Control elements in dynamically determined selectivity on a bifurcating surface

Bispericyclic Ambimodal Dimerization of Pentafulvene: The Origin of Asynchronicity and Kinetic Selectivity of the Endo Transition State

The propensity of fulvenes to undergo dimerization has long been known, although the in-depth mechanism and electronic behavior during dimerization are still elusive. Herein, we made an attempt to gain insights into the reactivity of pentafulvene for Diels-Alder (DA) and [6 + 4]-cycloadditions via conventional and ambimodal routes. The result emphasizes that pentafulvene dimerization preferentially proceeds through a unique bifurcation mechanism where two DA pathways merge together to produce two degenerate [4 + 2]-cycloadducts from a single TS. Despite the [6 + 4]-cycloadduct being thermodynamically preferred, [4 + 2]-cycloaddition reactions are kinetically driven. Singlet biradicaloid is involved in through-space 6e- delocalization as a secondary orbital interaction that originates asynchronicity and stabilizes the bispericyclic transition state (TS). The transformation of various actively participating intrinsic bonding orbitals (IBOs) unambiguously forecasts the formation of multiple products from a single TS and rationalizes the mechanism of ambimodal reactions that are rather difficult to probe with other analyses. The changes in active IBOs clearly distinguish the conventional reactions from bifurcation reactions and can be employed to characterize and confirm the ambimodal mechanism. This report gains a crucial theoretical insight into the mechanism of bifurcation, the origin of asynchronicity, and electronic behavior in ambimodal TS, which will certainly be of enormous value for future studies.

Substituent effects on the selectivity of ambimodal [6+4]/[4+2] cycloaddition

In this work, we report a density functional theory (DFT) study and a dynamical trajectory study of substituent effects on the ambimodal [6+4]/[4+2] cycloaddition proposed for 1,3,5,10,12-cycloheptadecapentaene, referred to as cycloheptadecapentaene. The proposed cycloaddition proceeds through an ambimodal transition state, which results in both a [6+4] adduct a [4+2] adduct directly. The [6+4] adduct can be readily converted to the [4+2] adduct via a Cope rearrangement. We study the selectivity of the reaction with regard to the position of substituents, steric effects of substituents, and electronic effects of substituents. In the dynamical trajectory study, we find that nitro-substituted reactants lead to a new product from the ambimodal transition state via the hetero Diels-Alder reaction, and this new product can then be converted to a [4+2] adduct by a hetero [3, 3]-sigmatropic rearrangement. These results may provide insights for designing more bridged heterocyclic compounds.

Modeling Multi-Step Organic Reactions: Can Density Functional Theory Deliver Misleading Chemistry?

Many organic reactions are characterized by a complex mechanism with a variety of transition states and intermediates of different chemical natures. Their correct and accurate theoretical characterization critically depends on the accuracy of the computational method used. In this work, we study a complex ambimodal cycloaddition with five transition states, two intermediates, and three products, and we ask whether density functional theory (DFT) can provide a correct description of this type of complex and multifaceted reaction. Our work fills a gap in that most systematic benchmarks of DFT for chemical reactions have considered much simpler reactions. Our results show that many density functionals not only lead to seriously large errors but also differ from one another in predicting whether the reaction is ambimodal. Only a few of the available functionals provide a balanced description of the complex and multifaceted reactions. The parameters varied in the tested functionals are the ingredients, the treatment of medium-range and nonlocal correlation energy, and the inclusion of Hartree-Fock exchange. These results show a clear need for more benchmarks on the mechanisms of large molecules in complex reactions.

Running Wild through Dirhodium Tetracarboxylate-Catalyzed Combined CH(C)-Functionalization/Cope Rearrangement Landscapes: Does Post-Transition-State Dynamic Mismatching Influence Product Distributions?

A special type of C-H functionalization can be achieved through C-H insertion combined with Cope rearrangement (CHCR) in the presence of dirhodium catalysts. This type of reaction was studied using density functional theory and ab initio molecular dynamics simulations, the results of which pointed to the dynamic origins of low yields observed in some experiments. These studies not only reveal intimate details of the complex reaction network underpinning CHCR reactions but also further cement the generality of the importance of nonstatistical dynamic effects in controlling Rh2L4-promoted reactions.

Binomial Uncertainty in Molecular Dynamics-Based Reactions Analysis

Molecular Dynamics-based reaction analysis is an indispensable tool for studying processes defying the transition-state theory (TST), where the product ratios do not follow energies of transition states. The main class of such processes is ambimodal reactions, which have a post-transition-state bifurcation, so that several products form via a single transition state. Multiple runs of molecular dynamics allow one to sample the space of possibilities and ultimately predict the product ratio without relying on TST; however, no techniques for estimating the reliability of the prediction were proposed so far. Here we show that dynamics runs follow the same rules as die rolls, which paves a simple way for estimating their uncertainty and, accordingly, the number of runs necessary to achieve the required accuracy. Remarkably, we find that the majority of such studies carried out in the last 5 years use far too few runs, so that the product ratios predicted in them can be off by >50% in more than 50% of cases.

Pericyclic Cascade Reactions Affording Thienyl- and Benzo[b]thienyl-Fused Architectures: A Synthetic and Density Functional Theory Analysis of Asynchronous Diels-Alder Reactions of Thioarylmaleimides

Herein, we report the synthesis and characterization of a series of thioarylmaleimides and their varied propensity toward highly selective domino Diels-Alder (D-A)/rearrangement, D-A/ene/elimination, and D-A/oxidation reactions to give three types of thienyl-fused architectures. Stereochemical assignment was achieved using a combination of nuclear magnetic resonance (NMR) studies, gauge independent atomic orbital (GIAO) NMR chemical shift calculations, and DP4+ analysis. Transition-state calculations support an asynchronous concerted mechanism and provide support for rationalizing the observed regio- and stereoselectivity.

Discovery and bioinspired total syntheses of unprecedented sesquiterpenoid dimers unveiled bifurcating [4 + 2] cycloaddition and target differentiation of enantiomers

[4 + 2] cycloaddition has led to diverse polycyclic chiral architectures, serving as novel sources for organic synthesis and biological exploration. Here, an unprecedented class of cadinane sesquiterpene [4 + 2] dimers, henryinins A-E (1-5), with a unique 6/6/6/6/6-fused pentacyclic system, were isolated from Schisandra henryi. The divergent total syntheses of compounds 1-5 and their enantiomers (6-10) were concisely accomplished in eight linear steps using a protection-free approach. Mechanistic studies illustrated the origin of selectivity in the key [4 + 2] cycloaddition as well as the inhibition of reaction pathway bifurcation via desymmetrization. The chemical proteomics results showed that a pair of enantiomers shared common targets (PRDX5 C100 and BLMH C73) and had unique targets (USP45 C588 for 4 and COG7 C419 for 9). This work provides experimental evidence for the discovery of unprecedented cadinane dimers from selective Diels-Alder reaction and a powerful strategy to explore the biological properties of natural products.

Ambimodal Addition-Coupled Electron Transfer Mechanism in a Pb(IV)-Promoted Oxidative Dearomatization Reaction

The mechanism of the Pb(IV)-promoted phenol oxidative dearomatization reaction has been traditionally attributed to a carbocation mechanism. In 2011, Pettus reported an oxidative dearomatization reaction leading to a mixture of a formal [5 + 2] and a C-O bond formation product. By employing density functional theory and quasi-molecular dynamics calculations, it was demonstrated that the reaction does not occur through a carbocation intermediate but instead proceeds through an addition-coupled electron transfer (ACET) mechanism. Moreover, the ACET exhibits ambimodality, wherein a transition state results in 4-6 distinct outcomes through post-TS bifurcation. The reported selectivity can be effectively rationalized by a newly proposed mechanism.

Accelerated Entropic Path Sampling with a Bidirectional Generative Adversarial Network

The role of entropy in mediating the dynamic outcomes of chemical reactions remains largely unknown. To evaluate the change of entropy along post-transition state paths, we have previously developed entropic path sampling that computes configurational entropy from an ensemble of reaction trajectories. However, one major caveat of this approach lies in its high computational demand: about 2000 trajectories are needed to converge the computation of an entropic profile. Here, by leveraging a deep generative model, we developed an accelerated entropic path sampling approach that evaluates entropic profiles using merely a few hundred reaction dynamic trajectories. The new method, called bidirectional generative adversarial network-entropic path sampling, can enhance the estimation of probability density functions of molecular configurations by generating pseudo-molecular configurations that are statistically indistinguishable from the true data. The method was established using cyclopentadiene dimerization, in which we reproduced the reference entropic profiles (derived from 2480 trajectories) using merely 124 trajectories. The method was further benchmarked using three reactions with symmetric post-transition-state bifurcation, including endo-butadiene dimerization, 5-fluoro-1,3-cyclopentadiene dimerization, and 5-methyl-1,3-cyclopentadiene dimerization. The results indicate the existence of a "hidden entropic intermediate", which is a dynamic species that binds to a local entropic maximum where no free energy minimum is formed.

Computational Design of a Tetrapericyclic Cycloaddition and the Nature of Potential Energy Surfaces with Multiple Bifurcations

An ambimodal transition state (TS) that leads to formation of four different pericyclic reaction products ([4 + 6]-, [2 + 8]-, [8 + 2]-, and [6 + 4]-cycloadducts) without any intervening minima has been designed and explored with DFT computations and quasiclassical molecular dynamics. Direct dynamics simulations propagated from the ambimodal TS show the evolution of trajectories to give the four cycloadducts. The topography of the PES is a key factor in product selectivity. A good correlation is observed between geometrical resemblance of the products to the ambimodal TS (measured by the RMSD) and the ratio of products formed in the dynamics simulations.

Symmetric Post-Transition State Bifurcation Reactions with Berry Pseudomagnetic Fields

We investigate how the Berry force (i.e., the pseudomagnetic force operating on nuclei as induced by electronic degeneracy and spin-orbit coupling (SOC)) might modify a post-transition state bifurcation (PTSB) reaction path and affect product selectivity for situations when multiple products share the same transition state. To estimate the magnitude of this effect, Langevin dynamics are performed on a model system with a valley-ridge inflection (VRI) point in the presence of a magnetic field (that mimics the Berry curvature). We also develop an analytic model for such selectivity that depends on key parameters such as the surface topology, the magnitude of the Berry force, and the nuclear friction. Within this dynamical model, static electronic structure calculations (at the level of generalized Hartree-Fock with spin-orbit coupling (GHF+SOC) theory) suggest that electronic spin induced Berry force effects may indeed lead to noticeable changes in methoxy radical isomerization.

C-H Insertion in Dirhodium Tetracarboxylate-Catalyzed Reactions despite Dynamical Tendencies toward Fragmentation: Implications for Reaction Efficiency and Catalyst Design

Rh-catalyzed C-H insertion reactions to form β-lactones suffer from post-transition state bifurcations, with the same transition states leading to ketones and ketenes via fragmentation in addition to β-lactones. In such a circumstance, traditional transition state theory cannot predict product selectivity, so we employed ab initio molecular dynamics simulations to do so and provide a framework for rationalizing the origins of said selectivity. Weak interactions between the catalyst and substrate were studied using energy decomposition and noncovalent interaction analyses, which unmasked an important role of the 2-bromophenyl substituent that has been used in multiple β-lactone-forming C-H insertion reactions. Small and large catalysts were shown to behave differently, with the latter providing a means of overcoming dynamically preferred fragmentation by lowering the barrier for the recombination of the product fragments in the grip of the large catalyst active site cavity.

Total Synthesis and Prediction of Ulodione Natural Products Guided by DFT Calculations

A biomimetic synthetic strategy has resulted in a two-step total synthesis of (±)-ulodione A and the prediction of two potential natural products, (±)-ulodiones C and D. This work was guided by computational investigations into the selectivity of a proposed biosynthetic Diels-Alder dimerization, which was then utilized in the chemical synthesis. This work highlights how biosynthetic considerations can both guide the design of efficient synthetic strategies and lead to the anticipation of new natural products.

Superresolved Motions of Single Molecular Catalysts during Polymerization Show Wide Distributions

The motion of single molecular ruthenium catalysts during and after single turnover events of ring-opening metathesis polymerization is imaged through single-molecule superresolution tracking with a positional accuracy of ±32 nm. This tracking is achieved through the real-time incorporation of spectrally tagged monomer units into active polymer chain ends during living polymerization; thus, by design, only active-catalyst motion is detected and imaged, without convolution by inactive catalysts. The catalysts show diverse individualistic diffusive behaviors with respect to time that persist for up to 20 s. Catalysts occupy three mobility populations: quasi-stationary (23%), intermediate (53%, 65 nm), and large (24%, 145 nm) step sizes. Differences in catalyst mobility populations also exist between individual aggregates (p < 0.001). Such differential motion indicates widely different local catalyst microenvironments during the catalytic turnover. These mobility differences are uniquely observable through single-catalyst microscopy and are not measurable through traditional ensemble analytical techniques for characterizing the behavior of molecular catalysts, such as nuclear magnetic resonance spectroscopy. The measured distributions of active molecular catalyst motions would not be readily predictable through modeling or first-principles, and the range likely impacts individual catalyst turnover rate and selectivity. This range plausibly contributes to property distributions observable in bulk polymers, such as molecular weight polydispersity (e.g., 1.9 in this system), leading to a revised understanding of the mechanistic, microscale origins of macroscale polymer properties.

Collective Synthesis of Illudalane Sesquiterpenes via Cascade Inverse Electron Demand (4 + 2) Cycloadditions of Thiophene S,S-Dioxides

Thiophene S,S-dioxides are underutilized tools for the de novo construction of benzene rings in organic synthesis. We report a collective synthesis of nine illudalane sesquiterpenes using bicyclic thiophene S,S-dioxides as generalized precursors to the indane core of the natural products. Exploiting furans as unusual dienophiles in this inverse electron demand Diels-Alder cascade, this concise and convergent approach enables the synthesis of these targets in as little as five steps. Theoretical studies rationalize the reactivity of thiophene S,S-dioxides with both electron-poor and electron-rich dienophiles and reveal reaction pathways involving either nonpolar pericyclic or bifurcating ambimodal cycloadditions. Overall, this work demonstrates the wider potential of thiophene S,S-dioxides as convenient and flexible precursors to polysubstituted arenes.

Reaction Space Projector (ReSPer) for Visualizing Dynamic Reaction Routes Based on Reduced-Dimension Space

To analyze chemical reaction dynamics based on a reaction path network, we have developed the "Reaction Space Projector" (ReSPer) method with the aid of the dimensionality reduction method. This program has two functions: the construction of a reduced-dimensionality reaction space from a molecular structure dataset, and the projection of dynamic trajectories into the low-dimensional reaction space. In this paper, we apply ReSPer to isomerization and bifurcation reactions of the Au₅ cluster and succeed in analyzing dynamic reaction routes involved in multiple elementary reaction processes, constructing complicated networks (called "closed islands") of nuclear permutation-inversion (NPI) isomerization reactions, and elucidating dynamic behaviors in bifurcation reactions with reference to bundles of trajectories. Interestingly, in the second application, we find a correspondence between the contribution ratios in the ability to visualize and the symmetry of the morphology of closed islands. In addition, the third application suggests the existence of boundaries that determine the selectivity in bifurcation reactions, which was discussed in the phase space. The ReSPer program is a versatile and robust tool to clarify dynamic reaction mechanisms based on the reduced-dimensionality reaction space without prior knowledge of target reactions.

Kinetic Analysis of a Reaction Path Network Including Ambimodal Transition States: A Case Study of an Intramolecular Diels-Alder Reaction

This study proposes a methodology for the kinetic analysis of a reaction path network including ambimodal transition states (TSs), through which an ensemble of trajectories bifurcates to multiple minima in a phenomenon called dynamical bifurcation. The proposed methodology consists of three techniques: an automated reaction path search to construct a reaction path network including ambimodal TSs, an ab initio molecular dynamics simulation to evaluate the branching ratio, and the definition of rate constants incorporating this ratio. Applying the procedure to a Diels-Alder reaction, it was found that the inclusion of dynamical bifurcations is necessary to explain the experimental reaction yield of a byproduct. In addition, it was verified that the products take 10¹³ s to reach thermal equilibrium and that the experimental selectivity is determined by the dynamical bifurcations.

Computational investigation of cycloadditions between cyclopentadiene and tropone-3,4-dimethylester

Thermally promoted cycloaddition reactions of tropone-3,4-dimethylester and cyclopentadiene have been investigated using density functional theory calculations at the M06-2X level and the CBS-QB3 method.

Stereoelectronic and dynamical effects dictate nitrogen inversion during valence isomerism in benzene imine

Non-classical processes such as heavy-atom tunneling and post transition-state dynamics govern stereoselectivity for benzene imine ⇌ 1H-azepine.

Post-spin crossing dynamics determine the regioselectivity in open-shell singlet biradical recombination

Comprehensive computational studies reveal unique dynamic effects in a multi-spin-state reaction that determine the regioselectivity of a biradical recombination process.

Heavy-Atom Kinetic Isotope Effects: Primary Interest or Zero Point?

Chemists have many options for elucidating reaction mechanisms. Global kinetic analysis and classic transition-state probes (e.g., LFERs, Eyring) inevitably form the cornerstone of any strategy, yet their application to increasingly sophisticated synthetic methodologies often leads to a wide range of indistinguishable mechanistic proposals. Computational chemistry provides powerful tools for narrowing the field in such cases, yet wholly simulated mechanisms must be interpreted with great caution. Heavy-atom kinetic isotope effects (KIEs) offer an exquisite but underutilized method for reconciling the two approaches, anchoring the theoretician in the world of calculable observables and providing the experimentalist with atomistic insights. This Perspective provides a personal outlook on this synergy. It surveys the computation of heavy-atom KIEs and their measurement by NMR spectroscopy, discusses recent case studies, highlights the intellectual reward that lies in alignment of experiment and theory, and reflects on the changes required in chemical education in the area.

Influence of Water and Enzyme on the Post-Transition State Bifurcation of NgnD-Catalyzed Ambimodal [6+4]/[4+2] Cycloaddition

The enzyme NgnD catalyzes an ambimodal cycloaddition that bifurcates to [6+4]- and [4+2]-adducts. Both products have been isolated in experiments, but it remains unknown how enzyme and water influence the bifurcation selectivity at the femtosecond time scale. Here, we study the impact of water and enzyme on the post-transition state bifurcation of NgnD-catalyzed [6+4]/[4+2] cycloaddition by integrating quantum mechanics/molecular mechanics quasiclassical dynamics simulations and biochemical assays. The ratio of [6+4]/[4+2] products significantly differs in the gas phase, water, and enzyme. Biochemical assays were employed to validate computational predictions. The study informs how water and enzyme affect the bifurcation selectivity through perturbation of the reaction dynamics in the femtosecond time scale, revealing the fundamental roles of condensed media in dynamically controlling the chemical selectivity for biosynthetic reactions.

Bifurcating reactions: distribution of products from energy distribution in a shared reactive mode

Bifurcating reactions yield two different products emerging from one single transition state and are therefore archetypal examples of reactions that cannot be described within the framework of the traditional Eyring's transition state theory (TST). With the growing number and importance of these reactions in organic and biosynthetic chemistry, there is also an increasing demand for a theoretical tool that would allow for the accurate quantification of reaction outcome at low cost. Here, we introduce such an approach that fulfils these criteria, by evaluating bifurcation selectivity through the energy distribution within the reactive mode of the key transition state. The presented method yields an excellent agreement with experimentally reported product ratios and predicts the correct selectivity for 89% of nearly 50 various cases, covering pericyclic reactions, rearrangements, fragmentations and metal-catalyzed processes as well as a series of trifurcating reactions. With 71% of product ratios determined within the error of less than 20%, we also found that the methodology outperforms three other tested protocols introduced recently in the literature. Given its predictive power, the procedure makes reaction design feasible even in the presence of complex non-TST chemical steps.

Reactive Mode Composition Factor (RMCF) analysis is a powerful tool to forecast the product distribution of bifurcating reactions through analysis of the kinetic energy distribution within the first transition state traversed by the reacting system.

Mechanisms and Dynamics of Synthetic and Biosynthetic Formation of Delitschiapyrones: Solvent Control of Ambimodal Periselectivity

The mechanism and dynamics for the formation of the delitschiapyrone family of natural products are studied by density functional theory (DFT) calculations and quasiclassical molecular dynamics simulations with DFT and xTB. In the uncatalyzed reaction, delitschiapyrones A and B are formed by Diels-Alder reactions through a single transition state and a post-transition state bifurcation that favors formation of delitschiapyrone B. In water and most likely in the enzyme, the acidic hydroxyquinone ionizes, and the resulting conjugate base undergoes cycloaddition preferentially to delitschiapyrone A. We demonstrate a new type of biosynthetic transformation and variable selectivity from a (4 + 2)/(4 + 3) ambimodal transition state.

Pathway Bifurcations in the Activation of Allylic Halides by Palladium and Their Influence on the Dynamics of η1 and η3 Allyl Intermediates

Transition-metal-catalyzed allylic substitution often exhibits complex product selectivity patterns, which have been primarily attributed to π ↔ σ ↔ π isomerization of the η¹ and η³ allyl intermediates. Product selectivity may be even further complicated if η¹- and η³-allyls share a single transition state (TS), leading to their formation resulting in a post-transition-state bifurcation (PTSB). In this work, density functional theory calculations using ab initio molecular dynamics (AIMD) have been carried out that support the presence of a PTSB in Pd-catalyzed allylic halide activation directly influencing product selectivity. The AIMD results initiated from the TS predict the η¹-allyl to be favored in the gas phase and a low dielectric (ε < 2.5) for trialkylphosphines, while the selectivity shifts toward the η³-allyl in higher dielectrics. The minimum energy path is also predicted to shift in product preference, consistent with the dynamics predictions. The bifurcation in allylic chloride activation is predicted to largely favor the η³-allyl at any solvent polarity. A PTSB was also discovered to be present in Ni and Pt allylic activation but with less bifurcation. These results offer a unique view into the mechanism of metal-catalyzed allylic substitution.

Computational Exploration of the Mechanism of Critical Steps in the Biomimetic Synthesis of Preuisolactone A, and Discovery of New Ambimodal (5 + 2)/(4 + 2) Cycloadditions

Computational studies with ωB97X-D density functional theory of the mechanisms of the steps in Trauner's biomimetic synthesis of preuisolactone A have elaborated and refined mechanisms of several unique processes. An ambimodal transition state has been identified for the cycloaddition between an o-quinone and a hydroxy-o-quinone; this leads to both (5 + 2) (with H shift) and (4 + 2) cycloaddition products, which can in principle interconvert via α-ketol rearrangements. The origins of periselectivity of this ambimodal cycloaddition have been investigated computationally with molecular dynamics simulations and tested further by an experimental study. In the presence of bicarbonate ions, the deprotonated hydroxy-o-quinone leads to only the (5 + 2) cycloaddition adduct. A new mechanism for a benzilic acid rearrangement resulting in ring contraction is proposed.

Huisgen's 1,3-Dipolar Cycloadditions to Fulvenes Proceed via Ambimodal [6+4]/[4+2] Transition States

Huisgen's 1960 announcement of the concept of 1,3-dipolar cycloadditions was published the year before Alder's study of the reaction of diazomethane and dimethylfulvene. The diazomethane reaction was studied again in 1970 by Houk et al. and shown to give a [6+4] adduct. Padwa's nitrile ylide cycloaddition to dimethylfulvene (1978) gave [6+4] and [4+2] adducts. We performed computational studies of these reactions with density functional theory (DFT) and show that they involve ambimodal [6+4]/[4+2] transition states that can lead to either type of cycloadduct from one transition state. We dedicate this paper to the extraordinary life and humanity of Rolf Huisgen, and to the undying influence of his discoveries on chemistry.

Dynamical Trajectory Study of the Transannular [6+4] and Ambimodal Cycloaddition in the Biosynthesis of Heronamides

We report the dynamical trajectory study of the transannular [6+4] and ambimodal cycloaddition proposed in the biosynthesis of heronamide natural products. The originally proposed bifurcation of the potential energy surface is found to strongly favor the formation of the [6+4] product, both in the gas phase and in an explicit water environment, as evidenced by our trajectory simulations. The detailed information on how the bonds are formed and how water influences the bonding dynamics was analyzed at the femtosecond time scale.

Nonstatistical Reaction Dynamics

Nonstatistical dynamics is important for many chemical reactions. The Rice-Ramsperger-Kassel-Marcus (RRKM) theory of unimolecular kinetics assumes a reactant molecule maintains a statistical microcanonical ensemble of vibrational states during its dissociation so that its unimolecular dynamics are time independent. Such dynamics results when the reactant's atomic motion is chaotic or irregular. Intrinsic non-RRKM dynamics occurs when part of the reactant's phase space consists of quasiperiodic/regular motion and a bottleneck exists, so that the unimolecular rate constant is time dependent. Nonrandom excitation of a molecule may result in short-time apparent non-RRKM dynamics. For rotational activation, the 2J + 1 K levels for a particular J may be highly mixed, making K an active degree of freedom, or K may be a good quantum number and an adiabatic degree of freedom. Nonstatistical dynamics is often important for bimolecular reactions and their intermediates and for product-energy partitioning of bimolecular and unimolecular reactions. Post–transition state dynamics is often highly complex and nonstatistical.

Intramolecular vibrational energy redistribution and the quantum ergodicity transition: a phase space perspective

The onset of facile intramolecular vibrational energy flow can be related to features in the connected network of anharmonic resonances in the classical phase space.

AFIR explorations of transition states of extended unsaturated systems: automatic location of ambimodal transition states

Based on the artificial force induced reaction (AFIR) method, we proposed a procedure to systematically explore ambimodal transition states (TSs) that cause the dynamical bifurcation.

Prediction of the [4 + 2]- and [5 + 4]-cycloaddition reactions in zig-zag carbon nanotubes via an ambimodal transition state: density functional theory calculations

A unique type of chemical reaction known as an ambimodal reaction has drawn tremendous attention owing to its intriguing feature of forming multiple (two or more) products from the same (single) transition state. In contrast to conventional reactions, bifurcation of the potential energy surface takes place in ambimodal reactions. Density functional theory (DFT) based calculations were performed to probe the Diels–Alder (DA) cycloaddition reactions of various carbon nanotubes (CNTs) with 1,3-butadiene. The present investigation reveals the possibility of ambimodal transition state formation on a potential energy surface (PES) corresponding to an unusual [5 + 4]-cycloadduct along with the conventional [4 + 2]-cycloadduct. The ground state of the [5 + 4]-cycloadduct obtained from butadiene and the H-terminated CNTs is a triplet (³T) state, but on the other hand the [4 + 2]-cycloadduct is a singlet (¹S) state. The [5 + 4]-adduct is energetically more stable in comparison with the [4 + 2]-adduct. The possibility of the formation of the [5 + 4]-adduct is validated using frontier molecular orbitals. The length of the nanotube significantly influences the overall kinetics and thermodynamics of the reaction.

A DFT study has been performed to unveil the ambimodal reaction in H-terminated CNTs.

Bond Memory in Dynamically Determined Stereoselectivity

The carboborative ring contraction of cyclohexenes exhibits an abnormal selectivity pattern in which a formally concerted double migration gives rise to predominant but not exclusive inversion products. In dynamic trajectories, the inversion and retention products are formed from the same transition state, and the trajectories accurately account for the experimental product ratios. The unusual origin of the selectivity is the dynamically retained non-equivalence of newly formed versus pre-existing bonds after the first bond migration.

Rearrangement and nucleophilic trapping of bicyclo[4.1.0]hept-2-yl derived nonclassical bicyclobutenium ions

Here we describe the synthesis of two specifically labelled 13C isotopologues of cis-2-(4-nitrophenoxy)bicyclo[4.1.0]heptane and their solvolysis reactions in trifluoroethanol. By using one- and two-dimensional 1H- and 13C-NMR spectroscopy, we characterized the pathways for the rearrangement of these isotopologues to give 13C-labelled 4-(2,2,2-trifluoroethoxy)cycloheptene. We show that the initially formed cationic intermediate undergoes a degenerate rearrangement, which does not reach equilibrium before nucleophilic capture of the cation. Moreover, we show that the nonclassical carbocation, cyclohept-3-ene(3,1,4-deloc)ylium, gives an approximate 6:1 ratio of the cis- to trans-diastereomeric 2-(2,2,2-trifluoroethoxy)bicyclo[4.1.0]heptane as reaction intermediates that subsequently solvolyze to the 4-(2,2,2-trifluoroethoxy)cycloheptene product.