Dynamic Effects Responsible for High Selectivity in a [3,3] Sigmatropic

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Dynamic Effects Responsible for High Selectivity in a [3,3] Sigmatropic Rearrangement Featuring a Bispericyclic Transition State Roberto Villar López, Olalla Nieto Faza, and Carlos Silva López* Departamento de Química Orgánica, Universidade de Vigo, Campus Lagoas-Marcosende, 36310 Vigo, Spain S Supporting Information *

ABSTRACT: Bispericyclic transition states appear when two independent pericyclic transition states merge into one. They are a particular case of the more general ambimodal concept applied to a transition state that connects reactants with two or more products involving reaction path bifurcations through valley-ridge inflections. In the present computational work, the first example of a bifurcating sigmatropic reaction featuring a bispericyclic transition state is reported for a cyclohexane featuring opposing methylene and a vinylidene fragments. Perhalogenation of a C−C bond in this substrate imparts a strong desymmetrization to the bifurcating potential energy surface. These systems undergo the [3,3] sigmatropic rearrangement with high selectivity, with a preferred product that depends on which halogen decorates the C−C bond. We have found that dynamic effects have a paramount role in the selectivity observed for these reactions.

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transition state in a boat conformation.12 Under these circumstances, a substituted allene undergoes a preferred rotation on a nonsymmetric substrate. During this study we initially analyzed the simplest and symmetrical substrate R1 (Figure 2). This cyclic system

INTRODUCTION One of the most remarkable achievements of physical organic chemistry in the last century occurred when Woodward and Hoffmann published their symmetry rules,1,2 which govern the selectivity of pericyclic reactions with seemingly no exception. Two decades later, a second level of selectivity was described for electrocyclic reactions, coined torquoselectivity by Houk. It may be defined as the selectivity for outward or inward rotation of the substituents of a breaking/forming C−C bond.3,4 There has been significant interest in exploring the frontiers of application of these symmetry rules and, in particular, on reactions proceeding with torquoselectivity.5−7 In this exploration, we have reported torquoselectivity in a wide range of reactions, including anionic, cationic, and neutral electrocyclizations, and expanded its application to some diradicalclosing processes.8−11 Very recently, we also found a torquoselectivity-like effect in a [3,3]-sigmatropic rearrangement (see Figure 1). For such an effect to operate, we concluded that the sigmatropic reaction has to occur through a

Figure 2. Two possible [3,3] sigmatropic pathways starting from substrate R1 and leading to degenerate products P1a and P1b.

featuring exocyclic allene and alkene fragments is known experimentally to furnish the sigmatropic products under harsh thermal conditions.13,14 This process operates without any level of selectivity, other than that dictated by the WH rules (supra− supra, compatible with the geometric constrains of the cyclic system, see Figure 2). Interestingly, the transition state associated with this reaction exhibited some unexpected Figure 1. Torquoselectivity observed in sigmatropic rearrangements of conformationally controlled substrates reacting via boat transition states. © 2017 American Chemical Society

Received: February 22, 2017 Published: April 7, 2017 4758

DOI: 10.1021/acs.joc.7b00425 J. Org. Chem. 2017, 82, 4758−4765

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The Journal of Organic Chemistry

cycloadditions, relating bispericyclic transition states and bifurcations.17−20 Recently, Houk et al. introduced the more general term ambimodal, defining it as a single transition state which leads to two or more products.21,22 Effects on product formation for this kind of topology have been not only computed but also experimentally observed.23 According to their definitions, bispericyclic structures would be particular cases of the ambimodal concept, with two sets of stabilizing cyclic aromatic orbital interactions that can lead to two different pericyclic reaction products. 24 In these reactions, the ambimodal transition state is commonly connected with a second transition state through a valley−ridge inflection (a VRI25−27 is a point where the potential energy surface valley changes into a ridge). The concept of sequential transition states and VRIs has also drawn the attention of Birney, who explored these topographical features of the potential energy surface in the field of pericyclic and pseudopericyclic reactions.28−30 Surfaces featuring sequential transition states and, as a result, VRIs, involve bifurcations in the vicinity of the VRI point (see Figure 5).31 Depending on the shape of the

features. Due to its symmetry, this structure possesses two equivalent C−C bonds that can participate (and be broken) in the sigmatropic rearrangement (C4−C5 and C7−C8 in Figure 2). Hence, this substrate may undergo a sigmatropic reaction via two degenerate pathways leading to products (P1a and P1b)15 depending on which C−C bond is involved in the rearrangement (see Figure 2). We, however, did not find two degenerate transition states associated with the cleavage of these two C−C bonds, but just one, TS1. Figure 3 illustrates the main features of the only transition state found for the sigmatropic rearrangement of R1. The

Figure 3. Fully optimized geometry (at the M06-2X/Def2TZVPP level of theory) of TS1.

structure of this transition state maintains the symmetry of the substrate, at the expense of featuring not two, but three, bonds being partially broken (C2C9, C4−C5, and C7−C8: the first being formed in the reaction and one of the two last ones being broken in the product). As a result, this transition state apparently adopts a structure that can be viewed as the superimposed transition states for the two canonical sigmatropic rearrangements that the substrate can suffer. Analysis of the normal mode associated with the imaginary frequency confirmed that the bond between the cumulene carbon of the allene (C2) and the terminal carbon of the exocyclic alkene moiety (C9) is being formed, whereas the other two bonds (C4−C5 and C7−C8) are being broken. According to the previous description, it seems that TS1 belongs to a special group of transition states that has been only described for a few cycloaddition reactions but that have also been suggested in other pericyclic processes and are termed bispericyclic transition states. These structures appear when two independent pericyclic transition states merge into one. The concept of pericyclic transition states merging is not new; Woodward and Katz suggested in 1959 a superposition of transition states for the Diels−Alder and Cope rearrangements of endo dicyclopentadiene (see Figure 4).16 Caramella and coworkers described the topology of the potential energy surface or this and other systems in the framework of Diels−Alder

Figure 5. Generic bifurcation on a potential energy surface showing the VRI point between the two transition states. Products P and P′ can be interconverted through TS2.

potential energy surface, bifurcations may be classified as symmetric or asymmetric.26 On a symmetric bifurcation, the two products are isoenergetic, so that two sequential transition states TS1 and TS2 are connected by a coordinate lying on a symmetry hyperplane of the potential energy surface (it separates the two basins like a mirror plane), and this coordinate is the minimum energy path (MEP).17−20 In this scenario, the probability for a reacting molecule to funnel into one or the other basin is exactly the same, and the bifurcation yields product molecules in an obvious 1:1 ratio. Taking into account that all of the trajectories on this kind of surface pass through the same rate-limiting transition state and that both product basins are symmetric, a 1:1 ratio is easily justified and dynamic effects in these reactions pass unnoticed. However, in an asymmetric PES, all of the trajectories still pass through a common rate-limiting transition state, but the product basins are different, and the sequential transition states create a topology near the ridge area that determines the selectivity of the reaction and the formation of products (often in a non-1:1

Figure 4. Two endo dimerization paths of cyclopentadiene and a merged bispericyclic transition state reported by Caramella et al.17−20 4759


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transition state displays shortened C−C bond lengths for the perhalogenated bond. On the contrary, chlorination and bromination impart the opposite distortion to TS1Cl and TS1Br, both displaying longer C−C bonds for the halogenated branch. In the three cases, the C4−C5 and C7−C8 bonds are stretched with respect to the reactant, suggesting that they may be also breaking in these transition states. A geometric analysis of TS1X therefore points toward some degree of bispericyclic nature in these transition states (see Figure 7). This

ratio) in a process that is purely governed by the dynamics of the reaction, irrespective of the common TS. To date, several PES bifurcations in sigmatropic reactions have been reported, but none of them involve a bispericyclic transition state (they usually involve ambimodal transition states bifurcating into a sigmatropic and a diradical pathway).32−35 Since the original work by Caramella,17−20 such types of transition states have only been found in cycloadditions occurring along bifurcating pathways.22,24,36−38 To the best of our knowledge, therefore, we have found the first example of a bifurcation in a sigmatropic rearrangement with a bispericyclic transition state. With these results in mind involving a bispericyclic transition state in a symmetric reaction path bifurcation, we decided to explore the possibility of imposing asymmetry on the system while preserving both the ambimodal nature of the transition state and the bifurcation on the potential energy surface. If successful, selectivity could be obtained exclusively from reaction dynamics.39−42

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RESULTS AND DISCUSSION Starting from R1 (Figure 2), in an attempt to desymmetrize the structure, several substitution patterns were considered. A perhalogenation strategy was used in order to achieve a substantial difference in the nature and dissociation energies of the breaking C−C bonds while minimizing geometrical distortions. Perfluorination, perchlorination, and perbromination of one of the cleaving C−C bonds was therefore conducted, and the reaction profiles and characteristics of the resulting transition states were analyzed (see Figure 6). Figure 7. Optimized geometries for transition states TS1 (top left), TS1F (top right), TS1Cl (bottom left), and TS1Br (bottom right). Displacement vectors associated with the imaginary frequency and key bond lengths are shown.

participation of a bispericyclic transition structure, however, seems to decrease in the sequence H, F, Cl, Br since the degree of asymmetry in the breaking bonds increases up to a situation where one single bond is significantly stretched (2.31 Å) whereas the other is only slightly stretched (1.59 Å) with respect to the reactant bond lengths (1.56 and 1.52 Å, respectively). The anisotropy of the current induced density (ACID) was thus computed in order to identify areas of delocalized electron density at the transition states. These calculations are also in good agreement with at least a partial bispericyclic nature at the transition states. The ACID isodensity is present at both C−C bonds, although it is significantly reduced for the more asymmetric structures, TS2Cl and TS2Br (see Figure 8). The geometric features of the second transition state (TS2X) are coherent with the interconversion process between the two products P1aX and P1bX (the C2−C9 bond is fully formed and unaffected in this transition state, whereas the C4−C5 and C7−C8 bonds alternatively form and cleave in the normal mode associated with the imaginary frequency; see the Supporting Information). In the case of an asymmetric PES, the topological relation between the transition states TS1X and TS2X cannot be fully determined through IRC calculations. IRC calculations on asymmetric surfaces connect the transition state with only one of the products, ignoring the presence of bifurcations.24 Thus, we can only resort to simulations that include dynamic effects and depart from the

Figure 6. Two possible [3,3] sigmatropic rearrangements starting from the substrate R1X proceeding through a common transition state TS1X to lead the products P1aX and P1bX.

Analysis of the Potential Energy Surface and Transition Structures. Calculations on the systems illustrated in Figure 6 were performed in order to locate the stationary points of the PES and characterize their rearranging mechanisms. Two first-order saddle points labeled TS1X and TS2X were found for the three halogenated substrates. As expected, the three pairs of transition structures display significant distortion in terms of the C4−C5 and C7−C8 distances. Surprisingly, however, this distortion is not in the same direction. In the perfluorinated substrate R1F the initial 4760


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coordinate (the eigenvectors of the imaginary frequency) and in the thermodynamics of the reaction. As illustrated in Figure 7, the normal mode that activates the sigmatropic reaction is strongly delocalized for the parent system (TS1), with larger contributions at the forming C−C bond and smaller ones in C4−C5 and C7−C8. For the perfluorinated system, the nonhalogenated bond is longer than the halogenated one (1.88 vs 1.68 Å), and the normal mode is strongly localized in the more stretched branch. Perchlorination and perbromination impart the opposite asymmetry, and the displacement vectors are arranged accordingly, with stronger contributions on the more stretched, halogenated bonds. The thermodynamic stability of the products shows a similar trend. The reaction of the parent system is a degenerated transformation, leaving both channels with the same energy. Upon perfluorination, P1bF (which involves the cleavage of the nonhalogenated C−C bond) is thermodynamically favored by 10 kcal/mol. Perchlorination and perbromination, however, favor P1aX, the product resulting from the cleavage of the halogenated C−C bond. Dynamic Effects. As we previously mentioned, selectivity, in an asymmetric bifurcating PES, is governed by the dynamics of the process. As a consequence, computational work based only on locating the stationary points on the potential energy surface yields an inadequate description of the reaction.43−47 Interestingly, we have seemingly found a system in which, by selecting the appropriate perhalogenation pattern, the imparted asymmetry in TS1 can be controlled. This has the potential to drive the reaction selectivity toward one product or the other just by preparing the correctly decorated substrate. To study this possibility, dynamic effects were considered for the [3,3] sigmatropic rearrangement of R1F and R1Cl via Born− Oppenheimer molecular dynamics.48−50 In order to have a benchmark to which we could establish comparisons and also as a control experiment in our dynamics calculations, we carried out the same study with the symmetric PES of the parent model R1. Figure 9 shows a paradigmatic example of dynamic effects on a symmetric bifurcating PES. Of 200 trajectories started from TS1, 100 trajectories reached the P1a basin and 99 arrived to the product; only one of the trajectories recrossed back to reactants. This almost identical percentage of trajectories reaching both products confirms the expected 1:1 ratio for this type of PES. A more detailed analysis of the trajectories reveals that, in some cases, the molecular system crosses TS1 in such a good alignment with the ridge that it proceeds on the ridge well beyond the second transition state, hence entering the product basins with wide amplitudes due to more energy being deposited in modes orthogonal to the reaction chanel.

Figure 8. Anisotropy of the current induced density (isodensity at 0.015 au) for transition states TS1, TS1F, TS1Cl, and TS1Br. The three halogenated structures are shown in two orientations so that both C− C bonds participating in the bispericyclic transition states process can be seen.

minimum energy pathway to obtain a reliable picture of the PES shape in the surroundings of TS1 and TS2. Energetics for the stationary points involved in the sigmatropic rearrangement of R1 and R1X can be found in Table 1. The overall features of the potential energy surface do not change significantly from the symmetric model to the halogenated counterpart. Activation energies are high (40−47 kcal/mol), in good agreement with the severe experimental conditions reported by Hopf.13,14 The asymmetry imposed in these systems has a clear impact not only on the geometrical features of the transition states but also on the normal mode associated with the reaction

Table 1. Relative Free Energies for the [3,3] Sigmatropic Rearrangement of R1 and the Halogenated Derivatives Included in Figure 6a,b structure

ΔG

structure

ΔG

structure

ΔG

structure

ΔG

R1 TS1 TS2 P1a P1b

0.0 41.0 36.9 −11.5 −11.5

R1F TS1F TS2F P1aF P1bF

0.0 45.8 43.6 −6.9 −10.9

R1Cl TS1Cl TS2Cl P1aCl P1bCl

0.0 44.8 35.8 −18.9 −10.7

R1Br TS1Br TS2Br P1aBr P1bBr

0.0 46.7 37.4 −18.5 −10.5

a

R1 and R1X have been used as the reference to obtain the relative free energies. bAll energies computed at the M062X/Def2TZVPP level of theory (298 K and 1 atm). 4761


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in the reaction of R1F with respect to the rate-limiting transition state (TS1F). We hypothesize that, starting from the symmetric potential energy surface described for R1, a desymmetrization of the structure through perfluorination in R1F leads to a transition state located off-center with respect to the product basins. The immediate effect of this situation is, from the transition state, a widening of the entry channel to one of the product basins and, conversely, the tightening of the entrance to the other basin. The latter is therefore entropically disfavored with respect to the former, and as a consequence, selectivity is observed in the formation of products. This qualitative visualization of the potential energy surface is also consistent with the dynamic bottlenecks observed in the P1aF basin; the tight entrance implies more chances of a highly tangential trajectory entering the product basin, and that correlates again with wider amplitudes and even the formation of loops as the system descends into the product well instead of following the more or less direct fall into the basin observed in the other cases. This interpretation of the characteristics of the potential energy surface at the rate-limiting transition state and the ridge area is consistent with the location of TS1F and TS2F with respect to the line bisecting the plot in Figure 10 (this line in R1 defined rigorously the separation between the two product basins). In the asymmetric bifurcation found for R1F, the rate-limiting transition state (TS1F) is off-diagonal and displaced toward the P1bF basin, contrary to the second transition state (TS2F) that is found displaced off-diagonal but toward the P1aF basin. This clearly indicates that TS1F is very well aligned with the entrance channel to the P1bF basin and that the P1aF basin has a relatively inaccessible entrance channel. An inventory of the 200 trajectories initiated from TS1F shows the following results: • 178 trajectories, 89% of the total, were found to reach the P1bF basin. • 18 trajectories, 9% of the total, were found to reach the P1aF basin. • 4 trajectories, 2% of the total, were found to be unproductive. They did not proceed to either product but recrossed the TS and headed back toward the reactant basin. The data listed above confirm the great difference between the control experiment and the asymmetrically bifurcating potential energy surface. It is noteworthy that recoiling trajectories to the reactant basin reported for TS1F, although minimal (2%), are more numerous than in the model system. The productive trajectories also feature striking differences with respect to the control experiment. The simulated product ratio is 10:1 in favor of P1bF, very far from the 1:1 ratio expected for R1. The large P1bF/P1aF ratio obtained represents a very high selectivity for the [3,3] sigmatropic rearrangement of R1F which stems exclusively from dynamic effects. Interestingly, Carpenter proposed in 1992 a geometry-based method to predict product ratios due to dynamic effects that circumvent the need for running trajectories.51 This simple approach implies projecting the eigenvector of the reaction coordinate along the distance vectors between the transition state and the products. The ratio between the projections provides a structure-based estimation of expected product ratios. The dot product values obtained in this approach were 39.6 and 3.9 for P1bF and P1aF, which are in excellent agreement with the 10:1 ratio obtained through dynamic calculations.

Figure 9. Quasiclassical trajectories of the parent model R1 reaching the P1a or P1b product basins from TS1. The location of the second transition state associated with the bifurcation (TS2) is also indicated.

Figure 10 provides a completely different picture. A simple visual analysis of the trajectories obtained shows that most of

Figure 10. Quasiclassical trajectories for the substrate with a perfluorinated C−C bond R1F reaching the P1aF or P1bF product basins from TS1F. The location of the second transition state associated with the bifurcation (TS2F) is also indicated.

them proceed to P1bF, coinciding with the asymmetry described above for TS1F. Furthermore, dynamic bottlenecks around 2.8 and 3.7 Å for the C7−C8 bond length can be observed in those trajectories entering the P1aF basin, whereas no bottleneck was observed for any trajectory in the rearrangement of R1 and no bottleneck is shown for the trajectories of R1F reaching the P1bF basin. These observations are indicative of a very different topology of the product basins 4762


The Journal of Organic Chemistry The static calculations described above suggested that both perchlorination and perbromination of a C−C bond subject to participate in the sigmatropic rearrangement would provide the reverse selectivity. In order to confirm this hypothesis, we also collected 200 trajectories for the rearrangement of TS1Cl, and the results obtained are summarized in Figure 11. Interestingly,

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CONCLUSIONS

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COMPUTATIONAL METHODS

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ASSOCIATED CONTENT

In this work, we report the first example of a bifurcating sigmatropic reaction featuring a bispericyclic transition state (TS1). The structure of this transition state arises from the partial merging of the two possible degenerate pathways from substrate R1 to P1a and P1b products. This merged pathway implies two sequential transiton states; the former is rate limiting, and the latter is the point of the mechanism where the path bifurcates into the product basins. A strong desymmetrization of the bifurcating potential energy surface was achieved through perhalogenation of one C−C bond in R1. The ambimodal nature of the rate-limiting transition state is clearly maintained for TS1F. The chlorinated and brominated substrates show transition states preserving some structural features of the bispericyclic transition state (elongated bond lengths and in phase stretching motion in the normal mode associated with the reaction coordinate), but their dynamic behavior suggests that a valley−ridge may not connect two sequential transition states. Interestingly, the asymmetry imposed upon halogenation is opposite when using F than when considering Cl and Br. These systems undergo the [3,3] sigmatropic rearrangement to furnish P1bX and P1aX with quite significant levels of selectivity. The perchlorinated and perbrominated substrates furnish the product of CX2−CX2 cleavage, whereas the nonfluorinated C−C bond is broken in the fluorinated system. Dynamic effects have a paramount role in the selectivity observed for these reactions.

Figure 11. Quasiclassical trajectories for the substrate with a perchlorinated C−C bond R1Cl reaching the P1aCl or P1bCl product basins from TS1Cl. The location of the second transition state associated with the bifurcation (TS2Cl) is also indicated.

Throughout this work, the Konh−Sham formulation of the density functional theory was employed.52,53 The meta-hybrid exchangecorrelation functional, M06-2X, by Zhao and Truhlar54 was used with the triple-ζ quality Def2TZVPP basis set for all of the static calculations. All geometry optimizations have been carried out using tight convergence criteria in order to obtain accurate stationary points. Such accuracy in the geometries also required a pruned grid for numerical integration with 99 radial shells and 590 angular points per shell. Analysis of the normal modes obtained via diagonalization of the Hessian matrix was used to confirm the topological nature of each stationary point. The wave function stability for each optimized structure has also been checked.55 The ACID56,57 was computed using CSGT.58 Dynamic trajectory experiments within the Born−Oppenheimer approximation were run at the UM06-2X/Def2SVP level.59−61 Mixing of the HOMO−LUMO orbitals was performed at every step of the trajectories to allow for the convergence into the open-shell solution of the SCF in steps where diradical character may arise in the structures. Two sets of 200 trajectories were run from transition states TS1, TS1F, and TS1Cl, respectively, with environmental conditions of 300 K and 1 atm. Initial velocities were assigned via random vibrational sampling. Four hundred true random numbers were obtained from atmospheric noise as provided by random.org.62 All trajectories were integrated with a stepsize of 0.2 fs, and an initial phase was selected in the direction of products from the starting transition state. Trajectory steps were recorded every 0.25 amu1/2 bohr and were stopped after 800 steps (ca. 480 ps) or when they arrived at the product basin. See the Supporting Information for more details. All calculations performed in this work have been carried out with the Gaussian 09 program.63

in this case, the asymmetrization imposed by the halogen substitution is so severe that the reaction only proceeds to a single product formation. Figure 11 illustrates that TS2Cl is too offset with respect to the location of the rate-limiting transition state (TS1Cl). During the 200 trajectories collected in this work, the surroundings of TS2Cl are visited by only three trajectories which nevertheless proceed to formation of P1aCl. It is noteworthy that for this substrate even these three highly excited trajectories are funneled to the reacting channel without the large amplitudes found for R1F, suggesting that this channel is significantly more steep, concentrating all the trajectories in a narrow corridor. Figure 11 also shows that about 15% of the trajectories recoil back to reactants for the perchlorinated substrate. In view of this experiment, and despite the fact that the geometry and the normal mode associated with the imaginary frequency for TS1Cl was consistent with some degree of bispericyclic character, the reaction for the perchlorinated, and by extension the perbrominated substrate, cannot be unambiguously described as examples of processes with ambimodal transition states. The reaction dynamic trajectories computed from TS1Cl only produce P1aCl, suggesting that this TS connects R1Cl only with this product. A ridge between TS1Cl and TS2Cl could not be confirmed through dynamic calculations. It could be the case that this reaction does not feature an ambimodal transition state, or that, if it does, one of the basins is extremely inaccessible due to a skewed ridge and results in complete selectivity toward P1aCl.

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.joc.7b00425. 4763


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CF energies and thermal corrections, Cartesian coordinates, number of imaginary frequencies for all computed structures, and details on the setup of the trajectory calculations (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +34 986813268. ORCID

Roberto Villar López: 0000-0002-9278-9752 Olalla Nieto Faza: 0000-0001-8754-1341 Carlos Silva López: 0000-0003-4955-9844 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the Centro de Supercomputación de Galicia (CESGA) for time on HPC infrastructures. Ministerio de Economiá y Competitividad (MINECO, PCTQ2016-75023C2-2-P) and Xunta de Galicia (EM2014/040) are also acknowledged for financial support. We are grateful to Prof. Barry Carpenter for kindly providing a copy of the Newton code and for insightful discussions on this chemistry.

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DEDICATION Dedicated to the Memory of Prof. Dieter Cremer, outstanding scientist, mentor and friend. REFERENCES

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Dynamic Effects Responsible for High Selectivity in a [3,3] Sigmatropic

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