Designing Reactions with Post-Transition-State Bifurcations: Asynchronous Nitrene Insertions into C–C σ Bonds

Abstract

•A recipe for designing reactions with post-transition-state bifurcations is provided•A model for selectivity control for such reactions is presented Deep understanding of the factors controlling reactivity and selectivity for chemical reactions empowers chemists to control product distributions and design reactions with desired outcomes. The work described here provides a recipe for designing reactions with post-transition-state bifurcations (PTSBs)—reactions in which a single transition state leads directly to two (or more) products. This type of reaction does not conform to the usual pictures of reactivity presented to students but has recently reared its head in fields as diverse as organometallic chemistry and natural products biosynthesis. By demonstrating that such a reaction can be designed rationally, we exert a degree of dominance over the lack of available data on such reactions, but our ability to design does not guarantee that we fully understand. Although we provide a working model for controlling selectivity for reactions with PTSBs, we hope it will be refined through future work in pursuit of deeper understanding. Discoveries of chemical reactions with potential energy surfaces with post-transition-state bifurcations are increasing in frequency. Although such potential energy surface features are often discovered accidentally, we demonstrate here that they can be designed rationally. We describe a process for designing such reactions and apply it to the design of a nitrene addition/alkyl-shift reaction with a post-transition state bifurcation. We examine substituent effects on this reaction and propose a dynamics-based model for selectivity control. Discoveries of chemical reactions with potential energy surfaces with post-transition-state bifurcations are increasing in frequency. Although such potential energy surface features are often discovered accidentally, we demonstrate here that they can be designed rationally. We describe a process for designing such reactions and apply it to the design of a nitrene addition/alkyl-shift reaction with a post-transition state bifurcation. We examine substituent effects on this reaction and propose a dynamics-based model for selectivity control. The formation of two or more products in a chemical reaction is typically attributed to competition between pathways with different rate-determining transition-state structures (TSSs). In an increasing number of cases, however, the formation of two or more products has been ascribed to pathways that bifurcate after a common TSS—pathways that split not at a subsequent shared minimum (intermediate) but on the downslope following the shared (ambimodal) TSS.1Ess 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: 7592-7601Crossref PubMed Scopus (276) Google Scholar, 2Hare S.R. Tantillo D.J. Post-transition state bifurcations gain momentum – current state of the field.Pure Appl. Chem. 2017; 89: 679-698Crossref Scopus (105) Google Scholar Such reactions are said to involve post-transition-state bifurcations (PTSBs), and the ratio of products formed is controlled by dynamic effects1Ess 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: 7592-7601Crossref PubMed Scopus (276) Google Scholar, 2Hare S.R. Tantillo D.J. Post-transition state bifurcations gain momentum – current state of the field.Pure Appl. Chem. 2017; 89: 679-698Crossref Scopus (105) Google Scholar, 3Carpenter B.K. Dynamic behavior of organic reactive intermediates.Angew. Chem. Int. Ed. 1998; 37: 3340-3350Crossref PubMed Google Scholar, 4Rehbein J. Carpenter B.K. Do we fully understand what controls chemical selectivity?.Phys. Chem. Chem. Phys. 2011; 13: 20906-20922Crossref PubMed Scopus (137) Google Scholar, 5Black 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: 12860-12865Crossref PubMed Scopus (146) Google Scholar, 6Yang Z. Houk K.N. The dynamics of chemical reactions: atomistic visualizations of organic reactions, and homage to van’t Hoff.Chem. Eur. J. 2018; 24: 3916-3924Crossref PubMed Scopus (31) Google Scholar, 7Lourderaj U. Park K. Hase W.L. Classical trajectory simulations of post-transition state dynamics.Int. Rev. Phys. Chem. 2008; 27: 361-403Crossref Scopus (134) Google Scholar, 8Ma X. Hase W.L. Perspective: chemical dynamics simulations of non-statistical reaction dynamics.Philos. Trans. A Math. Phys. Eng. Sci. 2017; 375https://doi.org/10.1098/rsta.2016.0204Crossref PubMed Scopus (49) Google Scholar, 9Nyman G. Computational methods of quantum reaction dynamics.Int. J. Quant. Chem. 2014; 114: 1183-1198Crossref Scopus (24) Google Scholar, 10Salem L. Narcissistic reactions. Synchronism vs. nonsynchronism in automerizations and enantiomerizations.Acc. Chem. Soc. 1971; 4: 322-328Crossref Scopus (82) Google Scholar, 11Wang I.S.Y. Karplus M. Dynamics of organic reactions.J. Am. Chem. Soc. 1973; 95: 8160-8164Crossref Scopus (120) Google Scholar rather than by differences in energies of transition states. A general potential energy surface (PES) involving a PTSB is presented in Figure 1; in this figure, TSS1 is the ambimodal TSS and TSS2 is a distinct TSS along a pathway interconverting the two products. Both products can be formed via pathways involving monotonic decreases in energy from TSS1. Evidence for PTSBs (still primarily theoretical) has been described for various isomerizations, carbocation rearrangements, C–H insertions, cycloadditions, and nucleophilic substitutions.1Ess 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: 7592-7601Crossref PubMed Scopus (276) Google Scholar, 2Hare S.R. Tantillo D.J. Post-transition state bifurcations gain momentum – current state of the field.Pure Appl. Chem. 2017; 89: 679-698Crossref Scopus (105) Google Scholar Although PES features such as PTSBs are of fundamental interest, we aim to delineate guidelines for (1) designing reactions with PTSBs and (2) predicting product selectivity for such reactions without having to resort to extensive dynamics simulations. Here, we describe and validate a strategy for the former and describe some progress with the latter. Our simple (in retrospect; it was not obvious at the outset) approach is to find a reaction that interconverts two molecules by way of a TSS (that would be TSS2 in Figure 1) that we can envision accessing from another reaction with a higher energy TSS (TSS1 in Figure 1). This approach would be straightforward if putative TSS2 has an electronic structure usually associated with a PES minimum. Two initial candidates for this type of reaction rose to the top of our list of possibilities: (1) carbocation rearrangements with TSSs resembling classical secondary carbocations12Tantillo D.J. The carbocation continuum in terpene biosynthesis—where are the secondary cations?.Chem. Soc. Rev. 2010; 39: 2847-2854Crossref PubMed Scopus (126) Google Scholar, 13Tantillo D.J. Recent excursions to the borderlands between the realms of concerted and stepwise: carbocation cascades in natural products biosynthesis.J. Phys. Org. Chem. 2008; 21: 561-570Crossref Scopus (121) Google Scholar, 14Hare S.R. Tantillo D.J. Dynamic behavior of rearranging carbocations – implications for terpene biosynthesis.Beilstein J. Org. Chem. 2016; 12: 377-390Crossref PubMed Scopus (53) Google Scholar and (2) dyotropic rearrangements with TSSs resembling tetrahedral intermediates associated with acyl substitution reactions.15Gutierrez O. Tantillo D.J. Analogies between synthetic and biosynthetic reactions in which [1,2]-alkyl shifts are combined with other events: dyotropic, Schmidt, and carbocation rearrangements.J. Org. Chem. 2012; 77: 8845-8850Crossref PubMed Scopus (46) Google Scholar We will discuss the former in a separate report but describe the latter in detail here. The reaction of interest is a twist on the Schmidt-Aubé reaction, a reaction that, over the past 25 years, has become a go-to method for the preparation of fused and bridged lactams, including those with twisted amide substructures.16Aube J. Milligan G.L. Intramolecular Schmidt reaction of alkyl azides.J. Am. Chem. Soc. 1991; 113: 8965-8966Crossref Scopus (202) Google Scholar For example, synthesis of protonated 2-quinuclidone, along with a smaller amount of a [3.2.1] isomer, was accomplished with a Schmidt-Aubé reaction (Scheme 1).17Tani K. Stoltz B.M. Synthesis and structural analysis of 2-quinuclidonium tetrafluoroborate.Nature. 2006; 441: 731-734Crossref PubMed Scopus (212) Google Scholar The results of previous quantum chemical computations indicated that acid-catalyzed Schmidt-Aubé reactions likely involve two-step mechanisms consisting of (1) rapid formation of a tetrahedral azidohydrin intermediate and (2) concerted loss of N2 and shifting of the alkyl group antiperiplanar to it (the rate-determining step).18Gutierrez O. Aubé J. Tantillo D.J. Mechanism of the acid-promoted intramolecular Schmidt reaction: theoretical assessment of the importance of lone pair–cation, cation−π, and steric effects in controlling regioselectivity.J. Org. Chem. 2012; 77: 640-647Crossref PubMed Scopus (34) Google Scholar Thus, the reaction shown in Scheme 1 is expected not to involve a PTSB but rather competing pathways with separate TSSs for alkyl shift and N2 loss leading to each product; our calculations confirm this expectation (see Experimental Procedures and Supplemental Information Section S1 for details). To convert this reaction to one with a PTSB, we sought to make the tetrahedral intermediate into a TSS for interconversion of the two products by a concerted dyotropic rearrangement with asynchronous bond-shifting events.15Gutierrez O. Tantillo D.J. Analogies between synthetic and biosynthetic reactions in which [1,2]-alkyl shifts are combined with other events: dyotropic, Schmidt, and carbocation rearrangements.J. Org. Chem. 2012; 77: 8845-8850Crossref PubMed Scopus (46) Google Scholar, 19Fernández I. Cossío F.P. Sierra M.A. Dyotropic reactions: mechanisms and synthetic applications.Chem. 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Chem. 2006; 71: 5876-5880Crossref PubMed Scopus (145) Google Scholar might be used to avoid the imine, i.e., nitrene generation would be expected to lead to structures resembling TSS1; these could then form the undesired imine or go on to our proposed bifurcation (see Supplemental Information for additional details on other competing reactions). This scenario would presumably involve an additional PTSB preceding TSS1 (which could be investigated in the future for various means of generating nitrenes). A similar PES was found for the homologous reaction shown in Scheme 2 (n = 2) and the bottom of Figure 3.Scheme 21,2-Alkyl-Shift/Nitrene-Addition/1,2-Alkyl-Shift Reaction (n = 1, 2)View Large Image Figure ViewerDownload Hi-res image Download (PPT) Several trajectories in the reactant direction led to a prototropic shift rather than a 1,2-alkyl shift, suggesting that the reverse pathway from TSS1 also bifurcates. Those were considered unproductive for our analysis. Quasiclassical dynamics trajectory calculations3Carpenter B.K. Dynamic behavior of organic reactive intermediates.Angew. Chem. Int. Ed. 1998; 37: 3340-3350Crossref PubMed Google Scholar, 4Rehbein J. Carpenter B.K. Do we fully understand what controls chemical selectivity?.Phys. Chem. Chem. Phys. 2011; 13: 20906-20922Crossref PubMed Scopus (137) Google Scholar, 5Black 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: 12860-12865Crossref PubMed Scopus (146) Google Scholar, 6Yang Z. Houk K.N. The dynamics of chemical reactions: atomistic visualizations of organic reactions, and homage to van’t Hoff.Chem. Eur. J. 2018; 24: 3916-3924Crossref PubMed Scopus (31) Google Scholar, 7Lourderaj U. Park K. Hase W.L. Classical trajectory simulations of post-transition state dynamics.Int. Rev. Phys. Chem. 2008; 27: 361-403Crossref Scopus (134) Google Scholar, 8Ma X. Hase W.L. Perspective: chemical dynamics simulations of non-statistical reaction dynamics.Philos. Trans. A Math. Phys. Eng. Sci. 2017; 375https://doi.org/10.1098/rsta.2016.0204Crossref PubMed Scopus (49) Google Scholar, 9Nyman G. Computational methods of quantum reaction dynamics.Int. J. Quant. Chem. 2014; 114: 1183-1198Crossref Scopus (24) Google Scholar, 10Salem L. Narcissistic reactions. Synchronism vs. nonsynchronism in automerizations and enantiomerizations.Acc. Chem. Soc. 1971; 4: 322-328Crossref Scopus (82) Google Scholar, 11Wang I.S.Y. Karplus M. Dynamics of organic reactions.J. Am. Chem. Soc. 1973; 95: 8160-8164Crossref Scopus (120) Google Scholar were performed for both systems, with trajectories initiated from TSS1. For the n = 1 system, 144 productive trajectories were obtained, all leading to the [3.2.1] product (consistent with the results of IRC calculations; see Supplemental Information Section S2 for details). Thus, although the PES appears to have a PTSB, this feature does not seem to influence the dynamical behavior. A different behavior was observed for the n = 2 system, for which 3 of 75 productive trajectories led to the [3.2.2] product and 72 led to the [4.2.1] product. In this system, the PES PTSB does appear to influence the dynamical behavior, albeit only slightly. Motivated by these results, we turned our attention to derivatives of the n = 2 system that might have a more balanced product distribution. Some of the many systems examined (see Supplemental Information Sections S3 and S4 for details) are illustrated in Figure 4; our first attempts involved adding strongly electron-withdrawing groups to weaken particular bonds.27Lemal D.M. Perspective on fluorocarbon chemistry.J. Org. Chem. 2004; 69: 1-11Crossref PubMed Scopus (348) Google Scholar, 28Borden W.T. Effects of electron donation into C–F σ* orbitals: explanations, predictions and experimental tests.Chem. 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The results of dynamics simulations on these systems are summarized in Table 1. As shown, inclusion of F or CF3 at the R1 position leads to more of the [3.2.2] product, making formation of this product competitive in several cases, e.g., NCH5 and NCH7. The trajectories leading to both products are illustrated in Figure 5 for NCH7, highlighting the balanced product distribution. Incorporating a F atom at the R2 position serves to enhance the formation of the [3.2.2] product, whereas incorporation of a F atom at the R3 position has a small opposing effect (see Experimental Procedures).Table 1Product Distributions Based on the Trajectories Obtained for Derivatives from Figure 4SubstituentsProductive Trajectories[3.2.2] (%)[4.2.1] (%)NCH1R1 = H, R2 = H, R3 = H754.096.0NCH2R1 = F, R2 = H, R3 = H11527.073.0NCH3R1 = H, R2 = F, R3 = H7916.583.5NCH4R1 = H, R2 = H, R3 = F761.398.7NCH5R1 = CF3, R2 = H, R3 = H5749.150.9NCH6R1 = CF3, R2 = H, R3 = F4729.870.2NCH7R1 = CF3; R2 = F; R3 = F4656.543.5 Open table in a new tab Figure 5Pathways to Competing ProductsShow full captionDynamics trajectories obtained for the net C–C insertion reaction of NCH7 to form the [3.2.2] (red lines) and [4.2.1] (blue lines) products. The locations of TSS1 and TSS2 are also indicated.View Large Image Figure ViewerDownload Hi-res image Download (PPT) Dynamics trajectories obtained for the net C–C insertion reaction of NCH7 to form the [3.2.2] (red lines) and [4.2.1] (blue lines) products. The locations of TSS1 and TSS2 are also indicated. We initially proposed that increased formation of the [3.2.2] product arises from repulsion between the lone pair at the nitrene center and fluorine lone pairs during bond shifting to form the [4.2.1] product. However, several lines of evidence argue against the validity of this hypothesis. First, TSS2 geometries that more closely resemble [3.2.2] products (and for which lone pairO– ↔ σ*C2–C1 interactions are predicted to be stronger) actually lead to smaller proportions of [3.2.2] product-forming trajectories (see Supplemental Information Section S4 for details). Second, N---C2–C3 angles in ambimodal TSS1s appear to be connected to product ratios—in general, the smaller that angle (which ranges from 80° to 91°; see Supplemental Information Section S4), the larger the proportion of [4.2.1] product that is formed. These observations would be consistent with a momentum effect: if a reacting molecule passing through the TSS1 region has its nitrogen atom (comparatively) near to C3, it prefers to insert into the C2–C3 bond to form the [4.2.1] product. Houk and co-workers have recently described geometric parameters of ambimodal TSSs that are predictive of product distributions for cycloadditions involving PTSBs.32Yang 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: 3061-3067Crossref PubMed Scopus (43) Google Scholar Third, examination of models of valley-ridge inflection (VRI) points (see Supplemental Information Section S5 for details on locating them) indicates that the more a VRI point resembles TSS2 (in terms of interatomic distances and angles; see Supplemental Information Section S4 for data), the more balanced a product distribution is observed, i.e., the more [3.2.2] product is formed. Noncovalent interaction (NCI) analysis33Johnson E.R. Keinan S. Mori-Sanchez P. Contreras-Garcia J. Cohen A.J. Yang W. Revealing noncovalent interactions.J. Am. Chem. Soc. 2010; 132: 6498-6506Crossref PubMed Scopus (5117) Google Scholar, 34Contreras-García J. Johnson E.R. Keinan S. Chaudret R. Piquemal J.P. Beratan D.N. Yang W. NCIPLOT: a program for plotting noncovalent interaction regions.J. Chem. Theory Comput. 2011; 7: 625-632Crossref PubMed Scopus (2321) Google Scholar also shows that VRI points for reactions with more balanced product distributions have additional stabilizing intramolecular interactions (e.g., apparent attractive interactions between F and N atoms); an example is shown in Figure 6 (see Supplemental Information Sections S6 and S7 for other structures). These observations lead us to conclude that reduced product selectivity results from favorable interactions that increase the residence time in the VRI region (“electrostatic drag”35Hare S.R. Pemberton R.P. Tantillo D.J. Navigating past a fork in the road: carbocation−π interactions can manipulate dynamic behavior of reactions facing post-transition-state bifurcations.J. Am. Chem. Soc. 2017; 139: 7485-7493Crossref PubMed Scopus (41) Google Scholar) and thereby mitigate momentum effects. In general, times to form [4.2.1] products were longer for systems with reduced selectivity (Figure 7; given that small amounts of [3.2.1] products are formed in some systems, we are not comfortable drawing conclusions using timing data for formation of [3.2.1] products), although the absence of a tight correlation implies that other factors are also at play.Figure 7Trajectory TimingsShow full captionAverage time of trajectories forming [4.2.1] product with respect to the percentage of trajectories forming [3.2.2] product. R2 = 0.68 (not considering NCH3).View Large Image Figure ViewerDownload Hi-res image Download (PPT) Average time of trajectories forming [4.2.1] product with respect to the percentage of trajectories forming [3.2.2] product. R2 = 0.68 (not considering NCH3). The IRC profiles obtained from TSS1 for all NCH derivatives are presented in Figure 8. All IRC pathways lead to [4.2.1] products. Although these profiles do not differ much on the reactant side of TSS1, the pathways downhill toward product do, displaying substituent-dependent asynchrony, manifested as differences in the prominence of the “shoulder” at ∼5 amu−1/2 bohr.12Tantillo D.J. The carbocation continuum in terpene biosynthesis—where are the secondary cations?.Chem. Soc. Rev. 2010; 39: 2847-2854Crossref PubMed Scopus (126) Google Scholar, 13Tantillo D.J. Recent excursions to the borderlands between the realms of concerted and stepwise: carbocation cascades in natural products biosynthesis.J. Phys. Org. Chem. 2008; 21: 561-570Crossref Scopus (121) Google Scholar, 14Hare S.R. Tantillo D.J. Dynamic behavior of rearranging carbocations – implications for terpene biosynthesis.Beilstein J. Org. Chem. 2016; 12: 377-390Crossref PubMed Scopus (53) Google Scholar, 36Nouri D.H. Tantillo D.J. Hiscotropic rearrangements: hybrids of electrocyclic and sigmatropic reactions.J. Org. Chem. 2006; 71: 3686-3695Crossref PubMed Scopus (39) Google Scholar, 37Cremer D. Wu A. Kraka E. The mechanism of the reaction FH + H2C=CH2 → H3CCFH2. Investigation of hidden intermediates with the unified reaction valley approach.Phys. Chem. Chem. Phys. 2001; 3: 674-687Crossref Scopus (37) Google Scholar, 38Kraka E. Cremer D. Computational analysis of the mechanism of chemical reactions in terms of reaction phases: hidden intermediates and hidden transition states.Acc. Chem. Res. 2010; 43: 591-601Crossref PubMed Scopus (132) Google Scholar The most asynchronous pathways are observed for systems that lead to the most [3.2.2] product in dynamics simulations, NCH5–NCH7. Flattening of the PES in this shoulder region is consistent with more escape toward [3.2.2] product; i.e., flatter surfaces should correspond to longer residence times and more extensive sampling of configuration space in the VRI region. In summary, we have made progress toward the two aims described above. With respect to aim (1), we laid out a strategy for designing reactions with PTSBs and showed that it is viable, although there were, unsurprisingly, hiccups along the way. This strategy involves finding a structure that should lie on the pathway interconverting two minima but which can also be accessed via a different reaction. If the structure in question is a PES minimum, then there is nothing special about the reaction network: the “different reaction” merely produces an intermediate that can convert to either of two products via competing TSSs. However, if the structure in question is a TSS, then the “different reaction” involves a PTSB, and product selectivity should be under dynamic control.39Burns J.M. Computational evidence for a reaction pathway bifurcation in Sasaki-type (4 + 3)-cycloadditions.Org. Biomol. Chem. 2018; 16: 1828-1836Crossref PubMed Google Scholar How does one find such a TSS? The approach laid out here is to look for a reaction with a putative intermediate that seems highly unlikely to have a significant lifetime, i.e., if an organic chemist is uncomfortable writing down such an intermediate in an arrow-pushing mechanism, then it is a candidate for TSS2 in a reaction with a PTSB.