Pathways for Concerted [2 + 2] Cycloaddition to Cumulenes - The

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Cite This: J. Org. Chem. XXXX, XXX, XXX−XXX

Pathways for Concerted [2 + 2] Cycloaddition to Cumulenes David M. Lemal* Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States S Supporting Information *

ABSTRACT: A computational search has revealed concerted pathways for [2 + 2] cycloaddition of ethylene to all 10 of the cumulenes with the formula XCY, where X, Y = C, N, O, and S. Four different concerted pathways have been found, three of them pseudopericyclic plus another based on sp-hybridized carbon. In the case of 2 of the 16 possible cycloadditions, a pair of novel three-membered ring intermediates has been discovered. As simple model reactions, cycloaddition of ethylene to formaldehyde, thioformaldehyde, and formaldimine is also described.

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INTRODUCTION

When the landmark series of papers by Woodward and Hoffmann on the conservation of orbital symmetry appeared in 1965,1 the stereoselective thermal [2 + 2] cycloadditions of ketene stood out as an anomaly. The [2 + 2] cycloadditions were orbital symmetry-forbidden to occur concertedly and therefore should be inhibited by high activation barriers and display lack of stereocontrol. Woodward and Hoffmann later rationalized the apparent concertedness of these cycloadditions by proposing that they occur antarafacially on the ketene with a perpendicular approach of the reactants.2 This model made the reactions allowed pericyclic processes and correctly predicted stereochemistry, but the required geometry is awkward to achieve. In subsequent decades a number of computational studies of the cycloaddition of ethylene to ketene established its transition state geometry,3−7 somewhat different from that envisioned by Woodward and Hoffmann, but these reports offered a variety of explanations for how and why the reaction works. In 1976, we recognized that there are cyclic, concerted processes that are not subject to orbital symmetry (topology) constraints.8 We coined the term pseudopericyclic to describe them and offered the following definition. A pseudopericyclic reaction is a concerted transformation whose primary changes in bonding compass a cyclic array of atoms, at one (or more) of which nonbonding and bonding atomic orbitals interchange roles. The role interchange means a “disconnection” in the cyclic array because the orbitals switching function are mutually orthogonal. The ethylene−ketene reaction is pseudopericyclic,9 occurring concertedly by virtue of a role switch at oxygen, as will be discussed below. In the present investigation, we have explored computationally the reactions of ethylene with each of the 10 cumulenes having the formula XCY, where X and Y are C, O, N, and S. Ethylene was chosen, not to find practical reactions, but for the sake of simplicity. The goal has been to find concerted pathways where possible and to discover how Nature’s wiles would circumvent orbital topology forbiddenness in each case. © XXXX American Chemical Society

RESULTS AND DISCUSSION

Calculations have been carried out at the B3LYP/cc-PVDZ+ level of theory.10 Where transition states for concerted reaction have been found, they have been shown to have a single imaginary frequency, and IRC calculations have confirmed that they connect reactants with adducts. Because even unrestricted singlet DFT transition state calculations always lead to a closedshell configuration, it is also important to determine whether the open-shell (diradicaloid) configuration does not lie lower in energy, thereby precluding concerted reaction. That will happen if the HOMO−LUMO energy difference is smaller than the electron pairing energy. Whether this is the case has been determined approximately for every transition state by carrying out a UDFT calculation with mixing of the HOMO and LUMO of the closed-shell species.11 The literature describes an array of methods of varying sophistication and effectiveness for analysis of cyclic reactions,12 but in this study we have simply focused on transition state geometry plus in some cases geometric changes occurring elsewhere along the reaction pathway. The use of functionals other than B3LYP and/or multireference methods can lead to transition states different from those described here. We regard this work as providing a conceptual framework for further, in-depth study by others in the future. To assist in understanding the cumulene reactions, we began by examining three simpler cycloadditions, those of ethylene with formaldehyde, thioformaldehyde, and formaldimine (Scheme 1). This was worthwhile because the sp-hybridized carbon and additional double bond of the cumulenes are complicating factors. Concerted transition states were found for Scheme 1

Received: July 30, 2017

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DOI: 10.1021/acs.joc.7b01911 J. Org. Chem. XXXX, XXX, XXX−XXX

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The Journal of Organic Chemistry all three (Figure 1), but only that for formaldehyde survived the configuration test. A lower-lying open-shell (diradicaloid)

Figure 2. Ethylene−formaldehyde transition state, illustrating how bonding takes place with the oxygen lone pair.

In the discussion below of the cumulene cycloadditions, groups of reactions that share a common mechanism are discussed together. A few diradicaloid transition states like those noted above have been found, but no systematic attempt has been made in this investigation to find stepwise pathways that might have barriers lower than those of the concerted processes. Ten-Electron Planar Pseudopericyclic Cycloadditions. The five reactions shown in Scheme 2 were found to have Scheme 2

Figure 1. Concerted transition states for addition of ethylene to formaldehyde (TS1), thioformaldehyde (TS2), and formaldimine (TS3). Lengths of the newly forming bonds are shown in angstrom (Å) units.

planar concerted transition states (Figure 3). Consider, for example, the carbonyl sulfide adduct 8. Because the carbonyl π bond appears to be oriented perpendicular to the ring plane in TS8, it appears that ethylene has added to a CS π bond lying in the ring plane. But that would be orbital topology-forbidden to occur in concert. Inspection of the transition state leading to adduct 4 (TS4) reveals what actually occurs. Because the N− CH3 group lies in the ring plane, the CN π bond must be oriented perpendicular to the plane, with the carbonyl π bond in the plane. It follows that one end of the ethylene bonds to the π bond of the carbonyl and the other end more slowly bonds to the nitrogen lone pair. Forbiddenness is circumvented by virtue of orbital “disconnections” at the two heteroatoms, places where bonding and nonbonding orbitals interchange roles (Figure 4).13−15 Thus, this reaction and the other four in this group involving carbon dioxide, carbon disulfide, and carbonyl sulfide are planar pseudopericyclic processes, each involving 10 electrons.16,17 Eight-Electron Nonplanar Pseudopericyclic Reactions. Cycloadditions of ethylene to ketene to give cyclobutanone (9),3−7 to thioketene to give cyclobutanethione (10),18 and to methyl isothiocyanate to give thiolactam 11 are shown in Scheme 3. The corresponding transition states (TS9−TS11) appear in Figure 5, where it is clear that the leading new C−C bond is forming nearly in the nodal plane of the CC and CN π bonds of the cumulenes. So addition is occurring to

configuration was found for both the formaldimine and thioformaldehyde transition states. All three of the closed-shell transition states are similar and all asynchronous to a varying degree. In each case the leading new bond forms by ethylene’s attack at the carbon end of the πbond of the substrate. The approach is angled a little above head-on to bring the heteroatom lone pair closer to the CH2 group that forms the lagging bond. From the orientation of that CH2, it is clear that the bond is directed well above the nucleus of the heteroatom and thus toward the lone pair, as illustrated in Figure 2 for the formaldehyde transition state. The π-bond becomes an oxygen lone pair in the product. The interchange of orbital roles at the heteroatom makes the reaction pseudopericyclic and therefore oblivious to the orbital topology rules. This is a six-electron pseudopericyclic process. Given the absence of a heteroatom, concerted cycloaddition of ethylene to itself would require a pericyclic transition state, i.e., antarafacial addition to one of the reactants. No such transition state could be found, as C−H and H−H steric repulsion interfered with achieving the awkward geometry necessary. B


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The Journal of Organic Chemistry

Figure 3. Planar transition states for cycloaddition of ethylene to methyl isocyanate (TS4), carbon dioxide (TS5), carbon disulfide (TS6), and carbonyl sulfide (TS7 and TS8). Lengths of the newly forming bonds are shown in angstrom (Å) units.

Figure 5. Transition states for ethylene addition to ketene (TS9), thioketene (TS10), and methyl isothiocyanate (TS11).

Figure 4. Diagram of the ethylene−methylisocyanate cycloaddition. Electron shifts shown in black are happening in-plane, and those in red are out-of-plane. Figure 6. Diagram of the ethylene−ketene reaction. Electron shifts in black are occurring roughly in the plane of the paper, while those in red are out-of-plane.

Scheme 3

on, thereby facilitating overlap with ketene’s CC π bond as the lagging bond develops. Six-Electron Nonplanar Pseudopericyclic Reactions. Cycloaddition of ethylene to the carbonyl group of ketene and to the thiocarbonyl group of methylisothiocyanate is shown in Scheme 4. The transition states TS12 and TS13 for these reactions strongly resemble the simpler TS1 to TS3 because the leading bond is forming in the nodal plane of the CC and the π bond of the carbonyl and thiocarbonyl groups. As in the planar transition states shown above, role interchange takes place at the oxygen and sulfur atoms, with a lone pair forming the new π bond (Figure 6). The absence of a heteroatom to play that role at the other end of the cumulene requires the nonplanarity, as the lagging new C−C bond must form to the CC and CN π bonds. In the case of ketene, attack at the carbonyl π bond takes place at an angle somewhat above head-

Scheme 4

C


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The Journal of Organic Chemistry CN π bond, respectively, making that π bond formally not part of the transformation. (Figure 7). The six-electron

Figure 9. Top: HOMO of TS12. Bottom: HOMO-1 of TS13 (1.2 kcal/mol below the HOMO). Figure 7. Transition states for cycloaddition of ethylene to the carbonyl group of ketene (TS12) and the thiocarbonyl group of methyl isothiocyanate (TS13).

pseudopericyclic reactions are represented diagrammatically in Figure 8. An important difference between these transition

Figure 10. Cycloaddition of ethylene to the carbonyl group of methyl isocyanate, showing the transition state.

Figure 8. Diagram of the addition of ethylene to the carbonyl group of ketene. Electron shifts in black are occurring roughly in the plane of the paper, while that in red is out-of-plane.

states and the simpler models results from conjugation of the “uninvolved” π bond with the reacting heteroatom; that bond plays a major role in the transition state HOMO (HOMO-1 in the case of isothiocyanate), as shown in Figure 9. The geometry of transition state TS14 for cycloaddition of ethylene to the carbonyl group of methylisocyanate is quite different from that of TS12 and TS13 (Figure 10), but nevertheless the reaction is tentatively classified as six-electron pseudopericyclic. The leading bond is forming roughly 20° above head-on attack on the carbonyl π bond, thereby bringing the other end of the ethylene closer to the oxygen lone pair and lowering the angle at which the reactants approach each other (Figure 11). Attack at an angle above head-on to achieve better overlap for the lagging bond was noted for the simple cycloadditions discussed at the outset and for ketene cycloadditions. This interpretation notwithstanding, it is possible that TS14 belongs in the next section’s category, as discussed there. A Novel Solution for Forbiddenness. As a control reaction, we explored addition of ethylene to allene (Figure 12),19 assuming that the absence of a heteroatom would require either that the reaction fail or that it be pericyclic with a geometrically challenging (π2s, π2a) transition state. To our surprise, the reaction eluded both fates. We found a concerted

Figure 11. Transition state for the methyl isocyanate reaction. Arrows show that the cumulene is angled so as to bring the oxygen lone pair closer to the approaching CH2 group.

transition state (TS15, Figure 12) in the approach to which the leading new C−C bond begins to form at the central carbon of the allene with nearly equal overlap with the two orthogonal π orbitals. As the reaction evolves, the ends of the allene counterrotate about 130° starting from their original orientation 90° apart. This sequence of events is depicted in Figure 13. As that first bond forms in the horizontal plane, the central carbon rehybridizes, ultimately to ∼sp2, and there remains a vertical p orbital at the center of a variably twisting allylic π system (Figure 14). The lagging new bond forms at the end of that π system. Thus, the orthogonality of the central carbon orbitals allows the reaction to proceed concertedly. D


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The HOMO of the allene transition state (TS15) appears in Figure 15, with its twisted allylic system and ethylene p orbital

Figure 12. Cycloaddition of ethylene to allene, showing the transition state. Figure 15. HOMO of the closed-shell transition state (TS15) for the ethylene−allene cycloaddition.

directed toward the upper lobe of the terminal allene carbon. The allene transition state is the first among the cumulenes for which we have found a lower-lying open-shell configuration. Just 1.8 kcal/mol below the closed-shell species, this transition state has similar geometry. Although the closed-shell is presumably not a realizable transition state as judged at this level of theory, it has been discussed in some detail because it is useful both as a model and as an exemplar of a new concept. Cycloadditions of ethylene to the CC bond of Nmethylketenimine and to dimethylcarbodiimide are depicted in Scheme 5. The very close similarity in geometry between the Scheme 5

ketenimine’s TS16 and allene’s TS15 points to a parallel pathway (Figure 16). The dihedral angle between the methylene groups in allene’s TS15 is ∼50°, and the twists in the allylic systems in TS16 and TS17 are within several degrees of that value. The latter transition state, in which the twist is unsymmetrical, is displayed a bit differently to show the twist more clearly. Like allene’s TS15, N-methylketeneimine’s TS16 has a very slightly lower-lying (by 0.9 kcal/mol) open-shell configuration, but dimethylcarbodiimide’s TS17 does not. Thus, at least the last is in principle an accessible concerted transition state. As noted above, the reaction leading to adduct 14 may also belong in the allene category. The geometry of TS14 is similar to that of TS17, and the absence of a “handle” on the oxygen atom leaves unclear the orientation of its orbitals. Thus, the question of whether the oxygen performs a pseudopericyclic role switch as it does in several other transition states or behaves like the corresponding nitrogen in TS17 cannot be answered definitively. Cycloaddition via an Unusual Intermediate. There remain two reactions for consideration, cycloaddition to the thiocarbonyl group of thioketene and to the imine group of N-

Figure 13. Views along the pathway for the ethylene−allene reaction. Beginning at lower left and proceeding clockwise to the bottom structure, changes in the dihedral angle between the allene methylene groups are depicted from early along the reaction coordinate until the methylenecyclobutane product. The transition state is the third structure in this sequence.

Figure 14. Idealized orbital changes at the central carbon of allene as the reaction progresses.

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Figure 17. Polar intermediate 20 in the cycloaddition of ethylene with the thiocarbonyl bond of thioketene.

Figure 16. Transition states for reaction of ethylene with the CC bond of N-methylketenimine (TS16) and dimethylcarbodiimide (TS17), with allene’s TS15 included for comparison.

methylketenimine (Scheme 6). Both afforded another surprise, but it should be noted that these reactions are hypothetical Scheme 6 Figure 18. HOMO of intermediate 20.

lies 4.1 kcal/mol lower in enthalpy (Figure 19). Very different from 20, this diradical has a dipole moment of just 1.70 D. The

because the alternative mode of cycloaddition, to the CC bond, has a much lower barrier. In addition, an open-shell transition state was found a little below closed-shell TS18 and TS19 (1.3 and 2.2 kcal/mol, respectively). In the thioketene case, intrinsic reaction coordinate calculations on both transition states led to adduct 18 and, not to starting materials, but to the novel closed-shell intermediate 20 (Figure 17). This species comprises a distorted, cationic three-membered ring held together with two electrons and linked orthogonally with a thioenolate ion. Its HOMO, shown in Figure 18, represents ψ2 of the 4πelectron thioenolate anion. With its three-center, two-electron bonding, the ring is an in-plane cyclopropenium ion, in contrast to π-bonded cyclopropenium ions. Intermediate 20 has a dipole moment of 5.81 D and could be described as a “cyclopropenium thioenolate”.20 In the case of the hypothetical N-methylketenimine reaction to afford adduct 19, IRC calculations for closed-shell TS19 lead to both 19 and a nitrogen analogue of 20, again not to starting materials. However, corresponding to that closed-shell nitrogen-containing species there is an open-shell minimum 21 that

Figure 19. Diradical intermediate 21 from ethylene and Nmethylketenimine.

greater ability of sulfur as compared to nitrogen to accommodate negative charge is presumably responsible for the contrast.21 Comparison of the Pseudopericyclic Cycloadditions. Each of the heteroatoms N, O, and S appears in 7 of the 16 F


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The Journal of Organic Chemistry Table 1. Energetics of Cumulence Cycloadditionsa

cumulene cycloadditions. Of the 11 pseudopericyclic ones, TS4 to TS14 (assuming the last is pseudopericyclic), oxygen is present in 7 and plays the bonding-nonbonding role switch in each. Sulfur does the same in its six appearances, but in nitrogen’s four it plays that role only once. That oxygen does it better than sulfur is implied by the fact that addition to the carbonyl bond of ketene would be pseudopericyclic (TS12) while that to thioketene (TS18) would not [and addition to formaldehyde would be pseudopericyclic (TS1) but that to thioformaldehyde (TS2) would not]. Oxygen’s apparent superiority may be attributable to better orbital overlaps with a 2p than with a 3p orbital. In the pseudopericyclic reactions of both oxygen and sulfur, a lone pair becomes a part of either a new π bond or a new σ bond. Clearly, nitrogen is reluctant to participate in the role switch in either direction, and this may be due to the fact that its lone pair in the cumulene is not a p but an sp2 orbital. Unlike a p lone pair, the sp2 is angled away by ∼30° from perpendicular to the C−N σ bond, diminishing orbital overlap during reaction for both kinds of role switch. It may also be significant that in the single instance where nitrogen’s lone pair orbital in the starting material becomes a bonding one, addition to methylisocyanate (TS4), the nitrogen ends up in a fourmembered ring, not in a double bond. That means that the lone pair’s hybridization evolves to sp3, not p, a smaller change that may be easier to accomplish. Nitrogen’s resistance to using its lone pair is also reflected in the fact that N-methylketenimine (adding across the CC bond) and dimethylcarbodiimide react like allene.22 Energetics of the Cycloadditions. Enthalpies of activation and reaction are presented in Table 1 for the 16 cumulene cycloadditions that have been examined. For all but entries 18 and 19, a concerted transition state has been found, though for two others (15 and 16) there is a slightly lowerlying open-shell configuration. The numbers immediately make clear that most of the transformations would not be realizable in practice. Ethylene was selected as the universal addend for simplicity, but choice of appropriate substituents on the alkene and/or where possible on the cumulene could dramatically lower barriers. Even allowing for this, several of the concerted pathways represented in the table would not be achievable. Reasons include endothermicity; a prohibitively high barrier; and, in the case of an unsymmetrical cumulene, a lower barrier for the alternative reaction. Free energies of activation and reaction are substantially higher than the enthalpies in all cases because the entropy changes are all large and negative. While a number of diradicaloid transition states have been happened upon, as noted previously no search has been made for stepwise, diradical processes that could undercut the concerted pathways we have found. Despite these disclaimers, there are cumulenes in the table for which concerted [2 + 2] cycloadditions have been found and others for which they may be realizable. Ketene,23 of course, and electronegatively substituted isocyanate14 fall in the first category; thioketene (predicted to be more reactive than ketene)18 and perhaps electronegatively substituted carbodiimide are prospects for the second. Though allene and Nmethylketenimine have open-shell transition states a little below the concerted ones at the level of theory we have employed, appropriately substituted analogues may not. If so, they would also be promising candidates for concerted [2 + 2] cycloadditions.

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Enthalpies caculated at the B3LYP/cc-PVDZ+ level of theory are given in kcal/mol. bThe ΔH⧧ value shown is based on the concerted transition state, not the slightly lower open-shell one.

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CONCLUSIONS [2 + 2] Cycloaddition of ethylene to 10 cumulenes has been explored, a total of 16 reactions. Concerted transition states have been located for all but two of them, though in 2 of these 14 cases a slightly lower-energy open-shell diradicaloid transition state was found. Thus, 12 of the reactions are predicted to be possible in principle via concerted pathways despite orbital topology forbiddenness. Four distinctly different pathways have been found, three of them pseudopericyclic plus a novel process exemplified by allene and based on sphybridized carbon. The pseudopericyclic transformations all depend upon a bonding-nonbonding orbital switch at a heteroatom (or two), and comparisons among these reactions have revealed an order of heteroatom ability to play that role. Oxygen is apparently somewhat better than sulfur, but both are far superior to nitrogen. This contrast may be attributable to doubly bonded oxygen and sulfur having p orbitals available for the role switch, whereas doubly bonded nitrogen has only an sp2 orbital. Exploring cycloaddition to thioketene and Nmethylketenimine resulted in the discovery of a pair of unusual three-membered ring intermediates, one highly polar and the other a diradical. As noted at the outset, this study has been carried out at a modest level of theory, but our findings provide a conceptual basis for future exploration. For a variety of reasons, most of the G


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(14) A planar, concerted transition state was found for the experimentally observed cycloaddition of chlorosulfonyl isocyanate with fluoroalkenes, but the 10-electron pseudopericyclic process was analyzed as pericyclic. Shellhamer, D. F.; Davenport, K. J.; Hassler, D. M.; Hickle, K. R.; Thorpe, J. J.; Vandenbroek, D. J.; Heasley, V. L.; Boatz, J. A.; Reingold, A. L.; Moore, C. E. J. Org. Chem. 2010, 75, 7913. (15) In a detailed ab initio investigation of [2 + 2] cycloadditions that included lactam formation from allene and isocyanic acid, the authors described as pericyclic the planar transition states they found. We classify them as 10-electron pseudopericyclic. Rode, J. E.; Dobrowolski, J. Cz. J. Phys. Chem. A 2006, 110, 3723. (16) The ethylene-carbon dioxide reaction has been correctly explained in ref 12. (17) [2 + 2] Cycloadditions of allene with carbon dioxide, carbon disulfide, and carbonyl sulfide have been examined as part of an extensive and thorough ab initio study of cumulene cycloadditions. The planar transition states leading to adducts I, III, VIII, and XVI were interpreted as pericyclic, but we regard them as 10-electron pseudopericyclic. Rode, J. E.; Dobrowolski, J. Cz. J. Phys. Chem. A 2006, 110, 207. (18) Ma, N. L.; Wong, M. W. Eur. J. Org. Chem. 2000, 1411. (19) For a review of [2 + 2] cycloaddition chemistry of allenes, see Alcaide, B.; Almendros, P.; Aragoncillo, C. Chem. Soc. Rev. 2010, 39, 783. (20) The enthalpy barrier for 1,2-bond shift in 20 to reach TS18 is 7.5 kcal/mol, but 20 is virtually isoenergetic with TS10. It is predicted by IRC calculations to undergo either one of two nearly barrierless processes: bond shift in the other direction to give 10 or reversion to starting materials. So although the transition state TS18 that led us to discover 20 is only hypothetical, that fragile intermediate is likely to be formed in the reaction of ethylene with thioketene to afford 10, especially in a polar solvent. An open-shell configuration for 20 is essentially degenerate with the closed. (21) IRC calculations on the open-shell counterpart of TS19 lead, not to 21, but to an open-chain diradical. (22) That resistance is manifest as well in the finding that formaldimine’s concerted transition state (TS3) lies nearly 20 kcal/ mol above its diradicaloid counterpart. (23) For a review of ketene cycloadditions, see Allen, A. D.; Tidwell, T. T. Chem. Rev. 2013, 113, 7287.

specific reactions we have examined would not be reducible to practice, but they have served well the purpose of this investigation: to discover when and how Nature can circumvent orbital-topology forbiddenness in a family of [2 + 2] cycloadditions. What has been learned should be applicable elsewhere where forbiddenness is a problem.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.joc.7b01911. Total energies and Cartesian coordinates for reactants, products, and transition states (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

David M. Lemal: 0000-0001-6218-1618 Notes

The author declares no competing financial interest.

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ACKNOWLEDGMENTS The author thanks the National Science Foundation for support of this work (grant no. CHE-0653935). REFERENCES

(1) Woodward, R. B.; Hoffmann, R. J. Am. Chem. Soc. 1965, 87, 395. Woodward, R. B.; Hoffmann, R. J. Am. Chem. Soc. 1965, 87, 2511. Hoffmann, R.; Woodward, R. B. J. Am. Chem. Soc. 1965, 87, 2046. Hoffmann, R.; Woodward, R. B. J. Am. Chem. Soc. 1965, 87, 4388. Hoffmann, R.; Woodward, R. B. J. Am. Chem. Soc. 1965, 87, 4389. (2) Woodward, R. B.; Hoffmann, R. Angew. Chem., Int. Ed. Engl. 1969, 8, 781. (3) Burke, L. A. J. Org. Chem. 1985, 50, 3149. (4) Houk, K. N. Pure Appl. Chem. 1989, 61, 643. (5) Wang, X. B.; Houk, K. N. J. Am. Chem. Soc. 1990, 112, 1754. (6) Bernardi, F.; Bottoni, A.; Robb, M. A.; Venturini, A. J. Am. Chem. Soc. 1990, 112, 2106. (7) (a) Valenti, E.; Pericas, M. A.; Moyano, A. J. Org. Chem. 1990, 55, 3582. (b) Yamabe, S.; Minato, T.; Osamura, Y. J. Chem. Soc., Chem. Commun. 1993, 450. (8) Ross, J. A.; Seiders, R. P.; Lemal, D. M. J. Am. Chem. Soc. 1976, 98, 4325. The pseudopericyclic idea was widely ignored until David Birney (Texas Tech) revived it in 1994 and ably carried it forward (along with others later) in a continuing series of experimental and theoretical investigations. Birney, D. M.; Wagenseller, P. E. J. Am. Chem. Soc. 1994, 116, 6262. (9) The theoretical analysis by Moyano et al. (ref 7a) was the only one that portrayed this reaction as pseudopericyclic, though they were apparently unaware of that term. (10) Jaguar, version 2014−4, Schrödinger, LLC, New York, 2014. Differences between open- and closed-shell transition states are expressed in terms of SCF energies. All other energy quantities reported are enthalpies. (11) Jaguar 8.4 User Manual; Schrödinger Press: New York, 2014; p 232. Several diradicaloid species have been discovered this way in the present investigation, but no systematic attempt has been made to find stepwise, diradical pathways for the [2 + 2] cycloadditions. (12) See, for example Lopez, R. V.; Faza, O. N.; Matito, E.; Lopez, C. S. Org. Biomol. Chem. 2017, 15, 435. (13) A theoretical study of the alkene−isocyanate [2 + 2] cycloaddition reaction found planar, concerted transition states but interpreted them as pericyclic. Cossio, F. P.; Lecea, B.; Lopez, X.; Roa, G.; Arrieta, A.; Ugalde, J. M. J. Chem. Soc., Chem. Commun. 1993, 1450. H


Pathways for Concerted [2 + 2] Cycloaddition to Cumulenes - The

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