Möbius Aromatics arising from a C=C=C ring component.


Sonsoles Martín-Santamaría, Balasundaram Lavan and Henry S. Rzepa*

Department of Chemistry, Imperial College of Science, Technology and Medicine, London, SW7 2AY, UK.


Replacement of one planar C=C unit in Hückel 4n+2 aromatic rings by a twisted C=C=C results in chiral 4n p Möbius aromatic rings.



The long history of aromatic chemistry is dominated by the concept of planar ring systems containing 4n+2 conjugated p electrons, the so-called Hückel rule of aromaticity. Heilbronner[1]in 1964 was the first to suggest that applying a so-called Möbius twist to the ring would create an aromatic species if 4n p electrons were conjugated. The Möbius concept has been widely applied to considering the aromaticity of pericyclic transition[2]states, but it is only recently that candidates for stable Möbius aromatics have been suggested. Schleyer and co-workers have reported that a Möbius twisted conformation of the 4n p system C9H9+ is aromatic[3]on the basis of calculated nucleus independent chemical shifts (NICS),2 a technique which appears reliable and useful at quantifying aromaticity. We recently reported calculations on two conformations of [16] annulene,[4]one being conventionally anti-aromatic, but the other having a pronounced Möbius-like twist not associated with any particular region of the ring. This isomer exhibited a NICS value consistent with mild aromaticity rather than anti-aromaticity. Here we suggest further candidates for consideration as Möbius aromatics.

Our initial focus was on the chiral species cycloheptatetraene 5. The presence of a C=C=C substructure in the 7-membered ring reduces the dihedral angle between the 1,3 allene substituents from 90° to 47-50°, which has the effect of breaking the degeneracy of the two highest occupied allene orbitals (Figure 1).§ Interaction of both resulting orbitals with the remaining ring p orbitals would create a similar Möbius topology to that envisaged by Heilbronner, the specific case of 5 resulting in what could be termed a [7] Möbius annulene or Möbannulene. A NICS calculation (-6.5 ppm, Table) establishes that this orbital interaction results in an aromatic system, although rather less so than benzene itself (NICS -10 ppm). The ~40° distortion at the allene unit in 5 is clearly destabilising, since the species is isolable only at low temperatures, dimerising at higher temperatures via a p2+p2 cycloaddition (a process known to be inhibited by bulky groups at the 1,3 positions[5]). The calculated bond lengths for 5 also show some alternation, indicative of a reactive species (Figure 2). The HOMO and HOMO-1 computed for 5 derive from the twisted allene system, but are now delocalised over the entire ring, and show Möbius topology (Figure 2). The HOMO for a pure Möbius aromatic would exhibit degeneracy,1 and although this is not true of 5, the energy difference (1.6eV/AM1) is less than that for allene at this twist angle (2.2eV, Figure 1).

As a ligand, 5 is unusual in binding metals to both "faces" concurrently (e.g 7),[6]but this is perhaps not unexpected if one considers it having only a single p-face! We also estimate one consequence of 5 (and its metal complexes) being chiral. Thus a typical model chiral auxilliary (e.g. R=CHClI or R=Camphorsultamil[7]) results in diastereoisomers differing in energy by about 0.4-0.6 kcal mol-1 (AM1), a relatively small discrimination, but possibly one capable of being increased by suitable design. 5 interconverts with its mirror image via the Hückel 4n+2 p aromatic 6 (cycloheptatrienylidene),[8]which at the correlated level (MP2) has recently been shown to be the transition state for this process (barrier ~27 kcal mol-1).

Elaborating the theme of substituting C=C=C for C=C (Table) we noted that the small ring systems 1 and 2 would be classified as anti-aromatic; 2 as a conventional 4-panti-aromatic Hückel system and 1 as a 4n+2 6-p Möbius anti-aromatic system. 1 appears not to exist as a minimum at the ab initio RHF level, whilst 2 reveals an anti-aromatic (positive) NICS value. No minimum for the anion 3 could be located for this putative 8-pMöbius aromatic, all optimisations resulting in the aromatic Hückel valence bond isomer 4, probably because twisting the allene component in 3 to accommodate a 6-membered ring requires too much energy. This is a lesser problem in the larger ring monocation 8, which appears to be a C2 symmetric 8-p Möbius system exhibiting NICS aromaticity, as is the 8-p dication 9. The singlet neutral form of 9/10 as an anti-aromatic 4n+2 10-p Möbannulene distorts to remove all symmetry and localise the bonds. The triplet neutral 9/10 retains C2 symmetry as might be expected of 4n+2 excited state Möbius aromatic, although the NICS value shows only slight aromaticity (-1.3 ppm). Chiral 12-pmonoanion 10 and the dianion 11 also show aromatic NICS values and have non-planar twisted geometries (Table). Each ring of the chiral bicyclic analogue of naphthalene 12 shows only modestly aromatic NICS values. In this instance, the carbene valence bond isomer 13, a bridged [10] 4n+2 Hückel aromatic annulene, is substantially lower in energy, making it unlikely that 12 is a viable synthetic target. System 14 is derived from the novel Hückel-aromatic S/N systems discovered by Rees and co-workers.[9]As an 8-pMöbius, 14 has an aromatic NICS value (Table). The 12-psystem 15 has a much smaller NICS value, which might be related to the larger dihedral angle at the allene termini (75°, Table 1) reducing the Möbius like orbital mixing (c.f. Figure 1). Our results do imply that optimum Möbius aromaticity may be achieved at allene twists of between ~30-60°.

Introducing two allene-like fragments into the system constitutes a double Möbius twist, for which the aromaticity prediction is again the Hückel 4n+2 rule. Thus both 17 and 18 have predicted to have Cs rather than C2 symmetry and they appear to act as 10-pbis-Möbius (Hückel) aromatics, the alkyne in 17 acting purely as a Hückel contributor (Figure 3a). The low NICS value for 18 is due to its substantial non-planarity. In contrast, the alkyne in the chiral 16 appears to act as a Möbius contributor (Figure 3b), with a modestly aromatic NICS value. This system is tantalisingly ambiguous: is it a 10-p annulene with a single Möbius twist, a 12-p system with a double Möbius twist or a 6-pexample of the recently reported trannulene aromaticity?[10]The triple Möbius system 19 cannot have C2 symmetry, but as a 12-psystem it would be expected to be Möbius aromatic. In fact, the NICS value reveals it to be non-aromatic, suggesting that this degree of orbital twisting results in little conjugation. Finally, we note that our analogy applied to trannulenes10 generates systems (c.f 20, Table) which appear less aromatic than the corresponding Hückel topology trannulenes (Table), but conform to a 4n rather than a 4n+2 rule for aromaticity.

We conclude that a diverse range of Möbius 4n p aromatic systems can be constructed by using a twisted allene fragment as an initiator, although the aromaticity as measured by computed NICS values is less than that for Hückel aromatics.

§ Computed 3D coordinates (as PDB files) and selected orbitals (as 3DMF files) are available online via the supplemental information associated with this article, at http://www.rsc.org/...
Table. Energies (kcal mol-1 for AM1, Hartree for RHF/6-31G(d)) and NICS values (ppm).

Species
AM1
RHF/6-31G(d)
NICS
Dihedral angle (o)a
1
155.3
b
-
8
2
147.1
-191.4899728
2.1
-
3
c
c
-
-
4
57.3
-230.0200
-9.8
-
5
95.7
-268.4477d
-6.5
51
6
117.0
-268.4241
-7.0
-
8
279.1
-306.6502
-5.6
65
9
575.9e
-344.6697
-3.3
86
10
96.8
-383.7313
-5.1
87
11
173.6
-347.4759f
-14.2
41
12
200.7
-420.9538
-4.7
37
13
178.5
-420.9954
-14.9
-
14
273.8
-963.7914
-10.9
27
15
72.9
-1415.9675
-0.4g
75
16
140.0
-344.1344
-3.3
67
17
229.2
-304.9946
-11.1
53
18
138.7
-306.2419
-2.1
50
19
175.5
-344.0594
+0.3
50
20ah
182.2
-422.0950
-5.7
65
20bh
181.0
-499.0069
+0.3
66
20h
183.4
-575.9171
-2.2
71
aDihedral angle between the two termini of the allene. b Converges to 2 on optimisation. c Converges to 4 on optimisation. d The energy for 5 was –270.2424 Hartree and the NICS value was –5.7 at the B3LYP/6-31G(d) level. eTriplet state energy of neutral form 133.0 kcal mol-1. f B3LYP/6-31G* values; RHF/6-31G* optimisation converges to a planar geometry. g Energy/NICS for 1,3,5,2,4-trithiadiazepine: –1378.1686/–9.3 at the RHF/6-31G(d) level. h 20a is the 12-panalogue of [10]-trannulene; 20b is the 14-p analogue of [12]-trannulene; 20 is the 16-panalogue of [14]-trannulene.


Figure 1. AM1 Allene Orbitals (HOMO and HOMO-1) as a function of 1,3 dihedral angle being (a) 90° (degenerate, -10.1 eV), (b) 45° (-9.0, -11.2 eV), 0° (-7.5, -12.5 eV)






Figure 2. Calculated geometry (Å, AM1 (RHF-6-31G*) [B3LYP/6-31G*] and form of the HOMO and HOMO-1 orbitals for 5.




Figure 3. Calculated AM1 form of the HOMO orbital for (a) 17 and (b)16.





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