1
Aromaticity on the edge of chaos: An ab initio study of the bimodal balance between aromatic and non-aromatic structures for 10π-dihetero[8]annulenes

Type: Goal | Advantage: None | Novelty: None | ConceptID: Goa1

2
The computed geometries of a class of 10π-annulenes containing two heteroatoms, which exhibit an acutely sensitive balance between π and σ influences upon ring planarity, reveal that the recent KMLYP hybridisation of the exchange functional in the DFT method is qualitatively superior to the more commonly used B3LYP hybrid for modelling the aromaticity of such systems.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con1

Introduction

3
Aromaticity as a concept has been dominated for most of its history by the study of benzenoid systems containing single or fused six-membered rings, and the recognition in the 1920s that this motif was associated both with ring planarity and with an “aromatic sextet” of electrons.1

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac1

4
Dewar in 1945 was the first to recognise unambiguous aromatic character in a larger (seven-membered) ring,2 although the potential for aromaticity in the eight-membered ring cyclooctatetraene (1) had been considered much earlier, most revealingly by Penney3 in 1934 and Lennard-Jones in .19374

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac2

5
The latter was apparently the first to conclude from Hückel-like calculations that this 8π system would exhibit strong bond alternation and relatively little stabilisation as a planar species.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac2

6
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 particular is remarkably prescient of the theories of conformational analysis developed some 15 years later by Barton.5

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac2

7
By 1945 in a review of non-benzenoid aromatic hydrocarbons, Baker6 felt able to conclude that “it is doubtful if the instability of cyclooctatetraene can be explained on grounds of angular strain alone”, although it was not until 1965 that Breslow7 formalised this apparent instability with the term 4n “anti-aromatic”, invoking what had by then become known as the Hückel 4n + 2/4n rule8 of aromaticity.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac2

8
We use term apparent instability because it has recently9 been argued in fact that such 4n “anti-aromatic” species are not destabilized electronically to any significant extent.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac2

9
Angular ring strain is avoided in larger monocyclic rings which also follow the 4n + 2 rule such as [14] or [18] annulene 210 by including transoid motifs to retain planarity or methano bridges11 to avoid close non-bonded contacts.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac3

10
The [9]annulene monoanion 3 with D9h symmetry appears to be the largest 10π annulene ring which is both planar and can accommodate all-cisoid motives.12

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac3

11
Somewhat surprisingly however, given the rather controversial origins surrounding the aromatic/non-aromatic/anti-aromatic character of the 4n1, less attention has been given to eight-membered rings involving instead 10 (and hence 4n + 2) rather than 8π electrons.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac3

12
Whilst the angular strain may be considered similar to that of 1, the presumption is that significantly more aromatic stabilisation will be present, hence tipping the balance towards planarity.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac3

13
The heterocyclic 10π 1,4-heteroannulenes 4 are one such a class for which a number of crystal structures have been reported.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac3

14
Remarkably, these exhibit wide variation in ring planarity and degree of bond alternation, in synchrony with the diatropic/non-diatropic NMR character of the molecules.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac3

15
This suggests that the balance between planarising aromaticity and non-planarising angular strain in these systems is a fine one.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac3

16
They may indeed be good examples of bimodal molecules where small changes to the substituents can invoke disproportionately large changes in their structure; a phenomenon which could be described as aromaticity on the edge of chaos.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac3

17
We considered that such bimodal molecules should serve as highly sensitive tests of modern quantitative electronic theories, since an accurate balance between ring strain, σ/π conjugation, bond delocalisation and associated electron correlation effects can often be a very difficult one to achieve in such theories.

Type: Hypothesis | Advantage: None | Novelty: None | ConceptID: Hyp1

18
Here we report a consistent set of calculations on such systems at two levels of theory, the standard B3LYP/6-31G(d) ab initio density functional procedure, and a newly reported13 rehybridisation known as KMLYP, in order to evaluate how sensitive the computed molecular geometries of such molecules are to variations in the computational method employed.

Type: Goal | Advantage: None | Novelty: None | ConceptID: Goa2

Computational procedure

19
Calculations were performed using Gaussian 98 (Rev A11)14 using standard optimization methods on all the known examples of ring system 4–6 for which crystal structures have been reported.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

20
To invoke the KMLYP functional, the following Gaussian route commands were used:13 #iop(5/45 = 10000557) iop(5/46 = 00000443) #iop(5/47 = 04481000)For reference, some calculations were also performed at the (computationally very much more expensive) MP2 correlated level.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod1

21
All final energies and geometries are available as electronic supplementary information (ESI).

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs1

22
Diatropic character was estimated using the NICS procedure as described by Schleyer and coworkers15.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod2

Results and discussion

23
Schleyer and Wannere16 have recently suggested that the degree of bond length alternation in both [14] and [18] annulene (2) may be significantly greater than inferred from the hitherto accepted (1995) analysis of the X-ray structure.10

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac4

24
Noting that the commonly used B3LYP/6-31G(d) ab initio density functional procedure associated little bond alternation with a poor prediction of the 1H NMR shifts6 of 2, they found that use of Kang and Musgrave's (KMLYP) rehybridisation13 of the density functional exchange terms predicted greater bond alternation but significantly also a much superior match between the computed 1H NMR shifts at this geometry and experiment.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac4

25
Following this suggestion, we considered it appropriate to also evaluate these two computational procedures for the bimodal series 4 to see if it represents an improved procedure for use when modelling molecules with aromatic properties.

Type: Goal | Advantage: None | Novelty: None | ConceptID: Goa3

26
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 an 81° dihedral angle for C3–O4–C5–C6 and an approximate C2 axis passing through the mid points of C2–C3 and C6–C7.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac5

27
At the B3LYP/6-31G(d) level only one minimum corresponding to an almost planar structure could be located (Table 1); clearly this predicted geometry is qualitatively different from the crystal structure, and although crystal packing forces (no hydrogen bonding is possible) might explain the difference, there is little precedent for such large variation caused by this effect.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con2

28
In contrast, two minima were located at the KMLYP/6-31G(d) level; an essentially planar aromatic-like geometry equivalent to the B3LYP structure, and an apparent valence bond isomer (lower than the former by ΔG 1.4 kcal mol–1 following zero-point and entropy corrections) which matches the twisted crystal structure with a predicted C3–O4–C5–C6 angle of 78°.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res1

29
Similar results were obtained at the larger 6-311+G(3d,p) basis set level, indicating this result is not highly basis set dependent.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res2

30
The differing electronic nature of these two 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 system comprising almost orthogonal pπ-pπ overlap at e.g. O4–C5.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res3

31
Two valence bond isomers are also located at the MP2 correlated level, the non-planar being lower by 0.8 kcal mol–1.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs2

32
When the pyranonyl substituent is replaced by the modestly more electronegative chloroacetyl group, both B3LYP and KMLYP 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 in essential agreement with the crystal structure; the small experimental non-planarity (Table 1) may indeed now be due to crystal packing effects.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con3

33
No non-planar valence bond forms could be located at either level, although this does not preclude their existence as very shallow stationary points.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con3

34
Also of interest is the parent ring system (4, XYO, RH).17b

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj1

35
Only a single planar minimum is predicted at B3LYP and KMLYP levels, with the NICS values indicating modest diatropicity.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res4

36
MP2 optimisation results in location of two minima, the planar one being 2.6 kcal mol–1 lower than the non-planar form.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs3

37
Experimentally,17b this system is reported as being planar in solution (from the 2,3JHH coupling constants), with 1H NMR shifts in a region (5.1–7.6 ppm) normally associated with diatropicity, but having a high olefin-like reactivity.

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac6

38
It is possible that both planar and non-planar valence isomers are present as an equilibrium mixture in solution, thus imparting dual characteristics to this molecule.

Type: Hypothesis | Advantage: None | Novelty: None | ConceptID: Hyp2

39
We therefore highlight this ring system as being close to a bimodal system on the edge of aromatic chaos, with relatively small changes to substituents apparently capable of invoking large changes in the geometry and aromaticity.

Type: Hypothesis | Advantage: None | Novelty: None | ConceptID: Hyp2

40
Exact planarity from both (solid-state) experiment and calculation 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 withdrawing ester group.19

Type: Result | Advantage: None | Novelty: None | ConceptID: Res5

41
Here again a significant difference between B3LYP and KMLYP is predicted, the latter appearing to be the more correct in terms of the computed bond lengths (no dihedral angles being reported for this system).

Type: Hypothesis | Advantage: None | Novelty: None | ConceptID: Hyp3

42
The N-dimethylamide group is predicted as intermediate in planarity between N-alkyl and N-ester, although the X-ray structure19 is quoted as being planar.

Type: Hypothesis | Advantage: None | Novelty: None | ConceptID: Hyp3

43
This molecule may be particularly finely balanced between planar aromaticity and non-planar non-aromaticity and may again be a good example of a bipolar aromatic molecule.

Type: Hypothesis | Advantage: None | Novelty: None | ConceptID: Hyp3

44
4, XYN-mesyl at the KMLYP level also shows subtle behaviour; a non-planar stationary point appears as a near inflexion point during geometry optimization, but the final geometry is almost planar; at the MP2 level the non planar form is a genuine minimum.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res6

45
Replacing a further ring carbon with a nitrogen heteroatom (5, XYN–CO2Me), Table 1) induces non-planarity which is more unambiguously predicted.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res7

46
For the mixed heteroatom series, planarity is both observed and computed for XO, YN-3,4,5-trimethoxyphenyl.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res8

47
With YN-Ts however, the crystal structure is described as “having considerable torsion”.20

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac7

48
Both MP2 and KMLYP optimizations result in location of such isomer (C3–O4–C5–C6 ≅93° and ≅82.5° respectively), although only with the former is the more stable the non-planar form (vis the similar KMLYP behaviour for 4, XYN-Mesyl).

Type: Result | Advantage: None | Novelty: None | ConceptID: Res9

49
The 1,4-dithiocine series (4, XYS)21,22 are all non-planar and equally well predicted with B3LYP and KMLYP, as is the oxathiocine (4, XO, YS).23

Type: Result | Advantage: None | Novelty: None | ConceptID: Res10

50
The series 4, XCH– are all predicted planar and are known25 to be diatropic (Table 1).

Type: Result | Advantage: None | Novelty: None | ConceptID: Res11

51
The (as yet unknown) parent system for 4, XO, YS, RH however shows another amplified difference between B3LYP and KMLYP.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res12

52
Valence bond isomers were located at both levels; for the former, the planar aromatic form was 3.0 kcal mol–1 lower, with KMLYP the non-aromatic form was 0.7 kcal mol–1 more stable.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res12

53
The existence of a locatable transition state between the two valence forms suggests these minima may not simply be artifacts of the single reference KMLYP (and MP2) procedures, but genuine (aromatic and non-aromatic) isomers straddling a Möbius-type26 transition state (C3–O4–C5–C6 ≅38°/KMLYP) which represents the least stable configuration for the 4n + 2 π electrons present.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con4

54
The analogy would be to planar 1 being the least stable 4n electronic configuration between two non-planar non-aromatic minima and hence a transition state connecting them.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con4

55
The seven-ring analogue 6 (XYZNH) is predicted both slightly non-planar and diatropic; the only two known crystal structures of this 10π ring system (XYZNR27 and XYZSe28) likewise reveal non-planarity.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res13

56
Finally, we note that only known example of a 6π four membered ring system (7, RCl, R′2,4,6-tri-t-butylphenyl) is also non-planar,29 but the origins of this are unlikely to be angular strain and are more likely associated either with poor pπpπ overlaps or a high degree of electron repulsion in a small ring.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con5

Conclusions

57
We argue here that molecules such as 4–6 are good examples of bipolar systems on the chaotic edge of aromaticity, where small changes of substitution on either the ring or the heteroatom can induce large (but predictable) changes to both the degree of delocalisation of the double bonds, reflected in the corresponding planarity and hence aromaticity of the system.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con6

58
As such, they serve to provide challenging tests of modern quantitative electronic structure theories.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con6

59
Of these, we suggest that the KMLYP/6-31(d) method appears capable of predicting this sensitivity more reliably than the older B3LYP treatment.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con7

60
We propose that synthesis and accurate structure determination of a more comprehensive set of substituted heteroaromatics such as 4 or 6 could serve as a novel type of reference library which could serve as the basis for developing even better hybridisations of density functional and other methods.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con8