Statistical Theory for the Kinetics and Dynamics of Roaming Reactions

An experimental and computational study of the unimolecular-decay reaction of diethyl-substituted Criegee intermediate (C2H5)2COO

We have performed direct kinetic measurements to determine the thermal unimolecular-decay rate coefficient of (C2H5)2COO as a function of temperature (223-296 K) and pressure (4-100 torr) using time-resolved UV-absorption spectroscopy. The stabilised (C2H5)2COO Criegee intermediate was produced by photolysing 3-bromo-3-iodopentane ((C2H5)2CIBr) with 213 nm radiation in the presence of O2. We performed quantum-chemistry calculations and master-equation simulations to complement the experimental work. At 296 K and 100 torr, we measure 1530 ± 440 s-1 (2σ) for the unimolecular-decay rate coefficient, and both the experiments and simulations indicate that the reaction is effectively at the high-pressure limit under these conditions. Key parameters in the master-equation model were optimised using the experimental results, and phenomenological rate coefficients were then computed to facilitate the use of the present results in modelling. A roaming channel that forms (R/S)-2-hydroxypentan-3-one was included in the master-equation model. We also performed similar calculations for the unimolecular-decay reaction of (CH3)2COO to improve the kinetic modelling of our previous work [J. Peltola et al., Phys. Chem. Chem. Phys., 2022, 24, 5211-5219].

Reduced Cost Computation and Exploitation of Accurate Radial Interaction Potentials for Barrier-Less Processes

Barrier-less steps are typical of radical and ionic reactions in the gas-phase, which often take place in extreme environments such as the combustion reactors operating at very high temperatures or the interstellar medium, characterized by ultralow temperatures and pressures. The difficulty of experimental studies in conditions mimicking these environments suggests that computational approaches can provide a valuable support. In this connection, the most advanced treatments of these processes in the framework of transition state theory are able to deliver accurate kinetic parameters provided that the underlying potential energy surface is sufficiently accurate. Since this requires a balanced treatment of static and dynamic correlation (which play different roles in different regions), very sophisticated and expensive quantum chemical approaches are required. One effective solution of this problem is offered by the computation of accurate one-dimensional radial potentials, which are then used to correct the results of a Monte Carlo sampling performed by cheaper quantum chemical approaches. In this paper, we will show that, for a large panel of different barrier-less reaction steps, the radial potential is ruled by the R-4 term and that addition of a further R-6 contribution provides quantitative agreement with the reference points. The consequences of this outcome are not trivial, since the reference potential can be fitted by a very limited number of points possibly with a nonlinear spacing. In the case of reaction steps ruled by long-range transition states, generalized expressions are also given for computing reaction rates in the framework of the phase-space theory. All these improvements pave the way toward the computation of reaction rates for barrier-less reactions involving large molecules.

UV-Induced Reaction Pathways in Bromoform Probed with Ultrafast Electron Diffraction

For many chemical reactions, it remains notoriously difficult to predict and experimentally determine the rates and branching ratios between different reaction channels. This is particularly the case for reactions involving short-lived intermediates, whose observation requires ultrafast methods. The UV photochemistry of bromoform (CHBr3) is among the most intensely studied photoreactions. Yet, a detailed understanding of the chemical pathways leading to the production of atomic Br and molecular Br2 fragments has proven challenging. In particular, the role of isomerization and/or roaming and their competition with direct C-Br bond scission has been a matter of continued debate. Here, gas-phase ultrafast megaelectronvolt electron diffraction (MeV-UED) is used to directly study structural dynamics in bromoform after single 267 nm photon excitation with femtosecond temporal resolution. The results show unambiguously that isomerization contributes significantly to the early stages of the UV photochemistry of bromoform. In addition to direct C-Br bond breaking within <200 fs, formation of iso-CHBr3 (Br-CH-Br-Br) is observed on the same time scale and with an isomer lifetime of >1.1 ps. The branching ratio between direct dissociation and isomerization is determined to be 0.4 ± 0.2:0.6 ± 0.2, i.e., approximately 60% of molecules undergo isomerization within the first few hundred femtoseconds after UV excitation. The structure and time of formation of iso-CHBr3 compare favorably with the results of an ab initio molecular dynamics simulation. The lifetime and interatomic distances of the isomer are consistent with the involvement of a roaming reaction mechanism.

Computational Modeling of the Conformation-Dependent Atmospheric Reactivity of Criegee Intermediates

The impacts of Criegee intermediates (CIs) on atmospheric chemistry depend significantly on the CI conformation. In this Perspective, I highlight examples of how electronic structure and statistical rate theory calculations, in conjunction with experiment, have revealed conformation-dependent details of both CI ground-state reactivity and electronic excitation. Calculations using single-reference electronic structure methods and conventional transition state theory have predicted that CIs with syn-alkyl or syn-vinyl substituents isomerize rapidly to vinyl hydroperoxides (VHPs) or dioxoles, both of which can decompose rapidly under atmospheric conditions. Ongoing computational research on hydroxyl radical (OH) roaming initiated by VHP dissociation requires the application of multireference electronic structure methods and variational transition state theory. CIs that lack both syn-alkyl and syn-vinyl substituents undergo either bimolecular reaction or π* ← π electronic excitation in the atmosphere. Accurate predictions of CI ultraviolet-visible spectra require multireference calculations with large active spaces and at least a second-order perturbative treatment of dynamic electron correlation. The extent to which electronic spectra can be diagnostic of the presence of specific CI conformers varies significantly with CI chemical identity.

Roaming in acetaldehyde

We investigate roaming in the photodissociation of acetaldehyde (CH3CHO), providing insights into the contrasting roaming dynamics observed for this molecule compared to formaldehyde. We carry out trajectory studies for full-dimensional acetaldehyde, supplemented with an analysis of a two-degree-of-freedom restricted model and obtain evidence for two distinct roaming pathways. Trajectories exhibit roaming at both shorter (9-11.5 au) and larger (14.5-22.9 au) maximum CH3-HCO separations, characterized by differing amounts of HCO rotation. No roaming trajectories were found in the intervening gap region. The roaming dynamics near 14.5-22.9 au are well-reproduced by the restricted model and involve passage through a centrifugal barrier, analogous to formaldehyde roaming. However, the shorter-range 9-11.5 au roaming appears unique to acetaldehyde and is likely facilitated by repulsive interactions absent in the simplified models. Phase space analysis reveals that this additional roaming pathway is inaccessible in the reduced dimensionality system. The findings suggest that acetaldehyde's increased propensity for roaming compared to formaldehyde may arise from the presence of multiple distinct roaming mechanisms rather than solely the higher roaming fragment mass.

OH Roaming during the Ozonolysis of α-Pinene: A New Route to Highly Oxygenated Molecules?

The formation of low-volatility organic compounds in the ozonolysis of α-pinene, the dominant atmospheric monoterpene, provides an important route to aerosol formation. In this work, we consider a previously unexplored set of pathways for the formation of highly oxygenated molecules in α-pinene ozonolysis. Pioneering, direct experimental observations of Lester and co-workers have demonstrated a significant production of hydroxycarbonyl products in the dissociation of Criegee intermediates. Theoretical analyses indicate that this production arises from OH roaming-induced pathways during the OO fission of the vinylhydroperoxides (VHPs), which in turn come from internal H transfers in the Criegee intermediates. Ab initio kinetics computations are used here to explore the OH roaming-induced channels that arise from the ozonolysis of α-pinene. For computational reasons, the calculations consider a surrogate for α-pinene, where two spectator methyl groups are replaced with H atoms. Multireference electronic structure calculations are used to illustrate a variety of energetically accessible OH roaming pathways for the four VHPs arising from the ozonolysis of this α-pinene surrogate. Ab initio transition-state theory-based master equation calculations indicate that for the dissociation of stabilized VHPs, these OH roaming pathways are kinetically significant with a branching that generally increases from ∼20% at room temperature up to ∼70% at lower temperatures representative of the troposphere. For one of the VHPs, this branching already exceeds 60% at room temperature. For the overall ozonolysis process, these branching ratios would be greatly reduced by a limited branching to the stabilized VHP, although there would also be some modest roaming fraction for the nonthermal VHP dissociation process. The strong exothermicities of the roaming-induced isomerizations/additions and abstractions suggest new routes to fission of the cyclobutane rings. Such ring fissions would facilitate further autoxidation reactions, thereby providing a new route for producing highly oxygenated nonvolatile precursors to aerosol formation.

Theoretical Kinetics Predictions for Reactions on the NH2O Potential Energy Surface

Recent modeling studies of ammonia oxidation, which are motivated by the prospective role of ammonia as a zero-carbon fuel, have indicated significant discrepancies among the existing literature mechanisms. In this study, high-level theoretical kinetics predictions have been obtained for reactions on the NH2O potential energy surface, including the NH2 + O, HNO + H, and NH + OH reactions. These reactions have previously been highlighted as important reactions in NH3 oxidation with high sensitivity and high uncertainty. The potential energy surface is explored with coupled cluster calculations, including large basis sets and high-level corrections to yield high-accuracy (∼0.2 kcal/mol 2σ uncertainty) estimates of the stationary point energies. Variational transition state theory is used to predict the microcanonical rate constants, which are then incorporated in master equation treatments of the temperature- and pressure-dependent kinetics. For radical-radical channels, the microcanonical rates are obtained from variable reaction coordinate transition state theory implementing directly evaluated multireference electronic energies. The analysis yields predictions for the total rate constants as well as the branching ratios. We find that the NO + H2 channel contributes 10% of the total NH2 + O flux at combustion temperatures, although this channel is not included in modern NH3 oxidation mechanisms. Modeling is used to illustrate the ramifications of these rate predictions on the kinetics of NH3 oxidation and NOx formation. The present results for NH2 + O are important for predicting the chain branching and formation of NO in the oxidation of NH3 and thermal DeNOx.

OH Roaming and Beyond in the Unimolecular Decay of the Methyl-Ethyl-Substituted Criegee Intermediate: Observations and Predictions

Alkene ozonolysis generates short-lived Criegee intermediates that are a significant source of hydroxyl (OH) radicals. This study demonstrates that roaming of the separating OH radicals can yield alternate hydroxycarbonyl products, thereby reducing the OH yield. Specifically, hydroxybutanone has been detected as a stable product arising from roaming in the unimolecular decay of the methyl-ethyl-substituted Criegee intermediate (MECI) under thermal flow cell conditions. The dynamical features of this novel multistage dissociation plus a roaming unimolecular decay process have also been examined with ab initio kinetics calculations. Experimentally, hydroxybutanone isomers are distinguished from the isomeric MECI by their higher ionization threshold and distinctive photoionization spectra. Moreover, the exponential rise of the hydroxybutanone kinetic time profile matches that for the unimolecular decay of MECI. A weaker methyl vinyl ketone (MVK) photoionization signal is also attributed to OH roaming. Complementary multireference electronic structure calculations have been utilized to map the unimolecular decay pathways for MECI, starting with 1,4 H atom transfer from a methyl or methylene group to the terminal oxygen, followed by roaming of the separating OH and butanonyl radicals in the long-range region of the potential. Roaming via reorientation and the addition of OH to the vinyl group of butanonyl is shown to yield hydroxybutanone, and subsequent C-O elongation and H-transfer can lead to MVK. A comprehensive theoretical kinetic analysis has been conducted to evaluate rate constants and branching yields (ca. 10-11%) for thermal unimolecular decay of MECI to conventional and roaming products under laboratory and atmospheric conditions, consistent with the estimated experimental yield (ca. 7%).

Mechanistic and Kinetic Investigations on Decomposition of Trifluoromethanesulfonyl Fluoride in the Presence of Water Vapor and Electric Field

As a potential insulation gas to replace sulfur hexafluoride (SF₆) due to environmental concerns, trifluoromethanesulonyl fluoride (CF₃SO₂F) has attracted great interests in various high-voltage electric applications. Thermal stability of CF₃SO₂F plays an important role in the rational design of the gas-insulated electric equipment. Unimolecular decomposition of CF₃SO₂F was investigated using high-level ab initio methods including the explicitly correlated RCCSD(T)-F12, the composite ROCBS-QB3, and the multireference RS2 extrapolated to complete basis set limit on the basis of M06-2X-, B2PLYPD3-, and CCSD-optimized geometrical parameters. Rate coefficients and decomposition temperatures were simulated using master equations. CF₃SO₂F decomposes predominantly via a simple C-S bond cleavage to form CF₃ and SO₂F, accompanied by a roaming induced F-abstraction detour to release CF₄ and SO₂, or isomerizes via CF₃ migration to the more stable CF₃OSFO followed by the production of CF₂O and SOF₂. Various characteristic decomposition products (e.g., CF₄, C₂F₆, CF₂O, SO₂, SOF₂, SO₂F₂, CF₃H, and so on.) have been identified theoretically through secondary reactions and hydrolysis of CF₃SO₂F in the presence of water vapor. Electronic structures and stability of CF₃SO₂F could be affected significantly by the external electric field orientated along the S-C bond. The field-dependent electron-molecule capture rates support that CF₃SO₂F is superior to SF₆ in dielectric strength. The present computational findings shed light on the practical use of CF₃SO₂F as the replacement gas for SF₆.

Concluding Remarks on Faraday Discussion on Unimolecular Reactions

This Faraday Discussion, marking the centenary of Lindemann’s explanation of the pressure-dependence of unimolecular reactions, presented recent advances in measuring and computing collisional energy transfer efficiencies, microcanonical rate coefficients, pressure-dependent...

Quantum resonances and roaming dynamics in formaldehyde photodissociation

The unimolecular dissociation of formaldehyde is studied via excitation to the à band at several excitation energies from just below the ground state radical dissociation threshold to 5000 cm-1 above...

Spiers Memorial Lecture: theory of unimolecular reactions

One hundred years ago, at an earlier Faraday Discussion meeting, Lindemann presented a mechanism that provides the foundation for contemplating the pressure dependence of unimolecular reactions. Since that time, our...

Orbiting resonances in formaldehyde reveal coupling of roaming, radical, and molecular channels

[Figure: see text].

Probing the Charge-Transfer Potential Energy Surfaces by the Photodissociation of [Ar-N2]. J Phys Chem Lett 2021;12:4012-4017. [PMID: 33877828 DOI: 10.1021/acs.jpclett.1c00798]

Chemical reaction pathways and product state correlations of gas-phase ion-molecule reactions are governed by the involved potential energy surfaces (PESs). Here, we report the photodissociation dynamics of charge-transfer complex [Ar-N₂]⁺, which is the intermediate of the model system of the Ar⁺ + N₂ → Ar + N₂⁺ reaction. High-resolution recoiling velocity images of photofragmented N₂ and N₂⁺ from different dissociation channels exhibit a vibrational state-specific correlation, revealing the nonadiabatic charge-transfer mechanisms upon the photodissociation of [Ar-N₂]⁺. The state-resolved product branching ratios have yielded an accurate determination of the resonant charge-transfer probabilities. This work provides a powerful approach to elucidating the detailed dynamics of chemical events of charge-transfer complex [Ar-N₂]⁺ and to probing the state-to-state charge-transfer PESs.

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.

Experimental and Theoretical Investigations of the Radical-Radical Reaction: N2H3 + NO2

The N₂H₃ + NO₂ reaction plays a key role during the early stages of hypergolic ignition between N₂H₄ and N₂O₄. Here for the first time, the reaction kinetics of N₂H₃ in excess NO₂ was studied in 2.0 Torr of N₂ and in the narrow temperature range 298-348 K in a pulsed photolysis flow-tube reactor coupled to a mass spectrometer. The temporal profile of the product, HONO, was determined by direct detection of the m/z +47 amu ion signal. For each chosen [NO₂], the observed [HONO] trace was fitted to a biexponential kinetics expression, which yielded a value for the pseudo-first-order rate coefficient, k', for the reaction of N₂H₃ with NO₂. The slope of the plot of k' versus [NO₂] yielded a value for the observed bimolecular rate coefficient, k_obs, which could be fitted to an Arrhenius expression of (2.36 ± 0.47) × 10^-12 exp((520 ± 350)/T) cm³ molecule^-1 s^-1. The errors are 1σ and include estimated uncertainties in the NO₂ concentration. The potential energy surface of N₂H₃ + NO₂ was investigated by advanced ab initio quantum chemistry theories. It was found that the reaction occurs via a complex reaction mechanism, and all of the reaction channels have transition state energies below that of the entrance asymptote. The radical-radical addition forms the N₂H₃NO₂ adducts, while roaming-mediated isomerization reactions yield the N₂H₃ONO isomers, which undergo rapid dissociation reactions to several sets of distinct products. The RRKM multiwell master equation simulations revealed that the major product channel involves the formation of trans-HONO and trans-N₂H₂ below 500 K and the formation of NO + NH₂NHO above 500 K, which is nearly pressure independent. The pressure-dependent rate coefficients of the product channels were computed over a wide pressure-temperature range, which encompassed the experimental data.

Roaming Reactions and Dynamics in the van der Waals Region

Roaming reactions were first clearly identified in photodissociation of formaldehyde 15 years ago, and roaming dynamics are now recognized as a universal aspect of chemical reactivity. These reactions typically involve frustrated near-dissociation of a quasibound system to radical fragments, followed by reorientation at long range and intramolecular abstraction. The consequences can be unexpected formation of molecular products, depletion of the radical pool in chemical systems, and formation of products with unusual internal state distributions. In this review, I examine some current aspects of roaming reactions with an emphasis on experimental results, focusing on possible quantum effects in roaming and roaming dynamics in bimolecular systems. These considerations lead to a more inclusive definition of roaming reactions as those for which key dynamics take place at long range.

Reaction Profiles and Kinetics for Radical-Radical Hydrogen Abstraction via Multireference Coupled Cluster Theory

Radical-radical abstractions in hydrocarbon oxidation chemistry are disproportionation reactions that are generally exothermic with little or no barrier yet are underappreciated and poorly studied. Such challenging multireference electronic structure problems are tackled here using the recently developed state-specific multireference coupled cluster methods Mk-MRCCSD and Mk-MRCCSD(T), as well as the companion perturbation theory Mk-MRPT2 and the established MRCISD, MRCISD+Q, and CASPT2 approaches. Reaction paths are investigated for five prototypes involving radical-radical hydrogen abstraction: H + BeH → H₂+ Be, H + NH₂ → H₂ + NH, CH₃ + C₂H₅ → CH₄ + C₂H₄, H + C₂H₅ → H₂ + C₂H₄, and H + HCO → H₂ + CO. Full configuration interaction (FCI) benchmark computations for the H + BeH, H + NH₂, and H + HCO reactions prove that Mk-MRCCSD(T) provides superior accuracy for the interaction energies in the entrance channel, with mean absolute errors less than 0.3 kcal mol^-1 and percentage deviations less than 10% over the fragment separations of relevance to kinetics. To facilitate combustion studies, energetics for the CH₃ + C₂H₅, H + C₂H₅, and H + HCO reactions were computed at each level of theory with correlation-consistent basis sets (cc-pVXZ, X = T, Q, 5) and extrapolated to the complete basis set (CBS) limit. These CBS energies were coupled with CASPT2 projected vibrational frequencies along a minimum energy path to obtain rate constants for these three reactions. The rigorous Mk-MRCCSD(T)/CBS results demonstrate unequivocally that these three reactions proceed with no barrier in the entrance channel, contrary to some earlier predictions. Mk-MRCCSD(T) also reveals that the economical CASPT2 method performs well for large interfragment separations but may deteriorate substantially at shorter distances.

Imaging the infrared multiphoton excitation and dissociation of propargyl chloride

Infrared multiphoton excitation is combined with UV excitation and state-resolved probes of Cl(²P_3/2), Cl*(²P_1/2), and HCl to study the photochemistry of propargyl chloride. The results show evidence both of infrared multiphoton dissociation on the ground electronic state and infrared multiphoton excitation followed by UV dissociation. The results are interpreted with the aid of a full characterization of the stationary points on the ground state using ab initio methods, as well as our recent experimental and theoretical characterization of the UV photochemistry of the molecule. The data suggest elimination of HCl on the ground electronic state produces linear propadienylidene as a coproduct over a roaming-like transition state that accesses the Cl-H-C abstraction geometry. This identification is supported by separate chirped-pulse microwave studies in a quasi-uniform flow also reported here.

UV photofragmentation dynamics of acetaldehyde cations prepared by single-photon VUV ionization

UV excitation of cold acetaldehyde cations prepared by single-photon VUV ionization results in remarkably rich photochemistry.

Water and a Borohydride/Hydronium Intermediate in the Borane-Catalyzed Hydrogenation of Carbonyl Compounds with H2 in Wet Ether: A Computational Study

We have computationally evaluated water as an active Lewis base (LB) and introduced the borohydride/hydronium intermediate in the mechanism of B(C₆F₅)₃-catalyzed hydrogenation of carbonyl compounds with H₂ in wet/moist ether. Our calculations extend the known frustrated Lewis pair mechanism of this reaction toward the inclusion of water as the active participant in all steps. Although the definition of the zero-energy point interweaves in comparison of the scenarios with and without water, we will be able to show that (i) water (hydrogen bonded to its molecular environment) can, in principle, act as a reasonably viable LB in cooperation with the borane Lewis acid such as B(C₆F₅)₃ but relatively a strong borane-water complexation can be the hindering factor; (ii) the herein-proposed borohydride/hydronium intermediates with the hydronium cation having three OH···ether hydrogen bonds or a combination of the OH···ether/OH···ketone hydrogen bonds appear to be as valid as the previously considered borohydride/oxonium or borohydride/oxocarbenium intermediates; (iii) the proton-coupled hydride transfer from the borohydride/hydronium to a ketone (acetone) has a reasonably low barrier. Our findings could be useful for better mechanistic understanding and further development of the aforementioned reaction.

Structurally Flexible Oxocarbenium/Borohydride Ion Pair: Dynamics of Hydride Transfer on the Background of Conformational Roaming

We apply Born-Oppenheimer molecular dynamics to the practically significant [dioxane-H⁽⁺⁾-acetone][(C₆F₅)₃B-H^(-)] and [Et₂O-H⁽⁺⁾-OCPr₂][(C₆F₅)₃B-H^(-)] ion pair intermediates. Dynamics of hydride transfer in cation/anion ion pair takes place on the background of large-amplitude configurational changes. Geometry of oxocarbenium/borohydride ion pairs is flexible, meaning that we uncover significant actual structural disorder at a finite temperature. Therefore, although the starting structure can be fairly close to the configurational area of the hydride transfer transition state (TS) and despite a low potential energy barrier (ca. 1.5 kcal/mol, according to the literature), already at T ≈ 325 K the system can remain ignorant of the TS region and move round and about ("roam") in the configurational space for a period of time in the range between 10 and 100 ps. This indicates structural flexibility of oxocarbenium/borohydride ion pair on apparently a flat potential energy "landscape" of cation/anion interaction, and this has not been taken into consideration by the free energy estimations in static considerations made thus far. The difference between the dynamics-based representation of the system versus the static representation amounts to the difference between quasi-bimolecular versus unimolecular descriptions of the hydride transfer step.

What is special about how roaming chemical reactions traverse their potential surfaces? Differences in geodesic paths between roaming and non-roaming events

With the notable exception of some illustrative two-degree-of-freedom models whose surprising classical dynamics has been worked out in detail, theories of roaming have largely bypassed the issue of when and why the counterintuitive phenomenon of roaming occurs. We propose that a useful way to begin to address these issues is to look for the geodesic (most efficient) pathways through the potential surfaces of candidate systems. Although roaming manifests itself in an unusual behavior at asymptotic geometries, we found in the case of formaldehyde dissociation that it was the pathways traversing the parts of the potential surface corresponding to highly vibrationally excited reactants that were the most revealing. An examination of the geodesics for roaming pathways in this region finds that they are much less tightly defined than the geodesics in that same region that lead directly to dissociation (whether into closed-shell products or into radical products). Thus, the broader set of options available to the roaming channel gives it an entropic advantage over more conventional reaction channels. These observations suggest that what leads to roaming in other systems may be less the presence of a localized "roaming transition state," than the existence of an entire region of the potential surface conducive to multiple equivalent pathways.

Theories and simulations of roaming

The phenomenon of roaming in chemical reactions has now become both commonly observed in experiment and extensively supported by theory and simulations. Roaming occurs in highly-excited molecules when the trajectories of atomic motion often bypass the minimum energy pathway and produce reaction in unexpected ways from unlikely geometries. The prototypical example is the unimolecular dissociation of formaldehyde (H₂CO), in which the "normal" reaction proceeds through a tight transition state to yield H₂ + CO but for which a high fraction of dissociations take place via a "roaming" mechanism in which one H atom moves far from the HCO, almost to dissociation, and then returns to abstract the second H atom. We review below the theories and simulations that have recently been developed to address and understand this new reaction phenomenon.

Products from the Oxidation of n-Butane from 298 to 735 K Using Either Cl Atom or Thermal Initiation: Formation of Acetone and Acetic Acid-Possible Roaming Reactions?

The oxidation of 2-butyl radicals (and to a lesser extent 1-butyl radicals) has been studied over the temperature range of 298-735 K. The reaction of Cl atoms (formed by 360 nm irradiation of Cl₂) with n-butane generated the 2-butyl radicals in mixtures of n-C₄H₁₀, O₂, and Cl₂ at temperatures below 600 K. Above 600 K, 2-butyl radicals were produced by thermal combustion reactions in the absence of chlorine. The yields of the products were measured by gas chromatography using a flame ionization detector. Major products quantified include acetone, acetic acid, acetaldehyde, butanone, 2-butanol, butanal, 1- and 2- chlorobutane, 1-butene, trans-2-butene, and cis-2-butene. At 298 K, the major oxygenated products are those expected from bimolecular reactions of 2-butylperoxy radicals (butanone, 2-butanol, and acetaldehyde). As the temperature rises to 390 K, the butanone decreases while acetaldehyde increases because of the increased rate of 2-butoxy radical decomposition. Acetone and acetic acid first appear in significant yield near 400 K, and these species rise slowly at first and then sharply, peaking near 525 K at yields of ∼25 and ∼20 mol %, respectively. In the same temperature range (400-525 K), butanone, acetaldehyde, and 2-butanol decrease rapidly. This suggests that acetone and acetic acid may be formed by previously unknown reaction channels of the 2-butylperoxy radical, which are in competition with those that lead to butanone, acetaldehyde, and 2-butanol. Above 570 K, the yields of acetone and acetic acid fall rapidly as the yields of the butenes rise. Experiments varying the Cl atom density, which in turn controls the entire radical pool density, were performed in the temperature range of 410-440 K. Decreasing the Cl atom density increased the yields of acetone and acetic acid while the yields of butanone, acetaldehyde, and 2-butanol decreased. This is consistent with the formation of acetone and acetic acid by unimolecular decomposition channels of the 2-butylperoxy radical, which are in competition with the bimolecular channels that form butanone, acetaldehyde, and 2-butanol. Such unimolecular decomposition channels would be unlikely to proceed through conventional transition states because those states would be very constrained. Therefore, the possibility that these decomposition channels proceed via roaming should be considered. In addition, we investigated and were unable to fit our data trends by a simplified ketohydroperoxide mechanism.

Flash Pyrolysis of t-Butyl Hydroperoxide and Di-t-butyl Peroxide: Evidence of Roaming in the Decomposition of Organic Hydroperoxides

Thermal decomposition of t-butyl hydroperoxide and di-t-butyl peroxide was investigated using flash pyrolysis (in a short reaction time of <100 μs) and vacuum-ultraviolet (λ = 118.2 nm) single-photon ionization time-of-flight mass spectrometry (VUV-SPI-TOFMS) at temperatures up to 1120 K and quantum computational methods. Acetone and methyl radical were detected as the predominant products in the initial decomposition of di-t-butyl peroxide via O-O bond fission. In the initial dissociation of t-butyl hydroperoxide, acetone, methyl radical, isobutylene, and isobutylene oxide products were identified. The novel detection of the unimolecular formation of isobutylene oxide, as supported by the computational study, was found to proceed via a roaming hydroxyl radical facilitated by a hydrogen-bonded intermediate. This new pathway could provide a new class of reactions to consider in the modeling of the low temperature oxidation of alkanes.

Theoretical Studies on the Kinetics of Multi-Channel Gas-Phase Unimolecular Decomposition of Acetaldehyde

Theoretical kinetic studies are performed on the multichannel thermal decomposition of acetaldehyde. The geometries of the stationary points on the potential energy surface of the reaction are optimized at the MP2(full)/6-311++G(2d,2p) level of theory. More accurate energies are obtained by single point energy calculations at the CCSD(T,full)/augh-cc-pVTZ+2df, CBS-Q and G4 levels of theory. Here, by application of steady-state approximation to the thermally activated species CH₃CHO* and CH₂CHOH* and performance of statistical mechanical manipulations, expressions for the rate constants for different product channels are derived. Special attempts are made to compute accurate energy-specific rate coefficients for different channels by using semiclassical transition state theory. It is found that the isomerization of CH₃CHO to the enol-form CH₂CHOH plays a significant role in the unimolecular reaction of CH₃CHO. The possible products of the reaction are formed via unimolecular decomposition of CH₃CHO and CH₂CHOH. The computed rate coefficients reveal that the dominant channel at low temperatures and high pressures is the formation of CH₂CHOH due to the low barrier height for CH₃CHO → CH₂CHOH isomerization process. However, at high temperatures, the product channel CH₃ + CHO becomes dominant.

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'.

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 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.

Roaming dynamics in ion-molecule reactions: phase space reaction pathways and geometrical interpretation

A model Hamiltonian for the reaction CH4(+) -> CH3(+) + H, parametrized to exhibit either early or late inner transition states, is employed to investigate the dynamical characteristics of the roaming mechanism. Tight/loose transition states and conventional/roaming reaction pathways are identified in terms of time-invariant objects in phase space. These are dividing surfaces associated with normally hyperbolic invariant manifolds (NHIMs). For systems with two degrees of freedom NHIMS are unstable periodic orbits which, in conjunction with their stable and unstable manifolds, unambiguously define the (locally) non-recrossing dividing surfaces assumed in statistical theories of reaction rates. By constructing periodic orbit continuation/bifurcation diagrams for two values of the potential function parameter corresponding to late and early transition states, respectively, and using the total energy as another parameter, we dynamically assign different regions of phase space to reactants and products as well as to conventional and roaming reaction pathways. The classical dynamics of the system are investigated by uniformly sampling trajectory initial conditions on the dividing surfaces. Trajectories are classified into four different categories: direct reactive and non-reactive trajectories, which lead to the formation of molecular and radical products respectively, and roaming reactive and non-reactive orbiting trajectories, which represent alternative pathways to form molecular and radical products. By analysing gap time distributions at several energies, we demonstrate that the phase space structure of the roaming region, which is strongly influenced by nonlinear resonances between the two degrees of freedom, results in nonexponential (nonstatistical) decay.