Torquoselectivity rules (discussed in Chapter 3.5 of my book) indicate that 3-phenylcyclobutene will ring-open to give the outward rotated product (Reaction 1). Houk and Tang report a seeming contradiction, namely the ring opening of 1 gives only the inward product 3 (Reaction 2).¹

B3LYP/6-31G* computations on the ring-opening of 4 indicate that the activation barrier for the outward path (leading to 5) is nearly 8 kcal mol^-1 lower than the barrier for the inward path (leading to 6, see Reaction 3). This is consistent with torquoselectivity rules, but what is going on in the experiment?

In the investigation of the isomerization of the outward to inward pathway, they discovered a low-energy pyran intermediate 7. This led to the proposal of the mechanism shown in Reaction 3. The highest barrier is for the electrocyclization that leads to the outward product 5. The subsequent barriers – the closing to the pyran 7 and then the torquoselective ring opening to 6 –  are about than 13 kcal mol^-1 lower in energy than for the first step. The observed product is the thermodynamic sink. And the nice thing about this mechanism is that torquoselection is preserved.

References

(1) Um, J. M.; Xu, H.; Houk, K. N.; Tang, W., "Thermodynamic Control of the Electrocyclic
Ring Opening of Cyclobutenes: C=X Substituents at C-3 Mask the Kinetic Torquoselectivity," J. Am. Chem. Soc. 2009, 131, 6664-6665, DOI: 10.1021/ja9016446.

InChIs

4: InChI=1/C16H16O6/c1-20-13(17)11-9-16(14(18)21-2,15(19)22-3)12(11)10-7-5-4-6-8-10/h4-9,12H,1-3H3
InChIKey=VBOGEHVOAGDMNG-UHFFFAOYAR

5: InChI=1/C16H16O6/c1-20-14(17)12(9-11-7-5-4-6-8-11)10-13(15(18)21-2)16(19)22-3/h4-10H,1-3H3/b12-9-
InChIKey=PZRWKBUUAFMPBC-XFXZXTDPBF

6: InChI=1/C16H16O6/c1-20-14(17)12(9-11-7-5-4-6-8-11)10-13(15(18)21-2)16(19)22-3/h4-10H,1-3H3/b12-9+
InChIKey=PZRWKBUUAFMPBC-FMIVXFBMBS

7: InChI=1/C16H16O6/c1-19-14(17)11-9-12(15(18)20-2)16(21-3)22-13(11)10-7-5-4-6-8-10/h4-9,13H,1-3H3/t13-/m0/s1
InChIKey=QSJZITDSTPMCEM-ZDUSSCGKBG

The importance of dynamics in simple reactions is made yet again in a recent study by Doubleday and Houk in 1,3-dipolar cycloadditions.¹ They looked at the reaction of acetylene or ethylene with either nitrous oxide, diazonioazanide, or methanediazonium. The transition state for these 6 reactions all show a concerted reaction. The transition vector has three major components; (a) symmetric formation/cleavage of the two new σ bonds, (b) bending of the dipolar component, or (c) symmetric bending of the hydrogens of ethylene or acetylene.

Classical trajectories were traced from the transition state back to reactant and forward to product. In the approach of the two fragments, the dipole bend vibrates, but then after the TS, it needs to bend quickly to close the 5-member ring. This means that the bending mode effectively has to “turn a corner” in phase space, and without energy in this mode, the molecules will simple bounce off of each other. Analysis of the reactants indicates significant vibrational excitation of the dipole bending mode.

References

(1) Xu, L.; Doubleday, C. E.; Houk, K. N., "Dynamics of 1,3-Dipolar Cycloaddition Reactions of Diazonium Betaines to Acetylene and Ethylene: Bending Vibrations Facilitate Reaction," Angew. Chem. Int. Ed. 2009, 48, 2746-2748, DOI: 10.1002/anie.200805906

What is the rate determining step in the Hajos-Parrish-Eder-Sauer-Wiechert reaction (reaction 1)? This basic question of the mechanism for the first example of the use of proline as a catalyst remains unanswered, though a recent paper by Meyer and Houk¹ does moves us forward.

Their ¹³C kinetic isotope effect study revealed that only the nucleophilic ketone (the carboyl of the butyl chain) experiences any significant effect, with a value of about 1.03. B3LYP/6-31G(d,p) computations of the three transition states shown below were performed for both the gas phase and solution using IEF-PCM. Calculations of the transition state for the formation of the C-C bond (TS3) predicts no kinetic isotope effect, indicating that it is not the rate limiting step, in conflict with previous² suggestions. The transition states for the formation of the carbinolamine (TS1) and formation of the iminium (TS2) both predict an isotope effect comparable with experiment. TS1 is about 3 kcal mol^-1 higher in energy than TS2. The authors conclude that a step prior to formation of the C-C is the rate limiting step of the Hajos-Parrish-Eder-Sauer-Wiechert reaction, but cannot discern between the two possibilities examined.

References

(1) Zhu, H.; Clemente, F. R.; Houk, K. N.; Meyer, M. P., "Rate Limiting Step Precedes C-C Bond Formation in the Archetypical Proline-Catalyzed Intramolecular Aldol Reaction," J. Am. Chem. Soc., 2009, 131, 1632-1633, DOI: 10.1021/ja806672y.

(2) Clemente, F. R.; Houk, K. N., "Computational Evidence for the Enamine
Mechanism of Intramolecular Aldol Reactions Catalyzed by Proline," Angew. Chem. Int. Ed., 2004, 43, 5766-5768, DOI: 10.1002/anie.200460916.

InChIs

2-methyl-2-(3-oxobutyl)cyclopentane-1,3-dione:
InChI=1/C10H14O3/c1-7(11)5-6-10(2)8(12)3-4-9(10)13/h3-6H2,1-2H3
InChIKey=OZBYSCPBJGAYMQ-UHFFFAOYAW

(3aS,7aS)-3a-hydroxy-7a-methyl-3,4,6,7-tetrahydro-2H-indene-1,5-dione:
InChI=1/C10H14O3/c1-9-4-2-7(11)6-10(9,13)5-3-8(9)12/h13H,2-6H2,1H3/t9-,10+/m1/s1
InChIKey=PUHCDQVSBDIJTM-ZJUUUORDBA

Concern about the use of DFT for general use in organic chemistry remains high; see my previous posts (1, 2, 3). Houk has now examined the reaction enthalpies of ten simple Diels-Alder reactions using a variety of functionals in the search for the root cause of the problem(s).¹

The ten reactions are listed in Scheme 1, and involve cyclic and acyclic dienes and either ethylene or acetylene as the dienophile. Table 1 lists the minimum and maximum deviation of the DFT enthalpies relative to the CBS-QB3 enthalpies (which are in excellent accord with experiment). Clearly, all of the DFT methods perform poorly, with significant errors in these simple reaction energies. The exception is the MO6-2X functional, whose errors are only slightly larger than that found with the SCS-MP2 method. Use of a larger basis set (6-311+G(2df,2p)) reduced errors only a small amount.

Table 1. Maximum, minimum and mean deviation of reaction enthalpies (kcal mol^-1) for the reactions in Scheme 1 using the 6-31+G(d,p) basis set.¹

In order to discern where the problem originates, they next explore the changes that occur in the Diels-Alder reaction: two π bonds are transformed into one σ and one π bond and the conjugation of the diene is lost, leading to (proto)branching in the product. Reactions 1-3 are used to assess the energy consequence of converting a π bond into a σ bond, creating a protobranch, and the loss of conjugation, respectively.

The energies of these reactions were then evaluated with the various functionals. It is only with the conversion of the π bond into a σ bond that they find a significant discrepancy between the DFT estimates and the CBS-QB3 estimate. DFT methods overestimate the energy for the π → σ exchange, by typically around 5 kcal mol^-1, but it can be much worse. Relying on cancellation of errors to save the day for DFT will not work when these types of bond changes are involved. Once again, the user of DFT is severely cautioned!

References

(1) Pieniazek, S. N.; Clemente, F. R.; Houk, K. N., "Sources of Error in DFT Computations of C-C Bond Formation Thermochemistries: π → σ Transformations and Error Cancellation by DFT Methods," Angew. Chem. Int. Ed. 2008, 47, 7746-7749, DOI: 10.1002/anie.200801843

Ken Houk has produced a very nice minireview on bifurcations in organic reactions.¹ This article is a great introduction to a topic that has broad implication for mechanistic concepts. Bifurcations result when a valley-ridge inflection point occurs on or near the intrinsic reaction coordinate. This inflection point allows trajectories to split into neighboring basins (to proceed to different products) without crossing a second transition state. In the examples discussed, the reactant crosses a single transition state and then leads to two different products. This is the so-called “two-step no intermediate” process.

I discuss the implications of these kinds of potential energy surfaces, and other ones of a pathological nature, in the last chapter of my book. Very interesting reaction dynamics often are the result, leading to a mechanistic understanding far from the ordinary!

References

(1) Ess, D. H.; Wheeler, S. E.; Iafe, R. G.; Xu, L.; Çelebi-Ölçüm, N.; Houk, K. N., "Bifurcations on Potential Energy Surfaces of Organic Reactions," Angew. Chem. Int. Ed. 2008, DOI: 10.1002/anie.200800918

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

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

Schleyer and Houk¹ offer a provocative paper examining the reference compounds that one chooses when trying to evaluate such concepts as ring strain energy and aromaticity. I discuss this at length in Chapter 2 of the book, focusing on the isodesmic, homodesmotic, and group equivalent reactions.

Their work starts with the isodesmic reaction

CH₃CH₂CH₃ + CH₄ → 2 CH₃CH₃

and note that this reaction is endothermic by 2.83 kcal mol^-1. They argue that 1,3-dialkyl interactions are stabilizing, and call this effect “protobranching”.

Gronert^2,3 has recently described the counterargument – that 1,3-dialkyl groups are repulsive – but whether the interaction is attractive or repulsive is not my concern here. Let’s proceed assuming that protobranching is in fact stabilizing.

Schleyer and Houk demonstrate that the stabilization of protobranching is nicely additive. In Table 1 are simple bond separation (isodesmic) reactions of straight-chain alkanes and cycloalkanes. This can then be extended to argue for why branched alkanes are more stable than their straight-chain analogues – namely, branched chains have more 1,3-dialkyl interactions and these are stabilizing. They note that the group separation reaction of iso-butane is more endothermic than that of pentane, yet the difference is neatly ascribed to protobranching.

Table 1. Energy of reactions and energy per protobranch (PB) using experimental heats of formation.

Now the interesting aspect is when this concept of protobranching is applied to ring systems. The conventional (homodesmotic) reaction for cyclopropane is

(CH₂)₃ + 3 C₂H₆ → 3 CH₃CH₂CH₃ ΔH = -27.7 kcal mol^-1

Schleyer and Houk argue that protobranching is not balanced in this reaction, and the consequence is that since propane is stabilized by about 2.8 kcal mol^-1, the reaction energy should be reduced by 8.4 kcal mol^-1. Thus the ring strain energy (RSE) of cyclopropane is 19.3 kcal mol^-1. This is essentially the value obtained when one employs the isodesmic reaction to evaluate the RSE of cyclopropane, namely

(CH₂)₃ + 3 CH₄ → 3 C₂H₆ ΔH = -19.2 kcal mol^-1

And this isodesmic reaction has balanced protobrancing (none!) on both sides. The reaction that balances protobranching (two on each side) for obtaining the RSE of cyclobutane is

(CH₂)₄ + 2 CH₄ → 2 CH₃CH₂CH₃ ΔH = -21.0 kcal mol^-1

Protobranching corrections need also be made to the question of aromatic stabilization energy or resonance energy of benzene. For example, since cyclohexane is invoked as one of the reference compounds in the following reaction, the resulting energy must be corrected for six protobranching interactions.

2 C₂H₄ + (CH₂)6 → (CH)₆ + 3 C₂H₆

The question now becomes “Is protobranching real and do we need to correct for it?” Further studies should be performed.

References

(1) Wodrich, M. D.; Wannere, C. S.; Mo, Y.; Jarowski, P. D.; Houk, K. N.; Schleyer, P. v. R., "The Concept of Protobranching and Its Many Paradigm Shifting Implications for Energy Evaluations," Chem. Eur. J. 2007, 13, 7731-7744, DOI: 10.1002/chem.200700602

(2) Gronert, S., "Evidence that Alkyl Substitution Provides Little Stabilization to Radicals: The C-C Bond Test and the Nonbonded Interaction Contradiction," J. Org. Chem., 2006, 71, 7045-7048, DOI: 10.1021/jo060797y.

(3) Gronert, S., "An Alternative Interpretation of the C-H Bond Strengths of Alkanes," J. Org. Chem., 2006, 71, 1209-1219, DOI: 10.1021/jo052363t.

The search for unusual potential energy surface topologies continues. Unusual surfaces can lead to dynamic effects that result in rates and product distributions dramatically divergent from that predicted by statistical theories. I addressed this topic in Chapter 7 of the book.

Houk has found another interesting example in the Diels-Alder reaction of cyclopentadiene with nitrostyrene 1.¹ The [4+2] adduct is 2, which can undergo a [3,3] Cope-like rearrangement to give 3. Product 3 can also result from a [2+4] Diels-Alder cycloaddition where cyclopentadiene acts as the dienophile.

Like some of the examples in Chapter 7, the potential energy surface, computed at B3LYP/6-31+G*, contains a single transition state (TS1) from reactants. Continuing on the reaction path past the transition state, a valley ridge inflection point (VRI) intervenes, causing the path to bifurcate: one path leads to 2 and the other leads to 3. In other words, a single transition state leads to two different products! TS1 is geometrically closer to 2 than 3, while TS2 lies closer to 3 than 2 (Figure 1). This topology directs most molecules to traverse a path over TS1 and on to 2. What is novel in this paper is that the acid-catalyzed reaction, using SnCl₄, shifts TS1 towards 3 and TS2 towards 2, leading to the opposite product distribution. The uncatalyzed reaction favors formation of 2 while the catalyzed reaction favors 3 over 2. Confirmation of this prediction awaits a molecular dynamics study.

TS1	TS1-Cat
TS2	TS2-Cat

Figure 1. B3LYP/6-31+G(d) optimized structures for TS1 and TS2.¹

References

(1) Celebi-Olcum, N.; Ess, D. H.; Aviyente, V.; Houk, K. N., “Lewis Acid Catalysis Alters the Shapes and Products of Bis-Pericyclic Diels-Alder Transition States,” J. Am. Chem. Soc., 2007, 129, 4528-4529. DOI: 10.1021/ja070686w

InChI

1: InChI=1/C8H7NO2/c10-9(11)7-6-8-4-2-1-3-5-8/h1-7H/b7-6+
2: InChI=1/C13H13NO2/c15-14(16)13-11-7-6-10(8-11)12(13)9-4-2-1-3-5-9/h1-7,10-13H,8H2
3: InChI=1/C13H13NO2/c15-14-9-12(10-5-2-1-3-6-10)11-7-4-8-13(11)16-14/h1-6,8-9,11-13H,7H2

A Stable Bis-allyl Intermediate on the Cope PES

As discussed in Chapter 3.2, the prototypical Cope rearrangement (the degenerate rearrangement of 1,5-hexadiene 1) is understood to proceed through a single concerted transition state. The concerted transition state 2 is described by three resonance structures (Scheme 1), and this allows for understanding the chameleonic nature of the substituted Cope rearrangement. For example, radical stabilizing groups at the 2 and 5 positions would favor the cyclohexyl-diyl structure.

Scheme 1

Schreiner computed the reaction path at BD(T)/cc-pVDZ//BLYP/6-31G* for 64 different variations of the Cope rearrangement.¹ A representative sampling from these is presented in Figure 1. The Cope rearrangements are found to fall into one of three categories. The first, called type 1, are concerted rearrangements. Type 2 rearrangements have two competing pathways: either through a concerted transition state or a diradical intermediate. The last group, type 3, comprises nonconcerted reactions with a cyclohexyl-diyl intermediate. Schreiner generalizes the results to the following rule: a nonconcerted reaction takes place when biradical intermediates are stabilized either by allyl or aromatic resonance.

Figure 1. Examples of the three type of Cope rearrangements. Relative energies, in kcal mol-1, were computed at BD(T)/cc-pVDZ//BLYP/6-31G*.1

Interestingly, Schreiner’s study identified reactions where the diyl is a stable intermediate, but he identified no case where the other extreme – two allyl radicals – appeared as a stable intermediate. Kertesz, in 2006, discovered just such an example with the Cope rearrangement of 3.² Using B3LYP and BPW91 computations with two different basis sets, he identified the stable diradical 5. This structure, shown in Figure 2, clearly has very long distances – 2.836 Å – separating the ends of the two “allylic” components. A true transition state 4 connects the reactant 3 with the intermediate 5 (see Figure 2). The activation energy is 6.3 kcal mol^-1 and the intermediate 5 lies 3.3 kcal mol^-1 above 3.

3	4	5
xyz file	xyz file	xyz file
Figure 2. B3LYP/6-31G(d) optimized structures of 3-5. Distances (Å) shown are between C1-C6 and C3-C4 of the hexadiene component of the Cope rearrangement.2

Why does a stable bis-allyl analogue exist on the Cope reaction surface of 3? In the prototype Diels-Alder reaction of 1,5-hexadiene, the possible bis-allyl intermediate (i.e., two isolated allyl radicals) is about 26 kcal mol^-1 higher in energy than the Cope transition state. Only with significant radical stabilization might one expect a bis-allyl intermediate to occur. One can consider 5 as composed of two bridged phenalenyl radicals (6). Phenalenyl radical is stable due to electron delocalization; its ESR spectrum has been observed, but it has not been isolated, instead dimerizing to give 7.³ In addition to the stabilization afforded by the extensive delocalization of the radical within the phenalenyl system, two phenalenyl systems can also interact through overlap of their π-systems, creating what has been termed π-dimerization.^4-6 MRMP2 computations suggest that the π-dimerization energy of 6 is 11 kcal mol^-1.⁷ While the geometry of 5 is not ideal for π-dimerization, its structure clearly indicates some stacking of the two phenalenyl fragments. Both the enhanced electron delocalization about the large phenalenyl system along with π-dimerization provides sufficient stabilization that the bis-allyl intermediate exits on the Cope rearrangement pathway. This now completes all of the options for how the Cope rearrangement may occur: either directly through a concerted transition state, or multi-step process with a 1,6-diyl intermediate or a bis-allyl intermediate.

Cope Rearrangement of 3-Vinylmethylenecyclobutane

3-Vinylmethylenecyclobutane 8 can undergo a myriad of thermal rearrangements involving [1,3]- and [3,3]-shifts.⁸ The Cope rearrangement of 8 to 9 has a barrier of 35.7 kcal mol^-1.⁹ This large barrier is consistent with cleavage of a C-C bond leading to a diradical intermediate.

Houk has recently confirmed the diradical nature of this rearrangement.¹⁰ The geometries of all reactants intermediates, products and transition states were optimized at UB3LYP/6-31+G(d) and single-point energies were evaluated at CASPT2(6,6)/6-31G(d). Two diradical intermediates, 10 and 11, lie 30.0 and 32.0 kcal mol^-1, respectively, above 8. These intermediates are separated by a small barrier, 1.5 kcal mol^-1 from 10, and a barrier of 2.0 kcal mol^-1 interconverts mirror versions of 10. All of these paths are sketched in Scheme 3 and the geometries of the critical points are displayed in Figure 3.

Scheme 3

8 xyz file
TS8-10 xyz file	TS8-11 xyz file
10 xyz file	TS10-11 xyz file	11 xyz file
TS11-9x xyz file	TS11-9n xyz file
9 xyz file

Figure 3. Optimized Structures of the critical points in Scheme 3.¹⁰

Only the reaction going forward from 11 can lead to product 9. There are two such routes, involving an exo or endo approach. They are of similar energy, and also very close in energy to that of the diradical intermediates. Houk concludes that the diradical intermediates “have substantial conformational freedom and very low barriers for forming stereo- and regioisomeric forms of the ring-enlarged product”, in agreement with the experimentally observed lack of any region- or stereoselectivity in the thermal reactions of 8. The computed barrier, 34.9 kcal mol^-1 for TS8-10, is in good accord with the experimental barrier of 35.7 kcal mol^-1.

A study by Jung¹¹ the year before actually inspired Houk’s work. Jung discovered that appropriately substituted vinylmethylcyclohexenes will undergo very selective Cope rearrangements; for example, thermolysis of 8a produces 9a in greater than 90% yield. This result is quite contrary to that normally observed for vinylmethylcyclohexene thermoylsis: many products with virtually complete scrambling of all stereochemical information.

Examination of the rearrangement of 8a is computationally prohibitive, so Houk looked at the effect of individual substituents. The role of the trialkylsiloxy group was evaluated through the rearrangement of 8b, leading to diradicals 10b and 11b (Scheme 4). The transition state leading to 11b is 1.5 kcal mol^-1 below that leading to 10b. This is opposite the relative ordering of the transition states in the parent reaction, indicating that siloxy substitution would favor the path that leads to direct Cope rearrangement, which must pass through 11. The preference for the opposite TS with the siloxy group results from its torquoselectivity (See Chapter 3.5) Since 11b is more stable than 10b, this would also help preserve the stereochemistry during the rearrangement.

Scheme 4

The effects of the terminal substituents were also evaluated. As shown in Scheme 5, the Cope rearrangement of 8b is predicted to proceed with distinct stereoselectivity. The ring opening step preferentially produces diradical intermediate 12 over 13. The ring forming step is also stereoselective: 12 cyclizes to 14 in a 3:1 ratio, while the ring closure of 13 predominantly gives 15. Overall, the rearrangement of 8b is predicted to give a product ratio 14:15 of 2:1. This is in accord with the Jung’s experimental observation.

Scheme 5

References

(1) Navarro-Vazquez, A.; Prall, M.; Schreiner, P. R., “Cope Reaction Families: To Be or Not to Be a Biradical,” Org. Lett. 2004, 6, 2981-2984, DOI: 10.1021/ol0488340

(2) Huang, J.; Kertesz, M., “Stepwise Cope Rearrangement of Cyclo-biphenalenyl via an Unusual Multicenter Covalent π-Bonded Intermediate,” J. Am. Chem. Soc. 2006, 128, 7277-7286, DOI: 10.1021/ja060427r

(3) Zheng, S.; Lan, J.; Khan, S. I.; Rubin, Y., “Synthesis, Characterization, and Coordination Chemistry of the 2-Azaphenalenyl Radical,” J. Am. Chem. Soc. 2003, 125, 5786-5791, DOI: 10.1021/ja029236o

(4) Goto, K.; Kubo, T.; Yamamoto, K.; Nakasuji, K.; Sato, K.; Shiomi, D.; Takui, T.; Kubota, M.; Kobayashi, T.; Yakusi, K.; Ouyang, J., “A Stable Neutral Hydrocarbon Radical: Synthesis, Crystal Structure, and Physical Properties of 2,5,8-Tri-tert-butyl-phenalenyl,” J. Am. Chem. Soc. 1999, 121, 1619-1620, DOI: 10.1021/ja9836242

(5) Suzuki, S.; Morita, Y.; Fukui, K.; Sato, K.; Shiomi, D.; Takui, T.; Nakasuji, K., “Aromaticity on the Pancake-Bonded Dimer of Neutral Phenalenyl Radical as Studied by MS and NMR Spectroscopies and NICS Analysis,” J. Am. Chem. Soc. 2006, 128, 2530-2531, DOI: 10.1021/ja058387z

(6) Takano, Y.; Taniguchi, T.; Isobe, H.; Kubo, T.; Morita, Y.; Yamamoto, K.; Nakasuji, K.; Takui, T.; Yamaguchi, K., “Hybrid Density Functional Theory Studies on the Magnetic Interactions and the Weak Covalent Bonding for the Phenalenyl Radical Dimeric Pair,” J. Am. Chem. Soc. 2002, 124, 11122-11130, DOI: 10.1021/ja0177197

(7) Small, D.; Zaitsev, V.; Jung, Y.; Rosokha, S. V.; Head-Gordon, M.; Kochi, J. K., “Intermolecular π-to-π Bonding between Stacked Aromatic Dyads. Experimental and Theoretical Binding Energies and Near-IR Optical Transitions for Phenalenyl Radical/Radical versus Radical/Cation Dimerizations,” J. Am. Chem. Soc. 2004, 126, 13850-13858, DOI: 10.1021/ja046770i

(8) Kozhushkov, S. I.; Kuznetsova, T. S.; Zefirov, N. S., “Mechanism of Thermal Isomerization of 3-Vinylmethylenecyclobutane into 4-Methylenecyclohexane,” Dokl. Akad. Nauk SSSR, 1988, 299, 1395-1399,

(9) Dolbier, W. R.; Mancini, G. J., “Non-concerted Thermal Reorganizations 3,3-Divinylmethylenecyclobutane,” Tetrahedron Lett. 1975, 16, 2141-2144, DOI: 10.1016/S0040-4039(00)72661-X.

(10) Zhao, Y. L.; Suhrada, C. P.; Jung, M. E.; Houk, K. N., “Theoretical Investigation of the Stereoselective Stepwise Cope Rearrangement of a 3-Vinylmethylenecyclobutane,” J. Am. Chem. Soc. 2006, 128, 11106-11113, DOI: 10.1021/ja060913e

(11) Jung, M. E.; Nishimura, N.; Novack, A. R., “Versatile Diastereoselectivity in Formal [3,3]-Sigmatropic Shifts of Substituted 1-Alkenyl-3-alkylidenecyclobutanols and Their Silyl Ethers,” J. Am. Chem. Soc. 2005, 127, 11206-11207, DOI: 10.1021/ja051663p

InChI

3: InChI=1/C34H26/c1-19-21-11-12-22-16-24-8-6-10-26-18-28-14-13-27-17-25-9-5-7-23(15-21)29(25)31(19)33(27,3)34(28,4)32(20(22)2)30(24)26/h5-18H,1-4H3/b12-11-/t33-,34+

5: InChI=1/C34H26/c1-19-23-11-12-25-17-29-9-6-10-30-18-26(22(4)32(21(25)3)34(29)30)14-13-24-16-28-8-5-7-27(15-23)33(28)31(19)20(24)2/h5-18H,1-4H3/b12-11-,14-13-

6: InChI=1/C13H9/c1-4-10-6-2-8-12-9-3-7-11(5-1)13(10)12/h1-9H

7: InChI=1/C26H18/c1-5-17-9-3-11-23-21(15-13-19(7-1)25(17)23)22-16-14-20-8-2-6-18-10-4-12-24(22)26(18)20/h1-16,21-22H

8: InChI=1/C7H10/c1-3-7-4-6(2)5-7/h3,7H,1-2,4-5H2

9: InChI=1/C7H10/c1-7-5-3-2-4-6-7/h2-3H,1,4-6H2