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] 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 Penney[3] in 1934 and Lennard-Jones in .1937[4] 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. 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] By 1945 in a review of non-benzenoid aromatic hydrocarbons, Baker[6] 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 Breslow[7] formalised this apparent instability with the term 4n “anti-aromatic”, invoking what had by then become known as the Hückel 4n + 2/4n rule[8] of aromaticity. We use term apparent instability because it has recently[9] been argued in fact that such 4n “anti-aromatic” species are not destabilized electronically to any significant extent.
Angular ring strain is avoided in larger monocyclic rings which also follow the 4n + 2 rule such as [14] or [18] annulene 2[10] by including transoid motifs to retain planarity or methano bridges[11] to avoid close non-bonded contacts. 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] 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. 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. The heterocyclic 10π 1,4-heteroannulenes 4 are one such a class for which a number of crystal structures have been reported. 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. This suggests that the balance between planarising aromaticity and non-planarising angular strain in these systems is a fine one. 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. 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. 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 reported[13] 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.
Schleyer and Wannere[16] 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] 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 shifts[6] of 2, they found that use of Kang and Musgrave's (KMLYP) rehybridisation[13] 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. 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.
The crystal structure of 1,4-dioxocine 4, XYO, R6-(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. 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.
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°. Similar results were obtained at the larger 6-311+G(3d,p) basis set level, indicating this result is not highly basis set dependent. The differing electronic nature of these two isomers is also reflected in the diatropic NMR character, as quantified using NICS values[15] (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. Two valence bond isomers are also located at the MP2 correlated level, the non-planar being lower by 0.8 kcal mol–1.
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 planar[17] (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. No non-planar valence bond forms could be located at either level, although this does not preclude their existence as very shallow stationary points. Also of interest is the parent ring system (4, XYO, RH).[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 planar one being 2.6 kcal mol–1 lower than the non-planar form. 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. 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. 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.
Exact planarity from both (solid-state) experiment and calculation is a feature of the parent 1,4-dihydro-1,4-diazocine (4, XYNH) and the 1,4-bis(trimethylsilyl) derivative,[18] but not so when the N-substituent is an electron withdrawing ester group.[19] 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). The N-dimethylamide group is predicted as intermediate in planarity between N-alkyl and N-ester, although the X-ray structure[19] is quoted as being planar. 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. 4, XYN-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. Replacing a further ring carbon with a nitrogen heteroatom (5, XYN–CO2Me), Table 1) induces non-planarity which is more unambiguously predicted.
For the mixed heteroatom series, planarity is both observed and computed for XO, YN-3,4,5-trimethoxyphenyl. With YN-Ts however, the crystal structure is described as “having considerable torsion”.[20] 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, XYN-Mesyl). The 1,4-dithiocine series (4, XYS)[21,22] are all non-planar and equally well predicted with B3LYP and KMLYP, as is the oxathiocine (4, XO, YS).[23] The series 4, XCH– are all predicted planar and are known[25] to be diatropic (Table 1). The (as yet unknown) parent system for 4, XO, YS, RH however shows another amplified difference between B3LYP and KMLYP. 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. 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-type[26] transition state (C3–O4–C5–C6 ≅38°/KMLYP) which represents the least stable configuration for the 4n + 2 π electrons present. 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.
The seven-ring analogue 6 (XYZNH) is predicted both slightly non-planar and diatropic; the only two known crystal structures of this 10π ring system (XYZNR[27] and XYZSe[28]) likewise reveal non-planarity. Finally, we note that only known example of a 6π four membered ring system (7, RCl, 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.