The click reaction has become a major workhorse of synthetic chemists since its proposal in 2001.¹ Despite its efficiencies, no clear-cut example of its use in nature has been reported until 2012, where Yu and co-workers speculated that it might be utilized in the biosynthesis of lycojaponicumin A and B.² Krenske, Patel, and Houk have examined the possibility of an enzyme activated click process in forming this natural product.³

First they examined the gas-phase intramolecular [3+2] reaction that takes 1 into 2.

They identified (at M06-2X/def2-TZVPP/M06-2X/6-31+G(d,p)) four different low-energy conformations of 1, of which three have the proper orientation for the cyclization to occur. The lowest energy conformer, the TS, and the product 2 are shown in Figure 1. The free energy activation barrier in the gas phase is 19.8 kcal mol^-1. Inclusion of water as an implicit solvent (through a TS starting from a different initial conformation) increases the barrier to 20.0 kcal mol^-1. Inclusion of four explicit water molecules, hydrogen bonded to the nitrone and enone, predicts a barrier of 20.5 kcal mol^-1. These values predict a slow reaction, but not totally impossible. In fact, Tantillo in a closely related work reported a theoretical study of the possibility of a [3+2] cyclization in the natural synthesis of flueggine A and virosaine, and found barriers of comparable size as here. Tantillo concludes that enzymatic activation is not essential.⁴

1

TS12

3

Table 1. M06-2X/6-31+G(d,p) optimized geometries of 1, TS12, and 2.

To model a potential enzyme, the Houk group created a theozyme whereby two water molecules act as hydrogen bond donors to the enone and the use of implicit solvent (diethyl ether) to mimic the interior of an enzyme. This theozyme model predicts a barrier of 15.3 kcal mol^-1, or a 2000 fold acceleration of the click reaction. The search for such an enzyme might prove quite intriguing.

References

(1) Kolb, H. C.; Finn, M. G.; Sharpless, K. B. "Click Chemistry: Diverse Chemical Function from a Few Good Reactions," Angew. Chem. Int. Ed. 2001, 40, 2004-2021, DOI: 10.1002/1521-3773(20010601)40:11<2004::AID-ANIE2004>3.0.CO;2-5.

(2) Wang, X.-J.; Zhang, G.-J.; Zhuang, P.-Y.; Zhang, Y.; Yu, S.-S.; Bao, X.-Q.; Zhang, D.; Yuan, Y.-H.; Chen, N.-H.; Ma, S.-g.; Qu, J.; Li, Y. "Lycojaponicumins A–C, Three Alkaloids with an Unprecedented Skeleton from Lycopodium japonicum," Org. Lett. 2012, 14, 2614-2617, DOI: 10.1021/ol3009478.

(3) Krenske, E. H.; Patel, A.; Houk, K. N. "Does Nature Click? Theoretical Prediction of an Enzyme-Catalyzed Transannular 1,3-Dipolar Cycloaddition in the Biosynthesis of Lycojaponicumins A and B," J. Am. Chem. Soc. 2013, 135, 17638-17642, DOI: 10.1021/ja409928z.

(4) Painter, P. P.; Pemberton, R. P.; Wong, B. M.; Ho, K. C.; Tantillo, D. J. "The Viability of Nitrone–Alkene (3 + 2) Cycloadditions in Alkaloid Biosynthesis," J. Org. Chem. 2014, 79, 432–435, DOI: 10.1021/jo402487d.

InChIs

1: InChI=1S/C16H21NO3/c1-11-8-12-10-14(18)13-4-2-6-17(20)7-3-5-16(12,13)15(19)9-11/h4,7,11-12H,2-3,5-6,8-10H2,1H3/b13-4-,17-7+
InChIKey=GVEYMXKHRRHCLV-KYGYAMEJSA-N

2: InChI=1S/C16H21NO3/c1-9-6-10-8-13(19)16-11(17-5-3-14(16)20-17)2-4-15(10,16)12(18)7-9/h9-11,14H,2-8H2,1H3/t9?,10-,11?,14?,15+,16-/m0/s1
InChIKey=QKFAOJHYKPBTKX-SGVNFLFUSA-N

The notion of tunneling control has been a topic of interest within this blog a number of times. As developed by Schreiner and Allen,^1,2 tunneling control is a third means for predicting (or directing) the outcome of a reaction, alongside the more traditionally recognized kinetic and thermodynamic control. Tunneling control occurs when tunneling through a higher barrier is preferred over tunneling through a lower barrier.

Kozuch and Borden propose another example of tunneling control, this time in the rearrangement of the noradamantyl carbene 1.³ This carbene can undergo a 1,2-carbon shift, driven by strain relief to form the alkene 2. The alternative as a 1,2-hydrogen shift that produces the alkene 3.

These two reaction pathways were explored using B3LYP/6-31G(d,p) computations coupled with canonical variational theory and small curvature tunneling corrections. Structures of the reactant 1 and the two transition states leading to the two products 2 and 3 are shown in Figure 1. The activation barrier at 300 K is 5.4 kcal mol^-1 leading to 2 and 8.6 kcal mol^-1 leading to 3. Tunneling is expected to be much more important for the hydrogen shift than for the carbon shift, but even including tunneling, the rate to form 2 is much faster than the rate to form 3 at 300 K.

1	TS 1→2	2
	TS 1→3	3

Figure 1. B3LYP/6 optimized structures of 1-3 and the transition states leading to 2 and 3.

The situation is reversed however at cryogenic temperatures (< 20 K). Tunneling is now the only route for the reactions to occur, and the rate for formation of 3 is dramatically greater than the rate of formation of 2, which is inhibited by the movement of the much heavier carbon atom. Perdeuteration of the methyl group of 1, which drastically slows the rate of tunneling in the path to 3, nonetheless still favors this pathway (forming d₃–3) over formation of d₃–2. Thus, at low temperatures the formation of 3 is the preferred product, a manifestation of tunneling control.

Kozuch and Borden end their paper with a hope that an experimentalist will examine this interesting case. I concur!

References

(1) Schreiner, P. R.; Reisenauer, H. P.; Ley, D.; Gerbig, D.; Wu, C.-H.; Allen, W. D. "Methylhydroxycarbene: Tunneling Control of a Chemical Reaction," Science 2011, 332, 1300-1303, DOI: 10.1126/science.1203761.

(2) Ley, D.; Gerbig, D.; Schreiner, P. R. "Tunnelling control of chemical reactions – the organic chemist’s perspective," Org. Biomol. Chem. 2012, 10, 3781-3790, DOI: 10.1039/C2OB07170C.

(3) Kozuch, S.; Zhang, X.; Hrovat, D. A.; Borden, W. T. "Calculations on Tunneling in the Reactions of Noradamantyl Carbenes," J. Am. Chem. Soc. 2013, 135, 17274-17277, DOI: 10.1021/ja409176u.

InChIs

1: InChI=1S/C11H16/c1-2-11-6-8-3-9(7-11)5-10(11)4-8/h8-10H,3-7H2,1H3
InChIKey=CXFJINASYYTBBV-UHFFFAOYSA-N

2: InChI=1S/C11H16/c1-7-10-3-8-2-9(5-10)6-11(7)4-8/h8-10H,2-6H2,1H3
InChIKey=XDANPUSLLJWVEK-UHFFFAOYSA-N

3: InChI=1S/C11H16/c1-2-11-6-8-3-9(7-11)5-10(11)4-8/h2,8-10H,1,3-7H2
InChIKey=JHEPVTWREMDEMG-UHFFFAOYSA-N

The concept of antiaromaticity is an outgrowth of the well-entrenched notion or aromaticity. While 4n+2 π-electron systems are aromatic, 4n π-electron systems should be antiaromatic. That should mean that antiaromatic systems are unstable. The cyclopropenyl anion 1a has 4 π-electrons and should be antiaromatic. Kass has provided computational results that strongly indicate it is not antiaromatic!¹

Let’s first look at the 3-cyclopropenyl cation 1c. Kass has computed (at both G3 and W1) the hydride affinity of 1c-4c. The hydride affinities of the latter three compounds plotted against the C=C-C⁺ angle is linear. The hydride affinity of 1c however falls way below the line, indicative of 1c being very stable – it is aromatic having just 2 π-electrons.

A similar plot of the deprotonation enthalpies leading to 1a-4d vs. C=C-C^– angle is linear including all four compounds. If 1a where antiaromatic, one would anticipate that the deprotonation energy to form 1a would be much greater than expected simply from the effect of the smaller angle. Kass suggests that this indicates that 1a is not antiaromatic, but just a regular run-of-the-mill (very) reactive anion.

A hint at what’s going on is provided by the geometry of the lowest energy structure of 1a, shown in Figure 1. The molecule is non-planar, having C_s symmetry. A truly antiaromatic structure should be planar, really of D_3h symmetry. The distortion from this symmetry reduces the antiaromatic character, in the same way that cyclobutadiene is not a perfect square and that cyclooctatraene is tub-shaped and not planar. So perhaps it is more fair to say that 1a has a distorted structure to avoid antiaromaticity, and that the idealized D_3h structure, does not exist because of its antiaromatic character.

References

(1) Kass, S. R. "Cyclopropenyl Anion: An Energetically Nonaromatic Ion," J. Org. Chem. 2013, 78, 7370-7372, DOI: 10.1021/jo401350m.

InChIs

1a: InChI=1S/C3H3/c1-2-3-1/h1-3H/q-1
InChIKey=IBTMQWIWZUYLHW-UHFFFAOYSA-N

1c: InChI=1S/C3H3/c1-2-3-1/h1-3H/q+1
InChIKey=IPKCFGQXHZKYLH-UHFFFAOYSA-N

Sorry I missed this paper from much earlier this year – it’s from a journal that’s not on my normal reading list. Anyways, here is another fantastic work from the Schreiner lab demonstrating the concept of tunneling control (see this post).¹ They prepare the t-butylhydroxycarbene 1 at low temperature to look for evidence of formation of possible products arising from a [1,2]-hydrogen shift (2), a [1,2]-methyl shift (3) or a [1,3]-CH insertion (4).

Schreiner performed CCSD(T)/cc-pVDZ optimizations of these compounds along with the transition states for the three migrations. The optimized geometries and relative energies are shown in Figure 1. The thermodynamic product is the aldehyde 2 while the kinetic product is the cyclopropane 4, with a barrier of 23.8 kcal mol^-1 some 3.5 kcal mol^-1 lower than the barrier leading to 2.

1 (0.0)	TS2 (27.3)	2 (-53.5)
	TS3 (31.0)	3 (-41.0)
	TS4 (23.8)	4 (-28.3)

Figure 1. CCSD(T)/cc-pVDZ optimized structures of 1-4 and the transition states for the three reaction. Relative energies in kcal mol^-1.

At low temperature (11 K), 1 is found to slowly convert into 2 with a half-life of 1.7 h. No other product is observed. Rates for the three reactions were also computed using the Wentzel-Kramers-Brillouin (WKB) method (which Schreiner and Allen have used in all of their previous studies). The predicted rate for the conversion of 1 into 2, which takes place at 11 K solely through a tunneling process, is 0.4h, in quite reasonable agreement with experiment. The predicted rates for the other two potential reactions at 11 K are 10³¹ and 10⁴⁰ years.

This is clearly an example of tunneling control. The reaction occurs not across the lowest barrier, but through the narrowest barrier.

References

(1) Ley, D.; Gerbig, D.; Schreiner, P. R. "Tunneling control of chemical reactions: C-H insertion versus H-tunneling in tert-butylhydroxycarbene," Chem. Sci. 2013, 4, 677-684, DOI: 10.1039/C2SC21555A.

InChI

1: InChI=1S/C5H10O/c1-5(2,3)4-6/h6H,1-3H3
InChIKey=ZGFKBRGJTPEEOC-UHFFFAOYSA-N

2: InChI=1S/C5H10O/c1-5(2,3)4-6/h4H,1-3H3

3: InChI=1S/C5H10O/c1-4(2)5(3)6/h6H,1-3H3
InChIKey=BZAZNULYLRVMSW-UHFFFAOYSA-N

4: InChI=1S/C5H10O/c1-5(2)3-4(5)6/h4,6H,3H2,1-2H3
InChIKey=MWWQKEGWQLBJBJ-UHFFFAOYSA-N

The role of dispersion in large systems is increasingly recognized as critical towards understanding molecular geometry. An interesting example is this study of acene dimers by Grimme.¹ The heptacene and nonacene dimers (1 and 2) were investigated with an eye towards the separation between the “butterfly wings” – is there a “stacked” conformation where the wings are close together, along with the “open” conformer?

The LPNO-CEPA/CBS potential energy surface of 1 shows only a single local energy minima, corresponding to the open conformer. B3LYP-D3 and B3LYP-NL, two different variations of dealing with dispersion (see this post), do a reasonable job at mimicking the LPNO-CEPA results, while MP2 indicates the stacked conformer is lower in energy than the open conformer.

B3LYP-D3 predicts both conformers for the nonacene dimer 2, and the optimized structures are shown in Figure 2. The stacked conformer is slightly lower in energy than the open one, with a barrier of about 3.5 kcal mol^-1. However in benzene solution, the open conformer is expected to dominate due to favorable solvation with both the interior and exterior sides of the wings.

open

stacked

Figure 1. B3LYP-D3/ef2-TZVP optimized structures of the open and stacked conformations of 2.

References

(1) Ehrlich, S.; Bettinger, H. F.; Grimme, S. "Dispersion-Driven Conformational Isomerism in σ-Bonded Dimers of Larger Acenes," Angew. Chem. Int. Ed. 2013, 41, 10892–10895, DOI: 10.1002/anie.201304674.

InChIs

1: InChI=1S/C60H36/c1-2-10-34-18-42-26-50-49(25-41(42)17-33(34)9-1)57-51-27-43-19-35-11-3-4-12-36(35)20-44(43)28-52(51)58(50)60-55-31-47-23-39-15-7-5-13-37(39)21-45(47)29-53(55)59(57)54-30-46-22-38-14-6-8-16-40(38)24-48(46)32-56(54)60/h1-32,57-60H
InChIKey=OYVUURMCCBPDLI-UHFFFAOYSA-N

2: InChI=1S/C76H44/c1-2-10-42-18-50-26-58-34-66-65(33-57(58)25-49(50)17-41(42)9-1)73-67-35-59-27-51-19-43-11-3-4-12-44(43)20-52(51)28-60(59)36-68(67)74(66)76-71-39-63-31-55-23-47-15-7-5-13-45(47)21-53(55)29-61(63)37-69(71)75(73)70-38-62-30-54-22-46-14-6-8-16-48(46)24-56(54)32-64(62)40-72(70)76/h1-40,73-76H
InChIKey=FTSMWBVFVPAXOB-UHFFFAOYSA-N

The singlet and triplet carbene is the topic of Chapter 4, especially sections 1 and 2. The ground state of methylene is the triplet, with one electron in the σ-orbital and one electron in the π-orbital, with the spins aligned. The lowest singlet state places the pair of electrons in the σ-orbital, and this state is about 9 kcal mol^-1 higher in energy than the triplet. The next lowest singlet state has one electron in each of the σ- and π-orbitals, with the spins aligned. The singlet state with both electrons in the π-orbital is the highest of these four states, some 60 kcal mol^-1 above the ground state triplet.

Hoffmann and Borden now pose the question “Can the doubly occupied π carbene (¹A₁-σ⁰π²) be the ground state with appropriate substitution?” The answer they find is yes!¹

The trick is to find a combination of substituents that will raise the energy of the σ-orbital and lower the energy of the π-orbital. The latter effect can be enhanced if the π-orbital can be a part of an aromatic (6e^–) ring.

Two of the best possibilities for identifying a ground state ¹A₁-σ⁰π² carbene are 1 and 2. The CASSCF/6-31G(d) optimized geometries of these two are shown in Figure 1. In 1, the nitrogen lone pairs act to destabilize the σ-orbital, while the aldehyde group acts as a withdrawing group to stabilize the π-orbital. The result is that the ¹A₁-σ⁰π⁶ state of 1 is predicted to be about 8 kcal mol^-1 more stable than the triplet state, as per CASPT2 and CCSD(T) computations.

An ever greater effect is predicted for 2. Here the nitrogen lone pairs adjacent to the carbene act to destabilize the σ-orbital. The empty π-orbital on B lowers the energy of the carbene π-orbital by making it part of the 6-electron aromatic ring. The ¹A₁-σ⁰π⁶ state of 2 is predicted to be about 25 kcal mol^-1 more stable than its triplet state!

1

2

Figure 1. CASSCF/6-31G(d) optimized geometries of the ¹A₁-σ⁰π⁶ states of 1 and 2.

References

(1) Chen, B.; Rogachev, A. Y.; Hrovat, D. A.; Hoffmann, R.; Borden, W. T. "How to
Make the σ⁰π² Singlet the Ground State of Carbenes," J. Am. Chem. Soc. 2013, 135, 13954-13964, DOI: 10.1021/ja407116e.

InChIs

1: InChI=1S/C5H2N2O2/c8-1-4-5(2-9)7-3-6-4/h1-2H
InChIKey=QDSVROXEBBWIOO-UHFFFAOYSA-N

2: InChI=1S/C3H3BN2/c1-4-2-6-3-5-1/h1-2,4H
InChIKey=MQJXDZBYOSOLST-UHFFFAOYSA-N

A long sought-after data point critical to the non-classical cation story has finally been obtained. The elusive x-ray crystal structure of a norbornyl cation was finally solved.¹ The [C₇H₁₁]⁺[Al₂Br₇]^– salt was crystallized in CH₂Br₂ at low temperature (40 K). This low temperature was needed to prohibit rotation of the norbornyl cation within the crystal (the cation is near spherical and so subject to relatively easy rotation within the crystal matrix) and hydride scrambling among the three carbons (C₁, C₂, and C₆) involved in the non-classical cation structure.

The authors report a number of different structures, all very similar, depending on slight differences in the crystals used. However, the important features are consistent with all of the structures. The cation is definitely of the non-classical type (see Figure 1) with the basal C₁-C₂ bond length of 1.39 Å similar that in benzene and long non-classical C₁-C₆ and C₂-C₆ distances of 1.80 Å. These distances match very well with the MP2(FC)/def2-QZVPP optimized distances of 1.393 and 1.825 Å, respectively.

Figure 1. X-ray structure of norbornyl cation.

References

(1) Scholz, F.; Himmel, D.; Heinemann, F. W.; Schleyer, P. v. R.; Meyer, K.; Krossing, I. "Crystal Structure Determination of the Nonclassical 2-Norbornyl Cation," Science 2013, 341, 62-64, DOI: 10.1126/science.1238849.

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.

Halskov, et al.¹ reported the interesting Diels-Alder selectivity shown in Scheme 1. The linear trienamine 1 did not undergo the Diels-Alder addition, while the less stable cross-conjugated diene 2 does react with 3 with high diastereo- and enantioselectivity. Their MPW1K/6-31+G(d,p) computations on a model system, carried out for a gas-phase environment, indicated a concerted mechanism, with thermodynamic control. However, the barrier for the reverse reaction for the kinetic product was computed to be greater than 30 kcal mol^-1, casting doubt on the possibility of thermodynamic control.

Scheme 1.

Houk and co-workers² have re-examined this reaction with the critical addition of performing the computation including the solvent effects. Since the stepwise alternatives involve the formation of zwitterions, solvent can be critical in stabilizing these charge-separated species, intermediates that might be unstable in the gas phase. Henry Rzepa has pointed out in his blog and on many comments in this blog about the need to include solvent, and this case is a prime example of the problems inherent in neglecting solvation.

Using models of the above reaction Houk located two zwitterionic intermediates of the Michael addition for both the reactions of 4 with 6 and of 5 with 6. The second step then involves the closure of the ring to give what would be Diels-Alder products. This is shown in Scheme 2. They were unable to locate transition states for any concerted pathways. The computations were done at M06-2x/def2-TZVPP/IEFPCM//B97D/6-31+G(d,p)/IEFPCM, modeling trichloromethane as the solvent.

Scheme 2. Numbers in italics are energies relative to 4 + 6.

The activation barrier for the second step in each reaction is very small, typically less than 5 kcal mol^-1, so the first step is rate determining. The lowest barrier is for the reaction of 5 leading to 9, analogous to the observed product. Furthermore, 9 is also the thermodynamic product. Thus, the regioselectivity is both kinetically and thermodynamically controlled through a stepwise reaction. This conclusion is only possible by including solvent in order to stabilize the zwitterionic intermediates, and should be a word of caution for everyone doing computations: be sure to include solvent for any reactions that involved charged or charge-separated species at any point along the reaction pathway!

References

(1) Halskov, K. S.; Johansen, T. K.; Davis, R. L.; Steurer, M.; Jensen, F.; Jørgensen, K. A. "Cross-trienamines in Asymmetric Organocatalysis," J. Am. Chem. Soc. 2012, 134, 12943-12946,
DOI: 10.1021/ja3068269.

(2) Dieckmann, A.; Breugst, M.; Houk, K. N. "Zwitterions and Unobserved Intermediates in Organocatalytic Diels–Alder Reactions of Linear and Cross-Conjugated Trienamines," J. Am. Chem. Soc. 2013, 135, 3237-3242, DOI: 10.1021/ja312043g.