Reaction Path Bifurcations Research Articles

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.

Visualization of reaction route map and dynamical trajectory in reduced dimension.

In the quantum chemical approach, chemical reaction mechanisms are investigated based on a potential energy surface (PES). Automated reaction path search methods enable us to construct a global reaction route map containing multiple reaction paths corresponding to a series of elementary reaction processes. The on-the-fly molecular dynamics (MD) method provides a classical trajectory exploring the full-dimensional PES based on electronic structure calculations. We have developed two reaction analysis methods, the on-the-fly trajectory mapping method and the reaction space projector (ReSPer) method, by introducing a structural similarity to a pair of geometric structures and revealed dynamic aspects affecting chemical reaction mechanisms. In this review, we will present the details of these analysis methods and discuss the dynamics effects of reaction path curvature and reaction path bifurcation with applications to the CH3OH + OH- collision reaction and the Au5 cluster branching and isomerization reactions.

Dynamic Effects Responsible for High Selectivity in a [3,3] Sigmatropic Rearrangement Featuring a Bispericyclic Transition State.

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.

ChemInform Abstract: Chemistry in Motion—off the MEP

AbstractReview: [79 refs.

Reaction Path Bifurcation in an Electrocyclic Reaction: Ring-Opening of the Cyclopropyl Radical.

Following previous work [J. Chem. Phys. 2013, 139, 154108] on a simple model of a reaction with a post-transition state valley ridge inflection point, we study the chemically important example of the electrocyclic cyclopropyl radical ring-opening reaction using direct dynamics and a reduced dimensional potential energy surface. The overall reaction requires con- or disrotation of the methylenes, but the initial stage of the ring-opening involves substantial internal rotation of only one methylene. The reaction path bifurcation is then associated with the relative sense of rotation of the second methylene. Clear deviations of reactive trajectories from the disrotatory intrinsic reaction coordinate (IRC) for the ring-opening are observed and the dynamical mechanism is discussed. Several features observed in the model system are found to be preserved in the more complex and higher dimensional ring-opening reaction. Most notable is the sensitivity of the reaction mechanism to the shape of the potential manifested as a Newtonian kinetic isotope effect upon deuterium substitution of one of the methylene hydrogens. Dependence of the product yield on frictional dissipation representing external environmental effects is also presented. The dynamics of the post-transition state cyclopropyl radical ring-opening are discussed in detail, and the use of low dimensional models as tools to analyze complicated organic reaction mechanisms is assessed in the context of this reaction.

Ene–Diene Transmissive Cycloaddition Reactions with Singlet Oxygen: The Vinylogous Gem Effect and Its Use for Polyoxyfunctionalization of Dienes

The singlet oxygen reactivities and regioselectivities of the model compounds 1b-d were compared with those of the geminal (gem) selectivity model ethyl tiglate (1a). The kinetic cis effect is k(E)/k(Z) = 5.2 for the tiglate/angelate system 1a/1a' without a change in the high gem regioselectivity. Further conjugation to vinyl groups enabled mode-selective processes, namely, [4 + 2] cycloadditions versus ene reactions. The site-specific effects of methylation on the mode selectivity and the regioselectivity of the ene reaction were studied for dienes 1e-g. A vinylogous gem effect was observed for the γ,δ-dimethylated and α,γ,δ-trimethylated substrates 1h and 1i, respectively. The corresponding phenylated substrates 1j-l showed similar mode selectivity, as monomethylated 1j exhibited exclusively [4 + 2] reactivity while the tandem products 12 and 14 were isolated from the di- and trimethylated substrates 1k and 1l, respectively. The vinylogous gem effect favors the formation of 1,3-dienes from the substrates, and thus, secondary singlet oxygen addition was observed to give hydroperoxy-1,2-dioxenes 19 and 20 in an ene-diene transmissive cycloaddition sequence. These products were reduced to give alcohols (16, 17, and 18) or furans (24 and 25), respectively, or treated with titanium(IV) alkoxides to give the epoxy alcohols 26 and 27. The vinylogous gem effect is rationalized by DFT calculations showing that biradicals are the low-energy intermediates and that no reaction path bifurcations compete.

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.

Do we fully understand what controls chemical selectivity?

Reaction rates and product selectivity of kinetically controlled reactions are not always sufficiently described by standard RRKM or TST theory. Reactions taking place on potential energy surfaces featuring a valley ridge inflection point belong to this class of reactions. Though various research groups could show that reaction path bifurcations are far from being an exception in organic reactions the underlying principles that govern product distributions of those bifurcating reaction pathways are yet not fully understood. This Perspective has the intention to provide an overview of how far our understanding and the development of the theoretical foundation have progressed.

Theoretical and experimental studies of the dissociation dynamics of methaniminium cation, CH2NH2+→CHNH++H2: Reaction path bifurcation

The unimolecular dissociation of CH2NH2+ has been investigated experimentally and theoretically. Kinetic energy release distribution was obtained by analyzing the mass-analyzed ion kinetic energy profile. Critical configurations along the reaction path were investigated by electronic structure calculations at the HF, MP2, QCISD, and B3LYP levels using the 6-31G** and 6-311+G** basis sets. Reaction path bifurcation was observed at all the levels. The bifurcation point was in the entrance region (before the transition state) at the HF level. This point moved to the exit region when the electron correlation effect was included at the MP2, QCISD, and B3LYP levels. A global potential energy surface incorporating this bifurcation feature was constructed by interpolation at the MP2/6-311+G** level. Classical trajectories were calculated on this surface and product mode-specific energies were evaluated. Based on these data, various experimental observations, lack of hydrogen scrambling in particular, could be adequately explained.

Bifurcation of reaction pathways: the set of valley ridge inflection points of a simple three-dimensional potential energy surface

This paper serves for the better understanding of the branching phenomenon of reaction paths of potential energy hypersurfaces in more than two dimensions. We apply the recently proposed reduced gradient following (RGF) method for the analysis of potential energy hypersurfaces having valley-ridge inflection (VRI) points. VRI points indicate the region of possible reaction path bifurcation. The relation between RGF and the so-called global Newton search for stationary points (Branin method) is shown. Using a 3D polynomial test surface, a whole 1D manifold of VRI points is obtained. Its relation to RGF curves, steepest descent and gradient extremals is discussed as well as the relation of the VRI manifold to bifurcation points of these curves.

Some thoughts on reaction-path following

Errors in reaction-path following have been examined with the aid of a simple model surface and a local correction scheme has been proposed. Two new fourth-order explicit methods for reaction-path following have been developed, and two potential-energy surfaces with analytical reaction paths have been constructed. Some aspects of reaction-path bifurcation are also discussed.

Quantum mechanical study of a reaction path bifurcation model

The feasibility of close coupling techniques for bifurcation processes is investigated using a simple model. Density contours and a flux map illustrate the bifurcation process. The relevance of this study to the theory of three-dimensional chemical reactions is discussed.

Natural Bifurcation Coordinates for Three-Dimensional Chemical Reactions

Three-dimensional atom-diatom collisions which can lead to two possible rearrangement products are considered under the restraint of near-linear intermediates. A coordinate system (natural bifurcation coordinates) is introduced to provide for smooth internal rotation of the system in the region of reaction path bifurcation; thus systems are allowed to ``wobble'' from one reaction path to the other. For both two- and three-dimensional reactions, the Hamiltonian operator is derived from the classical kinetic energy.