Prediction of Kinetic Product Ratios: Investigation of a Dynamically Controlled Case.

Of the various factors influencing kinetically controlled product ratios, the role of nonstatistical dynamics is arguably the least well understood. In this paper, reactions were chosen in which dynamics played a dominant role in product selection, by design. Specifically, the reactions studied were the ring openings of cyclopropylidene to allene and tetramethylcyclopropylidene to tetramethylallene (2,4-dimethylpenta-2,3-diene). Both reactions have intrinsic reaction coordinates that bifurcate symmetrically, leading to products that are enantiomeric once the atoms are uniquely labeled. The question addressed in the study was whether the outcomes─that is, which product well on the potential energy surface was selected─could be predicted from their initial conditions for individual trajectories in quasiclassical dynamics simulations. Hybrid potentials were developed based on cooperative interaction between molecular mechanics and artificial neural networks, trained against data from electronic structure calculations. These potentials allowed simulations of both gas-phase and condensed-phase reactions. The outcome was that, for both reactions, prediction of initial selection of product wells could be made with >95% success from initial conditions of the trajectories in the gas phase. However, when trajectories were run for longer, looking for "final" products for each trajectory, the predictability dropped off dramatically. In the gas-phase simulations, this drop off was caused by trajectories hopping between product wells on the potential energy surface. That behavior could be suppressed in condensed phases, but then new uncertainty was introduced because the intermolecular interactions between solute and bath, necessary to permit intermolecular energy transfer and cooling of the hot initial products, often led to perturbations of the initial directions of trajectories on the potential energy surface. It would consequently appear that a general ability to predict outcomes for reactions in which nonstatistical dynamics dominate remains a challenge even in the age of sophisticated machine-learning capabilities.

A Conical Intersection Influences the Ground State Rearrangement of Fulvene to Benzene.

The rearrangement of fulvene to benzene is believed to play an important role in the formation of soot during hydrocarbon combustion. Previous work has identified two possible mechanisms for the rearrangement─a unimolecular path and a hydrogen-atom-assisted, bimolecular path. Computational results to date have suggested that the unimolecular mechanism faces a barrier of about 74 kcal/mol, which makes it unable to compete with the bimolecular mechanism under typical combustion conditions. This computed barrier is about 10 kcal/mol higher than the experimental value, which is an unusually large discrepancy for modern electronic structure theory. In the present work, we have reinvestigated the unimolecular mechanism computationally, and we have found a second transition state that is approximately 10 kcal/mol lower in energy than the previously identified one and, therefore, in excellent agreement with the experimental value. The existence of two transition states for the same rearrangement arises because there is a conical intersection between the two lowest singlet states which occurs in the vicinity of the reaction coordinates. The two possible paths around the cone on the lower adiabatic surface give rise to the two distinct saddle points. The lower barrier for the unimolecular mechanism now makes it competitive with the bimolecular one, according to our calculations. In support of this conclusion, we have reanalyzed some previous experimental results on anisole pyrolysis, which leads to benzene as a significant product and have shown that the unimolecular and bimolecular mechanisms for fulvene → benzene must be occurring competitively in that system. Finally, we have identified that similar conical intersections arise during the isomerizations of benzofulvene and isobenzofulvene to naphthalene.

Low dimensional representations along intrinsic reaction coordinates and molecular dynamics trajectories using interatomic distance matrices.

Most chemical transformations (reactions or conformational changes) that are of interest to researchers have many degrees of freedom, usually too many to visualize without reducing the dimensionality of the system to include only the most important atomic motions. In this article, we describe a method of using Principal Component Analysis (PCA) for analyzing a series of molecular geometries (e.g., a reaction pathway or molecular dynamics trajectory) and determining the reduced dimensional space that captures the most structural variance in the fewest dimensions. The software written to carry out this method is called PathReducer, which permits (1) visualizing the geometries in a reduced dimensional space, (2) determining the axes that make up the reduced dimensional space, and (3) projecting the series of geometries into the low-dimensional space for visualization. We investigated two options to represent molecular structures within PathReducer: aligned Cartesian coordinates and matrices of interatomic distances. We found that interatomic distance matrices better captured non-linear motions in a smaller number of dimensions. To demonstrate the utility of PathReducer, we have carried out a number of applications where we have projected molecular dynamics trajectories into a reduced dimensional space defined by an intrinsic reaction coordinate. The visualizations provided by this analysis show that dynamic paths can differ greatly from the minimum energy pathway on a potential energy surface. Viewing intrinsic reaction coordinates and trajectories in this way provides a quick way to gather qualitative information about the pathways trajectories take relative to a minimum energy path. Given that the outputs from PCA are linear combinations of the input molecular structure coordinates (i.e., Cartesian coordinates or interatomic distances), they can be easily transferred to other types of calculations that require the definition of a reduced dimensional space (e.g., biased molecular dynamics simulations).

Environmental Processing of Lipids Driven by Aqueous Photochemistry of α-Keto Acids.

Sunlight can initiate photochemical reactions of organic molecules though direct photolysis, photosensitization, and indirect processes, often leading to complex radical chemistry that can increase molecular complexity in the environment. α-Keto acids act as photoinitiators for organic species that are not themselves photoactive. Here, we demonstrate this capability through the reaction of two α-keto acids, pyruvic acid and 2-oxooctanoic acid, with a series of fatty acids and fatty alcohols. We show for five different cases that a cross-product between the photoinitiated α-keto acid and non-photoactive species is formed during photolysis in aqueous solution. Fatty acids and alcohols are relatively unreactive species, which suggests that α-keto acids are able to act as radical initiators for many atmospherically relevant molecules found in the sea surface microlayer and on atmospheric aerosol particles.

Empirical Classification of Trajectory Data: An Opportunity for the Use of Machine Learning in Molecular Dynamics.

Classical Hamiltonian trajectories are initiated at random points in phase space on a fixed energy shell of a model two degrees of freedom potential, consisting of two interacting minima in an otherwise flat energy plane of infinite extent. Below the energy of the plane, the dynamics are demonstrably chaotic. However, most of the work in this paper involves trajectories at a fixed energy that is 1% above that of the plane, in which regime the dynamics exhibit behavior characteristic of chaotic scattering. The trajectories are analyzed without reference to the potential, as if they had been generated in a typical direct molecular dynamics simulation. The questions addressed are whether one can recover useful information about the structures controlling the dynamics in phase space from the trajectory data alone, and whether, despite the at least partially chaotic nature of the dynamics, one can make statistically meaningful predictions of trajectory outcomes from initial conditions. It is found that key unstable periodic orbits, which can be identified on the analytical potential, appear by simple classification of the trajectories, and that the specific roles of these periodic orbits in controlling the dynamics are also readily discerned from the trajectory data alone. Two different approaches to predicting trajectory outcomes from initial conditions are evaluated, and it is shown that the more successful of them has ∼90% success. The results are compared with those from a simple neural network, which has higher predictive success (97%) but requires the information obtained from the "by-hand" analysis to achieve that level. Finally, the dynamics, which occur partly on the very flat region of the potential, show characteristics of the much-studied phenomenon called "roaming." On this potential, it is found that roaming trajectories are effectively "failed" periodic orbits and that angular momentum can be identified as a key controlling factor, despite the fact that it is not a strictly conserved quantity. It is also noteworthy that roaming on this potential occurs in the absence of a "roaming saddle," which has previously been hypothesized to be a necessary feature for roaming to occur.

Mechanistic Description of Photochemical Oligomer Formation from Aqueous Pyruvic Acid.

The aqueous phase photochemistry of pyruvic acid, an important oxidation product of isoprene, is known to generate larger oligomeric species that may contribute to the formation of secondary organic aerosol in the atmosphere. Using high resolution negative mode electrospray ionization mass spectrometry, the aqueous photochemistry of dilute solutions of pyruvic acid (10, 1, and 0.5 mM) under anaerobic conditions was investigated. Even at the lowest concentration, covalently bonded dimers and trimers of pyruvic acid were observed as photochemical products. We calculate that it is energetically possible to photochemically generate parapyruvic acid, a dimer of pyruvic acid that is known to form via dark oligomerization processes. Subsequent photochemical reactions of parapyruvic acid with pyruvic acid form larger oligomeric products, such as 2,4-dihydroxy-2-methyl-5-oxohexanoic acid. A robust and relatively simple photochemical mechanism is discussed that explains both the conditional dependence and wide array of products that are observed.

Photochemical Synthesis of Oligomeric Amphiphiles from Alkyl Oxoacids in Aqueous Environments.

The aqueous phase photochemistry of a series of amphiphilic α-keto acids with differing linear alkyl chain lengths was investigated, demonstrating the ability of sunlight-initiated reactions to build molecular complexity under environmentally relevant conditions. We show that the photochemical reaction mechanisms for α-keto acids in aqueous solution are robust and generalizable across alkyl chain lengths. The organic radicals generated during photolysis are indiscriminate, leading to a large mixture of photoproducts that are observed using high-resolution electrospray ionization mass spectrometry, but these products are identifiable following literature photochemical mechanisms. The alkyl oxoacids under study here can undergo a Norrish Type II reaction to generate pyruvic acid, increasing the diversity of observed photoproducts. The major products of this photochemistry are covalently bonded dimers and trimers of the starting oxoacids, many of which are multi-tailed lipids. The properties of these oligomers are discussed, including their spontaneous self-assembly into aggregates.

Roaming: A Phase Space Perspective.

In this review we discuss the recently described roaming mechanism for chemical reactions from the point of view of nonlinear dynamical systems in phase space. The recognition of the roaming phenomenon shows the need for further developments in our fundamental understanding of basic reaction dynamics, as is made clear by considering some questions that cut across most studies of roaming: Is the dynamics statistical? Can transition state theory be applied to estimate roaming reaction rates? What role do saddle points on the potential energy surface play in explaining the behavior of roaming trajectories? How do we construct a dividing surface that is appropriate for describing the transformation from reactants to products for roaming trajectories? How should we define the roaming region? We show that the phase space perspective on reaction dynamics provides the setting in which these questions can be properly framed and answered. We illustrate these ideas by considering photodissociation of formaldehyde. The phase-space formulation allows an unambiguous description of all possible reactive events, which also allows us to uncover the phase space mechanism that explains which trajectories roam, as opposed to evolving toward a different reactive event.

Chemical Equilibria and Kinetics in Aqueous Solutions of Zymonic Acid.

The chemistry of pyruvic acid is of great interest due to its essential role in metabolism for all life and its role in atmospheric chemistry. Pyruvic acid under a wide range of conditions, including normal storage conditions, will spontaneously dimerize to form zymonic acid. We isolated zymonic acid and, using a variety of 1D and 2D NMR techniques, identified it as a single structure as a solid or dissolved in DMSO. When in aqueous solution, however, we identified a mixture of five different tautomers and hydrates in equilibrium with each other with no single dominant form. The kinetics of this conversion were studied in situ via NMR. The reactivity of the tautomers and hydrates in aqueous solution is investigated and discussed in terms of aqueous reaction mechanisms. There is strong evidence for a direct, reversible conversion from an enol to a geminal diol without passing through a ketone intermediate, which implies the reversible addition of water across a double bond under ambient conditions. Additionally, there is evidence for a base catalyzed lactone ring formation, which is in essence a base catalyzed esterification reaction. The equilibrium between pyruvic acid and its oligomers in aqueous solution is of consequence in the natural environment.

Gas-Phase Photolysis of Pyruvic Acid: The Effect of Pressure on Reaction Rates and Products.

In this work, we investigate the impact of pressure and oxygen on the kinetics of and products from the gas-phase photolysis of pyruvic acid. The results reveal a decrease in the photolysis quantum yield as pressure of air or nitrogen is increased, a trend not yet documented in the literature. A Stern-Volmer analysis demonstrates this effect is due to deactivation of the singlet state of pyruvic acid when the photolysis is performed in nitrogen, and from quenching of both the singlet and triplet state in air. Consistent with previous studies, acetaldehyde and CO2 are observed as the major products; however, other products, most notably acetic acid, are also identified in this work. The yield of acetic acid increases with increasing pressure of buffer gas, an effect that is amplified by the presence of oxygen. At least two mechanisms are necessary to explain the acetic acid, including one that requires reaction of photolysis intermediates with O2. These findings extend the fundamental understanding of the gas-phase photochemistry of pyruvic acid, highlighting the importance of pressure on the photolysis quantum yields and products.

The Study of Reactive Intermediates in Condensed Phases.

Novel experimental techniques and computational methods have provided new insight into the behavior of reactive intermediates in solution. The results of these studies show that some of the earlier ideas about how reactive intermediates ought to behave in solution were incomplete or even incorrect. This Perspective summarizes the new experimental and computational methods and draws attention to the shortcomings that their application has brought to light in previous models. Key areas needing further research are highlighted.

Toward Understanding the Roaming Mechanism in H + MgH → Mg + HH Reaction.

The roaming mechanism in the reaction H + MgH →Mg + HH is investigated by classical and quantum dynamics employing an accurate ab initio three-dimensional ground electronic state potential energy surface. The reaction dynamics are explored by running trajectories initialized on a four-dimensional dividing surface anchored on three-dimensional normally hyperbolic invariant manifold associated with a family of unstable orbiting periodic orbits in the entrance channel of the reaction (H + MgH). By locating periodic orbits localized in the HMgH well or involving H orbiting around the MgH diatom, and following their continuation with the total energy, regions in phase space where reactive or nonreactive trajectories may be trapped are found. In this way roaming reaction pathways are deduced in phase space. Patterns similar to periodic orbits projected into configuration space are found for the quantum bound and resonance eigenstates. Roaming is attributed to the capture of the trajectories in the neighborhood of certain periodic orbits. The complex forming trajectories in the HMgH well can either return to the radical channel or "roam" to the MgHH minimum from where the molecule may react.

Phase space barriers and dividing surfaces in the absence of critical points of the potential energy: Application to roaming in ozone.

We examine the phase space structures that govern reaction dynamics in the absence of critical points on the potential energy surface. We show that in the vicinity of hyperbolic invariant tori, it is possible to define phase space dividing surfaces that are analogous to the dividing surfaces governing transition from reactants to products near a critical point of the potential energy surface. We investigate the problem of capture of an atom by a diatomic molecule and show that a normally hyperbolic invariant manifold exists at large atom-diatom distances, away from any critical points on the potential. This normally hyperbolic invariant manifold is the anchor for the construction of a dividing surface in phase space, which defines the outer or loose transition state governing capture dynamics. We present an algorithm for sampling an approximate capture dividing surface, and apply our methods to the recombination of the ozone molecule. We treat both 2 and 3 degrees of freedom models with zero total angular momentum. We have located the normally hyperbolic invariant manifold from which the orbiting (outer) transition state is constructed. This forms the basis for our analysis of trajectories for ozone in general, but with particular emphasis on the roaming trajectories.

Phase Space Structures Explain Hydrogen Atom Roaming in Formaldehyde Decomposition.

We re-examine the prototypical roaming reaction--hydrogen atom roaming in formaldehyde decomposition--from a phase space perspective. Specifically, we address the question "why do trajectories roam, rather than dissociate through the radical channel?" We describe and compute the phase space structures that define and control all possible reactive events for this reaction, as well as provide a dynamically exact description of the roaming region in phase space. Using these phase space constructs, we show that in the roaming region, there is an unstable periodic orbit whose stable and unstable manifolds define a conduit that both encompasses all roaming trajectories exiting the formaldehyde well and shepherds them toward the H2···CO well.

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.

Prediction of enhanced solvent-induced enantioselectivity for a ring opening with a bifurcating reaction path.

Classical molecular dynamics simulations are reported for the deazetisation and ring opening of meso-2,3-difluoro-2,3-dimethyldiazocyclopropane in three solvents: CHCl3, CHFClBr and CH3CH(OH)CF3 (TFIPA). The achiral reactant leads to enantiomeric allene products, and the question addressed in the study is whether either of the chiral, enantiomerically pure solvents can induce significant enantiomeric excess in the products. The direct dynamics calculations use an empirical valence bond potential for the solute, with empirical parameters optimised against M06-2X/cc-pVTZ density functional results. The results reveal that the exothermic N2 loss and ring opening promote transient strong solvent-solute interactions within the first ∼100 fs of the reaction. Because of the bifurcating reaction path, these interactions occur at time when the "decision" about which enantiomer of the product to form has yet to be made (at least for many of the trajectories). Hence, it is possible in principle that the solvent could exert a larger-than-normal influence on the course of the reaction. In fact, the results reveal no such effect for CHFClBr but do predict that TFIPA should induce 15.2 ± 2.1% enantiomeric excess. This is roughly an order of magnitude larger than solvent-induced enantiomeric excesses found experimentally in reactions where the conversion of reactant(s) to enantiomeric products occur over separate transition states.

Nonstatistical dynamics on the caldera.

We explore both classical and quantum dynamics of a model potential exhibiting a caldera: that is, a shallow potential well with two pairs of symmetry related index one saddles associated with entrance/exit channels. Classical trajectory simulations at several different energies confirm the existence of the "dynamical matching" phenomenon originally proposed by Carpenter, where the momentum direction associated with an incoming trajectory initiated at a high energy saddle point determines to a considerable extent the outcome of the reaction (passage through the diametrically opposing exit channel). By studying a "stretched" version of the caldera model, we have uncovered a generalized dynamical matching: bundles of trajectories can reflect off a hard potential wall so as to end up exiting predominantly through the transition state opposite the reflection point. We also investigate the effects of dissipation on the classical dynamics. In addition to classical trajectory studies, we examine the dynamics of quantum wave packets on the caldera potential (stretched and unstretched). These computations reveal a quantum mechanical analogue of the "dynamical matching" phenomenon, where the initial expectation value of the momentum direction for the wave packet determines the exit channel through which most of the probability density passes to product.

Photoinitiated synthesis of self-assembled vesicles.

The aqueous photochemistry of 2-oxooctanoic acid (a single-tailed surfactant) results in the synthesis of a double-tailed surfactant product followed by spontaneous self-assembly into vesicles. The photochemical mechanism is detailed here, and the reaction products are identified using mass spectrometry. Then, the self-assembled vesicles are characterized using dynamic light scattering, fluorescence microscopy, and NMR. Further, their stability over time and in the presence of MgCl2 salt is demonstrated. This work contributes to membrane evolution through the provision of a prebiotic route for the synthesis of plausible membrane components and subsequent self-assembly of a primitive enclosure.