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

A 21st Century View of Allowed and Forbidden Electrocyclic Reactions

In 1965, Woodward and Hoffmann proposed a theory to predict the stereochemistry of electrocyclic reactions, which, after expansion and generalization, became known as the Woodward-Hoffmann Rules. Subsequently, Longuet-Higgins and Abrahamson used correlation diagrams to propose that the stereoselectivity of electrocyclizations could be explained by the correlation of reactant and product orbitals with the same symmetry. Immediately thereafter, Hoffmann and Woodward applied correlation diagrams to explain the mechanism of cycloadditions. We describe these discoveries and their evolution. We now report an investigation of various electrocyclic reactions using DFT and CASSCF. We track the frontier molecular orbitals along the intrinsic reaction coordinate and modeled trajectories and examine the correlation between HOMO and LUMO for thermally forbidden systems. We also investigate the electrocyclizations of several highly polarized systems for which the Houk group had predicted that donor-acceptor substitution can induce zwitterionic character, thereby providing low-energy pathways for formally forbidden reactions. We conclude with perspectives on the field of pericyclic reactions, including a refinement as the meaning of Woodward and Hoffmann's "Violations. There are none!" Lastly, we comment on the burgeoning influence of computations on all fields of chemistry.

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.

Understanding chemistry: from "heuristic (soft) explanations and reasoning by analogy" to "quantum chemistry"

"Soft theories," i.e., "heuristic models based on reasoning by analogy" largely drove chemistry understanding for 150 years or more. But soft theories have their limitations and with the expansion of chemistry in the mid-20th century, more and more inexplicable (by soft theory) experimental results were being obtained. In the past 50 years, quantum chemistry, most often in the guise of applied theoretical chemistry including computational chemistry, has provided (a) the underlying "hard evidence" for many soft theories and (b) the explanations for chemical phenomena that were unavailable by soft theories. In this publication, we define "hard theories" as "theories derived from quantum chemistry." Both soft and hard theories can be qualitative and quantitative, and the "Houk quadrant" is proposed as a helpful categorization tool. Furthermore, the language of soft theories is often used appropriately to describe quantum chemical results. A valid and useful way of doing science is the appropriate use and application of both soft and hard theories along with the best nomenclature available for successful communication of results and ideas.

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.

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.

Phase space geometry of isolated to condensed chemical reactions

The complexity of gas and condensed phase chemical reactions has generally been uncovered either approximately through transition state theories or exactly through (analytic or computational) integration of trajectories. These approaches can be improved by recognizing that the dynamics and associated geometric structures exist in phase space, ensuring that the propagator is symplectic as in velocity-Verlet integrators and by extending the space of dividing surfaces to optimize the rate variationally, respectively. The dividing surface can be analytically or variationally optimized in phase space, not just over configuration space, to obtain more accurate rates. Thus, a phase space perspective is of primary importance in creating a deeper understanding of the geometric structure of chemical reactions. A key contribution from dynamical systems theory is the generalization of the transition state (TS) in terms of the normally hyperbolic invariant manifold (NHIM) whose geometric phase-space structure persists under perturbation. The NHIM can be regarded as an anchor of a dividing surface in phase space and it gives rise to an exact non-recrossing TS theory rate in reactions that are dominated by a single bottleneck. Here, we review recent advances of phase space geometrical structures of particular relevance to chemical reactions in the condensed phase. We also provide conjectures on the promise of these techniques toward the design and control of chemical reactions.

Machine learning classification of disrotatory IRC and conrotatory non-IRC trajectory motion for cyclopropyl radical ring opening

Quasiclassical trajectory analysis is now a standard tool to analyze non-minimum energy pathway motion of organic reactions. However, due to the large amount of information associated with trajectories, quantitative analysis of the dynamic origin of reaction selectivity is complex. For the electrocyclic ring opening of cyclopropyl radical, more than 4000 trajectories were run showing that allyl radicals are formed through a mixture of disrotatory intrinsic reaction coordinate (IRC) motion as well as conrotatory non-IRC motion. Geometric, vibrational mode, and atomic velocity transition-state features from these trajectories were used for supervised machine learning analysis with classification algorithms. Accuracy >80% with a random forest model enabled quantitative and qualitative assessment of transition-state trajectory features controlling disrotatory IRC versus conrotatory non-IRC motion. This analysis revealed that there are two key vibrational modes where their directional combination provides prediction of IRC versus non-IRC motion.

Dynamics and decay rates of a time-dependent two-saddle system

The framework of transition state theory (TST) provides a powerful way for analyzing the dynamics of physical and chemical reactions. While TST has already been successfully used to obtain reaction rates for systems with a single time-dependent saddle point, multiple driven saddles have proven challenging because of their fractal-like phase space structure. This paper presents the construction of an approximately recrossing-free dividing surface based on the normally hyperbolic invariant manifold in a time-dependent two-saddle model system. Based on this, multiple methods for obtaining instantaneous (time-resolved) decay rates of the underlying activated complex are presented and their results discussed.

Photodissociation Dynamics of CO-Forming Channels on the Ground-State Surface of Methyl Formate at 248 nm: Direct Dynamics Study and Assessment of Generalized Multicenter Impulsive Models

The photodissociation dynamics of methyl formate in the electronic ground state S₀, initiated by a 248 nm-wavelength laser, is studied by direct dynamics simulations. We analyze five channels, where four of them have as products CH₃OH + CO, one leading to the formation of three fragments, H₂CO + H₂ + CO, and a channel characterized by a roaming transition state. The analysis of energy distribution among the degrees of freedom of the product and the comparison with experimental results previously published by other groups provide the ingredients to distinguish the examined dissociation pathways. The interpretation of the results proves that the characterization of dissociation mechanisms must rely on a dynamics approach involving multiple electronic states, including considerations on the features of the S₁/S₀ conical intersection. Here, we also assess the generalized multicenter impulsive model, GMCIM, that has been designed for dissociation processes with exit barriers, and the energy distribution in the products is predicted on the basis of information from the saddle points and the intrinsic reaction coordinates. Main features, advantages, limits, and future perspectives of the method are reported and discussed.

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.

Understanding and Predicting Post H-Atom Abstraction Selectivity through Reactive Mode Composition Factor Analysis

The selective functionalization of C-H bonds is one of the Grails of synthetic chemistry. In this work, we demonstrate that the selectivity toward fast hydroxylation or radical diffusion (known as the OH-rebound and dissociation mechanisms) following H-atom abstraction (HAA) from a substrate C-H bond by high-valent iron-oxo oxidants is already encoded in the HAA step when the post-HAA barriers are much lower than the preceding one. By applying the reactive mode composition factor (RMCF) analysis, which quantifies the kinetic energy distribution (KED) at the reactive mode (RM) of transition states, we show that reactions following the OH-rebound coordinate concentrate the RM kinetic energy on the motion of the reacting oxygen atom and the nascent substrate radical, whereas reactions following the dissociation channel localize most of their kinetic energy in H-atom motion. These motion signatures serve to predict the post-HAA selectivity, and since KED is affected by the free energy of reaction and asynchronicity (factor η) of HAA, we show that bimolecular HAA reactions in solution that are electron transfer-driven and highly exergonic have the lowest fraction of KED on the transferred H-atom and the highest chance to follow rebound hydroxylation. Finally, the RMCF analysis predicts that the H/D primary kinetic isotope effect can serve as a probe for these mechanisms, as confirmed in virtually all reported examples in the literature.

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.

Mechanisms and Beyond: Elucidation of Fluxional Dynamics by Exchange NMR Spectroscopy

Detailed mechanistic information is crucial to our understanding of reaction pathways and selectivity. Dynamic exchange NMR techniques, in particular 2D exchange spectroscopy (EXSY) and its modifications, provide indispensable intricate information on the mechanisms of organic and inorganic reactions and other phenomena, for example, the dynamics of interfacial processes. In this Review, key results from exchange NMR studies of small molecules over the last few decades are systemised and discussed. After a brief introduction to the theory, the key types of dynamic processes are identified and fundamental examples given of intra- and intermolecular reactions, which, in turn, could involve, or not, bond-making and bond-breaking events. Following that logic, internal molecular rotation, intramolecular stereomutation and molecular recognition will first be considered because they do not typically involve bond breaking. Then, rearrangements, substitution-type reactions, cyclisations, additions and other processes affecting chemical bonds will be discussed. Finally, interfacial molecular dynamics and unexpected combinations of different types of fluxional processes will also be highlighted. How exchange NMR spectroscopy helps to identify conformational changes, coordination and molecular recognition processes as well as quantify reaction energy barriers and extract detailed mechanistic information by using reaction rate theory in conjunction with computational techniques will be shown.

Lagrangian descriptors of driven chemical reaction manifolds

The persistence of a transition state structure in systems driven by time-dependent environments allows the application of modern reaction rate theories to solution-phase and nonequilibrium chemical reactions. However, identifying this structure is problematic in driven systems and has been limited by theories built on series expansion about a saddle point. Recently, it has been shown that to obtain formally exact rates for reactions in thermal environments, a transition state trajectory must be constructed. Here, using optimized Lagrangian descriptors [G. T. Craven and R. Hernandez, Phys. Rev. Lett. 115, 148301 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.148301], we obtain this so-called distinguished trajectory and the associated moving reaction manifolds on model energy surfaces subject to various driving and dissipative conditions. In particular, we demonstrate that this is exact for harmonic barriers in one dimension and this verification gives impetus to the application of Lagrangian descriptor-based methods in diverse classes of chemical reactions. The development of these objects is paramount in the theory of reaction dynamics as the transition state structure and its underlying network of manifolds directly dictate reactivity and selectivity.

Post-transition state bifurcations gain momentum – current state of the field

The existence of post-transition state bifurcations on potential energy surfaces for organic and biological reaction mechanisms has been known for decades, but recently, new reports of bifurcations have been occurring at a much higher rate. Beyond simply discovering bifurcations, computational chemists are developing techniques to understand what aspects of molecular structure and vibrations control the product selectivity in systems containing bifurcations. For example, the distribution of products seen in simulations has been found to be extremely sensitive to the local environment of the reacting system (i.e. the presence of a catalyst, enzyme, or explicit solvent molecules). The outlook for the future of this field is discussed, with an eye towards the application of the principles discussed here by experimental chemists to design a reaction setup to efficiently generate desired products.

Perspective: chemical dynamics simulations of non-statistical reaction dynamics

Non-statistical chemical dynamics are exemplified by disagreements with the transition state (TS), RRKM and phase space theories of chemical kinetics and dynamics. The intrinsic reaction coordinate (IRC) is often used for the former two theories, and non-statistical dynamics arising from non-IRC dynamics are often important. In this perspective, non-statistical dynamics are discussed for chemical reactions, with results primarily obtained from chemical dynamics simulations and to a lesser extent from experiment. The non-statistical dynamical properties discussed are: post-TS dynamics, including potential energy surface bifurcations, product energy partitioning in unimolecular dissociation and avoiding exit-channel potential energy minima; non-RRKM unimolecular decomposition; non-IRC dynamics; direct mechanisms for bimolecular reactions with pre- and/or post-reaction potential energy minima; non-TS theory barrier recrossings; and roaming dynamics.This article is part of the themed issue 'Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces'.

Cryptic post-transition state bifurcations that reduce the efficiency of lactone-forming Rh-carbenoid C-H insertions

Post-transition state bifurcations are described that lead to unexpected byproducts in Rh-promoted C–H insertion reactions.

Byproducts of chemical reactions are generally thought to result from the competition between two reaction pathways, each with its own rate-determining transition state structure. We show here, however, that pathways with a single transition state structure followed by a post-transition state bifurcation may also be a source of undesired products, especially those whose appearance is unexpected. The viability of this scenario for intramolecular C–H insertion reactions affording β-lactones via Rh-carbenoid intermediates is assessed through quantum chemical calculations on potential energy surfaces and quasi-classical molecular dynamics simulations. It appears that, in these cases, the rhodium catalyst is to blame for the accessibility of a second, unintended, pathway following the transition state structure for β-lactone formation that leads to fragmentation to a ketene and carbonyl compound. If an unexpected product is formed via a post-transition state bifurcation, conventional strategies for suppressing its formation are unlikely to succeed. Guidelines for recognizing the presence of a post-transition state bifurcation are described here, along with hints at means for controlling product distributions.

Deconstructing field-induced ketene isomerization through Lagrangian descriptors

Phase space contours (shown in color) constructed using the method of Lagrangian descriptors resolve the separatrices governing state transitions on the reaction-path potential energy surface (shown in white) for field-induced ketene isomerization.