(5 + 2)-Cycloaddition of Butadiene

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A pathway bifurcation in the (4+3)/(5+2) cycloaddition of butadiene and oxidopyrylium ylides: The significance of molecular orbital isosymmetry. Jed Marcus Burns, and Eric D. Boittier J. Org. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.joc.8b03236 • Publication Date (Web): 30 Jan 2019 Downloaded from http://pubs.acs.org on February 4, 2019

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The Journal of Organic Chemistry

A pathway bifurcation in the (4+3)/(5+2) cycloaddition of butadiene and oxidopyrylium ylides: The significance of molecular orbital isosymmetry. Jed M. Burns* and Eric D. Boittier School of Chemistry and Molecular Biosciences, The University of Queensland, St Lucia, 4067, QLD, Australia. [email protected], [email protected] CO (4+3)/ (5+2)cycloaddition

O Prod-1

O

O

O TS-1

O Prod-2

Abstract By drawing analogies from the dimerisation of cyclopentadiene, a novel reaction pathway bifurcation is uncovered in the cycloaddition of oxidopyrylium ylides and butadiene. Analysis of the potential energy surface (at the M06-2X/6-311+G(d,p) level of theory) in combination with Born-Oppenheimer Molecular Dynamics simulations (M06-2X/6-31+G(d)) demonstrate that both the (4+3)- and (5+2)-cycloaddition products are accessed from the same transition state. Key indicators of a pathway bifurcation (asynchronous bond formation, and a second transition state for the interconversion of the products) are also observed. The absence of a post-transition state bifurcation in the related oxidopyridinium systems of Krenske and Harmata is rationalised. Finally, the isosymmetry of the oxidopyrylium and cyclopentadiene molecular orbitals, as well as the presence of “secondary orbital interactions” are emphasised as the common source of non-statistical behaviour. Application of these principles will allow for the rapid identification of new reaction pathway bifurcations. Introduction Post-transition state bifurcations (PTSBs) are a chemical phenomenon whereby a single transition state connects a substrate to two (or more) products with no intervening minima.1-4 This behaviour, which contravenes the normal assumptions of traditional Transition State Theory, allows for the dynamic motion of the reacting system (the movement of atoms in the molecule as it passes through the transition state) to primarily determine the distribution of products.5-18 The transition states for reactions containing these features are often described as being bispericyclic (specifically when two discrete pericyclic reactions are observed to merge together),19-20 or ambimodal.15,18,21 At present, there are no experimentally relevant methods to control such processes.22 Moreover, there are no robust approaches to identify the presence of PTSBs in reactions a priori. This is concerning given predictions that a substantial number of reactions may be subject to nonstatistical dynamic effects.23 It is likely that significant quantities of material and time are

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wasted attempting to optimise reactions containing PTSB’s which are fundamentally predisposed to generating more than one product.24 It is therefore crucial to develop means for locating reactions which contain pathway bifurcations, and to control and harness this interesting phenomena. One of us (JMB) has previously alluded to “reaction planning principles” for the identification of reactions likely to contain pathway bifurcations.25 A component of this model will be disclosed below.26 Consider the frontier molecular orbitals of Caramella’s classic pathway bifurcation, the dimerization of cyclopentadiene CPD (Scheme 1, notably initially proposed by Woodward and Katz).19,27 Favourable orbital overlap occurs at the termini of and within the two systems, with one molecule acting as the antisymmetric HOMO component and the other the symmetric LUMO component (Scheme 1A). The endo approach of the reactant was (and continues to be) rationalised on the basis of favourable secondary orbital interactions until the discovery of the reaction pathway bifurcation.28,29 There are, however, other conjugated systems that can fulfil the required orbital symmetries, perhaps the simplest being the next higher homologue, the pentadienyl cation PD (Scheme 1B). The LUMO for the isolated cation PD would typically be constructed as LUMOPD A, but judicious substitution (e.g. an electron-donating group at C-2) could perturb the parent system to yield LUMOPD B, which could be considered the result of a linear combination of functional group orbitals (or the addition of a vacant p orbital to the LUMO of butadiene). We suspected such an orbital array would be present in oxidopyrylium OP, which was supported by calculation of the frontier molecular orbitals. Furthermore, reaction of OP with conjugated dienes (such as butadiene BD) would be expected to yield a pathway bifurcation between the competing (4+3)- and (5+2)-cycloadditions in a manner analogous to that of cyclopentadiene CPD (Scheme 1C).

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A) (4+2) BCPD-1

(3,3)sigmatropic

LUMOCPD

(2+4) CPD

TS-CPD HOMOCPD

BCPD-2

B)

A

B or

O

LUMOPD

LUMOOP

O

PD or

OP

HOMOPD HOMOOP C)

CO (4+3)/(5+2)cycloaddition?

O O BD

OP

O Prod-1

O

(3,3)sigmatropic

O

O TS-1

O Prod-2

Scheme 1: A) Caramella's pathway bifurcation in the dimerisation of cyclopentadiene CPD, B) Frontier molecular orbitals of the pentadienyl cation PD and oxidopyrylium ylide OP (calculated at the HF/6-31G(d) level of theory), C) Plausible pathway bifurcation in the cycloaddition of oxidopyrylium OP and butadiene BD. The insights discussed above led to the search for reaction pathway bifurcations in oxidopyrylium cycloadditions. While the reaction has been used extensively in synthesis,30-36 two reports by Sammes and Street,37 and Krenske and Harmata (deploying the related oxidopyridinium ylides),38 attracted our attention for their use of a butadiene reactant (Scheme 2). In some of the earliest work on oxidopyrylium cycloadditions, Sammes and Street noted that dienes, when reacted with OP (generated in situ from the deprotonation/elimination of acetate Pro-OP), yielded both the (5+2)- and (4+3)-products Prod-2 and Prod-1, with a preference for the (4+3)-products.37 Notably, the (5+2)-products (Prod-2A and B) were solely endo configured, implying a substantial preference for an endo TS (see below). More recently, Krenske and Harmata have documented the exclusive (4+3) cycloaddition of ester-substituted oxidopyridinium Harm-OP with a variety of dienes.38 Extensive computational investigation at the M06-2X/6-311+G(d,p)//M06-2X/6-31G(d) level of theory confirmed the preference for the (4+3)-product through the lowest energy exo 3/19



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transition state (see below), though experimentally both the endo and exo products were observed (for instance, reaction of penta-1,3-diene “methylbutadiene” MBD yields a 1:1 mixture of Prod-1D and Prod-1E). Sammes and Str eet

O

DCM 0 oC, 16 h

O DM

O

2eq NEt3

OP

CO

O

O

Prod-2A 8%

Prod-1A 49%

R O 1.8eq NEt3 DCM rt, 16 h

O IP

OP

O AcO

R

CO

O

O

Prod-2B 29%

Prod-1B R = Me or H 33%

O

2eq NEt3 DCM

O

O

O OP

Pro-OP

Kr enske and Har mata

MeOOC

O

O N Harm-OP

MeCN 80 oC 17 h

CO

MeOOC

Prod-1C 99%

MeOOC

O N

N

Harm-OP

MeOOC

MBD

MeOOC

85 oC 24 h

N BD

MeCN

CO

Prod-2C not obser ved

MeOOC

N Prod-1D exo

CO

1:1 70%

N Prod-1E endo

Scheme 2: Selected examples of oxidopyrylium OP and oxidopyridinium Harm-OP cycloadditions from Sammes and Street,37 and Krenske and Harmata.38 Results and Discussion Reaction profile We initially elected to model the cycloaddition of oxidopyrylium and butadiene at the M062X/6-311+G(d,p) level of theory (as used by Krenske and Harmata),38-39 with DCM solvation modelled implicitly using Truhlar’s SMD method.40 The free energy profile for the reaction is shown in Scheme 3. Geometries and free energies for the relevant transition states are shown in Figure 1. We determined the endo-configured TS-1 to be the lowest energy 4/19


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transition state structure, with a free energy barrier of 16.1 kcal/mol. This is consistent with the reaction conditions reported by Sammes and Street, whereby the transformation occurs easily at, or slightly below (0 oC), room temperature.37,41 Alternative structures, which may be more clearly recognised as (4+3)- or (5+2)-cycloaddition transition states (TS-3 and TS-6 to TS-8), were found to be higher in energy. The preference for TS-1 can again be ascribed to the favourable “secondary orbital interactions” between OP and BD. Intrinsic reaction coordinate (IRC) calculations for TS-1 support the ostensible (4+3)-character of the process, with the geometry smoothly connecting to the bicyclo[4.3.1]decanone, Prod-1. However, the cycloaddition is notably asynchronous (though still concerted) as the C1-C1’ bond is formed before the C4-C3’ (or C2-C5’) bond. Reoptimisation of structures after initial C1-C1’ bond formation located TS-2, which interconverts Prod-1 and Prod-2 via a (3,3)-sigmatropic rearrangement.42 It is important to note that the free energy barrier for the cycloaddition reaction (ΔG‡ = 16.1 kcal/mol) is significantly lower than that of the sigmatropic rearrangement (ΔG‡ = ~35 kcal/mol relative to Prod-2). Therefore, we assert that the distribution of (4+3)- and (5+2)-products observed by Sammes and Street under “kinetic” control is in fact determined dynamically in the initial cycloaddition step, and not as a result of subsequent interconversion. CO O

O

Prod-1

O

O BD

O

OP

O

O O

TS-1

TS-2

O Prod-2

see Figure 1

OP + BD

TS-1 | E‡ = 1.8 [2.2] E+ZPE‡ = 3.4 [3.8] H‡ = 2.7 [3.1] G‡ = 16.1 [16.4]

TS-2 -10.4 [-10.5] -7.2 [-7.3] -8.7 [-8.8] 6.5 [6.4]

Prod-2 -46.1 [-47.0] -41.4 [-42.3] -42.5 [43.4] -28.6 [-29.6] Prod-1 -47.5 [-48.0] -42.2 [-42.8] -43.5 [-44.0] -29.1 [-29.7]

Scheme 3: Energy profile (ΔE, ΔE + zero point energy (ZPE), ΔH and ΔG respectively) for the reaction of oxidopyrylium OP and butadiene BD calculated at the M06-2X/6311+G(d,p)//SMD(DCM) and M06-2X/6-31+G(d)//SMD(DCM) (square brackets) level of theory. Energies are in kcal/mol.

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4 2

1 3'

O

5'

O

O O

1'

TS-1 G‡ = 16.1 G‡ = 0.0

TS-2 6.5 -9.6

O O

O O

TS-3 (4+3) exo 18.3 2.2

TS-4 24.1 8.0

O O TS-6 (5+2) endo s-trans 18.1 2.0

O O TS-5 31.8 15.7

O O TS-7 (5+2) exo s-trans 18.2 2.1

O O TS-8 (5+2) exo s-cis 19.0 2.9

Figure 1: Transition states, geometries and free energies (ΔG‡) for the cycloaddition of oxidopyrylium OP and butadiene BD, calculated at the M06-2X/6-311+G(d,p)//SMD(DCM) level of theory. Note that the atom numbering for TS-1 will be used throughout. Free energies are in kcal/mol, bond lengths are in angstroms. With a view to confirming the presence of a pathway bifurcation (see below), we elected to investigate less computationally expensive levels of theory which would be suitable for Born-Oppenheimer Molecular Dynamics (BOMD) simulations.43-45 Geometries for TS-1 at differing levels of theory are shown in Figure 2. Transition state geometries reoptimized at the M06-2X/6-31G(d) level of theory (identical to that used by Krenske and Harmata) yielded structures which were slightly biased towards (4+3)-product formation evidenced by shortening of the C4-C3’ distance and lengthening of C2-C5’ (difference in bond length, bond = 0.27 Å vs 0.10 Å at the M06-2X/6-311+G(d,p)//SMD(DCM) level of theory). While B97XD yielded similar overall structures to M06-2X, the well-known B3LYP functional was unsuitable in reproducing the triple-zeta M06-2X results, being heavily skewed to the (4+3)product (bond = 0.41 Å). Addition of a diffuse function to the basis set (M06-2X/6-31+G(d)) in order to capture the polarisable character of the zwitterionic oxidopyrillium led to a lengthening of the forming C2-C5’ and C4-C3’ bonds. Finally, optimisation in implicit solvent yielded structures in close agreement to those obtained at the higher level of theory (bond =

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0.12 Å). The free energies for relevant structures calculated using M06-2X/631+G(d)//SMD(DCM) are reported in Scheme 3 and are in satisfactory agreement with the triple zeta results. The observed diversity in TS geometries has previously been noted as a hallmark of post-transition state bifurcations.4,24

O O TS-1

M06-2X/6-31G(d) bond = 0.27

M06-2X/6-311+G(d,p)//SMD(DCM) bond = 0.10

B97X-D/6-31G(d) bond = 0.24

M06-2X/6-31+G(d) bond = 0.20

B3LYP/6-31G(d) bond = 0.41

M06-2X/6-31+G(d)//SMD(DCM) bond = 0.12

Figure 2: Diversity in geometries of ambimodal TS-1 at different levels of theory, displaying the difference in the C4-C3’ and C2-C5’ bond lengths (bond). Distances are in angstroms (Å).

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Figure 3: Relaxed potential energy surface scan of area surrounding TS-1, modulating the C2-C5’ and C4-C3’ bond lengths, at the M06-2X/6-311+G(d,p)//M06-2X/6-31G(d) level of theory. Stylised trajectories are depicted as red arrows. Potential energy is in Hartrees, bond lengths are in angstroms (Å). Potential energy surface Visualisation of a bifurcation on the energy surface around TS-1 is understandably complicated by the need to account for three geometric variables (the “shared” C1-C1’ bond, and the “competing” C2-C5’ and C4-C3’ bond lengths) in addition to energy. In previous investigations, Houk and co-workers have used a composite variable of the difference between the competing bond lengths,6-7 whereas we used the shared and competing bond to demonstrate access to the minor product.25 In the current study, two different representations have been chosen (see Figure 3 and Figure 4). Figure 3 displays the relaxed potential energy surface surrounding TS-1, modulating the C2-C5’ and C4-C3’ bond lengths. Electronic energies (E) are presented, though results are similar with the addition of zero point energy (E + ZPE), as well as for free energies (G, see SI Figures S16-S19). The discontinuity between TS-1 and the adjacent surface is due to exothermic formation of the C1-C1’ bond, though it can be demonstrated that the two are smoothly connected (see SI Figures S14-S15). This is consistent with the course of the reaction along the minimum energy pathway. There is therefore a continuous downhill path from the transition state to both Prod-1 and Prod-2. Notably, geometries with slightly shorter C4-C3’ distances (2.82 Å, C2-C5’ = 2.99 Å) lead to Prod-1 while shorter C2-C5’ lengths (2.69 Å, C4-C3’ = 2.82 Å) lead to Prod-2 (as determined by “downhill” IRC calculations).

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Figure 4: Relaxed potential energy surface scan of area surrounding TS-1 (at the M06-2X/631G(d) level of theory) showing a downhill path to minor product Prod-2. The C2-C5’ and C1-C1’ bond lengths are varied while the C4-C3’ bond length is fixed. Potential energy is in Hartrees, bond lengths are in angstroms (Å). In addition to the analysis presented above, Figure 4 displays the potential energy surface varying the C1-C1’ and C2-C5’ bond lengths while fixing the C4-C3’ bond. While these conditions are non-physical, the resultant energy surface is descriptive. As before, there exists a continuously downhill path from TS-1 to the non-IRC product, Prod-2. Dynamics results In order to determine whether the observed post-transition state bifurcation was likely to be experimentally relevant, BOMD calculations were conducted (Figure 5).43-45 Given the demonstrated close agreement with the M06-2X/6-311+G(d,p) results, unrestricted M062X/6-31+G(d) was chosen (see above).46 Starting from TS-1, 100 trajectories with randomised normal mode energies and initial velocities (within a Boltzmann distribution of states) were generated and propagated both “forward” in the direction of the products and “backward” to confirm connection to the starting materials (see computational methods for details, and SI Figures S1-S10 for additional analysis). From this, 50 trajectories led to Prod-1 and 45 trajectories led to Prod-2, with 5 trajectories failing to reach any product after 200 steps (i.e. 120 fs) and instead “roaming” near the transition state region or recrossing to the starting materials. Inspection of the data reveals that trajectories initiated near TS-1 lead directly to either Prod-1 and Prod-2 in a mean time of ~89 fs, with the mean time for formation of the C1-C1’ bond being ~34 fs. The time between bond formation (~55 fs) is on the order of the lifetime of a C–C bond stretching frequency (30-60 fs, the preferred metric for reaction synchronicity)47 indicating that the reaction can be largely described as dynamically concerted, once again stressing that no intervening intermediate could be located.48 The time gap is of a similar magnitude to that calculated for the concerted asynchronous Diels–Alder cycloaddition of 2-hydroxybutadiene and cyanoacetylene (57 fs) by Houk, et al.47

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The product ratio determined from the BOMD calculations (~1:1) is in broad agreement with the results of Sammes and Street (Prod-1B, 33% yield, Prod-2B, 29% yield) and gives credence to the fact that the dynamics of the system are responsible for the observed product distribution, and not thermodynamic or kinetic factors. A curious observation is that an almost symmetric distribution of products is generated from an intrinsically assymetric transition state structure. The product distribution is in the order of what would be expected if the reaction were run under thermodynamic conditions (ΔΔGM06-2X/6-31+G(d) = 0.1 kcal/mol, coresponding to a ratio of ~1:1), but as stated previously the high barrier for TS-2 prevents their interconversion under the reported reaction conditions. To underscore this anomaly, Houk and co-workers have developed a linear regression analysis relating the difference in the "competing" bonds in the transition state structure to the ratio of products formed in ambimodal reactions,49 which in the current case would give a Prod-1:Prod-2 ratio of ~3:1 (2.4:1 when considering the M06-2X/6-311G(d,p) geometry). The discrepency (acknowledged by Houk, et al.) possibly stems from the use of bond lengths as an approximation for bond order.50 That being said, explicit calculation of the bond orders or interaction energies does not lead to a satifactory explanation. Wiberg bond indicies for TS1 calculated using the Natural Bond Orbital (NBO) method,51 are 0.0872 (C2-C5’) and 0.0672 (C4-C3’), counterintuitively yielding a higher bond order for the longer C2-C5’ bond. Second Order Perturbation Theory (SOPT) analysis gives interaction energies of 2.32 kcal/mol (C2C5’, from the C4’-C5’ , C1-C2 * interaction) and 2.71 kcal/mol (C4-C3’, from the C3’ , C3C4 * interaction). These results underscore the limitations of the static picture and suggest that features on the PES after the TS are responsible for the observed selectivity. More sophisticated procedures for predicting the product outcome of the reaction, especially Carpenter’s “vectorial decomposition” method,52-54 may be more appropriate for this system and will be investigated in the future.55

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Figure 5: Plot of 100 trajectories initiated near TS-1 (UM06-2X/6-31+G(d)//SMD(DCM)), tracking the C4-C3' and C2-C5' bond lengths. Distances are in angstroms (Å). Comparison to other systems A point that remains to be addressed is why a mixture of products is not observed in the related (4+3)-cycloaddition of Krenske and Harmata.38 The improved product specificity is likely due to the ester-substituent of the oxidopyridinium reactant, Harm-OP (Scheme 4).56 In contrast to the cycloaddition of OP, the exo transition state, Harm-TS-3 is preferred, leading exclusively to the (4+3)-product. Methyl ester substitution at the C4’ position would reduce the orbital coefficient at the adjacent C5’ position and thereby attenuate the stabilising interactions in the endo transition state, Harm-TS-1. With that being said, HarmTS-1, is calculated to only be 0.7 kcal/mol higher in energy than Harm-TS-3, meaning that under the reaction conditions it can be expected that ~20% of trajectories would pass through the endo transition state (calculated from the Eyring equation). If a post-transition state bifurcation does exist in this system then the (5+2)-product, Prod-2C, might be observed. On the other hand, and in contrast to TS-1, bond formation in Harm-TS-1 is calculated to be largely synchronous (C1-C1’ = 2.12 Å, C4-C3’ = 2.45 Å), and the difference in the “competing” bond lengths is substantial (C2-C5’ = 3.34 Å, Δbond = 0.89 Å). This suggests that even if a continuously downhill path is present from Harm-TS-1 to Prod-2, the amount of product formed may not be experimentally relevant. Indeed, of 25 trajectories initiated near Harm-TS-1, 23 led to Prod-1C with 2 recrossing to starting material (see SI Figure S11). Regardless of the dynamic preference, the reported reaction conditions (85 oC, sealed tube, 24 hrs) would favour the thermodynamic (4+3)-product, Prod-1C (ΔG = -14.4 kcal/mol), compared to Prod-2C (ΔG = -1.6 kcal/mol). The difference in the free energies of products

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can further be viewed as a result of the ester-substituent; a favourable push-pull electronic interaction exists in Prod-1C (a vinylogous amide) which is absent in Prod-2C (interactions which would also develop in Harm-TS-1 and Harm-TS-2).

Harm-TS-1

MeOOC O N MeOOC

Harm-TS-1 24.2

O

MeOOC

CO N

N

MeOOC

Prod-1C -14.4

O

Harm-OP

N Harm-TS-3 23.5 BD

MeOOC O N MeOOC

Harm-TS-2 24.8

O N Harm-TS-6 27.6

MeOOC

O N Prod-2C -1.6

Scheme 4: Selected computational results for the cycloaddition of oxidopyridinium HarmOP and butadiene BD by Krenske and Harmata.38 Free energies (ΔG and ΔG‡) are in kcal/mol, distances are in angstroms. The results of the current investigation underscores what is perhaps implicitly understood by some physical organic chemists but remains frequently unstated; secondary orbital interactions are indicators for possible reaction pathway bifurcations. This is borne out by the increasing number of reactions where secondary orbital interactions have originally been invoked in order to explain selectivity, and which later have been found to contain pathway bifurcations. These include Caramella’s dimerization of cyclopentadiene,19,57 and acrolein,58 (comprehensively investigated by Singleton),8,10-11 Itoh and Yamataka’s SN2 12/19


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displacement of bromoketones (the same orbital interactions determining stereoselectivity in the Felkin-Ahn model),59-60 our own report of the (4+3)-cycloaddition,25 as well as Houk, et al.61 and now the current system. Since its initial articulation, secondary orbital interactions have been used to explain the stereoselectivity of a number of reactions,62-64 and it is possible that such systems (with minimal manipulation) could yield new pathway bifurcations. In addition to the above point, we feel the current terminology does not satisfactorily convey the orbital characteristics of the cyclopentadiene and oxidopyrylium systems which lead to their similar behaviour in generating reaction pathway bifurcations. In the present investigation it is the isosymmetry of the (frontier) molecular orbitals of the two systems which has enabled the prediction of a new bifurcating reaction. In this context we would define molecular orbital isosymmetry as the condition of having similar, but not necessarily identical, arrangements in the phases and nodes of the orbitals (e.g. symmetric or antisymmetric with respect to a plane, or in-phase or out-of-phase for comparable atoms), especially when considering equivalent highest-occupied or lowest-unoccupied molecular orbitals (HOMO and LUMO).65 Chemical systems which contain PTSB may be extrapolated to others which are molecular orbital isosymmetric (or, at the pleasure of chemistry community, “iso-orbital” for short) in order to discover new post-transition state bifurcations. Conclusion In conclusion, the cycloaddition of oxidopyrylium ylides with butadiene has been shown to contain a PTSB, with the lowest energy transition state, TS-1, leading to both the (4+3)- and (5+2)-products, Prod-1 and Prod-2. Reoptimisation of geometries along the minimum energy path located a second transition state, TS-2, a (3,3)-sigmatropic rearrangement which interconverts the products. Calculation of the potential energy surface further confirmed that a continuously downhill path exists from TS-1 to both products. BOMD calculations determined a product ratio of 50:45, Prod-1:Prod-2, with the cycloaddition predicted to occur in a largely concerted asynchronous manner with minimal recrossing. These data are consistent with the product distribution observed experimentally by Sammes and Street.37 The results also provide an insight into the work of Krenske and Harmata,38 suggesting the presence of the ester-substituent supresses any bifurcating behaviour in the related oxidopyridinium system. The coincidence of secondary orbital interactions and PTSBs, and the elaboration of known bifurcating reactions to new orbital isosymmetric systems will greatly assist in the location of latent pathway bifurcations. Experimental Section Geometry optimisations and energy calculations were primarily implemented using the M06-2X functional,39 with the 6-311+G(d,p) basis set. The B3LYP,66-67 and B97X-D,68 functionals were also used in the comparison of transition state structures for TS-1. DCM solvation was modelled implicitly using Truhlar’s SMD method.40 The nature of all stationary points was confirmed by frequency analysis (0 imaginary frequencies for minima, 1 for transition state structures). When calculating the energy surface around TS-1, projected frequencies (using the Freq=projected keyword) were calculated for structures that were not stationary points.69

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Born–Oppenheimer Molecular Dynamics (BOMD) simulations were conducted in a manner similar to Lopez, et al,20 at the UM06-2X/6-31+G(d) level of theory.43-45 True random numbers (between 1-1,000,000,000) were gathered from random.org,70 and used as input seed numbers for the randomised initial normal mode energies and velocities (see SI for analysis of the initial distribution). One hundred trajectories were run under standard conditions (T = 300 K and 1 atm) in implicit solvent (SMD, DCM),40 and stopped when a forming bond, either C2-C5’ or C4-C3’, was less than 3.0 Bohr (~1.58 Å) or after 200 steps. A step size of 0.25 amu1/2Bohr (~0.6 femtoseconds) was used. The HOMO and LUMO orbitals were mixed to ensure that possible open-shell solutions were sampled in the course of the simulation (with the guess=mix keyword). In order to reduce computational cost while maintaining performance, force constants were updated every 12 steps. Previous investigations by Houk, et al.47 and Lopez, et al.20 have utilised similar values (12 and 7 respectively) while Paton, et al.71 in the course of investigating a radical cation Diels–Alder reaction has noticed no deterioration in results with values up to 99. All calculations were conducted using the Gaussian16 program.72 Data was analysed using Chemcraft,73 and Gaussview. Chemical graphics were generated with CYLview.74 Acknowledgements We acknowledge the National Computational Infrastructure (NCI, located at the Australian National University), the Queensland Cyber Infrastructure Foundation (QCIF) and the University of Queensland Research Computing Centre (UQ RCC) for access to supercomputing resources. J.M.B would like to thank Michael Harmata for his discussion of experimental data and warm conversation. The authors also thank Sevan Houston, Kylie Agnew-Francis, Timothy Vanden Berg and Peter Moore for their insights and comments. Supporting information Geometries, energies and number of frequencies for optimised structures, potential energy surfaces, and additional data from BOMD calculations. Conflict of interest The authors declare no conflict of interest.

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, 47, 7592-7601. (2) Birney, D. M. Theory, Experiment and Unusual Features of Potential Energy Surfaces of Pericyclic and Pseudopericyclic Reactions with Sequential Transition Structures. Curr. Org. Chem. 2010, 14, 1658-1668. (3) Rehbein, J.; Carpenter, B. K. Do We Fully Understand What Controls Chemical Selectivity? Phys. Chem. Chem. Phys. 2011, 13, 20906-20922. (4) Hare, S. R.; Tantillo, D. J. Post-Transition State Bifurcations Gain Momentum – Current State of the Field. Pure Appl. Chem. 2017, 89, 679-698.

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(5) Singleton, D. A.; Hang, C.; Szymanski, M. J.; Meyer, M. P.; Leach, A. G.; Kuwata, K. T.; Chen, J. S.; Greer, A.; Foote, C. S.; Houk, K. N. Mechanism of Ene Reactions of Singlet Oxygen. A Two-Step No-Intermediate Mechanism. J. Am. Chem. Soc. 2003, 125, 1319-1328. (6) Çelebi-Ölçüm, 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. (7) Çelebi-Ölçüm, N.; Ess, D. H.; Aviyente, V.; Houk, K. N. Effect of Lewis Acid Catalysts on Diels−Alder and Hetero-Diels−Alder Cycloadditions Sharing a Common Transition State. J. Org. Chem. 2008, 73, 7472-7480. (8) Thomas, J. B.; Waas, J. R.; Harmata, M.; Singleton, D. A. Control Elements in Dynamically Determined Selectivity on a Bifurcating Surface. J. Am. Chem. Soc. 2008, 130, 14544-14555. (9) Hong, Y. J.; Tantillo, D. J. A Potential Energy Surface Bifurcation in Terpene Biosynthesis. Nat. Chem. 2009, 1, 384-389. (10) Kelly, K. K.; Hirschi, J. S.; Singleton, D. A. Newtonian Kinetic Isotope Effects. Observation, Prediction, and Origin of Heavy-Atom Dynamic Isotope Effects. J. Am. Chem. Soc. 2009, 131, 8382-8383. (11) Wang, Z.; Hirschi, J. S.; Singleton, D. A. Recrossing and Dynamic Matching Effects on Selectivity in a Diels–Alder Reaction. Angew. Chem., Int. Ed. 2009, 48, 9156-9159. (12) Gonzalez-James, O. M.; Kwan, E. E.; Singleton, D. A. Entropic Intermediates and Hidden Rate-Limiting Steps in Seemingly Concerted Cycloadditions. Observation, Prediction, and Origin of an Isotope Effect on Recrossing. J. Am. Chem. Soc. 2012, 134, 1914-1917. (13) Andujar-De Sanctis, I. L.; Singleton, D. A. Racing Carbon Atoms. Atomic Motion Reaction Coordinates and Structural Effects on Newtonian Kinetic Isotope Effects. Org. Lett. 2012, 14, 5238-5241. (14) Hong, Y. J.; Tantillo, D. J. Biosynthetic Consequences of Multiple Sequential PostTransition-State Bifurcations. Nat. Chem. 2014, 6, 104-111. (15) Yu, P.; Patel, A.; Houk, K. N. Transannular [6 + 4] and Ambimodal Cycloaddition in the Biosynthesis of Heronamide A. J. Am. Chem. Soc. 2015, 137, 13518-13523. (16) Nieves-Quinones, Y.; Singleton, D. A. Dynamics and the Regiochemistry of Nitration of Toluene. J. Am. Chem. Soc. 2016, 138, 15167-15176. (17) Patel, A.; Chen, Z.; Yang, Z.; Gutiérrez, O.; Liu, H.-w.; Houk, K. N.; Singleton, D. A. Dynamically Complex [6+4] and [4+2] Cycloadditions in the Biosynthesis of Spinosyn A. J. Am. Chem. Soc. 2016, 138, 3631-3634. (18) Yu, P.; Chen, T. Q.; Yang, Z.; He, C. Q.; Patel, A.; Lam, Y.-h.; Liu, C.-Y.; Houk, K. N. Mechanisms and Origins of Periselectivity of the Ambimodal [6 + 4] Cycloadditions of Tropone to Dimethylfulvene. J. Am. Chem. Soc. 2017, 139, 8251-8258. (19) Caramella, P.; Quadrelli, P.; Toma, L. An Unexpected Bispericyclic Transition Structure Leading to 4+2 and 2+4 Cycloadducts in the Endo Dimerization of Cyclopentadiene. J. Am. Chem. Soc. 2002, 124, 1130-1131. (20) Villar López, R.; Faza, O. N.; Silva López, C. Dynamic Effects Responsible for High Selectivity in a [3,3] Sigmatropic Rearrangement Featuring a Bispericyclic Transition State. J. Org. Chem. 2017, 82, 4758-4765. (21) Pham, H. V.; Houk, K. N. Diels–Alder Reactions of Allene with Benzene and Butadiene: Concerted, Stepwise, and Ambimodal Transition States. J. Org. Chem. 2014, 79, 8968-8976. (22) For an example of dynamic control in silico see: Hare, S. R.; Pemberton, R. P.; Tantillo, D. J. Navigating Past a Fork in the Road: Carbocation−π Interactions Can Manipulate

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Dynamic Behavior of Reactions Facing Post-Transition-State Bifurcations. J. Am. Chem. Soc. 2017, 139, 7485-7493. (23) Kemsley, J. Dynamics Determine Enzyme Selectivity. Chem. Eng. News 2014, 92, 34-35. (24) Hare, S. R.; Tantillo, D. J. Cryptic Post-Transition State Bifurcations That Reduce the Efficiency of Lactone-Forming Rh-Carbenoid C-H Insertions. Chem. Sci. 2017, 8, 1442-1449. (25) Burns, J. M. Computational Evidence for a Reaction Pathway Bifurcation in Sasaki-Type (4 + 3)-Cycloadditions. Org. Biomol. Chem. 2018, 16, 1828-1836. (26) An alternative approach has just recently been described by Tantillo and Campos: Campos, R. B.; Tantillo, D. J. Designing Reactions with Post-Transition-State Bifurcations: Asynchronous Nitrene Insertions into C–C σ Bonds. Chem 2018. https://doi.org/10.1016/j.chempr.2018.10.019 (27) Woodward, R. B.; Katz, T. J. The Mechanism of the Diels-Alder Reaction. Tetrahedron 1959, 5, 70-89. (28) Woodward, R. B.; Hoffmann, R. The Conservation of Orbital Symmetry. Angew. Chem., Int. Ed. Engl. 1969, 8, 781-853. (29) The existence of secondary orbital interactions has been disputed (García, J. I.; Mayoral, J. A.; Salvatella, L. Do Secondary Orbital Interactions Really Exist? Acc. Chem. Res. 2000, 33, 658-664.) and vigorously defended (Wannere, C. S.; Paul, A.; Herges, R.; Houk, K. N.; Schaefer, H. F.; Von Ragué Schleyer, P. The existence of secondary orbital interactions. J. Comput. Chem. 2007, 28, 344-361.) (30) Wender, P. A.; Bi, F. C.; Buschmann, N.; Gosselin, F.; Kan, C.; Kee, J.-M.; Ohmura, H. Studies on Oxidopyrylium [5 + 2] Cycloadditions: Toward a General Synthetic Route to the C12-Hydroxy Daphnetoxins. Org. Lett. 2006, 8, 5373-5376. (31) Wender, P. A.; Buschmann, N.; Cardin, N. B.; Jones, L. R.; Kan, C.; Kee, J.-M.; Kowalski, J. A.; Longcore, K. E. Gateway Synthesis of Daphnane Congeners and Their Protein Kinase C Affinities and Cell-Growth Activities. Nat. Chem. 2011, 3, 615-619. (32) Burns, N. Z.; Witten, M. R.; Jacobsen, E. N. Dual Catalysis in Enantioselective Oxidopyrylium-Based [5 + 2] Cycloadditions. J. Am. Chem. Soc. 2011, 133, 14578-14581. (33) Ylijoki, K. E. O.; Stryker, J. M. [5 + 2] Cycloaddition Reactions in Organic and Natural Product Synthesis. Chem. Rev. 2013, 113, 2244-2266. (34) Simanis, J. A.; Law, C. M.; Woodall, E. L.; Hamaker, C. G.; Goodell, J. R.; Mitchell, T. A. Investigation of Oxidopyrylium-Alkene [5+2] Cycloaddition Conjugate Addition Cascade (C3) Sequences. Chem. Commun. 2014, 50, 9130-9133. (35) Witten, M. R.; Jacobsen, E. N. Catalytic Asymmetric Synthesis of 8-Oxabicyclooctanes by Intermolecular [5+2] Pyrylium Cycloadditions. Angew. Chem., Int. Ed. 2014, 53, 5912-5916. (36) Pellissier, H. Recent Developments in the [5+2] Cycloaddition. Adv. Synth. Catal. 2018, 360, 1551-1583. (37) Sammes, P. G.; Street, L. J. The Preparation and Some Reactions of 3-Oxidopyrylium. J. Chem. Soc., Perkin Trans. 1 1983, 1261-1265. (38) Fu, C.; Lora, N.; Kirchhoefer, P. L.; Lee, D. R.; Altenhofer, E.; Barnes, C. L.; Hungerford, N. L.; Krenske, E. H.; Harmata, M. (4+3) Cycloaddition Reactions of N-Alkyl Oxidopyridinium Ions. Angew. Chem., Int. Ed. 2017, 56, 14682-14687. (39) Zhao, Y.; Truhlar, D. G. The M06 Suite of Density Functionals for Main Group Thermochemistry, Thermochemical Kinetics, Noncovalent Interactions, Excited States, and Transition Elements: Two New Functionals and Systematic Testing of Four M06-Class Functionals and 12 Other Functionals. Theor. Chem. Acc. 2008, 120, 215-241.

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(40) Marenich, A. V.; Cramer, C. J.; Truhlar, D. G. Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions. J. Phys. Chem. B. 2009, 113, 6378-6396. (41) Discrepancies between the free energy of activation and the reported reaction time (16 h, though no comment is made as to whether this is optimised) are attributable to the oxidopyrylium OP being generated in situ from the elimination of the parent acetate ProOP, which has been shown to be the rate determining step. Kaufman, R. H.; Law, C. M.; Simanis, J. A.; Woodall, E. L.; Zwick, C. R.; Wedler, H. B.; Wendelboe, P.; Hamaker, C. G.; Goodell, J. R.; Tantillo, D. J.; Mitchell, T. A. Oxidopyrylium-Alkene [5 + 2] Cycloaddition Conjugate Addition Cascade (C3) Sequences: Scope, Limitation, and Computational Investigations. J. Org. Chem. 2018, 83, 9818-9838. (42) Both TS-1 and TS-2 are spin-unrestricted stable at the M06-2X/6-311+G(d,p) and M062X/6-31G(d)levels of theory. (43) Li, X.; Millam, J. M.; Schlegel, H. B. Ab Initio Molecular Dynamics Studies of the Photodissociation of Formaldehyde, H2CO→H2+CO: Direct Classical Trajectory Calculations by Mp2 and Density Functional Theory. J. Chem. Phys. 2000, 113, 10062-10067. (44) Millam, J. M.; Bakken, V. r.; Chen, W.; Hase, W. L.; Schlegel, H. B. Ab Initio Classical Trajectories on the Born–Oppenheimer Surface: Hessian-Based Integrators Using FifthOrder Polynomial and Rational Function Fits. J. Chem. Phys. 1999, 111, 3800-3805. (45) Chen, W.; Hase, W. L.; Schlegel, H. B. Ab Initio Classical Trajectory Study of H2CO→H2+CO Dissociation. Chem. Phys. Lett. 1994, 228, 436-442. (46) To stress the importance of appropriate method selection, in a preliminary test of 10 trajectories at the M06-2X/6-31G(d) level of theory, all led to the (4+3)-product. (47) Black, K.; Liu, P.; Xu, L.; Doubleday, C.; Houk, K. N. Dynamics, Transition States, and Timing of Bond Formation in Diels–Alder Reactions. Proc. Natl. Acad. Sci. U. S. A. 2012, 109, 12860-12865. (48) In the majority of cases, the formation of the product bond occurs without coincident shortening of the “competing” bond. As such, we would discourage a common interpretation that trajectories must pass through the second transition state (TS-2) in order to reach either Prod-1 or Prod-2. (49) Yang, Z.; Dong, X.; Yu, Y.; Yu, P.; Li, Y.; Jamieson, C.; Houk, K. N. Relationships between Product Ratios in Ambimodal Pericyclic Reactions and Bond Lengths in Transition Structures. J. Am. Chem. Soc. 2018, 140, 3061-3067. (50) The (4+3)/(4+2)-cycloaddition, investigated by us, and Houk, also features this aberrant behaviour. See ref. 25 and 61. (51) Reed, A. E.; Curtiss, L. A.; Weinhold, F. Intermolecular Interactions from a Natural Bond Orbital, Donor-Acceptor Viewpoint. Chem. Rev. 1988, 88, 899-926. (52) Peterson, T. H.; Carpenter, B. K. Estimation of Dynamic Effects on Product Ratios by Vectorial Decomposition of a Reaction Coordinate. Application to Thermal Nitrogen Loss from Bicyclic Azo Compounds. J. Am. Chem. Soc. 1992, 114, 766-767. (53) Carpenter, B. K. Intramolecular Dynamics for the Organic Chemist. Acc. Chem. Res. 1992, 25, 520-528. (54) Doubleday, C.; Suhrada, C. P.; Houk, K. N. Dynamics of the Degenerate Rearrangement of Bicyclo[3.1.0]Hex-2-Ene. J. Am. Chem. Soc. 2006, 128, 90-94. (55) We would like to thank a kind reviewer for drawing our attention to these reports. In addition to Carpenter’s method, we consider Doubleday and Houk’s geometric adaptation (ref 54) to be quite elegant, particularly in instances where the energy surface can be

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approximately modelled and products are formed directly (i.e. without trajectories “rebounding” off features on the PES). (56) A reviewer has suggested that the replacement of oxygen for nitrogen in oxidopyridinium may also contribute to differences in dynamic behaviour, and this is indeed correct. Our suspicion, however, is that the H to COOMe substitution (with the large change in electronic and orbital properties) is the principle determinant, as the nitrogen and oxygen atoms (and the iminium/enamine and oxocarbenium/vinyl ether functionalities so derived) are electronically similar. The impact of such substitution on the dynamic behaviour of ambimodal TSs will be investigated in a future report. (57) Caramella's investigation addressed this directly, in that it "... unexpectedly disclosed the origin of the endo selectivity and led to a simple rationalization that is quite different than usually thought," namely that the Salem-Houk SOI's were coincident with the presence of a PTSB. (58) Toma, L.; Quadrelli, P.; Caramella, P. Classical and Non-Classical Secondary Orbital Interactions and Coulombic Attraction in the Regiospecific Dimerization of Acrolein. Tetrahedron Lett. 2001, 42, 731-733. (59) Itoh, S.; Yoshimura, N.; Sato, M.; Yamataka, H. Computational Study on the Reaction Pathway of Α-Bromoacetophenones with Hydroxide Ion: Possible Path Bifurcation in the Addition/Substitution Mechanism. J. Org. Chem. 2011, 76, 8294-8299. (60) Nguyen Trong, A.; Eisenstein, O.; Lefour, J. M.; Tran Huu Dau, M. E. Orbital Factors and Asymmetric Induction. J. Am. Chem. Soc. 1973, 95, 6146-6147. (61) Chen, S.; Yu, P.; Houk, K. N. Ambimodal Dipolar/Diels–Alder Cycloaddition Transition States Involving Proton Transfers. J. Am. Chem. Soc. 2018, 140, 18124-18131. (62) Rondan, N. G.; Houk, K. N. Theory of Stereoselection in Conrotatory Electrocyclic Reactions of Substituted Cyclobutenes. J. Am. Chem. Soc. 1985, 107, 2099-2111. (63) Rudolf, K.; Spellmeyer, D. C.; Houk, K. N. Prediction and Experimental Verification of the Stereoselective Electrocyclization of 3-Formylcyclobutene. J. Org. Chem. 1987, 52, 37083710. (64) Dolbier, W. R.; Koroniak, H.; Houk, K. N.; Sheu, C. Electronic Control of Stereoselectivities of Electrocyclic Reactions of Cyclobutenes: A Triumph of Theory in the Prediction of Organic Reactions. Acc. Chem. Res. 1996, 29, 471-477. (65) Isoelectronicity (compounds with the same number of atoms and electrons) and isolobality (compounds with similar molecular orbitals, especially when extrapolating the reactivity of organic systems to transition metals, Hoffmann, R. Building Bridges Between Inorganic and Organic Chemistry (Nobel Lecture). Angew. Chem., Int. Ed. Engl. 1982, 21, 711-724.) are related concepts, but are not identical. The isolobal analogy does consider the symmetry properties of two analogous systems, but typically restricts itself to systems with the same number of atoms. We would propose that comparable systems can be orbital isosymmetric even if they differ in the number of constituent atoms or electrons (i.e. CPD, PD and OP; or ethene and hexatriene). (66) Becke, A. D. Density-Functional Thermochemistry. Iii. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648-5652. (67) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. B. 1988, 37, 785-789. (68) Chai, J.-D.; Head-Gordon, M. Long-Range Corrected Hybrid Density Functionals with Damped Atom–Atom Dispersion Corrections. Phys. Chem. Chem. Phys. 2008, 10, 6615-6620.

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(69) Baboul, A. G.; Schlegel, H. B. Improved Method for Calculating Projected Frequencies Along a Reaction Path. J. Chem. Phys. 1997, 107, 9413-9417. (70) RANDOM.ORG, https://www.random.org/ (71) Tan, J. S. J.; Hirvonen, V.; Paton, R. S. Dynamic Intermediates in the Radical Cation Diels–Alder Cycloaddition: Lifetime and Suprafacial Stereoselectivity. Org. Lett. 2018, 20, 2821-2825. (72) Gaussian 16, Revision A.03, M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, G. A. Petersson, H. Nakatsuji, X. Li, M. Caricato, A. V. Marenich, J. Bloino, B. G. Janesko, R. Gomperts, B. Mennucci, H. P. Hratchian, J. V. Ortiz, A. F. Izmaylov, J. L. Sonnenberg, D. Williams-Young, F. Ding, F. Lipparini, F. Egidi, J. Goings, B. Peng, A. Petrone, T. Henderson, D. Ranasinghe, V. G. Zakrzewski, J. Gao, N. Rega, G. Zheng, W. Liang, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, K. Throssell, J. A. Montgomery, Jr., J. E. Peralta, F. Ogliaro, M. J. Bearpark, J. J. Heyd, E. N. Brothers, K. N. Kudin, V. N. Staroverov, T. A. Keith, R. Kobayashi, J. Normand, K. Raghavachari, A. P. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, J. M. Millam, M. Klene, C. Adamo, R. Cammi, J. W. Ochterski, R. L. Martin, K. Morokuma, O. Farkas, J. B. Foresman, and D. J. Fox, Gaussian, Inc., Wallingford CT, 2016. (73) Chemcraft - graphical software for visualization of quantum chemistry computations. http://www.chemcraftprog.com (74) C. Y. Legault. http://www.cylview.org/index.html

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(5 + 2)-Cycloaddition of Butadiene

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