The nine methyl groups of nonamethylcyclopentyl cation 1 all interconvert with a barrier of 7 kcal mol^-1. However, at low temperature only partial scrambling occurs: there are two sets of methyl groups, one containing five groups and the other containing four methyl groups. The barrier for this scrambling is only 2.5 kcal mol^-1. While this behavior was found more than 20 years ago, Tantillo and Schleyer¹ only now have offered a complete explanation.

1

The ground state structure of 1 is shown in Figure 1 and has C₁ symmetry. The two pseudo-axial methyl groups adjacent to the cationic center show evidence of hyperconjugation: long C-C bonds and Me-C-C⁺ angles of 100°.

The transition state TS1¸also in Figure 1, is of C_s symmetry. This transition state leads to interchange of the pseudo-axial methyls, and interchange of the pseudo-equatorial methyls, but no exchange between the members of these two groups. The M06-2x/6-31+G(d,p) and mPW1PW91/6-31+G(d,p) estimate of this barrier is 1.5 and 2.5 kcal mol^-1, respectively. This agrees well with the experiment.

1
TS1	TS2

Figure 1. B3LYP/6-3+G(d,p) optimized geometries.

A second transition state TS2 was found and it corresponds with a twisting motion that interconverts an axial methyl with an equatorial methyl. This TS has C_s symmetry (shown in Figure 1) and the eclipsing interaction give rise to a larger barrier: 7.3 (M06-2x/6-31+G(d,p)) and 6.7 kcal mol^-1 (mPW1PW91/6-31+G(d,p)). So twisting through TS2 and scrambling through TS1 allows for complete exchange of all 9 methyl groups.

An interesting point also made by these authors is that these three structures represent the continuum of cationic structure: a classical (localized) cation in TS2, a bridged structure in TS1 and hyperconjugated cation in 1.

References

(1) Tantillo, D. J.; Schleyer, P. v. R. “Nonamethylcyclopentyl Cation Rearrangement Mysteries Solved,” Org. Lett. 2013, 15, 1725-1727, DOI: 10.1021/ol4005189.

InChIs

1: InChI=1S/C14H27/c1-10-11(2,3)13(6,7)14(8,9)12(10,4)5/h1-9H3/q+1
InChIKey=WUGVCUSQGLXERW-UHFFFAOYSA-N

One of the most widely recognized principles within organic chemistry is Hückel’s rule: an aromatic compound possesses 4n+2 π-electrons while an antiaromatic compound possesses 4n π-electrons. Much less well known is Baird’s rule:¹ the first excited triplet state will be aromatic if it has 4n π-electrons and antiaromatic if it has 4n+2 π-electrons.²

Schleyer used a number of standard methods for assessing aromatic character of a series of excited state triplets, including NICS values and geometric parameters.³ However, Schleyer has long been a proponent of an energetic assessment of aromaticity and it is only now in this recent paper⁴ that he and co-workers examine the stabilization energy of excited triplet states. The isomerization
stabilization energy (ISE)⁵ compares an aromatic (or antiaromatic) compound against a non-aromatic reference, one that typically is made by appending an exo-methylene group to the ring. So, to assess the ISE of the T₁ state of benzene, Reaction 1 is used. (Note that the inherent assumption here is that the stabilization energy of benzene is essentially identical to that of toluene.) At B3LYP/6-311++G(d,p) the energy of Reaction 1 is +13.5 kcal mol^-1. This reaction should be corrected for non-conservation of s-cis and s-trans conformers by adding on the energy of Reaction 2, which is +3.4 kcal mol^-1. So, the ISE of triplet benzene is +16.9 kcal mol^-1, indicating that it is antiaromatic. In contrast, the ISE for triplet cyclooctatetraene is -15.6 kcal mol^-1, and when corrected its ISE value is -24.7 kcal mol^-1, indicating aromatic character. These are completely consistent with Baird’s rule. Schleyer also presents an excellent correlation between the computed ISE values for the triplet state of 9 monocyclic polyenes and their NICS(1)_zz values.

I want to thank Henrik Ottosson for bringing this paper to my attention and for his excellent seminar on the subject of Baird’s rule on his recent visit to Trinity University.

References

(1) Baird, N. C. "Quantum organic photochemistry. II. Resonance and aromaticity in
the lowest 3ππ* state of cyclic hydrocarbons," J. Am. Chem. Soc. 1972, 94, 4941-4948, DOI: 10.1021/ja00769a025.

(2) Ottosson, H. "Organic photochemistry: Exciting excited-state aromaticity," Nat Chem 2012, 4, 969-971, DOI: 10.1038/nchem.1518.

(3) Gogonea, V.; Schleyer, P. v. R.; Schreiner, P. R. "Consequences of Triplet Aromaticity in 4nπ-Electron Annulenes: Calculation of Magnetic Shieldings for Open-Shell Species," Angew. Chem. Int. Ed. 1998, 37, 1945-1948, DOI: 10.1002/(SICI)1521-3773(19980803)37:13/14<1945::AID-ANIE1945>3.0.CO;2-E.

(4) Zhu, J.; An, K.; Schleyer, P. v. R. "Evaluation of Triplet Aromaticity by the
Isomerization Stabilization Energy," Org. Lett. 2013, 15, 2442-2445, DOI: 10.1021/ol400908z.

(5) Schleyer, P. v. R.; Puhlhofer, F. "Recommendations for the Evaluation of Aromatic Stabilization Energies," Org. Lett. 2002, 4, 2873-2876, DOI: 10.1021/ol0261332.

Jacobsen reports on another application of thiourea-based organocatalysts, this time for the
catalysis of hydroamination.¹ To support the synthetic effort, he examined the uncatalyzed intramolecular hydroamination that takes 1, through TS1 into product 2. The geometry of TS1 optimized at B3LYP/6-31+G(d,p) is shown in Figure 1. The computed barrier for this reaction is 22.2 kcal mol^-1. Using a model thiourea as the catalyst (MeHN)₂C=S, 3), Jacobsen locates a
catalyzed transition state TS2 shown in Figure 1. The activation barrier for this catalyzed reaction is 19.1 kcal mol^-1, suggesting that a thiourea can afford a real catalytic effect.

TS1

TS2

Figure 1. B3LYP/6-31+G(d,p) optimized geometries of TS1 and TS2(the catalyzed transition state).

Jacobsen then goes on to show that 4 can act as both an excellent catalyst for the hydroamination reaction along with inducing significant enantioselectivity. An example is Reaction 1, where 10 mol% of catalyst 3 gives an overall yield of 83% and an ee of 91%, while in the absence of catalyst the yield is only 8%.

References

(1) Brown, A. R.; Uyeda, C.; Brotherton, C. A.; Jacobsen, E. N. "Enantioselective Thiourea-Catalyzed Intramolecular Cope-Type Hydroamination," J. Am. Chem. Soc. 2013, 135, 6747-6749, DOI: 10.1021/ja402893z.

InChIs

1: InChI=1S/C5H11NO/c1-2-3-4-5-6-7/h2,6-7H,1,3-5H2
InChIKey=JUMXQRNWLGIKEI-UHFFFAOYSA-N

2: InChI=1S/C5H11NO/c1-5-3-2-4-6(5)7/h5,7H,2-4H2,1H3
InChIKey=YVBPNYXAQNAMLH-UHFFFAOYSA-N

3: InChI=1S/C3H8N2S/c1-4-3(6)5-2/h1-2H3,(H2,4,5,6)
InChIKey=VLCDUOXHFNUCKK-UHFFFAOYSA-N

4: InChI=1S/C44H49N3OS/c1-44(2,3)42(41(48)36-25-15-24-35(36)34-23-14-21-30-16-10-11-22-33(30)34)46-43(49)45-37-26-12-13-27-40(37)47-38(31-17-6-4-7-18-31)28-29-39(47)32-19-8-5-9-20-32/h4-11,14,16-23,28-29,35-37,40,42H,12-13,15,24-27H2,1-3H3,(H2,45,46,49)/t35-,36?,37-,40-,42-/m1/s1
InChIKey=OJMZMPGOFWBKAF-FDGFXIECSA-N