Myśliwiec and Stępień report on a new method for creating buckybowls.¹ The usual way had been to build from the inside outward. They opt instead to build from the outside in and have constructed the heterosubstitued bowl chrysaorole 1.

1

B3LYP/6-31G** optimizations reveal two conformers that are very close in energy: one has the butyl chains outstretched (1a) and one has the butyl arms internal or pendant (1b). These structures are shown in Figure 1. The depth of this bowl (1.96 Å) is quite a bit larger than in corranulene (0.87 Å). The agreement between the computed and experimental ¹³C and ¹H chemical shifts are excellent, supporting the notion that this gas phase geometry is similar to the solution phase structure. Though 1 is strained, 53.4 kcal mol^-1 based on B3LYP/6-31G** energies for Reaction 1 (which uses the parent of 1 – replacing the butyl groups with hydrogens), on a per sp² atom basis, it is no more strained than corranulene.

1a

1b

Figure 1. B3LYP/6-31G** optimized geometries of two conformers of 1.

This new synthetic strategy is likely to afford access to more unusual aromatic structures.

References

(1) Myśliwiec, D.; Stępień, M. "The Fold-In Approach to Bowl-Shaped Aromatic Compounds: Synthesis of Chrysaoroles," Angew. Chem. Int. Ed. 2013, 52, 1713-1717, DOI:10.1002/anie.201208547.

InChI

1: InChI=1S/C54H45N3/c1-4-7-16-55-49-19-31-10-12-33-21-51-45-27-39(33)37(31)25-43(49)44-26-38-32(20-50(44)55)11-13-34-22-52-46(28-40(34)38)48-30-42-36(24-54(48)57(52)18-9-6-3)15-14-35-23-53(47(45)29-41(35)42)56(51)17-8-5-2/h10-15,19-30H,4-9,16-18H2,1-3H3
InChIKey=VUUJVETWVYQACL-UHFFFAOYSA-N

I have discussed a few bowl-shaped aromatics in this blog (see for example this and this). Kuo and Wu now report on a few bowls derived from C₇₀-fullerenes.¹ The bowl 1 was synthesized (along with a couple of other derivatives) and its x-ray structure obtained. As anticipated this polyclic aromatic is not planar, but rather a definite bowl, with a bowl depth of 2.28 Å. This is less curved than when the fragment is present in C₇₀-fullerene.

Interestingly, this bowl does not invert through a planar transition state. The fully planar structure 1pl, shown in Figure 1, is 116 kcal mol^-1 above the ground state bowl structure, computed at B3LYP/cc-pVDZ. Rather, the molecule inverts through a twisted S-shaped structure 1TS, also shown in Figure 1. The activation barrier through 1TS is 80 kcal mol^-1. This suggests that 1 is static at room temperature, unlike corranulene which has an inversion barrier, through a planar transition state, of only 11 kcal mol^-1. The much more concave structure of 1 than corranulene leads to the greatly increased strain in its all-planar TS. This implies that properly substituted analogues of 1 will be chiral and configurationally stable. Not remarked upon is that the inversion pathway, which will interchange enantiomers when 1 is properly substituted, follows a fully chiral path, as discussed in this post.

1
1TS	1pl

Figure 1. B3LYP/cc-pVDZ optimized geometries of 1, 1TS, and 1pl.

Reference

(1) Wu, T.-C.; Chen, M.-K.; Lee, Y.-W.; Kuo, M.-Y.; Wu, Y.-T. "Bowl-Shaped Fragments of C₇₀ or Higher Fullerenes: Synthesis, Structural Analysis, and Inversion Dynamics," Angew. Chem. Int. Ed. 2013, 52, 1289-1293, DOI: 10.1002/anie.201208200.

InChIs

1: InChI=1S/C38H14/c1-3-17-21-11-7-15-9-13-23-19-5-2-6-20-24-14-10-16-8-12-22-18(4-1)27(17)33-35-29(21)25(15)31(23)37(35)34(28(19)20)38-32(24)26(16)30(22)36(33)38/h1-14H
InChIKey=KLCLRPVBVWXTPN-UHFFFAOYSA-N

Assessing the degree of aromaticity in a novel compound has been a much sought after prize, and is the topic of much of Chapter 2 in my book. An interesting approach is described in a recent JACS paper by Williams and Mitchell.¹ The interior methyl groups of 1 sit above and below the ring plane of the aromatic dihydropyrene and provide an interesting magnetic probe of the aromaticity; the chemical shift of these methyl groups are δ -4.06ppm, far upfield as they sit in the shielded region above the aromatic plane. Annelation of a benzene ring to give 2 should reduce the ring current, thereby reflecting a reduced aromatic character. In fact, the chemical shifts of the methyls in 2 are δ -1.58 ppm. This relatively large chemical shift difference provides a means for measuring the aromatic influence of other fused rings.

Suppose a different (non-benzene) ring were fused onto 1. Williams and Mitchell examined two such cases 3 and 4 (among others). These two compounds were prepared and studied by ¹H NMR and also by B3LYP/6-31G* computations. The optimized structures of 3 and 4 are shown in Figure 1.

The experimental chemical shifts of the interior methyl groups are δ -3.32 ppm. This downfield shift of the methyls relative to their position in 1 reflects some homoaromatic character of the cycloheptatrienyl ring. If we take the difference in the methyl chemical shifts in 1 and 2 to reflect the aromatic character of benzene (2.48 ppm), then the difference in the chemical shifts of 3 and 1 (0.74 ppm) indicates that the cycloheptatrienyl ring has 0.74/2.48*100 = 30% the (homo)aromatic character of benzene! Similarly, the methyl chemical shifts in 4 are δ -3.56 ppm, leading to an estimate of the aromatic character of the tropone ring of 20%.

3

4

Figure 1. B3LYP/6-31G* optimized geometries of 3 and 4.

In using NICS to estimate the aromatic character, they make use of the average value of the NICS in the four rings of the dihydropyrene fragment. The baseline comparison is then in the average NICS value of 1 compared to that in 5, a compound that has a similar geometry but without the aromatic character of the fused benzene ring. This difference is 11.42ppm. The analogous relationship is then 3 with 6 (a NICS difference of 3.81 ppm) and 4 with 7 (a NICS difference of 2.77ppm). This gives an estimate of the (homo)aromatic character of cycloheptatriene of 33% and the aromatic character of tropolone of 24%. This NICS estimates are in great agreement with the experimental values from the proton chemical shifts.

References

(1) Williams, R. V.; Edwards, W. D.; Zhang, P.; Berg, D. J.; Mitchell, R. H. "Experimental Verification of the Homoaromaticity of 1,3,5-Cycloheptatriene and Evaluation of the Aromaticity of Tropone and the Tropylium Cation by Use of the Dimethyldihydropyrene Probe," J. Am. Chem. Soc. 2012, 134, 16742-16752, DOI: 10.1021/ja306868r.

InChIs

1: InChI=1S/C26H32/c1-23(2,3)21-13-17-9-11-19-15-22(24(4,5)6)16-20-12-10-18(14-21)25(17,7)26(19,20)8/h9-16H,1-8H3/t25-,26-
InChIKey=SEGNSURCRWXVRS-DIVCQZSQSA-N

2: InChI=1S/C30H34/c1-27(2,3)21-15-19-13-14-20-16-22(28(4,5)6)18-26-24-12-10-9-11-23(24)25(17-21)29(19,7)30(20,26)8/h9-18H,1-8H3/t29-,30-/m1/s1
InChIKey=JQXZCWYPFGGVNF-LOYHVIPDSA-N

3: InChI=1S/C33H40/c1-20-13-21(2)15-27-26(14-20)28-18-24(30(3,4)5)16-22-11-12-23-17-25(31(6,7)8)19-29(27)33(23,10)32(22,28)9/h11-12,14-19H,13H2,1-10H3/t32-,33-/m1/s1
InChIKey=MUBRTBMPRBJVOC-CZNDPXEESA-N

4: InChI=1S/C33H38O/c1-19-13-25-26(14-20(2)29(19)34)28-18-24(31(6,7)8)16-22-12-11-21-15-23(30(3,4)5)17-27(25)32(21,9)33(22,28)10/h11-18H,1-10H3/t32-,33-/m1/s1
InChIKey=OWIRQHSHEVFPPM-CZNDPXEESA-N

Corranulene 1 is a bowl-shaped aromatic compound. It inverts through a planar transition state with a barrier of at 11.5 kcal mol^-1. What changes would be found if one per-phenylated corranulene, making 2?

Scott¹ has prepared 2a-c by arylating corranulene using phenylboroxin and palladium acetate and repeating this arylation four times. Amazing to me is that the yield of 2c is 54%! The BMK/cc-pVDZ optimized structure of 2a is shown in Figure 1. One can readily see that the bowl is nearly flat (click on the image to activate Jmol; the x-ray structure of 2b has the bowl depth of only 0.248 Å, compared to a depth of 0.87 Å in 1.

Interestingly, 2 inverts through a chiral TS (shown in Figure 1) so that inversion does not create the enantiomer! The computed barrier height is only 2.5 kcal mol^-1.

2a

2aTS

Figure 1. BMK/cc-pVDZ optimized structures of 2a and the bowl inversion transition state 2aTS.

The flatter bowl results in longer bonds and wider angles about the rim of 2 than in 1. As one might expect, 2a is very strained: the BMK/cc-pVDZ estimation is that 2 is 53 kcal mol^-1 more strained than 1, using the homodesmotic Reaction 1. In total, this is a real nice study of using strain to alter shape.

References

(1) Zhang, Q.; Kawasumi, K.; Segawa, Y.; Itami, K.; Scott, L. T. "Palladium-Catalyzed C–H Activation Taken to the Limit. Flattening an Aromatic Bowl by Total Arylation," J. Am. Chem. Soc., 2012, 134, 15664-15667, DOI: 10.1021/ja306992k

InChIs

1: InChI=1S/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-UHFFFAOYSA-N

2a: InChI=1S/C80H50/c1-11-31-51(32-12-1)61-62(52-33-13-2-14-34-52)72-65(55-39-19-5-20-40-55)66(56-41-21-6-22-42-56)74-69(59-47-27-9-28-48-59)70(60-49-29-10-30-50-60)75-68(58-45-25-8-26-46-58)67(57-43-23-7-24-44-57)73-64(54-37-17-4-18-38-54)63(53-35-15-3-16-36-53)71(61)76-77(72)79(74)80(75)78(73)76/h1-50H
InChIKey=OGBCICIRFDLAPN-UHFFFAOYSA-N

2b: InChI=1S/C120H130/c1-111(2,3)81-51-31-71(32-52-81)91-92(72-33-53-82(54-34-72)112(4,5)6)102-95(75-39-59-85(60-40-75)115(13,14)15)96(76-41-61-86(62-42-76)116(16,17)18)104-99(79-47-67-89(68-48-79)119(25,26)27)100(80-49-69-90(70-50-80)120(28,29)30)105-98(78-45-65-88(66-46-78)118(22,23)24)97(77-43-63-87(64-44-77)117(19,20)21)103-94(74-37-57-84(58-38-74)114(10,11)12)93(73-35-55-83(56-36-73)113(7,8)9)101(91)106-107(102)109(104)110(105)108(103)106/h31-70H,1-30H3
InChIKey=UQHBWLRORHEQNL-UHFFFAOYSA-N

2c: InChI=1S/C80H40Cl10/c81-51-21-1-41(2-22-51)61-62(42-3-23-52(82)24-4-42)72-65(45-9-29-55(85)30-10-45)66(46-11-31-56(86)32-12-46)74-69(49-17-37-59(89)38-18-49)70(50-19-39-60(90)40-20-50)75-68(48-15-35-58(88)36-16-48)67(47-13-33-57(87)34-14-47)73-64(44-7-27-54(84)28-8-44)63(43-5-25-53(83)26-6-43)71(61)76-77(72)79(74)80(75)78(73)76/h1-40H
InChIKey=MMASAVXWJRDYLD-UHFFFAOYSA-N

The activation energy for the 5-endo-dig reaction of the anion 1 is anomalously low compared to its 4-endo-dig and 6-endo-dig analogues. Furthermore, the TS is quite early, earlier than might be expected based on the Hammond Postulate. Alabugin and Schleyer have examined this reaction and found some interesting results.¹

First, NICS(0) values for a series of related intermolecular anionic attack at alkynes show some interesting trends (Table 1). Two of the transition states look like they might be aromatic: the TSs for the 3-exo-dig and the 5-endo-dig reaction have NICS(0) values that are quite negative. However, given the geometry of these TSs, particularly the close proximity of the σ bonds to the ring center, one might be concerned about contamination of these orbitals. So, NICS(0)_MOzz computations, which look at the tensor component perpendicular to the ring using just the π-MOs, shows that the 3-exo-dig is likely non-aromatic (NICS(0)_MOzz is near zero), the TS for the 4-endo-dig reaction is antiaromatic (NICS(0)_MOzz very positive) and the TS for the 5-endo-dig reaction is aromatic (NICS(0)_MOzz is very negative. So this last reaction is the first example of an aromatic transition that is not for a pericyclic reaction!

Table 1. NICS(0) and NICS(0)_MOzz for the TS of some anionic alkyne cyclizations.

These authors argue that the reaction of 1 is an “aborted” sigmatropic shift. A normal pericyclic reaction is a single step with a single (concerted) transition state. An interrupted sigmatropic shift has an intermediate that lies higher in energy than the reactants, such as in the Bergman cyclization of an enediyne. The aborted sigmatropic shift has an intermediate that lies lower in energy than the reactants, such as in the cyclization of 1.

References

(1) Gilmore, K.; Manoharan, M.; Wu, J. I. C.; Schleyer, P. v. R.; Alabugin, I. V. "Aromatic Transition States in Nonpericyclic Reactions: Anionic 5-Endo Cyclizations Are Aborted Sigmatropic Shifts," J. Am. Chem. Soc. 2012, 134, 10584–10594, DOI: 10.1021/ja303341b

Hoffmann¹ reports on a number of new benzene dimer structures, notably 5-8, whose RIJCOSX-MP2/cc-pVTZ² structures are shown in Figure 1. A few of these new dimers are only somewhat higher in energy than the known dimers 1-4. The energies of these dimers, relative to two isolated benzene molecules, are listed in Table 1.

1	2
3	4
5	6
7	8

Figure 1. RIJCOSX-MP2/cc-pVTZ optimized geometries of 1-8.

Table 1. Energy (kcal mol^-1) of the dimers relative to two benzene molecules and activation energy for reversion to two benzene molecules.

The energy for reversion of the isomers 5-8 to two isolated benzene molecules is calculated to be fairly large, and so they should be stable relative to that decomposition mode. They also examined a series of other decomposition modes, including [1,5]-hydrogen migration, all of which had barriers of 21 kcal mol^-1 or greater, retrocyclization ([2+2]), for which they could not locate transition states, electrocyclic ring opening (Cope), with barriers of at least 17 kcal mol^-1 and dimerization – some of which had relatively small enthalpic barriers of 4-5 kcal mol^-1. However, the dimerizations all have very unfavorable entropic activation barriers.

So, the conclusion is that all of the novel dimers (4–8) can be reasonable expected to hang around for some time and therefore are potential synthetic targets.

References

(1) Rogachev, A. Yu.; Wen, X.-D.; Hoffmann, R. "Jailbreaking Benzene Dimers," J.
Am. Chem. Soc., 2012, 134, 8062-8065, DOI:10.1021/ja302597r

(2) Kossmann, S.; Neese, F. "Efficient Structure Optimization with Second-Order Many-Body Perturbation Theory: The RIJCOSX-MP2 Method," J. Chem. Theory Comput., 2010, 6, 2325-2338, DOI: 10.1021/ct100199k

InChIs

1: InChI=1S/C12H12/c1-2-6-10-9(5-1)11-7-3-4-8-12(10)11/h1-12H/t9-,10+,11-,12+
InChIKey=WMPWOGVJEXSFLI-UHFFFAOYSA-N

2: InChI=1S/C12H12/c1-2-6-10-9(5-1)11-7-3-4-8-12(10)11/h1-12H/t9-,10+,11+,12-
InChIKey=WMPWOGVJEXSFLI-IWDIQUIJSA-N

3: InChI=1S/C12H12/c1-2-4-12-10-7-5-9(6-8-10)11(12)3-1/h1-12H/t9?,10?,11-,12+
InChIKey=ONVDJSCNMCYFTI-CAODYFQJSA-N

4: InChI=1S/C12H12/c1-2-10-4-3-9(1)11-5-7-12(10)8-6-11/h1-12H
InChIKey=BCBHEUOKKNYIAT-UHFFFAOYSA-N

5: InChI=1S/C12H12/c1-2-6-10-9(5-1)11-7-3-4-8-12(10)11/h1-12H/t9-,10-,11+,12+/m1/s1
InChIKey=WMPWOGVJEXSFLI-WYUUTHIRSA-N

6: InChI=1S/C12H12/c1-2-4-12-10-7-5-9(6-8-10)11(12)3-1/h1-12H/t9?,10?,11-,12-/m0/s1
InChIKey=ONVDJSCNMCYFTI-QQFIATSDSA-N

7: InChI=1S/C12H12/c1-2-6-10-9(5-1)11-7-3-4-8-12(10)11/h1-12H/t9-,10-,11-,12+/m1/s1
InChIKey=WMPWOGVJEXSFLI-KKOKHZNYSA-N

8: InChI=1S/C12H12/c1-2-6-10-9(5-1)11-7-3-4-8-12(10)11/h1-12H/t9-,10-,11-,12-
InChIKey=WMPWOGVJEXSFLI-NQYKUJLISA-N

How should one assess the aromatic stabilization energy of non-planar compounds like corannulene 1? The standard approach might be to employ the homodesmotic reaction, like Reaction 1. The energy of this reaction is however quite different whether one chooses s-cis or s-trans butadiene: 67.5 kcal mol^-1 with the former and 14.8 kcal mol^-1 with the latter. Exactly how one balances the total number of cis/trans relationships is problematic, but worse still is that Reaction 1 does not remove the effect of strain and non-planarity of 1.

Reaction 1
15 H₂C=CH-CH=CH₂ + 20 H₂C=C(CH₃)₂ → 1 + 10 H₂C=CH₂ + 20 H₂C=CH-CH₃

Dobrowolski, Ciesielski and Cyranski¹ propose a series of reactions that extend the isomerization stabilization energy concept of Schleyer. References are chosen that involve fixed alternate polyenes by appending methylene groups, creating radialene-like compounds. Reaction 2 and 3 are two such reactions that attempt to remove strain and non-planarity effects along with balancing the cis/trans relationships and potential H-H clashes between the pendant methylene groups. They report an additional 18 variations, because there is no unique method for portioning these effects.

Reaction 2

Reaction 3

Using B3LYP/6-311G** energies with zero-point vibrational energy, the reaction energies are 46.7 and 46.3 kcal mol^-1 for Reactions 2 and 3, respectively. Using all of the variations, the mean value is 44.7 kcal mol^-1 with a standard deviation of only 1.2 kcal mol^-1. It is clear that corranulene has a rather substantial artomatic stabilization energy, reflecting its decided aromatic character.

In a similar vein, they have also estimated the aromatic stabilization energy of coronene 2 as 58.4 kcal mol^-1, which, while clearly demonstrating the 2 is aromatic, it does not express any “superaromaticity”.

References

(1) Dobrowolski, M. A.; Ciesielski, A.; Cyranski, M. K. "On the aromatic stabilization of corannulene and coronene," Phys. Chem. Chem. Phys., 2011, 13, 20557-20563, DOI: 10.1039/C1CP21994D

InChIs

1: InChI=1S/C21H14/c1-3-13-6-7-15-10-11-16-9-8-14-5-4-12(2)17-18(13)20(15)21(16)19(14)17/h3-11H,1H2,2H3
InChIKey=ZJQHTVPYWDRMLD-UHFFFAOYSA-N

2: InChI=1S/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-UHFFFAOYSA-N

Novel aromatic (or at least potentially aromatic species) just keep on coming! Tobe has prepared this interesting ortho-quinodimethane derivative 1b.¹ Ortho-quinodimethane derivatives are rare, due to the high reactivity of the underlying structure 2. Known derivatives of 2 tend to undergo an electrocyclic rearrangement to the cyclobutanobenzene 3. Fusing the benzene rings should minimize this electrocyclization, and the mesityl substituents should minimize dimerization. In fact 1b is stable as a solid or in solution, even in solution exposed to air.

B3LYP/6-31G(d) computations are in nice agreement with the x-ray structure concerning the important C-C distances. The terminal rings have delocalized bonds, while the interior three rings exhibit bond alternation. The authors claim that 1 should be thought of as ortho-quinodimethane bridged by two benzene rings. There does seem to be a bit of diradical character, though temperature dependent NMR shows no broadening, so the singlet-triplet gap is large, and therefore 1 exhibits small diradical character.

The computed NICS(0) for 1a values are -3.94 for the terminal ring (indicative of an aromatic phenyl), +9.20 for the 5-member ring, and +5.42 for the middle ring. These can be compared to the NICS(0) value of +3.21 for the ring of 2 and +11.51 and +21.17 for the 6 and 5-member rings of 4, respectively. So, 1a expresses some antiaromatic character.

References

(1) Shimizu, A.; Tobe, Y., "Indeno[2,1-a]fluorene: An Air-Stable ortho-Quinodimethane Derivative," Angew. Chem. Int. Ed. 2011, 50, 6906-6910, DOI: 10.1002/anie.201101950

InChIs

1a: InChI=1/C20H12/c1-3-7-15-13(5-1)11-19-17(15)9-10-18-16-8-4-2-6-14(16)12-20(18)19/h1-12H
InChIKey=PJULCNAVAGQLAT-UHFFFAOYAS

1b: InChI=1/C38H32/c1-21-17-23(3)33(24(4)18-21)35-29-13-9-7-11-27(29)31-15-16-32-28-12-8-10-14-30(28)36(38(32)37(31)35)34-25(5)19-22(2)20-26(34)6/h7-20H,1-6H3
InChIKey=BMQDJJPSCFSAIJ-UHFFFAOYAA

2: InChI=1/C8H8/c1-7-5-3-4-6-8(7)2/h3-6H,1-2H2
InChIKey=XURVRZSODRHRNK-UHFFFAOYAV

3: InChI=1/C8H8/c1-2-4-8-6-5-7(8)3-1/h1-4H,5-6H2
InChIKey=UMIVXZPTRXBADB-UHFFFAOYAR

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

Bendikov and co-workers have examined the dimerization of linear acenes at M06-2x/6-31G(d).¹ They have looked at the formal forbidden [4+4] reaction that takes, for example, 2 molecules of benzene into three possible dimer products 1P_anti1-2, 1P_syn1-2, and 1P_syn1-4. The relative energies of these products increases in that order, and all three are much higher in energy than reactants; the lowest energy dimer is 1P_anti1-2, lying 47.4 kcal mol^-1 above two benzene molecules. Similarly, the dimerization of naphthalene is also endothermic, but the formation of the symmetric dimer of anthracene 3P-2,2’ is exothermic by 5.4 kcal mol^-1. This gibes nicely with the best estimate of -9 ± 3 kcal mol^-1.² Dimerization of the higher acenes are increasingly exothermic.

The transition state for the dimerization of benzene is concerted, though very asymmetric, as seen in Figure 1. Its energy is quite high (77.79 kcal mol^-1) and so this reaction can be completely discounted. The TS for the dimerization of naphthalene is also concerted and asymmetric, but the reaction pathway for the dimerization is stepwise, with a diradical intermediate. Furthermore, the highest barrier for this stepwise reaction is 33.3 kcal mol^-1. The activation energy of the back reaction (anthracene dimer to two anthrecene molecules) was measured 36.3 kcal mol^-1,³ and the computed barrier of 38.7 kcal mol^-1 is in nice agreement. The computed barriers for the dimerization of the higher acenes are predicted to be even lower than that of anthracene, consistent with the observation of dimers of these molecules.

1Panti1-2	1TSanti1-2
1P-42	1TS-42

Figure 1. M06-2x /6-31G(d) optimized structures.

I was curious that the authors did not consider the formally allowed [4+2] dimerization, leading for example to 1P-42. So, I optimized this product and the concerted transition state leading to it. These are shown in Figure 1. The barrier through this transition state is still very large (54.1 kcal mol^-1) but it is 23 kcal mol^-1 lower in energy than the barrier of the [4+4] reaction! The Product of the [4+2] is also lower in energy (by 9 kcal mol^-1) than 1P_anti1-2. It seems to me that this type of dimerization is worth examining too – though I must say I have not as yet looked to see if anyone has explored this already.

References

(1) Zade, S. S.; Zamoshchik, N.; Reddy, A. R.; Fridman-Marueli, G.; Sheberla, D.; Bendikov,
M., "Products and Mechanism of Acene Dimerization. A Computational Study," J. Am. Chem. Soc., 2011, 133, 10803-10816, DOI: 10.1021/ja106594v

(2) Grimme, S.; Diedrich, C.; Korth, M., "The Importance of Inter- and Intramolecular van der Waals Interactions in Organic Reactions: the Dimerization of Anthracene Revisited," Angew. Chem. Int. Ed., 2006, 45, 625-629, DOI: 10.1002/anie.200502440

(3) Greene, F. D., "Problems of stereochemistry in photochemical reactions in the anthracene area," Bull. Soc. Chim. Fr., 1960, 1356-1360

InChIs

Benzene: InChI=1/C6H6/c1-2-4-6-5-3-1/h1-6H
InChIKey=UHOVQNZJYSORNB-UHFFFAOYAH

1P_anti1-2: InChI=1/C12H12/c1-2-6-10-9(5-1)11-7-3-4-8-12(10)11/h1-12H
InChIKey=WMPWOGVJEXSFLI-UHFFFAOYAP

1P_syn1-2: InChI=1/C12H12/c1-2-6-10-9(5-1)11-7-3-4-8-12(10)11/h1-12H
InChIKey=WMPWOGVJEXSFLI-UHFFFAOYAP

1P_syn1-4: InChI=1/C12H12/c1-2-10-4-3-9(1)11-5-7-12(10)8-6-11/h1-12H
InChIKey=BCBHEUOKKNYIAT-UHFFFAOYAI

1P-42: InChI=1/C12H12/c1-2-4-12-10-7-5-9(6-8-10)11(12)3-1/h1-12H
InChIKey=ONVDJSCNMCYFTI-UHFFFAOYAY

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

3P-2,2’: InChI=1/C28H20/c1-2-10-18-17(9-1)25-19-11-3-4-12-20(19)26(18)28-23-15-7-5-13-21(23)27(25)22-14-6-8-16-24(22)28/h1-16,25-28H
InChIKey=JUTIJVADGQDBGY-UHFFFAOYAY

One of the ubiquitous examples of the Hückel rule is cyclooctatetraene dianion (COT^2-). This annulene has, presumably, 10 π electrons and therefore should be aromatic, satisfying the 4n+2 rule. Therefore, the molecule should be planar, right? Well, an article by Dominikowska and Palusiak call into question these assumptions.¹

COT^2-

First off, with either B3LYP or MP2 and a variety of basis sets, optimization of COT^2- starting from the tub-shape of COT itself led to the planar or nearly planar structure most of the time. The exceptions include B3LYP/6-311++G(d,p) and MP2/aug-cc-pVDZ. More interesting is that a number of the MP2 planar structures have one or more imaginary frequency; for example, MP2/6-311G has four imaginary frequencies.

I reoptimized a number of these structures assuming D_8h symmetry, and looked for the number of imaginary frequencies. B3LYP/6-311G(d,p) had no imaginary frequencies, but B3LYP/6-31++G(d,p) and B3LYP/6-311++G(d,p) had 2 and 4 imaginary frequencies, respectively. Many of the MP2 optimizations had imaginary frequencies, with MP2/6-311G(d,p) having 3 imaginary frequencies. The optimized structures of COT^2- at ωB97X-D/6-311G(d,p) had no imaginary frequencies but with the 6-311++G(d,p) basis set, it had two imaginary frequencies. Interestingly, Truhlar’s M06-2x functional with both 6-311G(d,p) and 6-311++G(d,p) gives no imaginary.

This is reminiscent of the situation with benzene and other arenes, where certain combinations of method and basis set gave multiple imaginary frequencies.² The ultimate culprit was identified as intramolecular basis set superposition error. Dominikowska and Palusiak discount this explanation here for two reasons. First, multiple imaginary frequencies are seen with the Dunning correlation consistent basis sets – MP2/aug-cc-pVDZ has 7 imaginary frequencies (though my computation at D_8h gives only one imaginary frequency), something not observed for benzene. Secondly, they noticed that in the non-planar COT^2- optimized structure there are bond paths connecting the hydrogens to non-nuclear attractors situated way outside the molecule. They suggest that the COT^2- might really be a Rydberg state, with the extra electrons located outside the molecule. This implies that the π system has only 8 electrons, giving the tub shape. They note that COT^2- has a very short lifetime and suggest that it is not an aromatic compound, a larger annulene congener of benzene, at all.

It would be interesting to see what would happen with COT^2- correcting for intramolecular basis set superposition error via the method of Asturiol, Duran and Salvador,³ which I described in this post. This correction led to planar benzene having no imaginary frequencies. This type of computation would help assess just what is going on here – is COT^2- afflicted with basis set problems or is it a very unusual, non-aromatic system?

References

(1) Dominikowska, J.; Palusiak, M., "Cyclooctatetraene dianion—an artifact?," J. Comput. Chem., 2011, 32, 1441-1448, DOI: 10.1002/jcc.21730

(2) Moran, D.; Simmonett, A. C.; Leach, F. E.; Allen, W. D.; Schleyer, P. v. R.; Schaefer, H. F., III, "Popular Theoretical Methods Predict Benzene and Arenes To Be Nonplanar," J. Am. Chem. Soc., 2006, 128, 9342-9343, DOI: 10.1021/ja0630285

(3)  Asturiol, D.; Duran, M.; Salvador, P., "Intramolecular basis set superposition error effects on the planarity of benzene and other aromatic molecules: A solution to the problem," J. Chem. Phys., 2008, 128, 144108, DOI: 10.1063/1.2902974