [8.9/7.6] Considerable torsion [8.2/13.9g ]

4, X=Y=S, R=6-Acetoxy ACXDTC,21 1256.41893/1254.75146 [2.5/2.4] 84.6 [86.4/87.7]

4, X=Y=S, R=8,9-Dimethyl-1,6-benzo DMBTOC,22

1260.83295/1259.16593 [2.1/2.0] 90.0, 96.2 [92.7/93.7]

4, X=S, Y=O (3,4,5,6-Tetrachloro-11,11-

dimethyl-2,7-oxathiabicyclo(6.4.0)dodeca-1(8),3,5-trien-9-one) FUVWEY,23

2852.64265/2849.43451 [2.2/2.1] 89.3 [85.3/86.5]

4, X=S, X=O 705.57218h /704.57509h [9.2/1.2] Unknown [0.0/74.2]4, X=CH, Y=S 669.09512/668.17759 [14.1/14.6] Diatropic by NMR25 [0.0/0.0]4, X=CH, Y=O 346.11046/345.41876 [13.5/13.5] Diatropic by NMR18 [0.0/0.0]

4, X=CH, Y=NH 326.24968/325.60088 [15.8/16.3] Diatropic by NMR18 [0.0/0.0]6, X=Y=Z=NH 320.79828/320.16244 [8.2/7.4] [36.7/12.5]

a Total energy (MP2): 381.42386 (planar), 381.41979 (non-planar). b Corrected for DG: 723.15206, Total energy (MP2): 722.61300.c Planar valence isomer; total energy (KMLYP/MP2) 723.29133/722.61166. Corrected for DG(KMLYP): 723.14989, NICS(KMLYP) 6.1.d Total energy (MP2): 1515.42207. e Non-planar isomer (MP2); 1515.42046, C3X4C5C6 dihedral 82.5. f Corrected for DG:

1179.53934. Total energy (MP2); 1139.55775. g Non-planar isomer; total energy (KMLYP/MP2) 1179.74319/1139.55812 Corrected forDG(KMLYP): 1179.53740. NICS(KMLYP) 1.2. C3X4C5C6 dihedral (KMLYP) 82.5. h Valence isomers; total energy (B3LYP/

KMLYP) 705.56747/704.57398 [1.6/8.6]. Transition state for interconversion (KMLYP): 704.57242 [4.1].

312 P h y s . C h e m . C h e m . P h y s . , 2 0 0 4 , 6 , 3 1 0 3 1 3 T h i s j o u r n a l i s Q T h e O w n e r S o c i e t i e s 2 0 0 4

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T h i s j o u r n a l i s Q T h e O w n e r S o c i e t i e s 2 0 0 4 P h y s . C h e m . C h e m . P h y s . , 2 0 0 4 , 6 , 3 1 0 3 1 3 313