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

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.

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.

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.

New Insights into the (A)Synchronicity of Diels–Alder Reactions: A Theoretical Study Based on the Reaction Force Analysis and Atomic Resolution of Energy Derivatives

In the present manuscript, we report new insights into the concept of (a)synchronicity in Diels–Alder (DA) reactions in the framework of the reaction force analysis in conjunction with natural population calculations and the atomic resolution of energy derivatives along the intrinsic reaction coordinate (IRC) path. Our findings suggest that the DA reaction transitions from a preferentially concerted mechanism to a stepwise one in a 0.10 Å window of synchronicity indices ranging from 0.90 to 1.00 Å. We have also shown that the relative position of the global minimum of the reaction force constant with respect to the TS is an alternative and quantifiable indicator of the (a)synchronicity in DA reactions. Moreover, the atomic resolution of energy derivatives reveals that the mechanism of the DA reaction involves two inner elementary processes associated with the formation of each of the two C-C bonds. This resolution goes on to indicate that, in asynchronous reactions, the driving and retarding components of the reaction force are mostly due to the fast and slow-forming C-C bonds (elementary processes) respectively, while in synchronous reactions, both elementary processes retard and drive the process concomitantly and equivalently.

Quasiclassical Direct Dynamics Trajectory Simulations of Organometallic Reactions

Homogeneous metal-mediated organometallic reactions represent a very large and diverse reaction class. Density functional theory calculations are now routinely carried out and reported for analyzing organometallic mechanisms and reaction pathways. While density functional theory calculations are extremely powerful to understand the energy and structure of organometallic reactions, there are several assumptions in their use and interpretation to define reaction mechanisms and to analyze reaction selectivity. Almost always it is assumed that potential energy structures calculated with density functional theory adequately describe mechanisms and selectivity within the framework of statistical theories, for example, transition state theory and RRKM theory. However, these static structures and corresponding energy landscapes do not provide atomic motion information during reactions that could reveal nonstatistical intermediates without complete intramolecular vibrational redistribution and nonintrinsic reaction coordinate (non-IRC) pathways. While nonstatistical intermediates and non-IRC reaction pathways are now relatively well established for organic reactions, these dynamic effects have heretofore been highly underexplored in organometallic reactions. Through a series of quasiclassical density functional theory direct dynamics trajectory studies, my group has recently demonstrated that dynamic effects occur in a variety of fundamental organometallic reactions, especially bond activation reactions. For example, in the C-H activation reaction between methane and [Cp*(PMe₃)Ir^III(CH₃)]⁺, while the density functional theory energy landscape showed a two-step oxidative cleavage and reductive coupling mechanism, trajectories revealed a mixture of this two-step mechanism and a dynamic one-step mechanism that skipped the [Cp*(PMe₃)Ir^V(H)(CH₃)₂]⁺ intermediate. This study also showed that despite a methane σ-complex being located on the density functional theory surface before oxidative cleavage and after reductive coupling, this intermediate is always skipped and should not be considered an intermediate during reactive trajectories. For non-IRC reaction pathways, quasiclassical direct dynamics trajectories showed that for the isomerization of [Tp(NO)(PMe₃)W(η²-benzene)] to [Tp(NO)(PMe₃)W(H)(Ph)], there are many dynamic reaction pathway connections due to a relatively flat energy landscape and π coordination is not necessary for C-H bond activation through oxidative cleavage. Trajectories also showed that dynamic effects are important in selectivity for ethylene C-H activation versus π coordination in reaction with Cp(PMe₃)₂Re, and trajectories provide a more quantitative model of selectivity than transition state theory. Quasiclassical trajectories examining Au-catalyzed monoallylic diol cyclizations showed dynamic coupling of several reaction steps that include alkoxylation π bond addition, proton shuttling, and water elimination reaction steps. Overall, these studies highlight the need to use direct dynamics trajectory simulations to consider atomic motion during reactions to understand organometallic reaction mechanisms and selectivity.

Machine Learning Analysis of Direct Dynamics Trajectory Outcomes for Thermal Deazetization of 2,3-Diazabicyclo[2.2.1]hept-2-ene

Experimentally, the thermal gas-phase deazetization of 2,3-diazabicyclo[2.2.1]hept-2-ene (1) results in the loss of N₂ and the formation of bicyclo products 3 (exo) and 4 (endo) in a nonstatistical ratio, with preference for the exo product. Here, we report unrestricted M06-2X quasiclassical trajectories initialized from the concerted N₂ ejection transition state that were able to replicate the experimental preference to form 3. We found that the 3:4 ratio results from the relative amounts of very fast (ballistic) exotype trajectories versus trajectories that lead to the 1,3-diradical intermediate 2. These quasiclassical trajectories provided a set of transition-state vibrational, velocity, momenta, and geometric features for the machine learning analysis. A selection of popular supervised classification algorithms (e.g., random forest) provided poor prediction of trajectory outcomes based on only transition-state vibrational quanta and energy features. However, these machine learning models provided more accurate predictions using atomic velocities and atomic positions, attaining ∼70% accuracy using initial conditions and between 85 and 95% accuracy at later reaction time steps. This increased accuracy allowed the feature importance analysis to reveal that, at the later-time analysis, the methylene bridge out-of-plane bending is correlated with trajectory outcomes for the formation of either the exo product or toward the diradical intermediate. Possible reasons for the struggle of machine learning algorithms to classify trajectories based on transition-state features is the heavily overlapping feature values, the finite but very large possible vibrational mode combinations, and the possibility of chaos as trajectories propagate. We examined this chaos by comparing a set of nearly identical trajectories that differed by only a very small scaling of the kinetic energies resulting from the transition-state reaction coordinate.

Unravelling the Keto-Enol Tautomer Dependent Photochemistry and Degradation Pathways of the Protonated UVA Filter Avobenzone

Avobenzone (AB) is a widely used UVA filter known to undergo irreversible photodegradation. Here, we investigate the detailed pathways by which AB photodegrades by applying UV laser-interfaced mass spectrometry to protonated AB ions. Gas-phase infrared multiple-photon dissociation (IRMPD) spectra obtained with the free electron laser for infrared experiments, FELIX, (600–1800 cm^–1) are also presented to confirm the geometric structures. The UV gas-phase absorption spectrum (2.5–5 eV) of protonated AB contains bands that correspond to selective excitation of either the enol or diketo forms, allowing us to probe the resulting, tautomer-dependent photochemistry. Numerous photofragments (i.e., photodegradants) are directly identified for the first time, with m/z 135 and 161 dominating, and m/z 146 and 177 also appearing prominently. Analysis of the production spectra of these photofragments reveals that that strong enol to keto photoisomerism is occurring, and that protonation significantly disrupts the stability of the enol (UVA active) tautomer. Close comparison of fragment ion yields with the TD-DFT-calculated absorption spectra give detailed information on the location and identity of the dissociative excited state surfaces, and thus provide new insight into the photodegradation pathways of avobenzone, and photoisomerization of the wider class of β-diketone containing molecules.

Mechanistic molecular motion of transition-metal mediated β-hydrogen transfer: quasiclassical trajectories reveal dynamically ballistic, dynamically unrelaxed, two step, and concerted mechanisms

Quasiclassical direct dynamics reveal new dynamical mechanisms for metal-alkyl to ethylene β-hydrogen transfer.

EVB and polarizable MM study of energy relaxation in fluorine–acetonitrile reactions

Many-body effects can impact on rates of energy transfer from a ‘hot’ DF solute to acetonitrile solvent.

A Trajectory-Based Method to Explore Reaction Mechanisms

The tsscds method, recently developed in our group, discovers chemical reaction mechanisms with minimal human intervention. It employs accelerated molecular dynamics, spectral graph theory, statistical rate theory and stochastic simulations to uncover chemical reaction paths and to solve the kinetics at the experimental conditions. In the present review, its application to solve mechanistic/kinetics problems in different research areas will be presented. Examples will be given of reactions involved in photodissociation dynamics, mass spectrometry, combustion chemistry and organometallic catalysis. Some planned improvements will also be described.

Dynamical Mechanism May Avoid High-Oxidation State Ir(V)-H Intermediate and Coordination Complex in Alkane and Arene C-H Activation by Cationic Ir(III) Phosphine

Organometallic reaction mechanisms are assumed to be appropriately described by minimum energy pathways mapped out by density functional theory calculations. For the two-step oxidative addition/reductive elimination mechanism for C-H activation of methane and benzene by cationic Cp*(PMe₃)Ir^III(CH₃), we report quasiclassical direct dynamics simulations that demonstrate the Ir^V-H intermediate is bypassed in a significant amount of productive trajectories initiated from vibrationally averaged velocity distributions of oxidative addition transition states. This organometallic dynamical mechanism is akin to the σ-bond metathesis pathway but occurs on the oxidative addition/reductive elimination energy surface and blurs the line between two- and one-step mechanisms. Quasiclassical trajectories also reveal that the momentum of crossing the reductive elimination structure always induces complete alkane and arene dissociation from the Ir metal center, skipping weak C-H σ and π coordination complexes. This suggests that these weak coordination complexes after reductive elimination are not necessarily on the reaction pathway and likely result from a solvent cage.

Labelling and determination of the energy in reactive intermediates in solution enabled by energy-dependent reaction selectivity

Any long-lived chemical structure in solution is subject to statistical energy equilibration, so the history of any specific structure does not affect its subsequent reactions. This is not true for very short-lived intermediates, since energy equilibration takes time. Here, this idea is applied to achieve the energy labeling of a reactive intermediate. The selectivity of the ring-opening α-cleavage reaction of 1-methylcyclobutoxy radical is found here to vary broadly depending on how the radical was formed. Reactions that provide little excess energy to the intermediate lead to high selectivity in the subsequent cleavage (measured as a kinetic isotope effect) while reactions that provide more excess energy to the intermediate exhibit lower selectivity. Allowing for the expected excess energy allows the prediction of the observed product ratios, and in turn the product ratios can be used to obtain a read-out of the energy present in a intermediate.