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. 2024 Apr 29;146(18):12758–12765. doi: 10.1021/jacs.4c02681

Molecular Dynamics Investigations of Dienolate [4 + 2] Reactions

Peng-Jui Chen †, Alexander Q Cusumano †, Kaylin N Flesch †, Christian Santiago Strong †, William A Goddard III ‡,*, Brian M Stoltz †,*
PMCID: PMC11082897  PMID: 38682865

Abstract

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We report quantum mechanics calculations and quasiclassical trajectory simulations of [4 + 2] reactions using three common dienolate substrates: siloxy dienes, Li dienolates, and conjugated Pd enolates. Asynchronous transition structures and unequal bond formation were invariably found, with average time gaps of developing bonds ranging from 26.5 to >251.0 fs. The results display a spectrum of dynamically concerted and stepwise [4 + 2] reactions, offering insights into the origin of the stereochemical outcomes of such reactions.

Introduction

[4 + 2] cycloadditions are among the most widely utilized reactions in organic synthesis because of their ability to readily construct complex motifs through the concomitant formation of two C–C bonds and up to four stereocenters.1 An important feature of canonical Diels–Alder reactions is its stereospecificity, which guarantees control over the relative stereochemistry at two centers of point chirality. Additionally, when the diene is suitably substituted, there is an additional element of stereoselectivity that must be considered regarding the relative facial bias of the two reactive partners. Fortunately, many [4 + 2] cycloadditions proceed with high levels of stereoselectivity and often favor the so-called “endo” product.1,2

[4 + 2] reactions involving nonpolarized or symmetrically polarized substrates generally follow a concerted and stereospecific mechanism (TS1).3 In contrast, polarized dienes and dienophiles can electronically support charge-separated intermediates (8); thus, reactions with polarized substrates may proceed via two separate C–C bond-forming events, and the stereochemical outcome in such processes may be determined by the stereoselectivity of the system (Figure 1A).4

Figure 1.

Figure 1

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(A) Potential concerted and stepwise [4 + 2] reaction pathways of nonpolarized and polarized dienes. (B) Siloxy diene [4 + 2] reactions. (C) Lithium base-promoted [4 + 2] reactions. (D) Pd-catalyzed asymmetric [4 + 2] cycloaddition. (E) Isolated intermediate from intended [4 + 2] reaction with Li dienolate.

Cyclohexenone-derived dienes are common polarized substrates utilized in [4 + 2] reactions for rapid access to ketone-containing [2.2.2] bicycles (e.g., 10, 13, and 16, Figure 1B–D), which are ubiquitous motifs in various complex natural products.5 Representative substrates include siloxy dienes (9),6 Li dienolates (12),7 and more recently, chiral conjugated Pd enolates reported by our lab (15, Figure 1B–D).8

Siloxy diene Diels–Alder cycloadditions are believed to afford [2.2.2] bicyclic products in a stereospecific manner with respect to the stereochemistry of the dienophile,9 which is consistent with a concerted pathway that lacks long-lived intermediates. Conversely, despite nearly identical reaction and stereochemical outcomes from [4 + 2] reactions with Li dienolates, Li dienolate reactions have typically been considered to involve stepwise double Michael additions because of their mild reaction conditions (e.g., −78 °C)10 and the observation of single Michael adducts (19) in certain reactions (Figure 1E), consistent with sequential conjugate addition pathways.11 Recently, our lab reported the catalytic asymmetric synthesis of [2.2.2] bicycles that proceed via chiral conjugated Pd enolates.8 While the stereochemistry of most products is consistent with that expected from Diels–Alder reactions (i.e., stereospecific with respect to the dienophile olefin geometry in addition to high endo/exo diastereoselectivity), it was ambiguous whether the reaction is, indeed, concerted and stereospecific or completely stereoselective.

One possible delineation between concerted and stepwise pathways depends on whether an intermediate and a second transition state is featured. On the potential energy surface (PES), a stepwise pathway would be characterized by two local maxima (transition structures) connected by a local minimum (intermediate) along the reaction coordinate (Figure 2, top PES). However, analysis solely based on electronic energy (i.e., the PES) can be misleading.12 For various pericyclic reactions, flat regions may exist along the reaction coordinate PES (Figure 2, middle PES). Molecules may spend extended amounts of time in these regions as long-lived intermediates despite the absence of a local potential energy minimum.13,14 Such scenarios can arise from the entropic penalty associated with the progression along the reaction coordinate, and consequently, these intermediates are often described as entropic intermediates, which exhibit shallow free energy minima but no potential energy minima. While these reactions appear concerted because of the lack of an intermediate on the PES, they can be dynamically stepwise if long-lived entropic intermediates are present.

Figure 2.

Figure 2

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Example PES of a stepwise [4 + 2] reaction (top), concerted [4 + 2] reaction (bottom), and a dynamically stepwise (one-step, two-stage) [4 + 2] reaction (middle).

As entropic intermediates are not potential energy minima, they are challenging to identify on the basis of transition structure and PES studies. This also leads to the difficulty in characterizing dynamically stepwise reactions. Complementary to transition state analysis, molecular dynamics simulations have been shown effective in describing reactions in a time-resolved manner, which is key to discerning dynamically concerted and stepwise processes.14,15

In the context of the Diels–Alder reaction, Houk and co-workers demonstrated that highly asynchronous transition structures (i.e., those with large differences in bond distances in the two forming bonds) may undergo two temporally distinct bond-forming steps, even in the absence of an intermediate on the PES. However, because the time gap between these steps is generally less than or equal to the period of a typical C–C bond stretch (∼30–60 fs), the authors defined these processes to be “dynamically concerted.”16

In this report, we present the results of molecular dynamics simulations of [4 + 2] reactions involving cyclohexenone-derived diene substrates to describe a spectrum of mechanisms from synchronous and dynamically concerted to asynchronous and dynamically stepwise. Our findings are consistent with the usual classifications of [4 + 2] reactions with siloxy dienes and Li dienolates and demonstrate the influence of substrate choice on possible stereochemical outcomes.

Experimental: Computational Methods

All quantum mechanics calculations were carried out with the ORCA program.17 Geometry optimizations, harmonic frequency calculations, and single-point energy evaluations were carried out with density functional theory (DFT). To locate saddle points of the reactions and propagate trajectories, the Perdew–Burke–Ernzerhof (PBE) functional18 paired with Becke–Johnson damped D4 dispersion corrections19 (PBE-D4) and implicit conductor-like polarizable continuum model (CPCM) for the respective solvents20 were used. For geometry optimization and harmonic frequency calculations, Pd is described by the def2-TZVP basis set21 and the ECP28MWB small-core (18 explicit valence electrons) quasi-relativistic pseudopotential,22 while C, H, N, and P are assigned the def2-SV(P) basis. Diffuse functions are added to oxygen (ma-def2-SV(P)).

Quasiclassical trajectories were initialized by normal mode sampling at the saddle points in which each normal mode includes zero-point energy, as well as a Boltzmann sampling of geometries corresponding to thermal energy available at the respective reaction temperatures with a randomized phase. Trajectories were propagated in the forward and reverse directions with a velocity–Verlet algorithm in 1.0 fs time steps, as implemented in Singleton’s Progdyn program,23 until either formation of cycloadduct (forming both C–C bond lengths < 1.5 Å), formation of starting material (the shorter C–C bond length > 3 Å and the longer > 4 Å), or reaching max time (500 fs).

Considering the size of the system, a hundred trajectories were sampled to maintain tractability, and we limited the DFT to the generalized gradient approximation (GGA) functional PBE for the dynamic simulations. To investigate the influence of DFT functional choice on simulation results, a suite of control experiments was performed on a model reaction using hybrid, metahybrid, and range-separated functionals. While simulations with different functionals yielded slightly variable results, all simulation results described in this report were performed with the same functionals for comparison. For additional details and discussion, see the Supporting Information (SI).

Results and Discussion

Molecular dynamics simulations provide time-resolved studies of pericyclic reactions, which enables identification of long-lived entropic intermediates in reactions where bond formations are not synchronous.13,14 Herein, we define the average time gap (Δt) as the difference in time between formation of the two developing C–C bonds and adopt 60 fs, approximately the period for a typical C–C bond stretch, as the time criterion to discern dynamically concerted and stepwise reactions, as proposed by Houk and co-workers.13 Previously, the Houk lab reported an average time gap of 3.9 fs in the symmetrical [4 + 2] reaction of butadiene and ethylene (TS1, Figure 3A).16 While more asynchronous transition structures led to time gaps of up to 56.5 fs (TS3, Figure 3A), the reported reactions are all deemed dynamically concerted.

Figure 3.

Figure 3

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(A) Examples of previously studied [4 + 2] reactions. (B) Rotation of dienophile bond in dynamical intermediates can lead to formation of diastereomers.

Conversely, highly polarized systems, such as cyclohexenone-derived dienolates, may lead to dynamically stepwise reactions. Dynamically stepwise [4 + 2] reactions would feature long-lived intermediates analogous to sequential Michael additions. These reactions are considered stereoselective, rather than stereospecific, because bond rotation of the intermediate about the dienophile is potentially allowed, which can lead to formation of additional diastereomers (Figure 3B).

To investigate the timing of the bond formations in [4 + 2] reactions with different cyclohexenone-derived substrates, we report the molecular dynamics simulations of three different cyclohexenone systems: siloxy dienes, Li dienolates, and conjugated Pd enolates.

2.1. Reactions with Siloxy Dienes

[4 + 2] reactions of siloxy dienes and dienophiles are generally considered to be concerted processes and are referred to as Diels–Alder reactions in the literature. Aiming to investigate whether these reactions are concerted in a dynamical sense, we studied the model intramolecular reaction of siloxy cyclohexadiene 25 (Figure 4A).

Figure 4.

Figure 4

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(A) Computed thermodynamics of intramolecular [4 + 2] reaction with siloxy diene. (B) Trajectories derived from molecular dynamics simulation originating from TS4.

Reported examples of [4 + 2] reactions with siloxy dienes are typically performed in the presence of Lewis acid catalysts or in high-boiling solvents at elevated temperatures. To eliminate potential influences of exogenous additives, our computations were performed for the additive-free reaction with the CPCM implicit solvation model for toluene. The vibrational frequency calculations and trajectory initialization in the molecular dynamics simulation are in accord with thermal energies available at 383.15 K.

Quantum mechanical (QM) calculations revealed an asynchronous transition state (TS4) for the modeled reaction with an imaginary frequency of 323 cm–1. Bond distances of C1–C2 (d1) and C3–C4 (d2) were found to be 2.08 and 2.71 Å, respectively. Comparison of the free energies of the transition state with the corresponding reactant indicates an activation energy barrier of 23.2 kcal/mol. From the identified transition state structure, molecular dynamics simulations were employed to further investigate the synchronicity of the bond formations.

In practice, molecules will be found with geometries distributed along the dividing surface defined by the calculated transition structure depending on the available thermal energy. To simulate this distribution, weighted Boltzmann sampling was performed to yield a set of starting points represented by the blue dots in Figure 4B. From these starting points, trajectories are propagated in both directions, which means that the atoms are assigned initial velocities of opposite signs for the two directions. The trajectories are subsequently plotted on a 2D potential energy surface defined by d1 and d2. Productive trajectories lead to the formation of the cycloadduct in one direction and separation of reactants in the other, while unproductive trajectories yield separated starting material (SM) in both propagated directions. These unproductive pathways are termed recrossing to the starting material (SM) and are omitted from the analysis of Δt.

For the modeled [4 + 2] reaction with siloxy diene (TS4), unproductive trajectories leading to SM recross were found to be minimal (3%). An average time gap of 26.5 fs (median of 24 fs, range of 0–73 fs) was derived from the 97 productive trajectories. The short Δt for the C–C bond formations suggests a highly synchronous reaction, thereby indicating that the reaction is dynamically concerted. Since bond rotations generally occur on picosecond time scales, rotation at the dienophile is extremely unlikely to occur during this time gap, and the stereochemistry of the reactants is relayed to that of the product through a perfectly stereoselective mechanism.

2.2. Reactions of Conjugated Li Enolates

Reported [4 + 2] reactions of Li dienolates have generally been thought of as stepwise processes through sequential Michael additions.24 This classification originates from the usually mild reaction conditions and specific examples in which intermediates with only one C–C σ-bond formed were isolated.11 Herein, we attempt to discuss the degree to which both intramolecular and intermolecular Li base-initiated [4 + 2] reactions (TS5–6) are concerted through molecular dynamics simulations.

Lithium enolates are known to form aggregates in organic solvents.25 Consequently, a description of the solvated Li dienolate species is required to depict the [4 + 2] reactions more accurately. As such reactions are typically performed in a mixture of hexanes and ethereal solvents, we considered a cubic Li tetramer structure reported for similar species in ethereal solvents.26

Computationally, this was achieved through the explicit expression of Li-coordinated species (27, Figure 5A). In addition to four diethyl ether molecules, the reactive dienolate and three methoxy anions were coordinated. These methoxy anions were used as surrogates for additional enolate species for computational simplicity. This Li enolate tetramer (27) is proposed to be in equilibrium with tetramer 28 where the reactive dienophile displaces the coordinated solvent.

Figure 5.

Figure 5

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(A) Model of a solvated Li enolate tetramer in ethereal solvent (formal charges are removed for simplicity and clarity). (B) Computed thermodynamics of intramolecular [4 + 2] reaction with Li dienolate. (C) Computed thermodynamics of intermolecular [4 + 2] reaction with Li dienolate. (D) Trajectories derived from a molecular dynamics simulation originating from TS5. (E) Trajectories derived from molecular dynamics simulation originating from TS6.

The reaction environment was subsequently simulated with reactive Li tetramer 28 using the CPCM implicit solvation model. The dielectric constant of the solvent was chosen to be 2.3, which corresponds to a 5:1 mixture of hexanes and diethyl ether.27 As low temperatures are generally required for such reactions, computations are in accordance with thermal energies available at 195.15 K.

TS5 and TS6 were found to have small energy barriers compared with those of the respective reactants, which is consistent with the typical low reaction temperatures. Similar to TS4 of siloxy diene, Li dienolate reactions exhibited asynchronous transition structures with bond distances of d1 and d2 in TS5 found to be 2.25 and 3.40 Å and d1 and d2 in TS6 to be 2.37 and 3.29 Å, respectively (Figure 5B,C).

Subsequent molecular dynamics simulations initiated from TS5 and TS6 revealed significantly different behavior from the reaction of siloxy diene 25. Both Li dienolate reactions exhibit substantially larger Δt, with the intramolecular reaction Δt (Figure 5B) found to be 251.0 fs and intermolecular reaction Δt = 154.5 fs (Figure 5C). These large time gaps indicate that Li dienolate systems tend to spend significant amounts of time as charge-separated intermediates 32 and 33 (Figure 5D,E), which is suggestive of dynamically stepwise processes. During the lifetime of charge-separated intermediates 32 and 33, free rotation of the C2–C4 σ-bond can lead to formation of diastereomers. Since bond rotations typically occur on a picosecond time scale, C3–C4 bond formation generally outcompetes bond rotation to afford the formal [4 + 2] adduct with stereochemistry analogous to the products of concerted mechanisms. Therefore, such processes are considered stereoselective rather than stereospecific as a concerted pathway.

Trajectory outcome distributions from TS5 and TS6 are also significantly different, despite the same ratio (63%) of productive trajectories. The majority of trajectories that were not productive for the intramolecular reaction (Figure 5B) led to long-lived intermediate 32 that persisted through the duration of the simulation, which was 500 fs. The previously calculated Δt does not include these 24 incomplete trajectories, and therefore, the Δt of the intramolecular reaction is likely to be even larger in reality. The remaining 13 trajectories from TS5 were found to reform reactant. In contrast, significant recrossing (35%) to starting material was observed from TS6 of the intermolecular reaction,28 and only two trajectories were incomplete.

Differences in various features of both the PES analysis and the molecular dynamics simulation were also observed as a consequence of whether the Li dienolate and dienophile were tethered. The initial bond length difference between d1 and d2 was found to be 1.15 Å for TS5, while this difference decreased to 0.92 Å for TS6. The two transition states were both characterized by a negative curvature on the PES but with magnitudes of 161 (TS5) and 119 cm–1 (TS6), respectively. While the distribution of the molecular dynamics simulation starting point geometries for TS5 and TS6 appear similar with regard to the initial d2, a tighter distribution along d1 is observed in intramolecular TS5.

In summary, our computational analysis of the intermolecular and intramolecular reactions with Li dienolates suggests that these reactions follow dynamically stepwise mechanisms with long-lived charge-separated intermediates having lifetimes of at least 154.5 fs for the intermolecular reaction and 251.0 fs for the intramolecular reaction. While the long intermediate lifetimes can potentially allow dienophile C–C σ-bond rotation, the C4 stereochemistry of the reactants is transferred to that of the [4 + 2] adducts in a stereoselective fashion. It was also observed that the presence of a tether between diene and dienophile leads to an increased time gap, significantly less recrossing to starting material, and substantially more incomplete trajectories.

2.3. Reactions of Conjugated Pd Enolates

Recently, our group reported the asymmetric decarboxylative [4 + 2] cycloaddition from catalytically generated Pd enolates as a unique approach to enantioenriched [2.2.2] bicyclic ketones (16). This reaction is envisioned to proceed via the intermediacy of a conjugated O-bound Pd enolate (15) that undergoes a formal intramolecular [4 + 2] cycloaddition with a pendant dienophile (Figure 6A). While the net transformation mirrors that of the Li enolates and siloxy dienes discussed previously, the chiral Pd enolate enables unprecedented control of absolute stereochemistry. Similar to both Li dienolates and siloxy dienes, the dienophile olefin geometry is generally reflected in the relative stereochemistry in the product of the Pd-catalyzed transformation (16). Our investigations of Li dienolates and siloxy dienes exemplify that analysis of product stereochemical outcome alone does not delineate between the possibilities of concerted stereospecific and dynamically stepwise stereoselective processes. Hence, while our initial report uncovered the origins of enantioselectivity, understanding the origin of the C2/C4 relative stereochemistry requires a time-resolved picture of bond formation.

Figure 6.

Figure 6

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(A) The decarboxylative asymmetric [4 + 2] cycloaddition of Pd enolates. (B) Trajectories derived from MD analysis of the bond-forming processes.

In analogy to the propylene-tethered intramolecular Li enolate cycloaddition (TS5), the transition structure for the net [4 + 2] reaction of conjugated Pd enolate 15 to transposed enolate 34 is highly asynchronous. The PES connecting 15 to 34 bears no minima between those of TS7 and 34. With C1–C2 (d1) and C3–C4 (d2) distances of 2.18 and 3.26 Å, respectively, TS7 has a Δd value of 1.08 Å—smaller than that of Li dienolate TS5 (Δd = 1.15 Å) but significantly greater than siloxy diene TS4 (Δd = 0.63 Å). TS7 is characterized by a negative curvature of the PES corresponding to −212 cm–1 compared with the flatter curvature of TS5 (−161 cm–1).

Quasiclassical dynamics were initiated from the normal-mode sampled TS7 starting points with a thermal energy corresponding to 333.15 K (Figure 6B). Our dynamics simulations reveal an average time difference between the C1–C2 and C3–4 bond formations (Δt) of 172.9 fs for the 90 productive trajectories (15 to 34). Of these trajectories, 81 present time gaps of >60 fs, while nine are classified as dynamically concerted (Δt ≤ 60 fs). The Δt values range from 19 to 405 fs with a standard deviation of 90.8 fs. Only eight trajectories display recrossing of the transition region to return to the starting enolate 15.

As with Li dienolate 28 and 30, significant time (up to 400 fs) is spent as a charge-separated intermediate (i.e., 35, Figure 6B). While this time corresponds to several C–C bond vibrational stretching periods, it remains a shorter time scale than that of C2–C4 bond rotation (≥1 ps). Hence, the dienophile olefin stereochemistry of 15 is relayed to that of product 34. Overall, the Pd enolate [4 + 2] is more concerted in nature than its Li enolate counterparts (28, 30) yet is more stepwise than the analogous reaction from siloxy diene 25.

Conclusions

We report molecular dynamics simulations of the [4 + 2] reactions of three classes of polarized dienes: siloxy dienes, Li dienolates, and conjugated Pd enolates. Analysis of the trajectories from our simulations demonstrates the reaction of a siloxy diene to be the most synchronous, with a time gap of only 26.5 fs and minimal recrossing to the starting material (3%). The intramolecular [4 + 2] reaction with conjugated Pd enolate exhibited more asynchronous behavior, with a time gap of 172.9 fs and 90% of the productive trajectories classified as dynamically stepwise. Finally, the reactions of Li dienolates were found to be the most asynchronous in nature. Both intramolecular and intermolecular [4 + 2] reactions of Li enolates were found to give time gaps of at least 154.5 and 251.0 fs with 95% and 100% of trajectories being considered dynamically stepwise, respectively.

In summary, these results affirm the tendency of certain polarized dienes to undergo [4 + 2] reactions with significant time differences between formation of the two new bonds. As long as this delay is shorter than the time required for a C–C σ-bond rotation, stereochemical information is preserved, thereby matching the stereospecificity of a concerted process. Understanding this time-resolved nature of bond formations is key to interpreting the stereochemical outcome of these processes and will aid the further developments and applications of [4 + 2] reactions.

Acknowledgments

The NIH-NIGMS (R35GM145239), Heritage Medical Research Investigators Program, and Caltech are thanked for the support of our research program. We further thank Professor Ken Houk for insightful discussions. The Caltech High Performance Computing Center is acknowledged for support of computational resources. P.-J.C. and C.S.S. would like to thank the NSF GRFP for funding. W.A.G. thanks the NSF (CBET-2311117) for support. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacs.4c02681.

  • Complete computational details (PDF)

  • Cartesian coordinates of the calculated structures (ZIP)

  • Sample Progdyn Files (ZIP)

  • QM energies and analysis (XLSX)

  • Sample trajectory animations (ZIP)

Author Contributions

§ P.-J.C and A.Q.C. contributed equally.

The authors declare no competing financial interest.

Supplementary Material

ja4c02681_si_001.pdf (386.6KB, pdf)
ja4c02681_si_002.zip (31.6KB, zip)
ja4c02681_si_003.zip (21.7KB, zip)
ja4c02681_si_004.xlsx (14.6KB, xlsx)
ja4c02681_si_005.zip (4.6MB, zip)

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  28. The trajectories leading to separation of reactants to starting material do not feature the charge-separated intermediate (33), which means that no bond formation (characterized by either C–C bond distance < 1.6 Å) was observed in these trajectories.

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