Perspective: chemical dynamics simulations of non-statistical reaction dynamics

Vibrationally Assisted Tunneling through the Bread of a Proton Sandwich─Connections to Dynamic Matching

Proton sandwiches are unusual nonclassical carbocations characterized by a five-center, four-electron bonding array which rapidly isomerize to lower energy isomers with three-center, two-electron bonding arrays via hydrogen migration transition states. These reactions are suspected to involve significant contributions from tunneling, even at relatively high temperatures, where tunneling effects are usually minimal. Machine-learning-accelerated ring-polymer, quasiclassical, and classical ab initio molecular dynamics simulations were used to investigate the effects of a flavor of dynamic matching that involves coupling of vibrational modes of the reactant to the transition structure mode with an imaginary frequency, and how quantum mechanical tunneling affects this coupling. These nonstatistical dynamic effects were quantified by analysis of momentum in the molecular dynamics simulations. We show the importance of momentum for reactivity with and without tunneling, how tunneling amplifies these benefits, and that vibrational modes can be leveraged to generate beneficial momentum.

Converting Second-Order Saddle Points to Transition States: New Principles for the Design of 4π Photoswitches

Molecular photoswitches have demonstrated potential for storing solar energy at the molecular level, with power densities comparable to commercial batteries and hydroelectric energy storage. However, development of efficient photoswitches is hindered by limitations in cyclability and optical properties of existing materials. We here demonstrate that certain limitations in photoswitches based on electrocyclizations stem from the issue of controlling competition between Woodward-Hoffmann allowed and forbidden pathways. Our approach moves beyond the traditional view of activation barriers and reveals that second-order saddle points are crucial in dictating the competition between disrotatory and conrotatory pathways. These insights suggest new opportunities to manipulate the competition between these pathways through geometric constraints, fundamentally altering the connectivity of the potential energy surface. Our study also emphasizes the necessity of multi-reference methods and the need to conduct higher-dimensional explorations for competing pathways beyond photoswitch design.

FeCl2-Mediated Rearrangement of Aminoperoxides into Functionalized Tetrahydrofurans: Dynamic Non-innocence of O-Ligands at an Fe Center Coordinates a Radical Cascade

The selective reaction of cyclic aminoperoxides with FeCl2 proceeds through a sequence of O-O and C-C bond cleavages, followed by intramolecular cyclization, yielding functionalized tetrahydrofurans in 44-82% yields. Replacing the peroxyacetal group in the peroxide structure with a peroxyaminal fragment fundamentally alters the reaction pathway. Instead of producing linear functionalized ketones, this modification leads to the formation of hard-to-access substituted tetrahydrofurans. Although the aminoperoxide cores undergo multiple bond scissions, this cascade is atom-economical. Computational analysis shows that the O-ligands at the Fe center have enough radical character to promote C-C bond fragmentation and subsequent cyclization. The stereoelectronic flexibility of oxygen, combined with iron's capacity to stabilize multiple reactive intermediates during the multistep cascade, explains the efficiency of this new atom-economic peroxide rearrangement.

Temperature effects on the branching dynamics in the model ambimodal (6 + 4)/(4 + 2) intramolecular cycloaddition reaction

C14H20 (tetradecapentaene) is a simple model system exhibiting post transition-state behavior, wherein both the (6 + 4) and (4 + 2) cycloaddition products are formed from one ambimocal transition state structure. We studied the bifurcation dynamics starting from the two ambimodal transition state structures, the chair-form and boat-form, using the quasi-classical trajectory, classical molecular dynamics, and ring-polymer molecular dynamics methods on the parameter-optimized semiempirical GFN2-xTB potential energy surface. It was found that the calculated branching fractions differ between the chair-form and boat-form due to the different nature in the IRC pathways. We also investigated the effects of temperature on bifurcation dynamics and found that, at higher temperatures, trajectories stay longer in the intermediate region of the potential energy surface.

Cavity induced modulation of intramolecular vibrational energy flow pathways

Recent experiments in polariton chemistry indicate that reaction rates can be significantly enhanced or suppressed inside an optical cavity. One possible explanation for the rate modulation involves the cavity mode altering the intramolecular vibrational energy redistribution (IVR) pathways by coupling to specific molecular vibrations in the vibrational strong coupling (VSC) regime. However, the mechanism for such a cavity-mediated modulation of IVR is yet to be understood. In a recent study, Ahn et al. [Science 380, 1165 (2023)] observed that the rate of alcoholysis of phenyl isocyanate (PHI) is considerably suppressed when the cavity mode is tuned to be resonant with the isocyanate (NCO) stretching mode of PHI. Here, we analyze the quantum and classical IVR dynamics of a model effective Hamiltonian for PHI involving the high-frequency NCO-stretch mode and two of the key low-frequency phenyl ring modes. We compute various indicators of the extent of IVR in the cavity-molecule system and show that tuning the cavity frequency to the NCO-stretching mode strongly perturbs the cavity-free IVR pathways. Subsequent IVR dynamics involving the cavity and the molecular anharmonic resonances lead to efficient scrambling of an initial NCO-stretching overtone state over the molecular quantum number space. We also show that the hybrid light-matter states of the effective Hamiltonian undergo a localization-delocalization transition in the VSC regime.

Trajectory-Based Time-Resolved Mechanism for Benzene Reductive Elimination from Cyclopentadienyl Mo/W Phenyl Hydride Complexes

Calculated potential energy structures and landscapes are very often used to define the sequence of reaction steps in an organometallic reaction mechanism and interpret kinetic isotope effect (KIE) measurements. Underlying most of this structure-to-mechanism translation is the use of statistical rate theories without consideration of atomic/molecular motion. Here we report direct dynamics simulations for an organometallic benzene reductive elimination reaction, where nonstatistical intermediates and dynamic-controlled pathways were identified. Specifically, we report single spin state as well as mixed spin state quasiclassical direct dynamics trajectories in the gas phase and explicit solvent for benzene reductive elimination from Mo and W bridged cyclopentadienyl phenyl hydride complexes ([Me2Si(C5Me4)2]M(H)(Ph), M = Mo and W). Different from the energy landscape mechanistic sequence, the dynamics trajectories revealed that after the benzene C-H bond forming transition state (often called reductive coupling), σ-coordination and π-coordination intermediates are either skipped or circumvented and that there is a direct pathway to forming a spin flipped solvent caged intermediate, which occurs in just a few hundred femtoseconds. Classical molecular dynamics simulations were then used to estimate the lifetime of the caged intermediate, which is between 200 and 400 picoseconds. This indicates that when the η2-π-coordination intermediate is formed, it occurs only after the first formation of the solvent-caged intermediate. This dynamic mechanism intriguingly suggests the possibility that the solvent-caged intermediate rather than a coordination intermediate is responsible (or partially responsible) for the inverse KIE value experimentally measured for W. Additionally, this dynamic mechanism prompted us to calculate the kH/kD KIE value for the C-H bonding forming transition states of Mo and W. Surprisingly, Mo gave a normal value, while W gave an inverse value, albeit small, due to a much later transition state position.

Non-IRC Mechanism of Bimolecular Reactions with Submerged Barriers: A Case Study of Si+ + H2O Reaction

Chemical reactions with submerged barriers may feature interesting dynamic behaviors that are distinct from those with substantial barriers or those entirely dominated by capture. The Si+ + H2O reaction is a prototypical example, involving even two submerged saddle points along the reaction path: one for the direct dissociation of H (H-dissociation SP) and another for H migration from the O-side to the Si-side (H-migration SP). We investigated the intricacies of this process by employing quasi-classical trajectory calculations on an accurate, full-dimensional ab initio potential energy surface. Through careful trajectory analysis, an interesting nonintrinsic reaction coordinate mechanism was found to play an important role in producing SiOH+ and H. This new pathway is featured as that the H atoms do not form HSiOH+ complexes along the minimum-energy path but directly dissociate into the products after passing through the H-migration SP. Furthermore, based on artificially scaled potential energy surfaces (PESs), the impact of barrier height on the reaction is also explored. This work provides new insights into the dynamics of the Si+ + H2O reaction and enriches our understanding of reactions with submerged barriers.

Dynamical Origin of Rebound versus Dissociation Selectivity during Fe-Oxo-Mediated C-H Functionalization Reactions

The mechanism of catalytic C-H functionalization of alkanes by Fe-oxo complexes is often suggested to involve a hydrogen atom transfer (HAT) step with the formation of a radical-pair intermediate followed by diverging pathways for radical rebound, dissociation, or desaturation. Recently, we showed that in some Fe-oxo reactions, the radical pair is a nonstatistical-type intermediate and dynamic effects control rebound versus dissociation pathway selectivity. However, the effect of the solvent cage on the stability and lifetime of the radical-pair intermediate has never been analyzed. Moreover, because of the extreme complexity of motion that occurs during dynamics trajectories, the underlying physical origin of pathway selectivity has not yet been determined. For the reaction between [(TQA_Cl)FeIVO]+ and cyclohexane, here, we report explicit solvent trajectories and machine learning analysis on transition-state sampled features (e.g., vibrational, velocity, and geometric) that identified the transferring hydrogen atom kinetic energy as the most important factor controlling rebound versus nonrebound dynamics trajectories, which provides an explanation for our previously proposed dynamic matching effect in fast rebound trajectories that bypass the radical-pair intermediate. Manual control of the reaction trajectories confirmed the importance of this feature and provides a mechanism to enhance or diminish selectivity for the rebound pathway. This led to a general catalyst design principle and proof-of-principle catalyst design that showcases how to control rebound versus dissociation reaction pathway selectivity.

Intramolecular Carboxyamidation of Alkyne-Tethered O-Acylhydroxamates through Formation of Fe(III)-Nitrenoids

We developed intramolecular carboxyamidations of alkyne-tethered O-acylhydroxamates followed by either thermally induced spontaneous or 4-(dimethylamino)pyridine-catalyzed O→O or O→N acyl group migration. Under iron-catalyzed conditions, the carboxyamidation products were generated in high yield from both Z-alkene and arene-tethered substrates. DFT calculations indicate that the iron-catalyzed carboxyamidation proceeds via a stepwise mechanism involving iron-imidyl radical cyclization followed by intramolecular acyloxy transfer from the iron center to the alkenyl radical center to furnish the cis-carboxyamidation product. Upon treatment with 4-(dimethylamino)pyridine, the Z-alkene-tethered carboxyamidation products underwent selective O→O acyl migration to generate 2-acyloxy-5-acyl pyrroles. Thermal O→N acyl migration occurs during carboxyamidation if the Z-alkene linker contains an alkyl or an aryl substituent at the β-position of the carbonyl group. On the other hand, the arene linker-containing compounds selectively undergo O→N acyl migration to generate N-acyl-3-acylisoindolinones, and the corresponding O→O acyl migration forming isoindole derivatives was not observed.

Possible Roles of Transition Metal Cations in the Formation of Interstellar Benzene via Catalytic Acetylene Cyclotrimerization

Polycyclic aromatic hydrocarbons (PAHs) are ubiquitous interstellar molecules. However, the formation mechanisms of PAHs and even the simplest cyclic aromatic hydrocarbon, benzene, are not yet fully understood. Recently, we reported the statistical and dynamical properties in the reaction mechanism of Fe+-catalyzed acetylene cyclotrimerization, whereby three acetylene molecules are directly converted to benzene. In this study, we extended our previous work and explored the possible role of the complex of other 3d transition metal cations, TM+ (TM = Sc, Ti, Mn, Co, and Ni), as a catalyst in acetylene cyclotrimerization. Potential energy profiles for bare TM+-catalyst (TM = Sc and Ti), for TM+NC--catalyst (TM = Sc, Ti, Mn, Co, and Ni), and for TM+-(H2O)8-catalyst (TM = Sc and Ti) systems were obtained using quantum chemistry calculations, including the density functional theory levels. The calculation results show that the scandium and titanium cations act as efficient catalysts in acetylene cyclotrimerization and that reactants, which contain an isolated acetylene and (C2H2)2 bound to a bare (ligated) TM cation (TM = Sc and Ti), can be converted into a benzene-metal-cation product complex without an entrance barrier. We found that the number of electrons in the 3d orbitals of the transition metal cation significantly contributes to the catalytic efficiency in the acetylene cyclotrimerization process. On-the-fly Born-Oppenheimer molecular dynamics (BOMD) simulations of the Ti+-NC- and Ti+-(H2O)8 complexes were also performed to comprehensively understand the nuclear dynamics of the reactions. The computational results suggest that interstellar benzene can be produced via acetylene cyclotrimerization reactions catalyzed by transition metal cation complexes.

Dynamic-dependent selectivity in a bisphosphine iron spin crossover C-H insertion/π-coordination reaction

Reaction pathway selectivity is generally controlled by competitive transition states. Organometallic reactions are complicated by the possibility that electronic spin state changes rather than transition states can control the relative rates of pathways, which can be modeled as minimum energy crossing points (MECPs). Here we show that in the reaction between bisphosphine Fe and ethylene involving spin state crossover (singlet and triplet spin states) that neither transition states nor MECPs model pathway selectivity consistent with experiment. Instead, single spin state and mixed spin state quasiclassical trajectories demonstrate nonstatistical intermediates and that C-H insertion versus π-coordination pathway selectivity is determined by the dynamic motion during reactive collisions. This example of dynamic-dependent product outcome provides a new selectivity model for organometallic reactions with spin crossover.

Direct Dynamics Trajectories Demonstrate Dynamic Matching and Nonstatistical Radical Pair Intermediates during Fe-Oxo-Mediated C-H Functionalization Reactions

The generally proposed mechanism for the reaction between non-heme Fe-oxo complexes and alkane C-H bonds involves a hydrogen atom transfer (HAT) reaction step with a radical pair intermediate that then has competitive radical rebound, dissociation, or desaturation pathways. Here, we report density functional theory-based quasiclassical direct dynamics trajectories that examine post-HAT reaction dynamics. Trajectories revealed that the radical pair intermediate can be a nonstatistical type intermediate without complete internal vibrational redistribution and post-HAT selectivity is generally determined by dynamic effects. Fast rebound trajectories occur through dynamic matching between the rotational motion of the newly formed Fe-OH bond and collision with the alkane radical, and all of this occurs through a nonsynchronous dynamically concerted process that circumvents the radical pair intermediate structure. For radical pair dissociation, trajectories proceeded to the radical pair intermediate for a very brief time, followed by complete dissociation. These trajectories provide a new viewpoint and model to understand the inherent reaction pathway selectivity for non-heme Fe-oxo-mediated C-H functionalization reactions.

Interstellar Benzene Formation Mechanisms via Acetylene Cyclotrimerization Catalyzed by Fe+ Attached to Water Ice Clusters: Quantum Chemistry Calculation Study

Benzene is the simplest building block of polycyclic aromatic hydrocarbons and has previously been found in the interstellar medium. Several barrierless reaction mechanisms for interstellar benzene formation that may operate under low-temperature and low-pressure conditions in the gas phase have been proposed. In this work, we studied different mechanisms for interstellar benzene formation based on acetylene cyclotrimerization catalyzed by Fe⁺ bound to solid water clusters through quantum chemistry calculations. We found that benzene is formed via a single-step process with one transition state from the three acetylene molecules on the Fe⁺(H₂O)_n (n = 1, 8, 10, 12 and 18) cluster surface. Moreover, the obtained mechanisms differed from those of single-atom catalysis, in which benzene is sequentially formed via multiple steps.

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

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

Portable Models for Entropy Effects on Kinetic Selectivity

Differences in entropies of competing transition states can direct kinetic selectivity. Understanding and modeling such entropy differences at the molecular level is complicated by the fact that entropy is statistical in nature; i.e., it depends on multiple vibrational states of transition structures, the existence of multiple dynamically accessible pathways past these transition structures, and contributions from multiple transition structures differing in conformation/configuration. The difficulties associated with modeling each of these contributors are discussed here, along with possible solutions, all with an eye toward the development of portable qualitative models of use to experimentalists aiming to design reactions that make use of entropy to control kinetic selectivity.

Energy Dispersion in Pyridinium-Water Nanodroplets upon Irradiation

Postirradiation dissociation of molecular clusters has been mainly studied assuming energy redistribution in the entire cluster prior to the dissociation. Here, the evaporation of water molecules from out-of-equilibrium pyridinium-water cluster ions was investigated using the recently developed correlated ion and neutral time-of-flight (COINTOF) mass spectrometry technique in combination with a velocity-map imaging (VMI) device. This special setup enables the measurement of velocity distributions of the evaporated molecules upon high-velocity collisions with an argon atom. The distributions measured for pyridinium-water cluster ions are found to have two distinct components. Besides a low-velocity contribution, which corresponds to the statistical evaporation of water molecules after nearly complete redistribution of the excitation energy within the clusters, a high-velocity contribution is also found in which the molecules are evaporated before the energy redistribution is complete. These two different evaporation modes were previously observed and described for protonated water cluster ions. However, unlike in the case of pure water clusters, the low-velocity part of the distributions for pyridinium-doped water clusters is itself composed of two distinct Maxwell-Boltzmann distributions, indicating that evaporated molecules originate in this case from out-of-equilibrium processes. Statistical molecular dynamics simulations were performed to (i) understand the effects caused in the ensuing evaporation process by the various excitation modes at different initial cluster constituents and to (ii) simulate the distributions resulting from sequential evaporations. The presence of a hydrophobic impurity in water clusters is shown to impact water molecule evaporation due to the energy storage in the internal degrees of freedom of the impurity.

Stereoelectronic and dynamical effects dictate nitrogen inversion during valence isomerism in benzene imine

Non-classical processes such as heavy-atom tunneling and post transition-state dynamics govern stereoselectivity for benzene imine ⇌ 1H-azepine.

Singlet Oxygen Oxidation of the Radical Cations of 8-Oxo-2'-deoxyguanosine and Its 9-Methyl Analogue: Dynamics, Potential Energy Surface, and Products Mediated by C5-O2 -Addition

8-Oxo-2'-deoxyguanosine (OG) is the most common DNA lesion. Notably, OG becomes more susceptible to oxidative damage than the undamaged nucleoside, forming mutagenic products in vivo. Herein the reactions of singlet O₂ with the radical cations of 8-oxo-2'-deoxyguanosine (OG^.+ ) and 9-methyl-8-oxoguanine (9MOG^.+ ) were investigated using ion-molecule scattering mass spectrometry, from which barrierless, exothermic O₂ -addition products were detected for both reaction systems. Corroborated by static reaction potential energy surface constructed using multi-reference CASPT2 theory and molecular dynamics simulated in the presence of the reactants' kinetic and internal energies, the C5-terminal O₂ -addition was pinpointed as the most probable reaction pathway. By elucidating the reaction mechanism, kinetics and dynamics, and reaction products and energetics, this work constitutes the first report unraveling the synergetic damage of OG by ionizing radiation and singlet O₂ .

Direct Dynamics Trajectories Reveal Nonstatistical Coordination Intermediates and Demonstrate that σ and π-Coordination Are Not Required for Rhenium(I)-Mediated Ethylene C-H Activation

The C-H activation reaction between Cp(PMe₃)₂Re and ethylene results in kinetic selectivity for the Re-vinyl hydride I over the thermodynamically more stable Cp(PMe₃)₂Re(η²-ethylene) π-complex II. While transition-state and variational transition-state structures were located for individual pathways leading to I and II, DFT and CCSD(T) energies predict a large kinetic selectivity of 10²-10⁴, which is incompatible with the experimental 10:1 ratio. DFT direct quasiclassical trajectories revealed that the transition states do not provide a qualitatively correct reaction mechanism or a quantitatively correct selectivity due to a nonstatistical σ-CH coordination intermediate that precedes the transition states for C-H activation and π coordination. Using metadynamics and quasiclassical direct dynamics, we show that trajectories for the reaction between Cp(PMe₃)₂Re and ethylene result in direct formation of either the Re-vinyl hydride I or the π-complex II. Trajectories leading to the Re-vinyl hydride skip σ-coordination and do not require π-coordination. Consistent with experiments, trajectory selectivity provides a relatively small kinetic selectivity for the Re-vinyl hydride.

Application of Reaction Path Search Calculations to Potential Energy Surface Fits

There has been significant progress in recent years in the use of machine learning techniques to model high-dimensional reactive potential energy surfaces using large-scale data obtained from ab initio electronic structure calculations. In these methods, the strategy used to gather data becomes a key issue as the molecular size increases. In this work, we examine the applicability of the reaction path search algorithm implemented in the Global Reaction Route Mapping (GRRM) code as a data-gathering approach. The electronic energies and gradients sampled by using the GRRM calculation are directly used in potential energy surface fitting to a permutationally invariant polynomial function. This simple approach was applied to the HNS and HCNO reaction systems, and we found that the fitted potential energy surfaces reasonably reproduce the features of the electronic structure calculations used in the GRRM calculations. This suggests that the GRRM sampling scheme can be used to construct an initial potential energy surface.

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.

Dynamic Effects on Migratory Aptitudes in Carbocation Reactions

Carbocation rearrangement reactions are of great significance to synthetic and biosynthetic chemistry. In pursuit of a scale of inherent migratory aptitude that takes into account dynamic effects, both uphill and downhill ab initio molecular dynamics (AIMD) simulations were used to examine competing migration events in a model system designed to remove steric and electronic biases. The results of these simulations were combined with detailed investigations of potential energy surface topography and variational transition state theory calculations to reveal the importance of nonstatistical dynamic effects on migratory aptitude.

Molecular Dynamics Simulations, Reaction Pathway and Mechanism Dissection, and Kinetics Modeling of the Nitric Acid Oxidation of Dicyanamide and Dicyanoborohydride Anions

Direct dynamics simulations of HNO₃ with dicyanamide anion DCA^- (i.e., N(CN)₂^-) and dicyanoborohydride anion DCBH^- (i.e., BH₂(CN)₂^-) were performed at the B3LYP/6-31+G(d) level of theory in an attempt to elucidate the primary and secondary reactions in the two reaction systems. Guided by trajectory results, reaction coordinates and potential energy diagrams were mapped out for the oxidation of DCA^- and DCBH^- by one and two HNO₃ molecules, respectively, in the gas-phase and in the condensed-phase ionic liquids using the B3LYP/6-311++G(d,p) method. The oxidation of DCA^- by HNO₃ is initiated by proton transfer. The most important pathway leads to the formation of O₂N-NHC(O)NCN^-, and the latter reacts with a second HNO₃ to produce O₂N-NHC(O)NC(O)NH-NO₂^-(DNB^-). The oxidation of DCBH^- by HNO₃ may follow a similar mechanism as that of DCA^-, producing two analogue products: O₂N-NHC(O)BH₂CN^- and O₂N-NHC(O)BH₂C(O)NH-NO₂^-. Moreover, two new, unique reaction pathways were discovered for DCBH^- because of its boron-hydride group: (1) isomerization of DCBH^- to CNBH₂CN^- and CNBH₂NC^- and (2) H₂ elimination in which the proton in HNO₃ combines with a hydride-H in DCBH^-. The Rice-Ramsperger-Kassel-Marcus (RRKM) theory was utilized to calculate reaction kinetics and product branching ratios. The RRKM results indicate that the formation of DNB^- is exclusively important in the oxidation of DCA^-, whereas the same type of reaction is a minor channel in the oxidation of DCBH^-. In the latter case, H₂ elimination becomes dominating. The RRKM modeling also indicates that the oxidation rate constant of DCBH^- is higher than that of DCA^- by an order of magnitude. This rationalizes the enhanced preignition performance of DCBH^- over DCA^- with HNO₃.

Experiments and Direct Dynamics Simulations That Probe η2-Arene/Aryl Hydride Equilibria of Tungsten Benzene Complexes

Key steps in the functionalization of an unactivated arene often involve its dihaptocoordination by a transition metal followed by insertion into the C-H bond. However, rarely are the η²-arene and aryl hydride species in measurable equilibrium. In this study, the benzene/phenyl hydride equilibrium is explored for the {WTp(NO)(PBu₃)} (Bu = n-butyl; Tp = trispyrazoylborate) system as a function of temperature, solvent, ancillary ligand, and arene substituent. Both face-flip and ring-walk isomerizations are identified through spin-saturation exchange measurements, which both appear to operate through scission of a C-H bond. The effect of either an electron-donating or electron-withdrawing substituent is to increase the stability of both arene and aryl hydride isomers. Crystal structures, electrochemical measurements, and extensive NMR data further support these findings. Static density functional theory calculations of the benzene-to-phenyl hydride landscape suggest a single linear sequence for this transformation involving a sigma complex and oxidative cleavage transition state. Static DFT calculations also identified an η²-coordinated benzene complex in which the arene is held more loosely than in the ground state, primarily through dispersion forces. Although a single reaction pathway was identified by static calculations, quasiclassical direct dynamics simulations identified a network of several reaction pathways connecting the η²-benzene and phenyl hydride isomers, due to the relatively flat energy landscape.

Bouncing off walls - widths of exit channels from shallow minima can dominate selectivity control

A selectivity model based on the widths of pathways to competing products, rather than barrier heights, is formulated for the butadiene + allyl cation reaction. This model was arrived at via analysis of stationary points, intrinsic reaction coordinates, potential energy surface shapes and direct dynamics trajectories, all determined using quantum chemical methods.

Gas-Phase Synthesis of 3-Vinylcyclopropene via the Crossed Beam Reaction of the Methylidyne Radical (CH; X2 Π) with 1,3-Butadiene (CH2 CHCHCH2 ; X1 Ag )

The crossed molecular beam reactions of the methylidyne radical (CH; X² Π) with 1,3-butadiene (CH₂ CHCHCH₂ ; X¹ A_g ) along with their (partially) deuterated counterparts were performed at collision energies of 20.8 kJ mol^-1 under single collision conditions. Combining our laboratory data with ab initio calculations, we reveal that the methylidyne radical may add barrierlessly to the terminal carbon atom and/or carbon-carbon double bond of 1,3-butadiene, leading to doublet C₅ H₇ intermediates with life times longer than the rotation periods. These collision complexes undergo non-statistical unimolecular decomposition through hydrogen atom emission yielding the cyclic cis- and trans-3-vinyl-cyclopropene products with reaction exoergicities of 119±42 kJ mol^-1 . Since this reaction is barrierless, exoergic, and all transition states are located below the energy of the separated reactants, these cyclic C₅ H₆ products are predicted to be accessed even in low-temperature environments, such as in hydrocarbon-rich atmospheres of planets and cold molecular clouds such as TMC-1.

Molecular Dynamics Simulations and Product Vibrational Spectral Analysis for the Reactions of NO2 with 1-Ethyl-3-methylimidazolium Dicyanamide (EMIM+DCA-), 1-Butyl-3-methylimidazolium Dicyanamide (BMIM+DCA-), and 1-Allyl-3-methylimidazolium Dicyanamide (AMIM+DCA-)

Direct dynamics trajectory simulations were carried out for the NO₂ oxidation of 1-ethyl-3-methylimidazolium dicyanamide (EMIM⁺DCA^-), which were aimed at probing the nature of the primary and secondary reactions in the system. Guided by trajectory results, reaction coordinates and potential energy diagrams were mapped out for NO₂ with EMIM⁺DCA^-, as well as with its analogues 1-butyl-3-methylimidazolium dicyanamide (BMIM⁺DCA^-) and 1-allyl-3-methylimidazolium dicyanamide (AMIM⁺DCA^-). Reactions of the dialkylimidazolium-dicyanamide (DCA) ionic liquids (ILs) are all initiated by proton transfer and/or alkyl abstraction between 1,3-dialkylimidazolium cations and DCA^- anion, of which two exoergic pathways are particularly relevant to their oxidation activities. One pathway is the transfer of a H^β-proton from the ethyl, butyl, or allyl group of the dialkylimidazolium cation to DCA^- that results in the concomitant elimination of the corresponding alkyl as a neutral alkene, and the other pathway is the alkyl abstraction by DCA^- via a second order nucleophilic substitution (SN₂) mechanism. The intra-ion-pair reaction products, including [dialkylimidazolium⁺ - H_C2⁺], alkylimidazole, alkene, alkyl-DCA, HDCA, and DCA^-, react with NO₂ and favor the formation of nitrite (-ONO) complexes over nitro (-NO₂) complexes, albeit the two complex structures have similar formation energies. The exoergic intra-ion-pair reactions in the dialkylimidazolium-DCA ILs account for their significantly higher oxidation activities over the previously reported 1-methyl-4-amino-1,2,4-triazolium dicyanamide [Liu, J.; J. Phys. Chem. B 2019, 123, 2956-2970] and for the relatively higher reactivity of BMIM⁺DCA^- vs AMIM⁺DCA^- as BMIM⁺ has a higher reaction path degeneracy for intra-ion-pair H^β-proton transfer and its H^β-transfer is more energetically favorable. To validate and directly compare our computational results with spectral measurements in the ILs, infrared and Raman spectra of BMIM⁺DCA^- and AMIM⁺DCA^- and their products with NO₂ were calculated using an ionic liquid solvation model. The simulated spectra reproduced all of the vibrational frequencies detected in the reactions of BMIM⁺DCA^- and AMIM⁺DCA^- IL droplets with NO₂ (as reported by Brotton et al. [ J. Phys. Chem. A 2018, 122, 7351-7377] and Lucas et al. [ J. Phys. Chem. A 2019, 123, 400-416]).

Nonstatistical Reaction Dynamics

Nonstatistical dynamics is important for many chemical reactions. The Rice-Ramsperger-Kassel-Marcus (RRKM) theory of unimolecular kinetics assumes a reactant molecule maintains a statistical microcanonical ensemble of vibrational states during its dissociation so that its unimolecular dynamics are time independent. Such dynamics results when the reactant's atomic motion is chaotic or irregular. Intrinsic non-RRKM dynamics occurs when part of the reactant's phase space consists of quasiperiodic/regular motion and a bottleneck exists, so that the unimolecular rate constant is time dependent. Nonrandom excitation of a molecule may result in short-time apparent non-RRKM dynamics. For rotational activation, the 2J + 1 K levels for a particular J may be highly mixed, making K an active degree of freedom, or K may be a good quantum number and an adiabatic degree of freedom. Nonstatistical dynamics is often important for bimolecular reactions and their intermediates and for product-energy partitioning of bimolecular and unimolecular reactions. Post–transition state dynamics is often highly complex and nonstatistical.

Tipping the balance: theoretical interrogation of divergent extended heterolytic fragmentations

Herein we interrogate a type of heterolytic fragmentation reaction called a 'divergent fragmentation' using density functional theory (DFT), natural bond orbital (NBO) analysis, ab initio molecular dynamics (AIMD), and external electric field (EEF) calculations. We demonstrate that substituents, electrostatic environment and non-statistical dynamic effects all influence product selectivity in reactions that involve divergent fragmentation pathways. Direct dynamics simulations reveal an unexpected post-transition state bifurcation (PTSB), and EEF calculations suggest that some transition states for divergent pathways can, in principle, be selectively stabilized if an electric field of the correct magnitude is oriented appropriately.

Real-time tracking of the entangled pathways in the multichannel photodissociation of acetaldehyde

The roaming mechanism, an unconventional reaction path, was discovered more than a decade ago in the studies of formaldehyde photodissociation, H₂CO → H₂ + CO. Since then, observations of roaming have been claimed in numerous photochemical processes. A closer examination of the presented data, however, revealed that evidence for roaming is not always unequivocal, and some of the conclusions could be misleading. We report here an in-depth, joint experimental and theoretical study of the title reaction. By tracking the time-evolution of the pair-correlated product state distributions, we decipher the competing, interwoven reaction pathways that lead to the radical (CH₃ + HCO) and molecular (CH₄ + CO) products. Possible roaming pathways are then elucidated and a more precise descriptor of the phenomenon is delineated.

Stable chaos and delayed onset of statisticality in unimolecular dissociation reactions

Statistical models provide a powerful and useful class of approximations for calculating reaction rates by bypassing the need for detailed, and often difficult, dynamical considerations. Such approaches invariably invoke specific assumptions about the extent of intramolecular vibrational energy flow in the system. However, the nature of the transition to the statistical regime as a function of the molecular parameters is far from being completely understood. Here, we use tools from nonlinear dynamics to study the transition to statisticality in a model unimolecular reaction by explicitly visualizing the high dimensional classical phase space. We identify generic features in the phase space involving the intersection of two or more independent anharmonic resonances and show that the presence of correlated, but chaotic, intramolecular dynamics near such junctions leads to nonstatisticality. Interestingly, akin to the stability of asteroids in the Solar System, molecules can stay protected from dissociation at the junctions for several picoseconds due to the phenomenon of stable chaos.

Intramolecular vibrational energy redistribution and the quantum ergodicity transition: a phase space perspective

The onset of facile intramolecular vibrational energy flow can be related to features in the connected network of anharmonic resonances in the classical phase space.

Experimental and DFT Studies on the Identity Exchange Reactions between Phenyl Chalcogen Iranium Ions and Alkenes

The gas-phase ion-molecule identity exchange reactions of phenyl chalcogen iranium ions with alkenes have been examined experimentally in a linear ion trap mass spectrometer by isotope labeling experiments. The nature of both the alkene and the chalcogen play crucial roles, with the bimolecular rates for π-ligand exchange following the order: [PhTe(c-C₆H₁₀)]⁺ + c-C₆D₁₀ > [PhTe(C₂D₄)]⁺ + C₂H₄ > [PhSe(c-C₆H₁₀)]⁺ + c-C₆D₁₀, with no reaction being observed for [PhSe(C₂D₄)]⁺ + C₂H₄, [PhS(C₂D₄)]⁺ + C₂H₄, and [PhS(c-C₆H₁₀)]⁺ + c-C₆D₁₀. The experimental results correlate with RRKM modeling and density functional theory (DFT) calculations, which also demonstrates that these reactions proceed via associative mechanisms. Natural bond orbital (NBO) analysis reveals a shift in the association complexes from a σ-hole interaction to ones mirroring the π-p⁺ and n-π* at the transition state in accordance with the rates of reaction.

Computational Study of the Reaction of 1-Methyl-4-amino-1,2,4-triazolium Dicyanamide with NO2: From Reaction Dynamics to Potential Surfaces, Kinetics and Spectroscopy

Direct dynamics trajectories were calculated at the B3LYP/6-31G(d) level of theory in an attempt to understand the reaction of 1-methyl-4-amino-1,2,4-triazolium dicyanamide (MAT⁺DCA^-) with NO₂. The trajectories revealed an extensive intra-ion-pair proton transfer in MAT⁺DCA^-. The reaction pathways of the ensuing HDCA (i.e., HNCNCN) and [MAT⁺ - H_C5⁺] (i.e., deprotonated at C5-H of MAT⁺) molecules as well as DCA^- with NO₂ were identified. The reaction of NO₂ with HDCA and DCA^- produces HNC(-ONO)NCN and NCNC(-ONO)N^- or NCNCN-NO₂^-, respectively, whereas that with [MAT⁺ - H_C5⁺] results in the formation of 5-O-MAT (i.e., 4-amino-2-methyl-2,4-dihydro-3 H-1,2,4-triazo-3-one) + NO and [MAT⁺ - H₂⁺] + HNO₂. Using trajectories for guidance, structures of intermediates, transition states and products, and the corresponding reaction potential surfaces were elucidated at B3LYP/6-311++ G(d,p). Rice-Ramsperger-Kassel-Marcus (RRKM) theory was utilized to calculate the reaction rates and statistical product branching ratios. A comparison of direct dynamics simulations with RRKM modeling results indicate that the reactions of NO₂ with HDCA and DCA^- are nonstatistical. To validate our computational results, infrared and Raman spectra of MAT⁺DCA^- and its reaction products with NO₂ were calculated using an ionic liquid solvation model. The calculated spectra reproduced the vibrational frequencies detected in an earlier spectroscopic study of MAT⁺DCA^- droplets with NO₂ [ Brotton , S. J. ; J. Phys. Chem. Lett. 2017 , 8 , 6053 ].

Pushing the limits of concertedness. A waltz of wandering carbocations

Among the array of complex terpene-forming carbocation cyclization/rearrangement reactions, the so-called "triple shift" reactions are among the most unexpected. Such reactions involve the asynchronous combination of three 1,n-shifts into a concerted process, e.g., a 1,2-alkyl shift followed by a 1,3-hydride shift followed by a second 1,2-alkyl shift. This type of reaction so far has been proposed to occur during the biosynthesis of diterpenes and the sidechains of sterols. Here we describe efforts to push the limits of concertedness in this type of carbocation reaction by designing, and characterizing with quantum chemical computations, systems that could couple additional 1,n-shift events to a triple shift leading, in principle to quadruple, pentuple, etc. shifts. While our designs did not lead to clear-cut examples of quadruple, etc. shifts, they did lead to reactions with surprisingly flat energy surfaces where more than five chemical events connect reactants and plausible products. Ab initio molecular dynamics simulations demonstrate that the formal minima on these surfaces interchange on short timescales, both with each other and with additional unexpected structures, allowing us a glimpse into a very complex manifold that allows ready access to great structural diversity.

Questions in natural products synthesis research that can (and cannot) be answered using computational chemistry

Questions of relevance to those working in the field of natural products synthesis that can be answered, at least in part, using computational chemistry approaches are described. Illustrative examples are provided, as are descriptions of limitations.

Singlet O2 Oxidation of a Deprotonated Guanine-Cytosine Base Pair and Its Entangling with Intra-Base-Pair Proton Transfer

We report an experimental and computational study on the ¹ O₂ oxidation of gas-phase deprotonated guanine-cytosine base pair [G ⋅ C-H]^- that is composed of 9HG ⋅ [C-H]^- and 7HG ⋅ [C-H]^- (pairing 9H- or 7H-guanine with N1-deprotonated cytosine), and 9HG ⋅ [C-H]^- _PT and 7HG ⋅ [C-H]^- _PT (formed by intra-base-pair proton transfer from the N1 of guanine to the N3 of [C-H]^- ). The conformer-averaged reaction product ions and cross section were measured over a center-of-mass collision energy range from 0.1 to 0.5 eV using a guided-ion-beam tandem mass spectrometer. To explore conformation-specific reactivity, collision dynamics of ¹ O₂ with each of the four [G ⋅ C-H]^- conformers was simulated at B3LYP/6-31G(d). Trajectories showed that the ¹ O₂ oxidation of the base pair entangles with intra-base-pair proton transfer, and prefers to occur in a collision when the base pair adopts a proton-transferred structure; trajectories also indicate that the 9HG-containing base pair favors stepwise formation of 4,8-endoperoxide of guanine, whereas the 7HG-containing base pair prefers concerted formation of guanine 5,8-endoperoxide. Using trajectory results as a guide, potential energy surfaces (PESs) along all possible reaction pathways were established using the approximately spin-projected ωB97XD/6-311++G(d,p)//B3LYP/6-311++G(d,p) method. PESs have not only rationalized trajectory findings but provided more accurate energetics and indicated that the proton-transferred base-pair conformers have lower activation barriers for oxidation than their non-proton-transferred counterparts.

Secondary Carbocations in the Biosynthesis of Pupukeanane Sesquiterpenes

The results of quantum chemical calculations on putative biosynthetic carbocation cyclization/rearrangements leading to pupukeanane and related sesquiterpenes indicate that a secondary carbocation proposed as an intermediate is not a minimum on the potential energy surface and instead resides in a region of the potential energy surface associated with a plateau containing multiple exit channels.