An alternative take on the nature of the interaction in π-stacking is offered by Wheeler and Houk.¹ They start by examining the binding between benzene and a series of 24 substituted benzenes. Two representative dimmers are shown in Figure 1, where the substituent is NO₂ or CH₂OH. As was noted in a number of previous studies,^2-6 the binding with any substituted benzene is stronger than the parent benzene dimer. Nonetheless, Wheeler and Houk point out that the binding energy has a reasonable correlation with σ_m. It appears that the benzene dimer itself is the outlier; the binding energy when the substituent is CH₂OH, whose σ_m value is zero, is bound more tightly than the benzene dimer. They conclude that there is a dispersive interaction between any substituent and the other benzene ring.

(a)	(b)
(c)	(d)

Figure 1. MO5-2X/6-31+G(d) optimized geometries of (a) C₆H₆-C₆H₅NO₂, (b) C₆H₆-C₆H₅CH₂OH, (c) C₆H₆-HNO₂, and (d) C₆H₆-HCH₂OH.¹

They next constructed an admittedly very crude model system whereby the substituted benzene C₆H₅X is replaced by HX; the corresponding models are also shown in Figure 1. The binding energies of these model dimmers correlates very well with the real dimmers, with r = 0.91. Rather than involving the interaction of the π-electrons, the origin of the enhanced binding in aromatic dimers involves electrostatic interactions of the substituent with the other aromatic ring – effectively the quadrupole of the unsubstituted ring interacts with the dipoles of the substituent and its ring system. In addition, the inherent dispersive interaction increase the binding.

References

(1) Wheeler, S. E.; Houk, K. N., "Substituent Effects in the Benzene Dimer are Due to Direct Interactions of the Substituents with the Unsubstituted Benzene," J. Am. Chem. Soc., 2008, 130, 10854-10855, DOI: 10.1021/ja802849j.

(2) Sinnokrot, M. O.; Sherrill, C. D., "Unexpected Substituent Effects in Face-to-Face π-Stacking Interactions," J. Phys. Chem. A, 2003, 107, 8377-8379, DOI: 10.1021/jp030880e.

(3) Sinnokrot, M. O.; Sherrill, C. D., "Substituent Effects in π-&pi Interactions: Sandwich and T-Shaped Configurations," J. Am. Chem. Soc., 2004, 126, 7690-7697, DOI: 10.1021/ja049434a.

(4) Sinnokrot, M. O.; Sherrill, C. D., "Highly Accurate Coupled Cluster Potential Energy Curves for the Benzene Dimer: Sandwich, T-Shaped, and Parallel-Displaced Configurations," J. Phys. Chem. A, 2004, 108, 10200-10207, DOI: 10.1021/jp0469517

(5) Lee, E. C.; Kim, D.; Jurecka, P.; Tarakeshwar, P.; Hobza, P.; Kim, K. S., "Understanding of Assembly Phenomena by Aromatic-Aromatic Interactions: Benzene Dimer and the Substituted Systems," J. Phys. Chem. A 2007, 111, 3446-3457, DOI: 10.1021/jp068635t.

(6) Grimme, S.; Antony, J.; Schwabe, T.; Mück-Lichtenfeld, C., "Density functional theory with dispersion corrections for supramolecular structures, aggregates, and complexes of
(bio)organic molecules," Org. Biomol. Chem. 2007, 741-758, DOI: 10.1039/b615319b

Schleyer continues his study of aromaticity with a paper¹ that picks up on the theme presented in one² I have previously blogged on – the relationship between a formally aromatic pyrazine and formally antiaromatic dihydropyrazine. He now examines the diazotetracene 1 and it dihydro analogue 2.¹ In terms of formal electron count, 1 should be aromatic, just like the all carbon analogue tetracene 3, and 2 should be antiaromatic.

Schleyer used the NICS_πzz values obtained in the center of each ring to evaluate the aromatic/antiaromatic character of these three molecules. These calculations were performed using canonical molecular orbitals and repeated using localized molecular orbitals. The results are similar for each method, and the canonical MO values are presented in Table 1. As expected for an aromatic compound, each ring of tetracene 3 has large negative NICS values, indicating that each ring is locally aromatic and the molecule as a whole is aromatic. The same is true for the diazotetracene 1. (In fact the NICS values for 1 and 3 are remarkably similar.) However, for 2, the dihydropyrazine ring has a positive NICS values, indicative of a locally antiaromatic ring. While the three phenyl rings have negative NICS values, these absolute values are smaller than for the rings of 1 or 3, indicating an attenuation of their aromaticity. Nonetheless, the sum of the NICS values of 2 is negative, suggesting that the molecule is globally aromatic, though only marginally so. This is due to the antiaromaticity of the dihydropyrazine ring being delocalized to some extent over the entire molecule. Schleyer, concludes that “large 4n π compounds […] are not appreciably destabilized relative to their 4n+2 π congeners.”

Table 1 NICS_πzz (ppm) for each ring of 1-3 and their sum.¹

References

(1) Miao, S.; Brombosz, S. M.; Schleyer, P. v. R.; Wu, J. I.; Barlow, S.; Marder, S. R.; Hardcastle, K. I.; Bunz, U. H. F., "Are N,N-Dihydrodiazatetracene Derivatives Antiaromatic?," J. Am. Chem. Soc., 2008, 130, 7339-7344, DOI: 10.1021/ja077614p.

(2) Miao, S.; Schleyer, P. v. R.; Wu, J. I.; Hardcastle, K. I.; Bunz, U. H. F., "A Thiadiazole-Fused N,N-Dihydroquinoxaline: Antiaromatic but Isolable," Org. Lett. 2007, 9, 1073-1076, DOI: 10.1021/ol070013i

InChIs

1: InChI=1/C18H12/c1-2-6-14-10-18-12-16-8-4-3-7-15(16)11-17(18)9-13(14)5-1/h1-12H

2: InChI=1/C16H10N2/c1-2-6-12-10-16-15(9-11(12)5-1)17-13-7-3-4-8-14(13)18-16/h1-10H

3: InChI=1/C16H12N2/c1-2-6-12-10-16-15(9-11(12)5-1)17-13-7-3-4-8-14(13)18-16/h1-10,17-18H

What is the topology of a molecule made of fused benzene rings? Hopf and co-workers have examined the case where the benzene rings are fused in an ortho arrangement to complete a circle, the so-called [n]circulenes 1_n.¹ They computed the series of [3]- to [20]circulene at B3LYP/6-31G(d).

The most common examples of this class are corannulene 1₅ and coronene 1₆. Hopf finds that the small circulenes, [3]- through [6]circulene, are bowls, consistent with many previous studies.

The larger circulenes fall into two distinct topological categories. [7]circulene through [16]circulene are saddles, as shown in Figure 1a. When the compounds are even larger, namely [17]- through [20]circulene, they adopt a helical topology, as seen in Figure 1b. Unfortunately, Hopf does not supply the optimized geometries; there is no supporting material at all. So I have reoptimized [12]circulene at B3LYP/6-31G(d) and [18]circulene at AM1. It is a real shame that authors do not routinely deposit their structures, that referees do not call out the authors on this, and that editors of journals do not demand full geometrical descriptions of all reported computed structures.

a)	b)
112: [12]circulene	118: [18]circulene

Figure 1. Optimized structures of (a) [12]circulene (B3LYP/6-31G(d)) and (b) [20]circulene (AM1).
Note the hydrogens have been omitted for clarity.

Hopf does not provide a comparison of structures and their energies. For example, what is the energy difference between the bowl and saddle topologies of [7]circulene or the energy difference between the saddle and helical topologies of [17]circulene?

The change in topology of the circulenes is fascinating. One wonders if this change is strictly a function of a stringing fused hexagons in a circle and minimizing the surface. Or is their some π-π stacking that leads to the saddle and helical topologies? Further details would be interesting – as would be examining other types of ciculenes as hinted by the authors at the end of the paper regarding isomeric kekulenes 2.

References

(1) Christoph, H.; Grunenberg, J.; Hopf, H.; Dix, I.; Jones, P. G.; Scholtissek, M.; Maier, G., "MP2 and DFT Calculations on Circulenes and an Attempt to Prepare the Second Lowest Benzolog, [4]Circulene," Chem. Eur. J. 2008, 14, 5604-5616, DOI: 10.1002/chem.200701837

InChIs

1₅: InChI=1/C20H10/c1-2-12-5-6-14-9-10-15-8-7-13-4-3-11(1)16-17(12)19(14)20(15)18(13)16/h1-10H
InChIKey: VXRUJZQPKRBJKH-UHFFFAOYAF

1₆: InChI=1/C24H12/c1-2-14-5-6-16-9-11-18-12-10-17-8-7-15-4-3-13(1)19-20(14)22(16)24(18)23(17)21(15)19/h1-12H
InChIKey: VPUGDVKSAQVFFS-UHFFFAOYAQ

1₁₂: InChIKey: FTLFLCQEVCSDMZ-UHFFFAOYAB

1₁₈: InChIKey: CRXJHICCESJVIG-UHFFFAOYAJ

The importance of the interactions between neighboring aromatic molecules cannot be overemphasized – π-π-stacking is invoked to explain the structure of DNA, the hydrophobic effect, molecular recognition, etc. Nonetheless, the nature of this interaction is not clear. In fact the commonly held notion of π-π orbital overlap is not seen in computations.

Grimme¹ has now carefully examined the nature of aromatic stacking by comparison with aliphatic analogues. He has examined dimers formed of benzene 1, naphthalene 2, anthracene 3, and teracene 4 and compared these with the dimers of their saturated analogues (cyclohexane 1s, decalin 2s, tetradecahydroanthracene 3s, and octadecahydrotetracene 4s. The aromatic dimmers were optimized in the T-shaped and stacked arrangements, and these are shown for 3 along with the dimer of 3s in Figure 1. These structures are optimized at B97-D/TZV(2d,2p) – a functional designed for van der Waals compounds. Energies were then computed at B2LYP-D/QZV3P, double-hybrid functional that works very well for large systems.

Figure 1. Optimized structures of 3s, 3t, and 3a.

The energies for formation of the complexes are listed in Table 1. The first interesting result here is that the benzene and naphthalene dimmers (whether stacked or T-shaped) are bound by about the same amount as their saturated analogues. Grimme thus warns that “caution is required to not overestimate the effect of the π system”.

Table 1. Complexation energy (kcal mol^-1)

The two larger aromatics here do show a significantly enhanced complexation energy than their saturated analogues, and Grimme refers to this extra stabilization as the π-π stacking effect (PSE). Energy decomposition analysis suggests that electrostatic interactions actually favor the complexation of the saturated analogues over the aromatics. However, Pauli exchange repulsion essentially cancels the electrostatic attraction for all the systems, and it is dispersion that accounts for the dimerization energy. Dispersion increases with size of the molecule, and “classical” dispersion forces (the R^-6 relationship) accounts for more than half of the dispersion energy in the saturated dimmers, while it is the non-classical, or orbital-based, dispersion that dominates in the stacked aromatic dimmers. Grimme attributes this to “special nonlocal electron correlations between the π electrons in the two fragments at small interplane distances”.

References

(1) Grimme, S., "Do Special Noncovalent π-π Stacking Interactions Really Exist?," Angew. Chem. Int. Ed., 2008, 47, 3430-3434, DOI: 10.1002/anie.200705157.

InChIs

1: InChI=1/C6H6/c1-2-4-6-5-3-1/h1-6H

1s: InChI=1/C6H12/c1-2-4-6-5-3-1/h1-6H2

2: InChI=1/C10H8/c1-2-6-10-8-4-3-7-9(10)5-1/h1-8H

2s: InChI=1/C10H18/c1-2-6-10-8-4-3-7-9(10)5-1/h9-10H,1-8H2

3: InChI=1/C14H10/c1-2-6-12-10-14-8-4-3-7-13(14)9-11(12)5-1/h1-10H

3s: InChI=1/C14H24/c1-2-6-12-10-14-8-4-3-7-13(14)9-11(12)5-1/h11-14H,1-10H2

4: InChI=1/C18H12/c1-2-6-14-10-18-12-16-8-4-3-7-15(16)11-17(18)9-13(14)5-1/h1-12H

4s: InChI=1/C18H30/c1-2-6-14-10-18-12-16-8-4-3-7-15(16)11-17(18)9-13(14)5-1/h13-18H,1-12H2

I have discussed Möbius aromatic systems in the book and in the blog. A new Möbius aromatic platform has been synthesized, where the porphyrin π-system is appropriately twisted. Osuka has prepared the hexaphyrins 1 and 2.¹ These possess a double-twist structure, and with its 28 π-electrons 1 should be antiaromatic and 2, having 26 π-electrons should be aromatic.

In fact, the x-ray structure of 1 displays significant bond alternation and the NH protons (in the interior of the molecule) have chemical shift far downfield (δ 14.95 and 12.35 ppm) – all consistent with antiaromatic character. On the other hand¸ while 2 exhibits little bond alternation, the NH protons are seen at 11.1 ppm, too far downfield for the interior positions of an aromatic compound!

Rzepa² has computed 1 and 2 at MPW1PW91/6-31G(d,p) for X=H and CF₃; the latter matches the experimentally prepared compounds. (Rzepa supplies very nice web-enabled access to his results through the supporting materials, and so I do not repeat his structures here. Please also see comments to this post.) As expected, both optimized structures of 1(X=H or X=CF₃) shows distinct bond localization and positive NICS values. The chemical shifts of the NH protons are far downfield, and in reasonable agreement with the experimental shifts. The optimized structures of 2 display bond delocalization and negative NICS values, indicative of aromaticity, as do the NH chemical shifts of 5.2 ppm (X=CF₃) or 3.8 ppm (X=H). These chemical shifts differ from the experiment. Rzepa locates a second less stable conformation 3, but its NH chemical shifts are at 10.9 and 10.1 ppm, in reasonable agreement with experiment. So, he concludes that 1 is antiaromatic and 2 is aromatic and both have a double-twist Möbius topology.

Tanaka, et al have reported the structure of the octaphyrin held in place by a complexed
metal, such as 4.³ A number of analogues have been prepared and their x-ray structure shows the single twist needed for Möbius topology. The NMR spectra are consistent with an aromatic system. And relevant to this blog, B3LYP/6-31G(d) (SDD for the heavy metals) NICS computations reveals a large negative value, -14.6 ppm for 5.

References

(1) Shimizu, S.; Aratani, N.; Osuka, A., "meso-Trifluoromethyl-Substituted
Expanded Porphyrins," Chem. Eur. J., 2006, 12, 4909-4918, DOI: 10.1002/chem.200600158

(2) Rzepa, H. S., "Lemniscular Hexaphyrins as Examples of Aromatic and Antiaromatic
Double-Twist Möbius Molecules," Org. Lett. 2008, DOI: 10.1021/ol703129z

(3) Tanaka, Y.; Saito, S.; Mori, S.; Aratani, N.; Shinokubo, H.; Shibata, N.; Higuchi, Y.; Yoon, Z. S.; Kim, K. S.; Noh, S. B.; Park , J. K.; Kim , D.; Osuka, A., "Metalation of Expanded Porphyrins: A Chemical Trigger Used To Produce Molecular Twisting and Möbius Aromaticity," Angew. Chem. Int. Ed., 2008, 47, 681-684, DOI: 10.1002/anie.200704407

InChIs

1(X=H): InChI=1/C30H22N6/c1-2-20-14-22-5-6-24(33-22)16-26-9-10-28(35-26)18-30-12-11-29(36-30)17-27-8-7-25(34-27)15-23-4-3-21(32-23)13-19(1)31-20/h1-18,31-32,35-36H/b19-13-,20-14-,21-13+,22-14-,23-15-,24-16-,25-15-,26-16-,27-17-,28-18+,29-17-,30-18-

InChIKey: LZQBSNZLFFXDHG-FXYKPCLQBX

1(X=CF₃): InChIKey: XMLQOLTZAIQLSA-UFROFZBYBD

2(X=H): InChI=1/C30H20N6/c1-2-20-14-22-5-6-24(33-22)16-26-9-10-28(35-26)18-30-12-11-29(36-30)17-27-8-7-25(34-27)15-23-4-3-21(32-23)13-19(1)31-20/h1-18,31,36H/b19-13-,20-14-,21-13-,22-14-,23-15-,24-16+,25-15+,26-16-,27-17-,28-18-,29-17-,30-18-

InChIKey: MMFGRQLRZMFRGC-NJRWMLEBBC

2(X=CF₃): InChIKey: FFCNJJQCGZCFGC-FJVZODTDBS

The novel cyclophanes 1 and 2 have now been synthesized.¹ An interesting question is whether the bent pyrenes portion of the two molecules remains aromatic. The bending angles is 93.8° in 1 and 95.8° in 2. This distortion is readily apparent in Figure 1, which presents their B3LYP/6-311G(d,p) optimized geometries. NICS computations were used to assess the aromaticity of the pyrene portion. The central rings of pyrene have NICS(0) = -4.4 ppm. The corresponding values in 1 and 2 are -4.5 ppm. The apical rings of pyrene have NICS(0)= -11.9 ppm, while the value is -11.1 ppm in 1 and -11.0 ppm in 2. These calculations indicate that the molecule retains much of the aromaticity of the parent pyrene despite the significant out-of-plane distortions.

Figure 1. B3LYP/6-311G(d,p) optimized geometries of 1 and 2.¹

1

2

References

(1) Zhang, B.; Manning, G. P.; Dobrowolski, M. A.; Cyranski, M. K.; Bodwell, G. J., "Nonplanar Aromatic Compounds. 9. Synthesis, Structure, and Aromaticity of 1:2,13:14-Dibenzo[2]paracyclo[2](2,7)-pyrenophane-1,13-diene," Org. Lett., 2008, 10, 273-276, DOI: 10.1021/ol702703b.

InChIs

1: InChI=1/C34H20/c1-3-7-31-27-17-23-13-15-25-19-28(20-26-16-14-24(18-27)33(23)34(25)26)32-8-4-2-6-30(32)22-11-9-21(10-12-22)29(31)5-1/h1-20H/b29-21-,30-22-,31-27-,32-28-
InChIKey=RYJKEGNHXVXOPX-LISLPQAZBN

2: InChI=1/C82H52/c1-9-25-53(26-10-1)71-73(55-29-13-3-14-30-55)77(59-37-21-7-22-38-59)81-67-49-63-45-47-65-51-68(52-66-48-46-64(50-67)69(63)70(65)66)82-78(60-39-23-8-24-40-60)74(56-31-15-4-16-32-56)72(54-27-11-2-12-28-54)76(58-35-19-6-20-36-58)80(82)62-43-41-61(42-44-62)79(81)75(71)57-33-17-5-18-34-57/h1-52H/b79-61-,80-62-,81-67-,82-68-
InChIKey=BKSFSTJXYFPKOG-IPILNRTDBN

What happens when antiaromatic rings stack? One can draw an MO interaction diagram for π-stacked cyclobutadiene dimer (Figure 1) and recognize at once that this cluster should be stabilized. In fact, it is reminiscent of an orbital diagram for an aromatic species!

Figure 1. MO Interaction diagram of stacked butadiene (modified from Ref 1).

Houk had examined just this dimer (1) in 1996 and located a D_4h critical point at CASSCF(8,8)/6-31G* (see Figure 2).² This structure is energetically below two isolated cyclobutadiene molecules; however, it is a second-order saddle point.

1

Figure 1. CASSCF(8,8)/6-31G* optimized structure of 1.

Schleyer has examined a series of superphanes constructed from anti- and aromatic rings linked by methano bridges, 2-7.¹ These structures were optimized at B3LYP/6-311+G** and their magnetic properties computed at GIAO-PW91. The optimized structures of 3 and 4 are shown in Figure 3.

3

4

Figure 3. B3LYP/6-311+G** optimized structures of 3 and 4.¹

The inter-ring separation (D) in these compounds is quite interesting (Table 1). It decreases in the series 2-4, with the distance in the latter compound of only 2.002 Å. The inter-ring distance is much larger in 5, which has two (aromatic) benzene rings. All of the other comounds (except 2) have shorter distances and these all involve antiaromatic rings. These short distances for the antiaromatic superphanes suggests stabilizing interactions between the rings, as indicated by the MO diagram of Figure 1.

Table 1. Inter-ring distance and NICS values for 2-7.¹

^aDistance (Å) between the carbon of one ring and the closest carbon of the second ring.

The NICS values are also interesting. Schleyer computed a variety of different NICS values, and we list here the isotropic NICS value at the cage center (NICS_cage) and the zz-component evaluated 1 Å above the ring on the outside face NICS(1)_zzring). The NICS(1)_zzring is perhaps the best measure of magnetic properties related to aromatic/antiaromatic character. All six compounds have rings that have negative values of NICS(1)_zzring, indicating of aromatic character. In fact, the value for 5 is less negative than for isolated benzene alone. This suggests that the stacked antiaromatic rings become aromatic, while the stacked aromatic rings become less aromatic. For all six compounds, the NICS_cage value is negative indicating diatropicity, associated with aromatic character – again consistent with the MO argument presented in Figure 1. To answer our lead off question, stacked antiaromatic rings are aromatic!

References

(1) Corminboeuf, C.; Schleyer, P. v. R.; Warner, P., "Are Antiaromatic Rings Stacked Face-to-Face Aromatic?," Org. Lett. 2007, 9, 3263-3266, DOI: 10.1021/ol071183y.

(2) Li, Y.; Houk, K. N., "The Dimerization of Cyclobutadiene. An ab Initio CASSCF Theoretical Study," J. Am. Chem. Soc. 1996, 118, 880-885, DOI: 10.1021/ja921663m.

InChIs

2: InChI=1/C9H6/c1-4-6-2-7-5(1)9(7)3-8(4)6/h1-3H2/q-2

3: InChI=1/C12H8/c1-5-7-2-8-6(1)10-3-9(5)11(7)4-12(8)10/h1-4H2

4: InChI=1/C15H10/c1-6-8-2-9-7(1)11-3-10(6)14-5-15(11)13(9)4-12(8)14/h1-5H2/q+2

5: InChI=1/C18H12/c1-7-9-2-10-8(1)12-3-11(7)15-5-16(12)18-6-17(15)13(9)4-14(10)18/h1-6H2

6: InChI=1/C21H14/c1-8-10-2-11-9(1)13-3-12(8)16-5-17(13)21-7-20(16)18-6-19(21)15(11)4-14(10)18/h1-7H2/q-2

7: InChI=1/C24H16/c1-9-11-2-12-10(1)14-3-13(9)17-5-18(14)22-7-21(17)23-8-24(22)20-6-19(23)15(11)4-16(12)20/h1-8H2

Robinson and Schleyer report the synthesis of and computations on the novel structure gallepin 1.¹ This is the gallium analogue of tropyllium, the prototype of a seven-member aromatic ring. Robinson actually prepared the bis-benzannulated analogue 2, which is found to coordinate to TMEDA in the crystal.

Schleyer computed (B3LYP/LANL2DZ) the gallepin portion of 2 in its naked form 3 and associated with trimethylamine 4. The crystal structure of 2 reveals that the 7 member ring is boat-shaped, and this is reproduced in the computed structure of 4. Interestingly, the naked gallepin is planar, suggestive of an aromatic structure. NICS_πZZ computations were performed to gauge the aromaticity of these compounds. The value for the 7-member ring is -9.0 in 4 and -9.9 in 3, indicating aromatic character. These values are less then in the parent gallepin 1, which has a value of -15.3, but this is the normal type of diminishment expected from benzannulation.
But borapin has a NICS_πZZ substantially more negative (-27.7) and so gallepins are less aromatic than borapins. Nonetheless, it is very interesting that aromaticity can be extended in this interesting way – different heteroatom and different ring size.

3	4

References

(1) Quillian, B.; Wang, Y.; Wei, P.; Wannere, C. S.; Schleyer, P. v. R.; Robinson, G. H., "Gallepins. Neutral Gallium Analogues of the Tropylium Ion: Synthesis, Structure, and Aromaticity," J. Am. Chem. Soc., 2007, 129, 13380-13381, DOI: 10.1021/ja075428d.

Peter Vollhardt and Ken Houk have teamed up on an interesting account of pericyclic reactions of molecules related to starphenylene.¹ This touches on the nature of aromatic compounds and pericyclic reaction mechanisms, topics I take up in a few places in the book.

Compound 1 rearranges at 120 °C to 3, and the presumed pathway is
through 2 – the simultaneous [2+2+2] ring opening through the all-disrotatory path.
However, the computed (B3LYP/6-31G(d) activation energy is 34.6 kcal mol^-1 for this path, much higher than the experimental activation enthalpy, which is 28.9 kcal mol^-1.

The alternative path is to sequential break the cyclobutene rings with the standard conrotatory stereochemistry. This would give 4 and the barrier is 32.5 kcal mol^-1, in better agreement with experiment. From here, there is a bond shift, which traverses a Möbius geometry – as proposed by Karney and Castro (see the book and also this previous post). An electrocylization, followed by a Diels-Alder cycloaddition completes the path to 3. The rate determining step is the first: 1 ↔ 4.

On the other hand, upon heating 5 produces 6. Here the computed barrier for the [2+2+2] reaction (32.6 kcal mol^-1) is in nice agreement with the experimental value (34.1 kcal mol^-1), while the stepwise pathway has a much higher barrier (39.9 kcal mol^-1). They did not locate the polycyclic analogue of 3 (namely, 7) in the reaction of 5. This may be due in part to the fact that the bond shift is accompanied by a loss of aromaticity.

References

(1) Eichberg, M. J. H., K. N.; Lehmann, J.; Leonard, P. W.; Märker, A.; Norton, J. E.; Sawicka, D.; Vollhardt, K. P. C. W., G. D.; Wolff, S., "The Thermal Retro[2+2+2] cycloaddition of Cyclohexane Activated by Triscyclobutenannelation: Concerted All-Disrotatory versus Stepwise Conrotatory Pathways to Fused [12]Annulenes," Angew. Chem. Int. Ed., 2007, 46, 6894-6898, DOI: 10.1002/anie.200702474

InChIs

1: InChI=1/C24H30/c1-2-8-14-13(7-1)19-20(14)22-17-11-5-6-12-18(17)24(22)23-16-10-4-3-9-15(16)21(19)23/h19-24H,1-12H2/t19-,20+,21-,22+,23-,24+

2: InChI=1/C24H30/c1-2-8-20-15-16-22-10-5-6-12-24(22)18-17-23-11-4-3-9-21(23)14-13-19(20)7-1/h13-18H,1-12H2/b14-13-,16-15-,18-17-,19-13-,20-15+,21-14+,22-16+,23-17+,24-18-

3: InChI=1/C24H30/c1-2-8-14-13(7-1)19-21-15-9-3-4-10-16(15)22-20(14)23(19)17-11-5-6-12-18(17)24(21)22/h19-24H,1-12H2

4: InChI=1/C24H30/c1-2-8-20-15-16-22-10-5-6-12-24(22)18-17-23-11-4-3-9-21(23)14-13-19(20)7-1/h13-18H,1-12H2/b14-13+,16-15+,18-17+,19-13-,20-15+,21-14+,22-16-,23-17-,24-18+

5: InChI=1/C24H18/c1-2-8-14-13(7-1)19-20(14)22-17-11-5-6-12-18(17)24(22)23-16-10-4-3-9-15(16)21(19)23/h1-12,19-24H/t19-,20+,21-,22+,23-,24+

6: InChI=1/C24H18/c1-2-8-20-15-16-22-10-5-6-12-24(22)18-17-23-11-4-3-9-21(23)14-13-19(20)7-1/h1-18H/b14-13-,16-15-,18-17-,19-13-,20-15+,21-14+,22-16+,23-17+,24-18-

7: InChI=1/C24H18/c1-2-8-14-13(7-1)19-21-15-9-3-4-10-16(15)22-20(14)23(19)17-11-5-6-12-18(17)24(21)22/h1-12,19-24H

I discuss the concept of σ-aromaticity in Chapter 2.3.1. The arguments for its existence in cyclopropane include surface delocalization of electron density, MO energies, an energetic stability greater than predicted by traditional assessments of its ring strain energy, and a negative value of its NICS(0) and NICS(1).

Fowler, Baker and Lillington have computed the ring current in cyclopropane, cyclobutane and cyclopentane.¹ The later two are computed for their planar conformations, which are not local minima, but make the graphical comparisons simpler. Unfortunately, I do not have electronic access to the journal article and so cannot link to their images, but the plots of the current density of cyclopropane clearly indicates a large diatropic current circling the outside of the ring. In the interior of the ring is a smaller paratropic current.

For this concept to have applicability, cyclobutane should express σ-antiaromaticity. The ring current map for cyclobutane does show a strong paratropic current in the inside of the ring with a weaker diatropic current on the outside of the ring. The current map of cyclopentane shows an interior paratropic and external diatropic currents of nearly identical magnitude, suggestive of a simple superposition of circulation due to five local bonds. Thus, cyclopropane expresses significant σ-aromaticity, cyclobutane is weakly σ-antiaromatic, and cyclopentane is non-aromatic.

References

(1) Fowler, P. W.; Baker, J.; Mark Lillington, M., "The Ring Current in Cyclopropane," Theor. Chem. Acta 2007, 118, 123-127, DOI: 10.1007/s00214-007-0253-2.

InChI:

cyclopropane: InChI=1/C3H6/c1-2-3-1/h1-3H2

cyclobutane: InChI=1/C4H8/c1-2-4-3-1/h1-4H2

cyclopentane: InChI=1/C5H10/c1-2-4-5-3-1/h1-5H2