Lemniscular Hexaphyrins as examples of aromatic and antiaromatic Double-twist Möbius molecules.

Henry S. Rzepa

Two reported hexaphyrins are anaylzed via measured and computed geometries and NMR-shieldings as examples of respectively 4n+2 π-electron aromatic and 4n π-electron antiaromatic double-twist Mobius ring systems, adopting a lemniscular/figure-eight topology with linking number L_K=2π. Partitioning L_K into local twist (T_W) and non-local writhe (W_R) appears insensitive to the aromatic/antiaromatic character.

Heilbronner postulated in 1964¹ that suitably sized [4n]-electron annulenes might exist as singlet species by adopting a conformation in which a Möbius-like single half-twist is imparted to the basis set of 2p atomic orbitals forming the cyclically conjugated system. More recently it was proposed that this class of chiral, and potentially aromatic, molecule be extended to include double and higher order half-twisted systems,² and this was followed by suggestions that a (hypothetical) [14] annulene^3a and 10-electron electrocyclic reaction^3b and a real class of molecules known as octaphyrins⁴ might be examples of such double-twist systems. The most prominent candidate for a single half-twist system is the [16]annulene 1 as achieved via a rational synthesis by Herges et al,⁵ but the degree of conjugation and associated aromaticity for this molecule has proven controversial.^4,6 In the present article, it is proposed that two recently synthesized chiral hexaphyrins⁷ constitute particularly well characterized examplars of respectively anti-aromatic and aromatic double half-twist Möbius molecules.

A doubly twisted "figure-eight", or lemniscular conformation of [14] annulene 2 has been calculated as being energetically accessible if suitably substituted.^3a Such a double half twisted (more generally any system with an even number of such twists) can be shown to follow a 4n+2 electron rule for singlet stability and potential aromaticity.⁸ Given however that two half-twists have to be sustained by the p_π manifold within a relatively small ring, some explanation was needed to account for the relative stability of this conformation. We suggested^8,9 this was the result of reduction of (overlap-reducing) local twists of adjacent p_π-p_π orbitals (quantified by the parameter T_w) by supercoiling of the central axis of the ring into three dimensions, a process known as writhing (quantified by the parameter W_R). Twist and writhe are formally related by L_k, the so-called linking number of the orbital basis set ribbon, via the relationship: L_k = T_w + W_R, where L_k is restricted to (positive or negative) integer values when expressed in units of "half-twist" (i.e. π).

L_k alone determines whether a cyclic array of 2p atomic orbitals must inevitably result in a phase shift (true for odd values of L_k) or whether it has no mandatory phase shift in this basis (true for even values of L_k). According to this scheme, the singly half twisted systems proposed first by Heilbronner, and exemplified by the [16]annulene 1 synthesized by Herges, belong to the L_k = odd category. Doubly half-twisted lemniscular systems of which 2 is an example, belong to the L_k = even category. These two types follow 4n and 4n+2 electron rules respectively. For the chiral conformation of the [14] annulene, it has been shown⁹ that the ribbon constructed from the 2p orbital basis set for 2 does indeed have the numerical value L_k=2, and that this is partitioned as T_w = 1.11 and W_r =0.89. Almost half of the undesirable (at least in terms of π-electronic conjugation) "twist" has been eliminated by conversion into "writhe" via bending of the central annulene curve into three dimensions. That such a chiral system can also be strongly aromatic was shown via a computed NICS(0) index¹⁰ which revealed a prominent diatropic ring current. This particular conformation of [14] annulene remains hypothetical; the issue is now whether any well characterized conjugated lemniscular molecules might be real exemplars of this type of aromaticity.

Two candidates 3 and 4 appear to deserve analysis in these terms. These are both hexaphyrins (calixa[6]phyrins) recently characterized by Osuka and co-workers⁷. Species 3 is a [28]hexaphyrin which follows a 4n π-electron rule, but it is easily oxidized by MnO₂ to 4, a system following a 4n+2 π--electron rule. The structures of both 3 and 4 have been determined crystallographically as having "figure-eight" lemniscular conformations, and both therefore may conform to the L_k = 2 classification noted above. Whereas 4 as a 4n+2 system might be expected to be magnetically diatropic and chirally aromatic, the 4n-electron 3 would be expected to be magnetically paratropic and (if L_k = 2/even) to be antiaromatic.

The ¹H NMR spectrum recorded for 3 certainly bears out its anti-aromaticity. The four NH protons point inwards, and are reported to have strongly deshielded chemical shifts (δ 14.95, 12.35 ppm) as appropriate for a paratropic ring current. The meso positions are occupied not by protons but by CF₃ groups, but protons here would be expected to be shielded upfield. The crystallographic structure also supports this by evidence of prominent bond length alternation. The two pairs of C-N lengths on the nitrogen bearing no hydrogen reveal an average Δ_r 0.072Å; the six pairs of C-C bond lengths centered at the meso positions show similar variation (Δ_r 0.079). The four pyrrole units with NH groups partition into a pair bearing two long (~1.46) and one short (1.33-1.34) bonds; the other pair reveals local bond equality (in a manner reminiscent of the Clar sextet)¹¹, all of which points to the essentially localized valence structure shown as the formula for 3.

The structure of 4 is in marked contrast, with average Δ_r 0.021, 0.009 and 0.015Å for the C-N, C-NH and meso C-C lengths respectively. It is clearly better represented by the mean of the valence bond form shown for 4 and its Kekule bond shifted isomer. The reported ¹H NMR is however more mysterious. The two inner-pointing NH protons are reported at 11.1 ppm, apparently also indicative of a paratropic rather than diatropic ring current. This observation led the authors⁷ to conclude that 4 was not in fact aromatic, despite its 26π-electron conjugation. The resulting contradiction between the delocalized bond lengths and this NH NMR shift was left unexplained.

In order to conform these various hypotheses, and to ascertain whether 4 is truly aromatic or not, density functional calculations and derived values for the computed magnetic shieldings of the protons (X=H, CF₃), the bond lengths around the rings, the NICS(0) index and selected values for L_k, T_w and W_r were conducted. The density functional hybrid/basis set combination mpw1pw91/6-31g(d,p) was employed,¹² since this has been demonstrated to provide reasonably accurate relative magnetic shieldings at feasible computational cost for systems of this size.¹³

At this theoretical level, the computed values for 3,X=CF₃ are: NICS(0) +4.9 ppm (WEO1) and average Δ_r 0.056/0.063Å for the C-N/meso C-C lengths respectively. The corresponding values for X=H are +9.7, 0.047/0.058. The relative magnetic shieldings (X=CF₃) were computed at the GIAO level with an applied solvation field (CPCM, solvent=dichloromethane) as 19.8 and 15.2 ppm, The observed values for the NH protons 3,X=CF₃ are around 3-4 ppm less than observed, but they do represent a room temperature averaged shift and not that of one specific conformer, and again indicate a paratropic ring current. The computed CH shifts for the pyrrole rings ranged from 9.0-6.3 ppm, compared with 7.4 - 6.8 observed; these are within the level of accuracy supported by the GIAO method for ¹H shifts. The averaged values for the ¹⁹F shifts differ by 1.8 ppm for the three non-equivalent pairs of trifluoromethyl substituents, compared with 2.1 ppm measured. With X=H, the computed NH shieldings show even greater downfield shifts of 22.9 and 17.9 ppm, suggesting that the meso CF₃ substitution attenuates the anti-aromaticity of this ring system.

The 26π system 4, X=CF₃/X=H shows opposite behaviour. The NICS(0) values are respectively -11.7 and -12.3 ppm (WEO1) characteristic of aromatic, diatropic molecules.² Average Δ_r values of 0.004, 0.003 and 0.003Å for the C-N, C-NH and meso C-C lengths respectively indicate virtually no bond length alternation and hence essentially complete aromatic delocalization.

Values for the linking number L_k and its components T_w and W_R were obtained by constructing a ribbon from the 2p atomic orbital basis set following the procedure reported previously.⁹ However, this procedure was based on carbocyclic annulenes for which only one unique ribbon can be constructed; with the phyrins, passage through the five-membered pyrrole ring offers several ways of constructing a ribbon based on a single continuous 2p AO path. Analysis of the bond lengths, as set out above, suggest that a route involving all the nitrogens better represents the conjugated pathway then the alternative involving instead the C=C atoms of pyrrole unit. Using this path, the values obtained for 3, X=H/3, X=CF₃ were L_k = 2/2, T_w = 1.31/??? and W_R =0.69/??π. The corresponding values for 4, X=H and 4, X=CF₃ were L_k = 2/2, T_w = 1.28/??? and W_R =0.72/??π. These values formally confirm both 3 and 4 as double-twisted Mobius rings from which a significant measure of local twist has been converted into writhe. The difference between the values of T_w and W_R for the anti-aromatic and aromatic rings is surprisingly small, given that an aromatic system might have been expected to induce a much smaller twist as a means of enhancing the conjugating delocalization at the expense of greater bending-derived writhing in the σ framework.

The computed NH chemical shift for 4, X=CF₃ (5.2 ppm) differs substantially from that measured for this system in chloroform (11.1 ppm), and can be considered outside the expected error of the GIAO method. It is however consistent with the shielded shift expected from the inside region of a diatropic ring current. The pyrrolic CH protons (8.9 - 6.0) do however match with the values reported (7.9 - 6.0). The NMR values for X=H are even clearer; the NH proton is predicted at the strongly shielded value of 3.8 ppm. The meso CH protons are also intriguing; the two close to the lemniscate cross-over region come between 4.9-5.5, whilst the outer four appear between 8.5-7.4, reminding that in a helical aromatic, the shielding/deshielding regions are not the simple cone associated with a purely planar aromatic.

A possible solution to the NH NMR shift paradox might be that the solution conformation differs from that of the crystal. Thus two alternative positions which the NH pyrrole units in 4 could adopt are shown as 5 and 6. Of these, 5 is marginally the more stable, although 8.3 kcal/mol less stable than 4 (computed with a chloroform solvation model). A small computed distorsion from exact C₂ symmetry is found for 5, X=CF₃, resulting in two NH peaks predicted at 10.9 and 10.1 ppm, although this is likely to average out at room temperatures because of conformational mobility. This average value of 10.5 ppm is close to the observed value of 11.1 ppm. The remaining ring protons are predicted between 8.3-6.8 ppm, compared with the observed values of 7.9-6.0. An attenuated NICS(0) of -6.8 ppm and average Δ_r values of 0.042, 0.007 and 0.042Å for the C-N, C-NH and meso C-C lengths indicate that 5 is less aromatic than 2, but clearly not yet non-aromatic, and most probably is not the same conformation/tautomer as the crystal structure.

Also included for completeness are the (hypothetical) systems 7 and 8, which represent respectively the further oxidation of 4 to a 24 π-electron and formally antiaromatic system, and reduction of the antiaromatic 3 to a 30 π-electron formally aromatic system. The NICS(0) index for 7 (WEO1) indicates it as non-aromatic, with CH resonances in the region 7-4-8.3 and alternating bonds; Δ_r (meso C-C) 0.099Å. More interesting is 8, X=CF₃, which manifests as the expected aromatic system (WEO1), non-alternating bonds (Δ_r (meso C-C) 0.007Å), inner-facing NH shifts in the region 1.1-3.2 ppm, and outer facing CH shifts of 5.1-6.4 (in the cross-over region) and 8.0-8.8 ppm. The calculated free energy of reduction (3, X=CF₃ + H₂ = 8, X=CF₃) of -6.4 kcal/mol appears synthetically viable.

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Web Enhanced Object 1. NICS(0) Values for Hexaphyrins

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