Post-transition State Bifurcation Research Articles

Molecular dynamics simulation study of post‐transition state bifurcation: A case study on the ambimodal transition state of dipolar/Diels–Alder cycloaddition

AbstractThe potential energy surfaces for the reactions of 1,3‐butadiene with 2‐hydroxythioacrolein and 2‐aminoacrolein exhibit ambimodal transition states leading to both dipolar (4 + 3) and Diels–Alder (4 + 2) cycloaddition products, thereby demonstrating a post transition state bifurcation feature. We have investigated the bifurcation dynamics of these reactions using three molecular dynamics (MD) methods: quasi‐classical trajectory, classical MD, and ring‐polymer MD simulations. The trajectory calculations were performed with the semiempirical GFN2‐xTB method with the element‐specific parameters optimized to reproduce the density‐functional theory calculations. The effect of water solvation was examined using an implicit solvation model, revealing significant differences in bifurcation dynamic between gas‐phase and solution‐phase reactions. Nuclear quantum effects were found to play a crucial role in the proton‐transfer process from the (4 + 3) intermediate to the (4 + 3) product in the case of the 2‐aminoacrolein reaction.

Dynamically or Kinetically Controlled? Computational Study of the Mechanisms of Electrophilic Aminoalkenylation of Heteroaromatics with Keteniminium Ions.

Quantum chemical calculations and molecular dynamics simulations were applied to study the electrophilic aminoalkenylation of heteroaromatics with keniminium ions. Post-transition state bifurcation (PTSB) was found in the electrophilic addition step for the aminoalkenylation of pyrroles and indoles, and the selectivity for these reactions was dynamically controlled. However, the aminoalkenylation of furan was kinetically controlled because no apparent PTSB was found in the electrophilic addition step. The substituents on the keteniminium ions can also affect the dynamic results for the aminoalkenylations to pyrroles: the C2-aminoalkenylated product is much more favored over the C3-aminoalkenylated product for keteniminium ions with electron-donating substituents, while the product ratio (C2 product/C3 product) decreased when stronger electron-withdrawing substituents were applied.

Machine learning‐assisted study of correlation between post‐transition‐state bifurcation and initial phase information at the ambimodal transition state

AbstractThe Diels–Alder cycloaddition of cyclopentadiene and nitroethene, the intramolecular cycloaddition between a diene and triene, and the Diels–Alder cycloaddition of 2‐hydroxyacrolein with 1,3‐butadiene involving post‐transition‐state bifurcation (PTSB) were studied. These cycloaddition reactions were investigated using quasi‐classical trajectory (QCT), classical molecular dynamics (MD), ring‐polymer molecular dynamics (RPMD) simulations, and supervised machine‐learning binary classification techniques. Room‐temperature dynamics simulations started from the ambimodal transition state (TS) using the QCT, classical MD, and RPMD methods presented similar dynamics. Binary classification revealed that the initial geometry displacement from the ambimodal TS for the Diels–Alder cycloaddition of cyclopentadiene and nitroethene contributed to the branching dynamics and that the initial momenta for the intramolecular cycloaddition between a diene and triene and the Diels–Alder cycloaddition of 2‐hydroxyacrolein with 1,3‐butadiene played a significant role in the bifurcation dynamics.

Molecular dynamics simulations and machine-learning assisted study of the reaction path bifurcation: Application to the intramolecular Diels–Alder cycloaddition between cyclobutadiene and butadiene

The intramolecular Diels–Alder cycloaddition between cyclobutadiene and butadiene, which involves post-transition-state bifurcation (PTSB), has been investigated using the ring-polymer molecular dynamics (RPMD), classical MD and quasi-classical trajectory (QCT) simulations, and supervised machine-learning (ML) technique. The branching fraction of this reaction strongly depends on the simulation temperature. While QCT, classical MD and RPMD simulations performed at room temperature, starting from the ambimodal transition state (TS), showed the similar dynamics, QCT overestimated the minor branching fraction at low temperature. The supervised machine-learning analysis revealed that the initial coordinates and momenta for low frequency modes at the ambimodal TS contribute to the branching dynamics. The classical MD and RPMD methods follow similar conditions to quantum Boltzmann distributions, whereas the artificially localized phase distribution, considering that the zero-point energy is wedged into the classical particles. As a result, the QCT method can provide inadequate bifurcation dynamics, such as the overestimation of the minor product.

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.

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.

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.

Post-Transition State Bifurcation in Iron-Catalyzed Arene Aminations

Recently, an iron-catalyzed meta-selective arene amination strategy was reported to show excellent regiocontrol, operational simplicity, and high atom and cost efficiencies. In this work, density functional theory (DFT) calculations and quasiclassical molecular dynamics (MD) simulations were carried out to study the mechanism of this reaction. Our computations revealed an unreported ambimodal attack of arene by hydroxylamine-O-sulfate, which forms not only σ-complex via electrophilic addition but also an aziridinium intermediate through energetically concerted electrophilic–nucleophilic additions. Quasiclassical trajectories suggest the orientation of the attacking NH2+ group with respect to arene control: (a) site selectivity of the post-transition state nucleophilic attack and (b) σ-complex/aziridinium selectivity on the bifurcating surface. The final amination products can be favorably generated via the ring opening of aziridinium intermediates, rearrangement of σ-complexes, and deprotonation of the resultant carbocations. Overall, our study illustrates a novel pathway in which an ambimodal reaction is incorporated into the standard SEAr mechanism.

Tuning the branching ratio in a symmetric potential energy surface with a post-transition state bifurcation using external time dependence

Chemical selectivity, as quantified by a branching ratio, is a phenomenon relevant for many organic chemical reactions. It may be exhibited on a potential energy surface (PES) that features a valley-ridge inflection point (VRI) in the region between two sequential index-1 saddles, with one saddle having higher energy than the other. Reaction occurs when a trajectory crosses the region of the higher energy saddle (the “entrance channel”) and approaches the lower energy saddle. On both sides of the lower energy saddle, there are two wells and the question we address is that given an initial ensemble of trajectories, what is the relative fraction of trajectories that enter each well. For a symmetric PES this fraction is 1:1. We consider a symmetric PES subject to a time-periodic forcing characterized by an amplitude, frequency, and phase. In this letter we analyze how the branching ratio depends on these three parameters.

Dynamically Bifurcating Hydride Transfer Mechanism and Origin of Inverse Isotope Effect for Heterodinuclear AgRu-Catalyzed Alkyne Semihydrogenation

The mechanism and heterodinuclear cooperative effects for AgRu-catalyzed alkyne semihydrogenation were analyzed with density-functional theory (DFT) and experiment. This combined effort revealed the following: (1) AgRu-catalyzed diphenylacetylene hydrogenation initially gives a kinetic mixture of cis-stilbene and trans-stilbene by an ionic Ag–H hydride transfer transition state and post-transition state bifurcation, which was identified by quasiclassical direct dynamics simulations. (2) The hydrogenation reaction exhibits an unexpected inverse kinetic isotope effect (KIE < 1) resulting from an inverse equilibrium isotope effect (EIE) for heterodinuclear H2/D2 activation. (3) The Ag–Ru heterodinuclear cooperative effective is critical for both H2 activation and vinylsilver protonolysis reaction steps. (4) Rate studies and computational analysis show that electron-donating groups accelerate catalysis.

Pathway Bifurcation in the (4 + 3)/(5 + 2)-Cycloaddition of Butadiene and Oxidopyrylium Ylides: The Significance of Molecular Orbital Isosymmetry.

By drawing analogies from the dimerization 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 rationalized. Finally, the isosymmetry of the oxidopyrylium and cyclopentadiene molecular orbitals as well as the presence of "secondary orbital interactions" are emphasized as the common source of nonstatistical behavior. Application of these principles will allow for the rapid identification of new reaction pathway bifurcations.

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

Summary 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.

Rearrangement of Hydroxylated Pinene Derivatives to Fenchone-Type Frameworks: Computational Evidence for Dynamically-Controlled Selectivity.

An acid-catalyzed Prins/semipinacol rearrangement cascade reaction of hydroxylated pinene derivatives that leads to tricyclic fenchone-type scaffolds in very high yields and diastereoselectivity has been developed. Quantum chemical analysis of the selectivity-determining step provides support for the existence of an extremely flat potential energy surface around the transition state structure. This transition state structure appears to be ambimodal, i.e., the fenchone-type tricyclic scaffolds are formed in preference to the competing formation of a bornyl (camphor-type) skeleton under dynamic control via a post-transition state bifurcation (PTSB).

Post-transition state bifurcations induce dynamical detours in Pummerer-like reactions.

A post-transition state bifurcation (PTSB) involved in a Pummerer-type rearrangement is characterized using density functional theory (DFT) calculations on potential energy stationary points and direct dynamics simulations. A sensitivity of the ratio of products produced via this PTSB to solvent dielectric constant is revealed and implications of such a dependence for selectivity control of organic reactions are discussed.

Computational evidence for a reaction pathway bifurcation in Sasaki-type (4 + 3)-cycloadditions.

The current report seeks to validate the existence of a post-transition state bifurcation in the Lewis acid-catalysed (4 + 3)-cycloaddition of butadiene and α-methoxy acrolein. Cycloaddition transition state (TS) structures are shown by intrinsic reaction coordinate (IRC) and potential energy surface (PES) scan calculations to connect directly to both (4 + 3)- and (4 + 2)-products. A second TS, a 1,2-sigmatropic shift which interconverts the products, was also located. Implicit solvent is observed to have a substantial effect of the course of the reaction, with the minimum energy path from the gas phase TS leading to (4 + 2)-product whereas the DCM solvent phase TS leads to (4 + 3)-product. On the basis of these data it is suggested that a number of previously reported (4 + 3)-cycloadditions may also possess reaction pathway bifurcations.

Nonstatistical dynamics on potentials exhibiting reaction path bifurcations and valley-ridge inflection points

We study reaction dynamics on a model potential energy surface exhibiting post-transition state bifurcation in the vicinity of a valley ridge inflection (VRI) point. We compute fractional yields of products reached after the VRI region is traversed, both with and without dissipation. It is found that apparently minor variations in the potential lead to significant changes in the reaction dynamics. Moreover, when dissipative effects are incorporated, the product ratio depends in a complicated and highly non-monotonic fashion on the dissipation parameter. Dynamics in the vicinity of the VRI point itself play essentially no role in determining the product ratio, except in the highly dissipative regime.