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. Author manuscript; available in PMC: 2026 Sep 1.
Published in final edited form as: J Am Chem Soc. 2026 Sep 2;148(34):36870–36877. doi: 10.1021/jacs.6c09105

Diradical Character of Cyclic Allenes Enables Their Thermal (2 + 2) Cycloadditions

Noah W Gilbertson 1,†, Allison T Hands 2,†, Jacob P Sorrentino 3, K N Houk 4, Neil K Garg 5
PMCID: PMC13527721  NIHMSID: NIHMS2206348  PMID: 42617096

Abstract

(2 + 2) Cycloadditions are a versatile transformation often employed in the synthesis of cyclobutanes. Such cycloadditions usually require the use of light or another synthetic workaround, given that thermal (2 + 2) cycloadditions are orbital symmetry-forbidden for unstrained all-suprafacial transition states. A unique type of (2 + 2) cycloaddition involves transient strained cyclic allenes, which proceed readily at ambient temperature without external stimuli. In the present study, computations and experiments show that the feasibility of these cycloadditions is tied to the inherent diradical character of the cyclic allenes. Moreover, comparative stereochemical transfer experiments for Diels–Alder and (2 + 2) cycloadditions are consistent with strained cyclic allenes having both closed- and open-shell character, thus rendering them diradicaloids. This study is expected to prompt the further strategic use of diradicaloids for the assembly of complex scaffolds.

Graphical Abstract

graphic file with name nihms-2206348-f0001.webp

INTRODUCTION

Cycloadditions are an indispensable method to rapidly build complex, polycyclic molecules.1,2 The present study concerns (2 + 2) cycloadditions, which provide a well-established means to assemble substituted cyclobutanes.3–6 Although thermal [πs2 + πs2] cycloadditions (i.e., 1 + 1→2, Figure 1A) are forbidden due to the molecular orbital considerations shown in 3,7–9 chemists have devised several workarounds for achieving (2 + 2) cycloadditions, including the use of ketenes 4,10 photochemical reactions involving α,β-unsaturated ketones 511 or other alkenes,12 Lewis acid activation,13 and/or photoexcitation. A complementary and understudied thermal approach involves the use of strained intermediates,14,15 specifically, strained cyclic allenes (e.g., 6) (Figure 1B).16–19 The first (2 + 2) cycloadditions of cyclic allenes were reported in the 1960s, and included the dimerization of 1,2-cyclohexadiene (6) to give 720,21 and trapping with styrene (8) to give 9.20,22 Subsequent studies by Christl, West, and others23–32 show that the methodology has practical value for the synthesis of compounds ranging from complex polycycles30–32 to modified DNA fragments,29 under mild reaction conditions.

Figure 1.

Figure 1.

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(A) Thermally forbidden (2 + 2) cycloaddition of ethylene (1) to form cyclobutane (2) with orbital interactions 3 and synthetic workarounds. (B) Dimerization of 1,2-cyclohexadiene (6) to form dimer 7, and trapping of 6 with styrene (8) to make cyclobutane 9. (C) Diradicaloid nature of cyclic allenes shown by concerted asynchronous (4 + 2) reaction of cyclic allene 10 and diene 11 (known; concerted process) and (2 + 2) cycloaddition of 10 and dienamine 13a driven by inherent diradical character (this study; proposed diradical process). Diradical character reported as nLUNO *100, calculated using CASSCF-(6,6)/cc-pVDZ level of theory.

Our laboratories and others have been intrigued by the mechanisms of strained cyclic allene cycloadditions leading to many theoretical studies, especially in recent years.33–48 We have previously examined (4 + 2) cycloadditions (i.e., 10 + 11→ 12, Figure 1C), which are found to proceed through thermally allowed concerted pathways.35,36,38 Those findings, coupled with the aforementioned consideration that [πs2 + πs2] cycloadditions are forbidden, make (2 + 2) cycloadditions of cyclic allenes an intriguing process.

Here, we probe the hypothesis that the diradicaloid nature of cyclic allenes is an important factor for the success of cyclic allene (2 + 2) cycloadditions. A diradicaloid is defined as “a system that is in between a diradical and a closed-shell molecule.”49 Despite some ambiguities in this definition, diradicaloids are especially intriguing as they can potentially engage in polar or radical processes due to their multireference character. Diradical character can be readily calculated using multireference complete active space self-consistent field (CASSCF) computations, a well-established method for studying open-shell singlet species.49–54 As will be utilized in this study, diradical character is typically quantified with the descriptor, y0, which is the computed occupation number of the lowest unoccupied natural orbital (LUNO).49,55 Diradicaloids have been studied for decades, including examples in the fields of acene chemistry, main group chemistry, and transition metal chemistry. Within the field of chemical synthesis, dimerization reactions are most well explored.56–63 Additionally, studies on 1,3-dipoles suggest diradical character correlates with reactivity.64–66 However, the use of diradicaloids in synthetically valuable fragment couplings to form complex structures is understudied. Our laboratories recently reported one such example for the reaction between cyclic allenes and bicyclobutanes, which gives bicyclohexane products of potential interest to medicinal chemists.34

We report an experimental and computational investigation of the thermal (2 + 2) cycloaddition between cyclic allene 10 and dienamine 13a to give 14a (Figure 1c).67,68 In addition to explaining regio- and diastereoselectivities, our studies suggest that the transformation proceeds through a diradical pathway. The diradicaloid nature of cyclic allenes (i.e., ~15% diradical character), which arises from its geometric distortion, is thought to be an important driving factor. These findings are expected to help fuel the further development of diradicaloid-enabled transformations of value to the synthetic community.

RESULTS AND DISCUSSION

Computational Evaluation of Reaction Mechanisms

Although computational studies of cyclic allene (4 + 2) and (3 + 2) cycloadditions have been performed,33,35,36,42–45 the examination of cyclic allene (2 + 2) cycloadditions remains limited.46 Prior studies of related systems have led to conflicting conclusions, suggesting either a stepwise47,48 or a concerted pathway.27 Thus, we sought to interrogate the mechanism for the reaction shown in Figure 2A, which was recently disclosed by our laboratory.32 Using a Kobayashi-type approach,17 also first used by Johnson to generate strained cyclic allenes,69 treatment of cyclic allene precursor 15 with dienamine 13a in the presence of fluoride gives cycloadduct 14a in 83% yield (17:1 d.r.). This complexity-generating (2 + 2) cycloaddition presumably proceeds via cyclic allene 10.

Figure 2.

Figure 2.

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(A) Experimental result of (2 + 2) cycloaddition using cyclic allene precursor 15 and dienamine 13a (3 equiv). (B) Potential reaction pathways, with a stepwise radical pathway being most favorable. The Ms group was used in place of the Ts protecting group in computational studies; 14b is the N-Ms analog of cycloadduct 14a. Calculations were performed at the ωB97X-D/def2-TZVPP/SMD(CH2Cl2)//ωB97X-D/def2-SVP/SMD(CH2Cl2) level of theory.

Computations for the reaction of cyclic allene 10 with dienamine 13b (the mesyl group was used in place of tosyl protecting group in computational studies) were performed using DFT at the ωB97X-D/def2-TZVPP/SMD(CH2Cl2)//ωB97X-D/def2-SVP/SMD(CH2Cl2) level of theory. This specific level of theory shows strong correlation to our experimental results and has been used to study a σ-bond insertion reaction of cyclic allenes, albeit using a different solvent model.34,70 Further details on how each computation was performed are available in the Supporting Information (see Part II.A).

Three likely pathways that could lead to the experimentally observed product were considered as shown in Figure 2B: a concerted pathway, a stepwise polar pathway, and a stepwise diradical pathway. For the concerted [πs2 + πa2] pathway (see TS-1), a transition state could not be found, suggesting this pathway is unlikely, as expected.8,9 For the stepwise polar reaction pathway (see TS-2), a transition state was indeed located for this process using a restricted DFT calculation. However, the wave function of the transition state was not stable with respect to the open-diradical wave function, suggesting this pathway was also disfavored. Additionally, computed Hirshfeld charges indicate minimal charge separation for the transformation, suggesting that the mechanism is likely not stepwise-polar.70 Finally, for the stepwise diradical pathway (see TS-3), a viable transition state was identified using an unrestricted DFT calculation. This transition state has a reasonable activation barrier of 19.2 kcal mol−1, involving C–C bond formation between the central carbon of the allene and the terminal carbon of the dienamine. This transition state (TS-3) leads to diradical 16, which leads to the corresponding cycloadduct 14b through radical recombination, as discussed below. Overall, these computational studies support a stepwise diradical pathway.

Having identified a plausible transition state for a stepwise diradical pathway, we computed the reaction coordinate for the aforementioned (2 + 2) cycloaddition (Figure 3). Initial C–C bond formation between cyclic allene 10 and dienamine 13b leads to diradical intermediate 16 via TS-3. This pathway ultimately gives rise to a doubly stabilized diradical intermediate, which is energetically favorable (see intermediate 16).70 Analogous to Diels–Alder cycloadditions of cyclic allenes,35,36,38 the central carbon of the cyclic allene approaches perpendicular to the reactive alkene terminus, as this approach allows for proper orbital alignment. As noted above, the transition state barrier is 19.2 kcal mol−1, consistent with the reaction occurring rapidly under ambient conditions. The length of the forming C–C bond is 2.16 Å, which is a reasonable C–C partial bond distance.34 The formation of diradical 16 is exergonic by 18.8 kcal mol−1. Subsequent radical recombination can lead to either of two diastereomers, 14b or 17, the former being the experimentally favored isomer. Transition states for both processes were found: TS-4a (ΔG‡ = 11.8 kcal mol−1) to give 14b and TS-4b (ΔG‡ = 13.5 kcal mol−1) to afford 17. TS-4a is favored by 1.7 kcal mol−1, consistent with the experimental observation that diastereomer 14b forms preferentially. We attribute the energy difference between TS-4a and TS-4b to steric interactions. Specifically, in TS-4b, H2′ of the dienamine and H1′ of the allene fragment are 2.38 Å apart, suggesting an unfavorable steric interaction. When compared to TS-4a, the analogous steric interaction is alleviated as H2 is 2.93 Å from H1 of the allene fragment. Overall, the reaction coordinate for the stepwise diradical pathway leading to 14b is in good accord with experimental observations.

Figure 3.

Figure 3.

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Calculated energy profile for the (2 + 2) cycloaddition of cyclic allene 10 and dienamine 13b via a stepwise radical pathway, consistent with the experimental reaction outcome (ωB97X-D/def2-TZVPP/SMD(CH2Cl2)//ωB97X-D/def2-SVP/SMD(CH2Cl2)). The Ms group was used in place of the Ts protecting group in computational studies. The SO2Me is omitted from the three-dimensional representation for clarity. All energies are reported in kcal mol−1.

Computational Study of Diradical Character and Distortion/Interaction Activation Strain (DIAS) Analysis

In typical (2 + 2) reactions of alkenes, photoexcitation or highly radical- or ion-stabilizing substituents are required to allow access to stepwise pathways and lead to cycloaddition. As such, we questioned what makes the cyclic allene (2 + 2) cycloaddition proceed so readily and what allows for the diradical pathway in the absence of photoexcitation. Previously, we suggested that geometric distortion (i.e., twisting, bending, and pyramidalization) of cyclic allenes leads to inherent diradical character present in cyclic allenes, which, in turn, enabled an unusual σ-bond insertion reaction.34 To interrogate if this property was also responsible for the (2 + 2) cycloaddition of cyclic allene 10 with dienamine 13b, we calculated diradical character (y0)55 across the reaction coordinate leading to diradical 16 (Figure 4A). CASSCF, the method of choice to assess diradical character, was used.34,49–53,70 In the ground state, the diradical character for cyclic allene 10 and alkene 13b are 15% and 11%, respectively. The diradical character for each fragment individually and the two together (“complex”) increases toward the transition state, leading to 18% diradical character in TS-3 (ΔG‡ = 19.2 kcal mol−1). Following C–C bond formation, the diradical character rises rapidly, eventually reaching 100% at diradical intermediate 16. We provide visualized natural orbitals and their energies along the reaction coordinate in the Supporting Information (see Part II.H).

Figure 4.

Figure 4.

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(A) Diradical character along the potential energy surface for the C–C bond formation of the (2 + 2) cycloaddition between cyclic allene 10 and 13b. (B) Diradical character along the potential energy surface for the first step of the (2 + 2) cycloaddition between dihydropyran 18 and 13b (ωB97X-D/def2-TZVPP/SMD(CH2Cl2)//ωB97X-D/def2-SVP/SMD(CH2Cl2)). Diradical character reported as nLUNO *100, calculated using CASSCF(6,6)/cc-pVDZ level of theory. (C) Distortion/interaction activation strain (DIAS) analysis for the first step of the reaction between cyclic allene 10 and 13b (TS-3) and dihydropyran 18 and 13b (TS-5) (CASSCF(6,6)/CASPT2/cc-pVDZ).

For comparison, an analogous study was performed for a reaction that does not readily take place under thermal conditions, the reaction of dihydropyran 18 in place of the strained cyclic allene 10 (see Figure 4B). The ground state diradical character of dihydropyran 18 is 8%, considerably lower compared to that of cyclic allene 10 (15%). This increases to 15% in the transition state TS-5 (ΔG‡ = 49.7 kcal mol−1), before rapidly rising to 100% in diradical 19. This process is endergonic, with 19 being 43.3 kcal mol−1 higher in energy than 18 and 10. Although the overall trends are similar in comparing the reaction of cyclic allene 10 and dihydropyran 18, the varying diradical characters (15% vs 8%), barriers of C–C bond formation (19.2 and 49.7 kcal mol−1), and correlations between the two parameters are notable. Cyclic allene 10 already has significant diradical character (15%), allowing for a low-barrier transition state (ΔG‡ = 19.2 kcal mol−1) with 18% diradical character, requiring minimal electronic reorganization. In the latter case involving dihydropyran 18, significant diradical character is seen in the transition state (15%), but because there is little diradical character in the reactant (8%), a greater degree of electronic reorganization is required, contributing to a prohibitively high activation barrier (49.7 kcal mol−1) to reach TS-5. Although the absolute values for calculated diradical character should not be overinterpreted, the smaller change in diradical character in the case of the cyclic allene reaction (15% in 10 to 18% in TS-3) suggests that high diradical character in the ground state, stemming from geometric distortion, makes possible what would otherwise be a high barrier process. We suspect the diradical character of the alkene reaction partner is less important, given that other alkenes are known to undergo (2 + 2) cycloadditions with cyclic allenes.31,32 We also note differences in resonance stabilization of the developing radicals; the development of an unstabilized secondary radical may contribute to the high reaction barrier to reach TS-5 (vs the resonance-stabilized allylic radical 16 being formed in the case of the cyclic allene reaction).

As shown in Figure 4C, we also performed distortion/interaction activation strain (DIAS) analysis71 for the reactions shown in Figure 4A,B. CASSCF(6,6)/CASPT2/cc-pVDZ single-point energy calculations are used, as this method has been used previously to study cyclic allenes engaging in radical reactivity.34 Further discussion of method selection is available in the Supporting Information, Part II.A and M. In the (2 + 2) reaction of cyclic allene 10 with dienamine 13b, the ΔE‡ to reach TS-3 was calculated to be −0.1 kcal mol−1, essentially zero.72 Of note, we find that the distortion energies for each reactant are quite small (i.e., Eallene–dist = −0.3 kcal mol−1 and Edienamine–dist = 1.6 kcal mol−1).73 The interaction energy (Einteraction) is also small, but favorable, and calculated to be only −1.4 kcal mol−1. Because of the existing distortion in the ground state structures and resulting high diradical character of both reactants, essentially no distortion is required to reach the transition state, and the barrier is mainly attributed to the unfavorable entropy of a bimolecular reaction. In contrast, the corresponding (2 + 2) reaction between dihydropyran 18 and dienamine 13b has a much higher energy of activation (ΔE‡ = 23.7 kcal mol−1).72 Significant geometric distortion is required for both reactants in order to achieve TS-5 (Edihydropyran–dist = 10.3 kcal mol−1 and Edienamine–dist = 7.9 kcal mol−1). In addition, the interaction energy was positive (Einteraction = 5.7 kcal mol−1),74 indicative of less favorable overlap and repulsive interactions in TS-5. Collectively, the results from this DIAS analysis suggest that the ease by which the (2 + 2) cycloaddition occurs is related to low distortion required to achieve the transition state TS-3, stemming from the distortion and diradical character inherent to cyclic allene 10. The favorable interaction energy in the reaction of allene 10 with 13b stems from the cyclic allene frontier molecular orbitals being helical with large coefficients on the central carbon of the allene.36

Kinetic Isotope Effect and Stereochemical Transfer Experiments

Experiments were performed to further assess the reaction mechanism, the first of which is shown in Figure 5. A kinetic isotope experiment using Singleton’s natural abundance (12C/13C) method was conducted on the reaction of cyclic allene precursor 15 and dienamine 13a to form cycloadduct 14a.75 This type of experiment provides insight into whether a transformation proceeds through a concerted mechanism or a stepwise mechanism, as the carbon atom involved in the product-determining step becomes fractionally enriched with the faster-reacting 12C isotope. For the experiment shown, k12C/13C = 1.001 ± 0.001 for the methylene carbon of 14a, while essentially no kinetic isotope effect (KIE) was observed at the quaternary center (1.001 ± 0.001). This indicates that the C–C bond between the central carbon of the cyclic allene intermediate 10 and the terminal position of dienamine 13a forms first, with the adjacent carbon of the dienamine experiencing no bond formation, supporting the stepwise mechanism. If a concerted mechanism was operative, the 12C/13C KIE would have presumably led to coefficients greater than one for both carbons in question, rather than just the methylene carbon.

Figure 5.

Figure 5.

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Natural abundance (12C/13C) kinetic isotope experiment between cyclic allene precursor 15 and dienamine 13a (3 equiv) supports a stepwise mechanism.

Finally, stereochemical transfer studies were performed to compare Diels–Alder versus (2 + 2) cycloadditions of cyclic allenes (Figure 6). These studies utilized azacyclic allene precursor 20, which can be accessed in enantioenriched form38 and possesses a methyl substituent that dictates regioselectivities. In the key Diels–Alder study, cycloaddition with dimethylfuran (21) occurs stereoselectively to give enantioenriched products 22 (Figure 6A).38,76 In contrast, the analogous reaction of azacyclic allene precursor 20 with dienamine 13a under nearly identical reaction conditions delivered cycloadduct 23 in low enantiomeric excess (ee) of 22% (Figure 6B). These results are consistent with the Diels–Alder cycloaddition proceeding through a concerted pathway, leading to excellent stereoretention, while the (2 + 2) cycloaddition occurs through a stepwise diradical pathway.77–79 Regarding the latter, the reaction outcome can be rationalized through a mechanism involving stereospecific generation of axially chiral allene 25 (from 20), which reacts with dienamine 13a to give diradical intermediate 26 (Figure 6C). Radical recombination of 26 would give 23, whereas C–C bond rotation, followed by radical recombination of ent-26 would furnish ent-23. The modest ee observed (i.e., 22%) is consistent with these two pathways occurring competitively (i.e., ΔGrecomb‡ ≈ ΔGrot‡).80 We calculate the ΔGrecomb‡ is 10.9 kcal mol−1 (N-Ms used in place of N-Ts).70 Although barriers for C–C bond rotation in alkanes are typically on the order of several kcal mol−1, a higher barrier (i.e., ΔGrot‡) is expected and reasonable given the sterically congested nature of the system.70,81,82 Overall, these results are indicative of the diradicaloid nature of cyclic allenes (24). Such species are unique in that they can behave as either closed-shell or open-shell species under almost identical reaction conditions.

Figure 6.

Figure 6.

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(A) (4 + 2) cycloaddition occurs with stereospecificity, indicative of the cyclic allene intermediate behaving as a closed-shell species. (B) (2 + 2) cycloaddition using 13a (3 equiv) occurs with low stereospecificity, suggestive that cyclic allene intermediates can also behave as an open-shell species. (C) Plausible mechanism for the formation of 23 with modest stereoselectivity.

CONCLUSION

Although thermal (2 + 2) cycloadditions are typically forbidden, such cycloadditions of strained cyclic allenes occur at ambient temperature. Computational studies show that these unusual reactions are related to the inherent diradical character of cyclic allenes. Moreover, stereochemical transfer experiments of (2 + 2) and (4 + 2) cycloadditions are consistent with strained cyclic allenes having the propensity to behave as either closed-shell or open-shell species, thus rendering them diradicaloids. This study not only explains why thermal (2 + 2) cycloadditions of strained cyclic allenes proceed so readily but also draws attention to the underexplored area of diradicaloids to strategically access structurally complex molecules.

Supplementary Material

SI

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacs.6c09105.

Materials and methods, detailed experimental procedures, compound characterization data, including NMR spectra, Cartesian coordinates, electronic energies, entropies, enthalpies, and Gibbs free energies (PDF)

xyz-files (ZIP)

ACKNOWLEDGMENTS

The authors are grateful to the NIH-NIGMS (R35 GM139593 for N.K.G.), the National Science Foundation (DGE-2034835 for A.T.H. and CHE-2452867 for K.N.H.), and the Trueblood Family (for N.K.G.) for financial support. These studies were supported by shared instrumentation grants from the NSF (CHE-8804), the NIH NCRR (S10RR025631), and the NIH ORIP (S10OD028644). Calculations were performed on the Hoffman2 cluster and the UCLA Institute of Digital Research and Education (IDRE) at UCLA. Huiling Shao and Matthew McVeigh are thanked for helpful discussions.

Footnotes

Complete contact information is available at: https://pubs.acs.org/10.1021/jacs.6c09105

The authors declare no competing financial interest.

Contributor Information

Noah W. Gilbertson, Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, United States.

Allison T. Hands, Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, United States.

Jacob P. Sorrentino, Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, United States

K. N. Houk, Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, United States

Neil K. Garg, Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, United States

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