The Roaming Atom: Straying from the Reaction Path in Formaldehyde Decomposition

Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces

In this Introduction, we show the basic problems of non-statistical and non-equilibrium phenomena related to the papers collected in this themed issue. Over the past few years, significant advances in both computing power and development of theories have allowed the study of larger systems, increasing the time length of simulations and improving the quality of potential energy surfaces. In particular, the possibility of using quantum chemistry to calculate energies and forces 'on the fly' has paved the way to directly study chemical reactions. This has provided a valuable tool to explore molecular mechanisms at given temperatures and energies and to see whether these reactive trajectories follow statistical laws and/or minimum energy pathways. This themed issue collects different aspects of the problem and gives an overview of recent works and developments in different contexts, from the gas phase to the condensed phase to excited states.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'.

Effects of microsolvation on a SN2 reaction: indirect atomistic dynamics and weakened suppression of reactivity

Systematic studies of microsolvation in the gas phase have enriched our knowledge of solvent effects. Here, the dynamics of a prototype S_N2 reaction of a hydrated fluoride ion with methyl iodide is uncovered employing direct dynamics simulations that show strikingly distinct features from those determined for an unsolvated system. An indirect scattering is found to prevail, which occurs dominantly by forming hydrated F^-(H₂O)-HCH₂I and F^-(H₂O)-CH₃I pre-reaction complexes at low energies, but proceeds through their water-free counterparts at higher energies. This finding is in strong contrast to a general evolution from indirect to direct dynamics with enhancing energy for the unsolvated substitution reactions, and this discrepancy is understood by the substantial steric hindrance introduced by a water molecule. As established in experiments, solvation suppresses the reactivity, whereas we find that this depression is remarkably frustrated upon raising the energy given that collision-induced dehydration essentially diminishes the water block for reactive collisions. The present study sheds light on how solute-solvent interactions affect the underlying dynamics at a deeper atomic level, thereby promoting our understanding of the fundamental solvent effects on chemical reactions in solution.

Bimolecular Reactions between Dimethylnitramine and Its Radical Decomposition Products

Bimolecular reactions between intact nitramines and their radical decomposition products can accelerate thermal decomposition, yet the detailed mechanisms of such reactions are not well understood. We have used density functional theory at the M06/6-311++G(3df,3pd) level to locate transition structures and compute 0 K activation barriers for various gas-phase reactions that may contribute to radical-assisted decomposition of dimethylnitramine (DMNA, (CH₃)₂NNO₂). Our calculations indicate that H abstraction from DMNA is the lowest-barrier mechanism for most radicals and a subsequent N-N β-scission in the alkyl radical 3 leads to an imine intermediate and NO₂. H abstraction is thus responsible for conversion of most radicals to NO₂. Also, among the nine radicals considered, NO is found to be least reactive and its reactions with DMNA yield dimethylnitrosoamine (DMNSA, (CH₃)₂NNO), a known product of DMNA decomposition.

Roaming-Mediated CH2NH Elimination from the Ionization of Aromatic Ethylamines

The ionization of aromatic ethylamines by photons or electrons leads to elimination of CH₂NH fragments, supposedly deriving from the McLafferty rearrangement involving intramolecular γ‐hydrogen transfer. Using tryptamine and phenethylamine as examples, the results reported here suggest that the McLafferty mechanism is inadequate for interpreting the observations of CH₂NH elimination due to much higher calculated appearance energy than experimentally measured values. Furthermore, by considering the roaming‐mediated effect, the calculated appearance energy for the elimination of CH₂NH fragments is reduced and matches well with the experimental results and verifies the existence of roaming‐mediated effect. This effect could potentially be extended to explain the general CH₂NH elimination of aromatic ethylamines. Due to the similar hydrogen transfer to that of the McLafferty mechanism, the roaming‐mediated effect was taken into account to suggest a novel mechanism, termed the “roaming‐modified McLafferty rearrangement”, that explains the observations of CH₂NH elimination in the ionization of aromatic ethylamines. This is a reasonable modification of the McLafferty rearrangement mechanism.

Competing pathways in the near-UV photochemistry of acetaldehyde

Time-resolved ion imaging measurements have been performed to explore the photochemistry of acetaldehyde at photolysis wavelengths spanning the range 265–328 nm.

Advances in spectroscopy and dynamics of small and medium sized molecules and clusters

Investigations of the spectroscopy and dynamics of small- and medium-sized molecules and clusters represent a hot topic in atmospheric chemistry, biology, physics, atto- and femto-chemistry and astrophysics.

Photochemical Reactions of Cyclohexanone: Mechanisms and Dynamics

Photochemistry of carbonyl compounds is of major importance in atmospheric and organic chemistry. The photochemistry of cyclohexanone is studied here using on-the-fly molecular dynamics simulations on a semiempirical multireference configuration interaction potential-energy surface to predict the distribution of photoproducts and time scales for their formation. Rich photochemistry is predicted to occur on a picosecond time scale following the photoexcitation of cyclohexanone to the first singlet excited state. The main findings include: (1) Reaction channels found experimentally are confirmed by the theoretical simulations, and a new reaction channel is predicted. (2) The majority (87%) of the reactive trajectories start with a ring opening via C-Cα bond cleavage, supporting observations of previous studies. (3) Mechanistic details, time scales, and yields are predicted for all reaction channels. These benchmark results shed light on the photochemistry of isolated carbonyl compounds in the atmosphere and can be extended in the future to photochemistry of more complex atmospherically relevant carbonyl compounds in both gaseous and condensed-phase environments.

Photodissociation dynamics of dinitrite at 355 nm: initiation of a reactive pathway

Dinitrites are effective nitrosating reagents in preparative chemistry and their decomposition products are involved in the atmospheric reaction of volatile organic compounds with nitrogen oxides (NO_x). In this work, photodissociation dynamics of five alkyl dinitrites were investigated by detecting the LIF spectra of the dissociation products and theoretical calculations. The results showed that the C-C bond connecting the two nitrosooxy (-ONO) functional groups was the weakest bond in vicinal dinitrites and aldehydes were the dissociation products. For dinitrites with two ONO groups separated by a CH₂ group, vinoxy and 1-methylvinoxy radicals were detected as the fragments via photodissociation, indicating a different mechanism compared to thermal decomposition. This observation demonstrated that a new reactive pathway could be initiated by photolysis of dinitrites.

Quantum and quasi-classical calculations for the S⁺ + H₂(v,j) → SH⁺(v',j') + H reactive collisions

State-to-state cross-sections for the S(+) + H2(v,j) → SH(+)(v',j') + H endothermic reaction are obtained using quantum wave packet (WP) and quasi-classical (QCT) methods for different initial ro-vibrational H2(v,j) over a wide range of translation energies. The final state distribution as a function of the initial quantum number is obtained and discussed. Additionally, the effect of the internal excitation of H2 on the reactivity is carefully studied. It appears that energy transfer among modes is very inefficient that vibrational energy is the most favorable for the reaction, and rotational excitation significantly enhances the reactivity when vibrational energy is sufficient to reach the product. Special attention is also paid to an unusual discrepancy between classical and quantum dynamics for low rotational levels while agreement improves with rotational excitation of H2. An interesting resonant behaviour found in WP calculations is also discussed and associated with the existence of roaming classical trajectories that enhance the reactivity of the title reaction. Finally, a comparison with the experimental results of Stowe et al. for S(+) + HD and S(+) + D2 reactions exhibits a reasonably good agreement with those results.

Thermal Decomposition of 3-Bromopropene. A Theoretical Kinetic Investigation

A detailed kinetic study of the gas-phase thermal decomposition of 3-bromopropene over wide temperature and pressure ranges was performed. Quantum chemical calculations employing the density functional theory methods B3LYP, BMK, and M06-2X and the CBS-QB3 and G4 ab initio composite models provide the relevant part of the potential energy surfaces and the molecular properties of the species involved in the CH2═CH-CH2Br → CH2═C═CH2 + HBr (1) and CH2═CH-CH2Br → CH2═CH-CH2 + Br (2) reaction channels. Transition-state theory and unimolecular reaction rate theory calculations show that the simple bond fission reaction ( 2 ) is the predominant decomposition channel and that all reported experimental studies are very close to the high-pressure limit of this process. Over the 500-1400 K range a rate constant for the primary dissociation of k2,∞ = 4.8 × 10(14) exp(-55.0 kcal mol(-1)/RT) s(-1) is predicted at the G4 level. The calculated k1,∞ values lie between 50 to 260 times smaller. A value of 10.6 ± 1.5 kcal mol(-1) for the standard enthalpy of formation of 3-bromopropene at 298 K was estimated from G4 thermochemical calculations.

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.

Recent Advances in Quantum Dynamics of Bimolecular Reactions

In this review, we survey the latest advances in theoretical understanding of bimolecular reaction dynamics in the past decade. The remarkable recent progress in this field has been driven by more accurate and efficient ab initio electronic structure theory, effective potential-energy surface fitting techniques, and novel quantum scattering algorithms. Quantum mechanical characterization of bimolecular reactions continues to uncover interesting dynamical phenomena in atom-diatom reactions and beyond, reaching an unprecedented level of sophistication. In tandem with experimental explorations, these theoretical developments have greatly advanced our understanding of key issues in reaction dynamics, such as microscopic reaction mechanisms, mode specificity, product energy disposal, influence of reactive resonances, and nonadiabatic effects.

Microsolvated F(-)(H2O) + CH3I S(N)2 Reaction Dynamics. Insight into the Suppressed Formation of Solvated Products

Microsolvation offers a bottom-up approach to investigate details of how solute-solvent interactions affect chemical reaction dynamics. The dynamics of the microsolvated S(N)2 reaction F(-)(H2O) + CH3I are uncovered in detail by using direct chemical dynamics simulations. Direct rebound and stripping and indirect atomic-level mechanisms are observed. The indirect events comprise ∼70% of the solvated reaction and occur predominantly via a hydrogen-bonded F(-)(H2O)···HCH2I prereaction complex. The reaction dynamics show propensity for the direct three-body dissociation channel F(-)(H2O) + CH3I → CH3F + I(-) + H2O after passing the reaction's dynamical bottleneck. The water molecule leaves the reactive system before traversing the postreaction region of the PES, where water transfer toward the product species occurs. This provides an insight into the very interesting finding of strongly suppressed formation of energetically favored solvated products for almost all SN2 reactions under microsolvation.

Theoretical insight into the wavelength-dependent photodissociation mechanism of nitric acid

The MS-CASPT2 method is used to study O(¹D) + HONO and OH + NO₂ photodissociation pathways of HNO₃ in the four lowest electronic singlet states.

A 1 + 1′ resonance-enhanced multiphoton ionization scheme for rotationally state-selective detection of formaldehyde via the à 1A2 ← X̃ 1A1 transition

The new 1 + 1′ REMPI scheme is well-suited for sensitive determination of rotational state distributions in formaldehyde.

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.

Dynamical, spectroscopic and computational imaging of bond breaking in photodissociation: roaming and role of conical intersections

Recent experimental and theoretical advances in the study of the dissociation of excited molecules are revealing unexpected mechanisms, when their outcomes are tackled by combining (i) space-time ion imaging of translational features, with (ii) spectroscopic probing of rotational and vibrational distributions; crucial is the assistance of (iii) the quantum chemistry of structural investigations of rearrangements of chemical bonds, and of (iv) the simulations of molecular dynamics to follow the evolution of selective bond stretching and breaking. Here we present results of such an integrated approach to methyl formate, HCOOCH3, the simplest of esters; the main focus is on the rotovibrationally excited CO (v=1) product and in general on the energy distribution in the fragments. Previous laser studies of dissociation into CO and CH3OH at a sequence of various wavelengths discovered signatures of a roaming mechanism by the late arrival of CO (v=0) products in time-of-flight ion imaging. Subsequent detailed investigations as a function of excitation energy provided the assessment of the threshold, which opens for triple breakdown into CO and further fragments H and CH3O, as spectroscopically characterized by ion imaging and FTIR respectively. Accompanying quantum mechanical electronic structure calculations and classical molecular dynamics simulations clarify the origin of these fragments through "roaming" pathways involving incipient radical intermediates at energies below the triple fragmentation threshold: a specific role is played by nonadiabatic transitions at a conical intersection between ground and excited states; alternative pathways focalize our attention to regions of the potential energy surfaces other than those in the neighbourhoods of saddle points along minimum energy paths: eventually this leads us to look for avenues in reaction kinetics beyond those of venerable transition state theories.

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.

Stereodynamical Origin of Anti-Arrhenius Kinetics: Negative Activation Energy and Roaming for a Four-Atom Reaction

The OH + HBr → H2O + Br reaction, prototypical of halogen-atom liberating processes relevant to mechanisms for atmospheric ozone destruction, attracted frequent attention of experimental chemical kinetics: the nature of the unusual reactivity drop from low to high temperatures eluded a variety of theoretical efforts, ranking this one among the most studied four-atom reactions. Here, inspired by oriented molecular-beams experiments, we develop a first-principles stereodynamical approach. Thermalized sets of trajectories, evolving on a multidimensional potential energy surface quantum mechanically generated on-the-fly, provide a map of most visited regions at each temperature. Visualizations of rearrangements of bonds along trajectories and of the role of specific angles of reactants' mutual approach elucidate the mechanistic change from the low kinetic energy regime (where incident reactants reorient to find the propitious alignment leading to reaction) to high temperature (where speed hinders adjustment of directionality and roaming delays reactivity).

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.

Modulation of inherent dynamical tendencies of the bisabolyl cation via preorganization in epi-isozizaene synthase

The relative importance of preorganization, selective transition state stabilization and inherent reactivity are assessed through quantum chemical and docking calculations for a sesquiterpene synthase (epi-isozizaene synthase, EIZS). Inherent reactivity of the bisabolyl cation, both static and dynamic, appears to determine the pathway to product, although preorganization and selective binding of the final transition state structure in the multi-step carbocation cascade that forms epi-isozizaene appear to play important roles.

Characterization of molecular channel in photodissociation of SOCl2 at 248 nm: Cl2 probing by cavity ring-down absorption spectroscopy

A primary elimination channel of the chlorine molecule in the one-photon dissociation of SOCl2 at 248 nm was investigated using cavity ring-down absorption spectroscopy (CRDS). By means of spectral simulation, the ratio of the vibrational population in the v = 0, 1, and 2 levels was evaluated to be 1 : (0.10 ± 0.02) : (0.009 ± 0.005), corresponding to a Boltzmann vibrational temperature of 340 ± 30 K. The Cl2 molecular channel was obtained with a quantum yield of 0.4 ± 0.2 from the X(1)A' ground state of SOCl2via internal conversion. The dissociation mechanism differs from a prior study where a smaller yield of <3% was obtained, initiated from the 2(1)A' excited state. Temperature-dependence measurements of the Cl2 fragment turn out to support our mechanism. With the aid of ab initio potential energy calculations, two dissociation routes to the molecular products were found, including one synchronous dissociation pathway via a three-center transition state (TS) and the other sequential dissociation pathway via a roaming-mediated isomerization TS. The latter mechanism with a lower energy barrier dominates the dissociation reaction.

Computational organic chemistry: bridging theory and experiment in establishing the mechanisms of chemical reactions

Understanding the mechanisms of chemical reactions, especially catalysis, has been an important and active area of computational organic chemistry, and close collaborations between experimentalists and theorists represent a growing trend. This Perspective provides examples of such productive collaborations. The understanding of various reaction mechanisms and the insight gained from these studies are emphasized. The applications of various experimental techniques in elucidation of reaction details as well as the development of various computational techniques to meet the demand of emerging synthetic methods, e.g., C-H activation, organocatalysis, and single electron transfer, are presented along with some conventional developments of mechanistic aspects. Examples of applications are selected to demonstrate the advantages and limitations of these techniques. Some challenges in the mechanistic studies and predictions of reactions are also analyzed.

Revealing a double-inversion mechanism for the F⁻+CH₃Cl SN2 reaction

Stereo-specific reaction mechanisms play a fundamental role in chemistry. The back-side attack inversion and front-side attack retention pathways of the bimolecular nucleophilic substitution (SN2) reactions are the textbook examples for stereo-specific chemical processes. Here, we report an accurate global analytic potential energy surface (PES) for the F(-)+CH₃Cl SN2 reaction, which describes both the back-side and front-side attack substitution pathways as well as the proton-abstraction channel. Moreover, reaction dynamics simulations on this surface reveal a novel double-inversion mechanism, in which an abstraction-induced inversion via a FH···CH₂Cl(-) transition state is followed by a second inversion via the usual [F···CH₃···Cl](-) saddle point, thereby opening a lower energy reaction path for retention than the front-side attack. Quasi-classical trajectory computations for the F(-)+CH₃Cl(ν1=0, 1) reactions show that the front-side attack is a fast direct, whereas the double inversion is a slow indirect process.

Insight into photofragment vector correlation by a multi-center impulsive model

A multi-center impulsive model has been recently developed to characterize the dynamic feature of fragment vector correlation in photodissociation of formaldehyde, H₂CO → CO + H₂, via both transition state and roaming pathways.

Roaming as the dominant mechanism for molecular products in the photodissociation of large aliphatic aldehydes

Photodissociation of isobutyraldehyde (C₃H₇CHO) at 248 nm is investigated using time-resolved Fourier-transform infrared emission spectroscopy to demonstrate the growing importance of the roaming pathway with increasing molecular size of aliphatic aldehydes.

HCN elimination from vinyl cyanide: product energy partitioning, the role of hydrogen–deuterium exchange reactions and a new pathway

A schematic diagram of HCN elimination channels from vinyl cyanide including a new CCdiss pathway.

Time-resolved photoionization spectroscopy of mixed Rydberg-valence states: indole case study

Time-resolved photoelectron imaging reveals subtle new mechanistic insight into the ultraviolet relaxation dynamics of gas-phase indole.