Theoretical and Computational Studies of Non-RRKM Unimolecular Dynamics

Quantum Chemical Interrogation of Reactions Promoted by Dirhodium Tetracarboxylate Catalysts─Mechanism, Selectivity, and Nonstatistical Dynamic Effects

ConspectusRh2L4 catalysts have risen in popularity in the world of organic synthesis, being used to accomplish a variety of reactions, including C-H insertion and cyclopropanation, and often doing so with high levels of stereocontrol. While the mechanisms and origins of selectivity for such reactions have been examined with computational quantum chemistry for decades, only recently have detailed pictures of the dynamic behavior of reacting Rh2L4-complexed molecules become accessible. Our computational studies on Rh2L4 catalyzed reactions are described here, with a focus on C-H insertion reactions of Rh2L4-carbenes. Several issues complicate the modeling of these reactions, each providing an opportunity for greater understanding and each revealing issues that should be incorporated into future rational design efforts. First, the fundamental mechanism of C-H insertion is discussed. While early quantum chemical studies pointed to transition structures with 3-center [C-H-C] substructures and asynchronous hydride transfer/C-C bond formation, recent examples of reactions with particularly flat potential energy surfaces and even discrete zwitterionic intermediates have been found. These reactions are associated with systems bearing π-donating groups at the site of hydride transfer, allowing for an intermediate with a carbocation substructure at that site to be selectively stabilized. Second, the possible importance of solvent coordination at the Rh atom distal to the carbene is discussed. While effects on reactivity and selectivity were found to be small, they turn out not to be negligible in some cases. Third, it is shown that, in contrast to many other transition metal promoted reactions, many Rh2L4 catalyzed reactions likely involve dissociation of the Rh2L4 catalyst before key chemical steps leading to products. When to expect dissociation is associated with specific features of substrates and the product-forming reactions in question. Often, dissociation precedes transition structures for pericyclic reactions that involve electrons that would otherwise bind to Rh2L4. Finally, the importance of nonstatistical dynamic effects, characterized through ab initio molecular dynamics studies, in some Rh2L4 catalyzed reactions is discussed. These are reactions where transition structures are shown to be followed by flat regions, very shallow minima, and/or pathways that bifurcate, all allowing for trajectories from a single transition state to form multiple different products. The likelihood of encountering such a situation is shown to be associated again with the likelihood of formation of zwitterionic structures along reaction paths, but ones for which pathways to multiple products are expected to be associated with very low or no barriers. The connection between these features and reduced yields of desired products are highlighted, as are the means by which some Rh2L4 catalysts modulate dynamic behavior to produce particular products in high yield.

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.

On the intramolecular vibrational energy redistribution dynamics of aromatic complexes: A comparative study on C6H6-C6H5Cl, C6H6-C6H3Cl3, C6H6-C6Cl6 and C6H6-C6H5F, C6H6-C6H3F3, C6H6-C6F6

Chemical dynamics Simulation studies on benzene dimer (Bz2) and benzene-hexachlorobenzene (Bz-HCB) as performed in the past suggest that the coupling between the monomeric (intramolecular) vibrational modes and modes generated due to the association of two monomers (intermolecular) has to be neither strong nor weak for a fast dissociation of the complex. To find the optimum coupling, four complexes are taken into consideration in this work, namely, benzene-monofluorobenzene, benzene-monochlorobenzene, benzene-trifluorobenzene (Bz-TFB), and benzene-trichlorobenzene. Bz-TFB has the highest rate of dissociation among all seven complexes, including Bz2, Bz-HCB, and Bz-HFB (HFB stands for hexafluorobenzene). The set of vibrational frequencies of Bz-TFB is mainly the reason for this fast dissociation. The mass of chlorine in Bz-HCB is optimized to match its vibrational frequencies similar to those of Bz-TFB, and the dissociation of Bz-HCB becomes faster. The power spectrum of Bz-TFB, Bz-HCB, and Bz-HCB with the modified mass of chlorine is also computed to understand the extent of the said coupling in these complexes.

Regular reaction dynamics in analytical form in the vicinity of symmetrical transition states. Central barrier crossings in SN2 reactions

When an activated complex, as defined in transition state theory (TST), has a polyhedral shape, its kinetic energy is found to be diagonal in a system of spherical polar coordinates. If, in addition, the polyhedron is characterized by a high symmetry, then its dynamics considerably simplifies. An application of this approach to the most symmetrical TS known to date, i.e., that which controls the Cl- + CH3Cl → ClCH3 + Cl- SN2 nucleophilic substitution, is presented and an analytical expression of its potential energy surface is provided. In a substantial range around the saddle point, approximate equations of motion for the two components of the reaction coordinate, i.e., the antisymmetrical stretching motion of the ClCCl core and the wagging motion of the hydrogen triad, can be derived in an analytical form. During an extensive period of time, the main component of the reaction coordinate is governed by an unexpectedly simple equation of motion that depends on a single initial condition, irrespective of the other ones and of the internal energy. Reactive trajectories are observed to form a perfectly collimated bundle characterized by undetectable dispersion, thereby giving a spectacular example of regular dynamics in an anharmonic potential. Regularity and collimation are brought about by local symmetry, which is a widespread feature of potential energy surfaces. Anharmonicity is observed to influence the dynamics only at a late stage. As energy increases, trajectories tend to fan out and to deviate from the analytical equation. For the wagging motion, chaos sets in at much lower energies.

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.

Theoretical Investigation of Dissociation versus Intramolecular Rearrangements in Aminohydroxymethylene

Aminohydroxymethylene (H₂N-C̈-OH) is the simplest aminooxycarbene which is a heteroatom stabilized carbene. This highly reactive molecule was prepared in an Ar matrix in a recent experimental work. Unimolecular reactivity of this astrochemically important molecule was investigated and only fragmentations were identified contrary to the observations of both fragmentations and intramolecular rearrangements in other hydroxycarbenes. These rearrangement reactions form the corresponding imine and carbonyl compounds. In the present work, direct chemical dynamics simulations of unimolecular chemistry of aminohydroxymethylene were performed in the gas phase to study atomic level dissociation mechanisms. Classical trajectories were generated on-the-fly using potentials and gradients computed at the density functional B3LYP/6-31+G* level of electronic structure theory. Simulation results showed that intramolecular rearrangements accompany fragmentations during the unimolecular decay process of aminohydroxymethylene. However, the average lifetime of the intermediate isomers were found to be only few picoseconds which might not have been long enough for detection in the experiments.

Dynamical Behavior of Aromatic Trimer Complexes in Unimolecular Dissociation Reaction at High Temperatures. Case Studies on C6H6-C6F6-C6H6 and C6H6 Trimer Complexes

The intramolecular vibrational energy redistribution (IVR) dynamics during unimolecular dissociation of aromatic trimers at high temperatures is the primary interest of this study. Chemical dynamics simulations are performed for the unimolecular dissociation of benzene-hexafluorobenzene-benzene (Bz-HFB-Bz) and benzene trimer (Bz-trimer) complexes at a temperature range of 1000-2000 K. Partial dissociation of both the complexes is observed, which leads to a dimer and a monomer in the dynamics. However, the probability of such dissociation was found much lower in the case of the Bz-trimer, which further decreases with the increase of temperature. The rate of partial dissociation of Bz-HFB-Bz is faster at 1500, 1800, and 2000 K, whereas the rate of complete dissociation of the Bz-trimer is significantly faster than Bz-HFB-Bz at all temperatures. This is just the opposite of the corresponding dimer's dissociation, where benzene-hexafluorobenzene (Bz-HFB) dissociates at a faster rate than the benzene dimer (Bz-dimer). Thus, the dissociation dynamics of the trimer is different than that of the dimer. Simulations with excited intramolecular and intermolecular modes of the trimer complexes reveal that energy flows from intermolecular to intramolecular modes of Bz-HFB-Bz more freely than the Bz-trimer, and the dissociation process becomes slower for the former. Calculated activation energies for both types of dynamics are much lower than the corresponding binding energies, which may be due to the anharmonicity. The Arrhenius equation with an anharmonic correction factor is considered to recalculate the activation energy and pre-exponential factor.

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.

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.

Dynamics of a gas-phase SNAr reaction: non-concerted mechanism despite the Meisenheimer complex being a transition state

The commonly accepted mechanism of the nucleophilic aromatic substitution (SNAr) reaction has been found to be governed by the nature of the Meisenheimer structure on the potential energy surface. A stable Meisenheimer intermediate favors a stepwise mechanism, while a Meisenheimer transition state favors a concerted mechanism. Here, we show by using a detailed potential energy map (using the DFT and DLPNO-CCSD(T)/CBS methods) and ab initio classical trajectory simulations that the F- + C6H5NO2 SNAr reaction involves a Meisenheimer transition state and follows a stepwise mechanism in contrast to the expected concerted pathway. The stepwise mechanism observed in the trajectory simulations takes place by the formation of various ion-dipole and σ-complexes. While the majority of the trajectories follow the multi-step mechanism and avoid the minimum energy path, a considerable fraction exhibit a roaming atom mechanism where the F atom hovers around the phenyl ring before the formation of the products.

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.

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.

Theoretical investigation of the dissociation chemistry of formyl halides in the gas phase

Halogen substituted analogues of formaldehyde, HXCO (X = F, Cl, Br, and I), play a crucial role in the degradation of stratospheric ozone.

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.

Theoretical investigation of the isomerization pathways of diazenes: torsion vs. inversion

Diazenes are an important family of organic compounds used widely in synthetic and materials chemistry. These molecules have a planar geometry and exhibit cis-trans isomerization. The simplest of all these molecules - diazene (N2H2) - has been subjected to several experimental and theoretical studies. Two mechanisms have been proposed for the cis-trans isomerization of diazene, which are an in-plane inversion and an out-of-plane torsion. The activation energies for these pathways are similar and the competition between these two mechanisms has been discussed in the literature based on electronic structure theory calculations. Three decades ago, a classical dynamics investigation of diazene isomerization was carried out using a model Hamiltonian and it was indicated that the in-plane inversion is forbidden classically because of a centrifugal barrier and the out-of-plane torsion is the only isomerization pathway. In the present work, we investigated the cis-trans isomerization dynamics of diazene using ab initio classical trajectory simulations at the CASSCF(2,2)/aug-cc-pVDZ level of electronic structure theory. The simulation results confirmed the presence of the aforementioned centrifugal barrier for the inversion and torsion was the only observed pathway. The calculations were repeated for a similar system (difluorodiazene, N2F2) and again the centrifugal barrier prevented the inversion pathway.

The separation of the reaction coordinate in transition state theory: Regularity and dimensionality reduction resulting from local symmetry

Local symmetry in a transition state is defined as the absence of cross terms involving the reaction coordinate in the Taylor expansion about a saddle point of a potential energy surface (i.e., by the assumption ∂²V/∂R∂q_j|_* = 0). Then, the plane R = R_* is, but in the immediate neighborhood of the saddle point only, a local plane of symmetry of the potential energy surface. When this decisive condition is met, together with a second requirement that the kinetic energy be diagonal, the reaction dynamics becomes extremely simple, even in a multidimensional system, because it is determined solely by the harmonic part of the potential, at least during the early stages of the evolution. The dimensionality of the system is then reduced, with the reaction coordinate neatly separated from the vibrational degrees of freedom. The latter are then spectators that can only interact among themselves. As a result of this local symmetry, the subset of reactive trajectories is, during an appreciable period of time, observed to form a bundle grouped around an average trajectory. The distance separating the centers of mass of the two dissociating fragments is the appropriate reaction coordinate. The dynamical reaction path, defined as the central curve of a reactive cylinder in phase space, can be derived in closed form as a surprisingly simple one-dimensional law of motion and can be said to derive from a 1D effective Hamiltonian. An alternative formulation of the problem is possible, in which bond lengths are adopted as internal coordinates, although the expression of the kinetic energy becomes much more complicated. Explicit conditions under which the reaction coordinate decouples from spectator modes can be stipulated.

A Better Understanding of the Unimolecular Dissociation Dynamics of Weakly Bound Aromatic Compounds at High Temperature: A Study on C6H6-C6F6 and Comparison with C6H6 Dimer

Chemical dynamics simulations are performed to study the unimolecular dissociation of the benzene (Bz)-hexafluorobenzene (HFB) complex at five different temperatures ranging from 1000 to 2000 K, and the results are compared with that of the Bz dimer at common simulation temperatures. Bz-HFB, in comparison with Bz dimer, possesses a much attractive intermolecular interaction, a very different equilibrium geometry, and a lower average quantum vibrational excitation energy at a given temperature. Six low-frequency modes of Bz-HFB are formed by Bz + HFB association which are weakly coupled with the vibrational modes of Bz and HFB. However, this coupling is found much stronger in Bz-HFB compared to the same in the Bz dimer. The simulations are done with very good potential energy parameters taken from the literature. Considering the canonical (TST) model, the unimolecular dissociation rate constant at each temperature is calculated and fitted to the Arrhenius equation. An activation energy of 5.0 kcal/mol and a pre-exponential factor of 2.39 × 10¹² s^-1 are obtained, which are of expected magnitudes. The responsible vibrational mode for dissociation is identified by performing normal-mode analysis. Simulations with random excitations of high-frequency Bz and HFB modes and low-frequency inter-Bz-HFB vibrational modes of the Bz-HFB complex are also performed. The intramolecular vibrational energy redistribution (IVR) time and the unimolecular dissociation rate constants are calculated from these simulations. The latter shows good agreement with the same obtained from simulation with random excitation of all vibrational modes.

Unimolecular Rate Constants versus Energy and Pressure as a Convolution of Unimolecular Lifetime and Collisional Deactivation Probabilities. Analyses of Intrinsic Non-RRKM Dynamics

Following work by Slater and Bunker, the unimolecular rate constant versus collision frequency, k_uni(ω, E), is expressed as a convolution of unimolecular lifetime and collisional deactivation probabilities. This allows incorporation of nonexponential, intrinsically non-RRKM, populations of dissociating molecules versus time, N( t)/ N(0), in the expression for k_uni(ω, E). Previous work using this approach is reviewed. In the work presented here, the biexponential f₁ exp(- k₁ t) + f₂ exp(- k₂ t) is used to represent N( t)/ N(0), where f₁ k₁ + f₂ k₂ equals the RRKM rate constant k( E) and f₁ + f₂ = 1. With these two constraints, there are two adjustable parameters in the biexponential N( t)/ N(0) to represent intrinsic non-RRKM dynamics. The rate constant k₁ is larger than k( E) and k₂ is smaller. This biexponential gives k_uni(ω, E) rate constants that are lower than the RRKM prediction, except at the high and low pressure limits. The deviation from the RRKM prediction increases as f₁ is made smaller and k₁ made larger. Of considerable interest is the finding that, if the collision frequency ω for the RRKM plot of k_uni(ω, E) versus ω is multiplied by an energy transfer efficiency factor β_c, the RRKM k_uni(ω, E) versus ω plot may be scaled to match those for the intrinsic non-RRKM, biexponential N( t)/ N(0), plots. This analysis identifies the importance of determining accurate collisional intermolecular energy transfer (IET) efficiencies.

Dissection of the multichannel reaction of acetylene with atomic oxygen: from the global potential energy surface to rate coefficients and branching dynamics

A global potential energy surface for the O(³P) + C₂H₂reaction is developed and the quasi-classical trajectory study on the potential energy surface reproduce the rate coefficient and product branching ratio.

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.

Detecting reactive islands using Lagrangian descriptors and the relevance to transition path sampling

It has been known for sometime now that isomerization reactions, classically, are mediated by phase space structures called reactive islands (RI). RIs provide one possible route to correct for the nonstatistical effects in the reaction dynamics. In this work, we map out the reactive islands for the two dimensional Müller-Brown model potential and show that the reactive islands are intimately linked to the issue of rare event sampling. In particular, we establish the sensitivity of the so called committor probabilities, useful quantities in the transition path sampling technique, to the hierarchical RI structures. Mapping out the RI structure for high dimensional systems, however, is a challenging task. Here, we show that the technique of Lagrangian descriptors is able to effectively identify the RI hierarchy in the model system. Based on our results, we suggest that the Lagrangian descriptors can be useful for detecting RIs in high dimensional systems.

Signatures of a Conical Intersection in Adiabatic Dissociation on the Ground Electronic State

Conical intersections are known to cause nonadiabatic transitions, but their effects on adiabatic dynamics are often ignored. Using the overtone-induced dissociation of the hydroxymethyl radical as an example, we demonstrate that ground-state O-H bond rupture is significantly affected by a conical intersection with an electronically excited state along the dissociation path, despite the much lower energy of the dissociating state than that of the conical intersection. In addition to lifetime differences, the geometric phase leads to a different H₂CO rotational state distribution compared with that obtained using the standard single-state adiabatic model, which constitutes a signature of the conical intersection.

The Unimolecular Reactions of CF3CHF2 Studied by Chemical Activation: Assignment of Rate Constants and Threshold Energies to the 1,2-H Atom Transfer, 1,1-HF and 1,2-HF Elimination Reactions, and the Dependence of Threshold Energies on the Number of F-Atom Substituents in the Fluoroethane Molecules

The recombination of CF₃ and CHF₂ radicals in a room-temperature bath gas was used to prepare vibrationally excited CF₃CHF₂* molecules with 101 kcal mol^-1 of vibrational energy. The subsequent 1,2-H atom transfer and 1,1-HF and 1,2-HF elimination reactions were observed as a function of bath gas pressure by following the CHF₃, CF₃(F)C: and C₂F₄ product concentrations by gas chromatography using a mass spectrometer as the detector. The singlet CF₃(F)C: concentration was measured by trapping the carbene with trans-2-butene. The experimental rate constants are 3.6 × 10⁴, 4.7 × 10⁴, and 1.1 × 10⁴ s^-1 for the 1,2-H atom transfer and 1,1-HF and 1,2-HF elimination reactions, respectively. These experimental rate constants were matched to statistical RRKM calculated rate constants to assign threshold energies (E₀) of 88 ± 2, 88 ± 2, and 87 ± 2 kcal mol^-1 to the three reactions. Pentafluoroethane is the only fluoroethane that has a competitive H atom transfer decomposition reaction, and it is the only example with 1,1-HF elimination being more important than 1,2-HF elimination. The trend of increasing threshold energies for both 1,1-HF and 1,2-HF processes with the number of F atoms in the fluoroethane molecule is summarized and investigated with electronic-structure calculations. Examination of the intrinsic reaction coordinate associated with the 1,1-HF elimination reaction found an adduct between CF₃(F)C: and HF in the exit channel with a dissociation energy of ∼5 kcal mol^-1. Hydrogen-bonded complexes between HF and the H atom migration transition state of CH₃(F)C: and the F atom migration transition state of CF₃(F)C: also were found by the calculations. The role that these carbene-HF complexes could play in 1,1-HF elimination reactions is discussed.

A Theoretical and Mass Spectrometry Study of Dimethyl Methylphosphonate: New Isomers and Cation Decay Channels in an Intense Femtosecond Laser Field

Using both mass spectrometry with intense femtosecond laser ionization and high-level computational methods, we have explored the structure and fragmentation patterns of dimethyl methylphosphonate (DMMP) cation. Extensive search of the geometries of both neutral and positively charged DMMP yields new isomers that are appreciably lower in total energy than those commonly synthesized using the Michaelis-Arbuzov reaction. The stability of the standard isomer with CH₃PO(OCH₃)₂ topology is found to be due to the presence of high barriers to isomer interconversion that involves several transition states. Our femtosecond laser ionization experiments show that the relative yields of the major dissociation products as a function of peak laser intensity correlate well with the theoretical estimates for the energies of the DMMP⁺ decay via various channels. In contrast, the peak laser intensities required for observation of minor dissociation products exhibit no correlation with the computed decay energies, which suggests that barrier heights and/or excited electronic states of DMMP⁺ determine its preferred fragmentation pathways in an intense femtosecond laser field.

Classical Dynamics Simulations of Dissociation of Protonated Tryptophan in the Gas Phase

Gas phase decomposition of protonated amino acids are of great interest due to their role in understanding protein and peptide chemistry. Several experimental and theoretical studies have been reported in the literature on this subject. In the present work, decomposition of the aromatic amino acid protonated tryptophan was studied by on-the-fly classical chemical dynamics simulations using density functional theory. Mass spectrometry and electronic structure theory studies have shown multiple dissociation pathways for this biologically relevant molecule. Unlike aliphatic amino acids, protonated tryptophan dissociates via NH₃ elimination rather than the usual iminium ion formation by combined removal of H₂O and CO molecules. Also, a major fragmentation pathway in the present work involves C_α-C_β bond fission. Results of the chemical dynamics simulations reported here are in overall agreement with experiments, and detailed atomic level mechanisms are presented.

Crossing the dividing surface of transition state theory. IV. Dynamical regularity and dimensionality reduction as key features of reactive trajectories

The atom-diatom interaction is studied by classical mechanics using Jacobi coordinates (R, r, θ). Reactivity criteria that go beyond the simple requirement of transition state theory (i.e., P_R* > 0) are derived in terms of specific initial conditions. Trajectories that exactly fulfill these conditions cross the conventional dividing surface used in transition state theory (i.e., the plane in configuration space passing through a saddle point of the potential energy surface and perpendicular to the reaction coordinate) only once. Furthermore, they are observed to be strikingly similar and to form a tightly packed bundle of perfectly collimated trajectories in the two-dimensional (R, r) configuration space, although their angular motion is highly specific for each one. Particular attention is paid to symmetrical transition states (i.e., either collinear or T-shaped with C_2v symmetry) for which decoupling between angular and radial coordinates is observed, as a result of selection rules that reduce to zero Coriolis couplings between modes that belong to different irreducible representations. Liapunov exponents are equal to zero and Hamilton's characteristic function is planar in that part of configuration space that is visited by reactive trajectories. Detailed consideration is given to the concept of average reactive trajectory, which starts right from the saddle point and which is shown to be free of curvature-induced Coriolis coupling. The reaction path Hamiltonian model, together with a symmetry-based separation of the angular degree of freedom, provides an appropriate framework that leads to the formulation of an effective two-dimensional Hamiltonian. The success of the adiabatic approximation in this model is due to the symmetry of the transition state, not to a separation of time scales. Adjacent trajectories, i.e., those that do not exactly fulfill the reactivity conditions have similar characteristics, but the quality of the approximation is lower. At higher energies, these characteristics persist, but to a lesser degree. Recrossings of the dividing surface then become much more frequent and the phase space volumes of initial conditions that generate recrossing-free trajectories decrease. Altogether, one ends up with an additional illustration of the concept of reactive cylinder (or conduit) in phase space that reactive trajectories must follow. Reactivity is associated with dynamical regularity and dimensionality reduction, whatever the shape of the potential energy surface, no matter how strong its anharmonicity, and whatever the curvature of its reaction path. Both simplifying features persist during the entire reactive process, up to complete separation of fragments. The ergodicity assumption commonly assumed in statistical theories is inappropriate for reactive trajectories.

Hydration Leads to Efficient Reactions of the Carbonate Radical Anion with Hydrogen Chloride in the Gas Phase

The carbonate radical anion CO₃^•- is a key intermediate in tropospheric anion chemistry. Despite its radical character, only a small number of reactions have been reported in the literature. Here we investigate the gas-phase reactions of CO₃^•- and CO₃^•-(H₂O) with HCl under ultrahigh vacuum conditions. Bare CO₃^•- forms OHCl^•- with a rate constant of 4.2 × 10^-12 cm³ s^-1, which corresponds to an efficiency of only 0.4%. Hydration accelerates the reaction, and ligand exchange of H₂O against HCl proceeds with a rate of 2.7 × 10^-10 cm³ s^-1. Quantum chemical calculations reveal that OHCl^•- is best described as an OH^• hydrogen bonded to Cl^-, while the ligand exchange product is Cl^-(HCO₃^•). Under tropospheric conditions, where CO₃^•-(H₂O) is the dominant species, Cl^-(HCO₃^•) is efficiently formed. These reactions must be included in models of tropospheric anion chemistry.

Frequency analysis of the laser driven nonlinear dynamics of HCN

We study the vibrational dynamics of a model for the HCN molecule in the presence of a monochromatic laser field. The variation of the structural behavior of the system as a function of the laser frequency is analyzed in detail using the smaller alignment index, frequency maps, and diffusion coefficients. It is observed that the ergodicity of the system depends on the frequency of the excitation field, especially in its transitions from and into chaos. This provides a roadmap for the possibility of bond excitation and dissociation in this molecule.

Cryptic post-transition state bifurcations that reduce the efficiency of lactone-forming Rh-carbenoid C-H insertions

Post-transition state bifurcations are described that lead to unexpected byproducts in Rh-promoted C–H insertion reactions.

Byproducts of chemical reactions are generally thought to result from the competition between two reaction pathways, each with its own rate-determining transition state structure. We show here, however, that pathways with a single transition state structure followed by a post-transition state bifurcation may also be a source of undesired products, especially those whose appearance is unexpected. The viability of this scenario for intramolecular C–H insertion reactions affording β-lactones via Rh-carbenoid intermediates is assessed through quantum chemical calculations on potential energy surfaces and quasi-classical molecular dynamics simulations. It appears that, in these cases, the rhodium catalyst is to blame for the accessibility of a second, unintended, pathway following the transition state structure for β-lactone formation that leads to fragmentation to a ketene and carbonyl compound. If an unexpected product is formed via a post-transition state bifurcation, conventional strategies for suppressing its formation are unlikely to succeed. Guidelines for recognizing the presence of a post-transition state bifurcation are described here, along with hints at means for controlling product distributions.

Dynamical Bifurcation in Gas-Phase XH- + CH3 Y SN 2 Reactions: The Role of Energy Flow and Redistribution in Avoiding the Minimum Energy Path

The gas-phase reactions of XH^- (X=O, S) + CH₃ Y (Y=F, Cl, Br) span nearly the whole range of S_N 2 pathways, and show an intrinsic reaction coordinate (IRC) (minimum energy path) with a deep well owing to the CH₃ XH⋅⋅⋅Y^- (or CH₃ S^- ⋅⋅⋅HF) hydrogen-bonded postreaction complex. MP2 quasiclassical-type direct dynamics starting at the [HX⋅⋅⋅CH₃ ⋅⋅⋅Y]^- transition-state (TS) structure reveal distinct mechanistic behaviors. Trajectories that yield the separated CH₃ XH+Y^- (or CH₃ S^- +HF) products directly are non-IRC, whereas those that sample the CH₃ XH⋅⋅⋅Y^- (or CH₃ S^- ⋅⋅⋅HF) complex are IRC. The IRCIRC/non-IRC ratios of 90:10, 40:60, 25:75, 2:98, 0:100, and 0:100 are obtained for (X, Y)=(S, F), (O, F), (S, Cl), (S, Br), (O, Cl), and (O, Br), respectively. The properties of the energy profiles after the TS cannot provide a rationalization of these results. Analysis of the energy flow in dynamics shows that the trajectories cross a dynamical bifurcation, and that the inability to follow the minimum energy path arises from long vibration periods of the X-C⋅⋅⋅Y bending mode. The partition of the available energy to the products into vibrational, rotational, and translational energies reveals that if the vibrational contribution is more than 80 %, non-IRC behavior dominates, unless the relative fraction of the rotational and translational components is similar, in which case a richer dynamical mechanism is shown, with an IRC/non-IRC ratio that correlates to this relative fraction.

Mechanistic details of energy transfer and soft landing in ala2-H(+) collisions with a F-SAM surface

Previous chemical dynamics simulations (Phys. Chem. Chem. Phys., 2014, 16, 23769-23778) were analyzed to delineate atomistic details for collision of N-protonated dialanine (ala2-H(+)) with a C8 perfluorinated self-assembled monolayer (F-SAM) surface. Initial collision energies Ei of 5-70 eV and incident angles θi of 0° and 45°, with the surface normal, were considered. Four trajectory types were identified: (1) direct scattering; (2) temporary sticking/physisorption on top of the surface; (3) temporary penetration of the surface with additional physisorption on the surface; and (4) trapping on/in the surface, by physisorption or surface penetration, when the trajectory is terminated. Direct scattering increases from 12 to 100% as Ei is increased from 5 to 70 eV. For the direct scattering at 70 eV, at least one ala2-H(+) heavy atom penetrated the surface for all of the trajectories. For ∼33% of the trajectories all eleven of the ala2-H(+) heavy atoms penetrated the F-SAM at the time of deepest penetration. The importance of trapping decreased with increase in Ei, decreasing from 84 to 0% with Ei increase from 5 to 70 eV at θi = 0°. Somewhat surprisingly, the collisional energy transfers to the F-SAM surface and ala2-H(+) are overall insensitive to the trajectory type. The energy transfer to ala2-H(+) is primarily to vibration, with the transfer to rotation ∼10% or less. Adsorption and then trapping of ala2-H(+) is primarily a multi-step process, and the following five trapping mechanisms were identified: (i) physisorption-penetration-physisorption (phys-pen-phys); (ii) penetration-physisorption-penetration (pen-phys-pen); (iii) penetration-physisorption (pen-phys); (iv) physisorption-penetration (phys-pen); and (v) only physisorption (phys). For Ei = 5 eV, the pen-phys-pen, pen-phys, phys-pen, and phys trapping mechanisms have similar probabilities. For 13.5 eV, the phys-pen mechanism, important at 5 eV, is unimportant. The radius of gyration of ala2-H(+) was calculated once it is trapped on/in the F-SAM surface and trapping decreases the ion's compactness, in part by breaking hydrogen bonds. The ala2-H(+) + F-SAM simulations are compared with the penetration and trapping dynamics found in previous simulations of projectile + organic surface collisions.

Dynamic Reaction Mechanisms of ClO(-) with CH3Cl: Comparison Between Direct Dynamics Trajectory Simulations and Experiment

We have investigated the dynamic reaction mechanisms of *ClO¯ with CH3Cl (the asterisk is utilized to label a different Cl atom). Ab initio molecular dynamics simulations at the MP2/6-31+G(d,p) level of theory have been employed to compute the dynamic trajectories. On the basis of our simulations, the dynamic reaction pathways for the bimolecular nucleophilic substitution (SN2) reaction channel and SN2-induced elimination reaction channel are clearly illustrated. For the SN2 reaction channel, some trajectories directly dissociate to the final products of CH3O*Cl and Cl¯, whereas the others involve the dynamic Cl¯···CH3O*Cl intermediate complex. As to the SN2-induced elimination reaction channel, the trajectories lead to the final products of CH2O, HCl, and *Cl¯ through the dynamic Cl¯···CH3O*Cl intermediate complex. More significantly, the product branching ratios of Cl¯ and *Cl¯ predicted by our simulations are basically consistent with previous experimental results (Villano et al. J. Am. Chem. Soc. 2009, 131, 8227-8233).

Dynamic behavior of rearranging carbocations - implications for terpene biosynthesis

This review describes unexpected dynamical behaviors of rearranging carbocations and the modern computational methods used to elucidate these aspects of reaction mechanisms. Unique potential energy surface topologies associated with these rearrangements have been discovered in recent years that are not only of fundamental interest, but also provide insight into the way Nature manipulates chemical space to accomplish specific chemical transformations. Cautions for analyzing both experimental and theoretical data on carbocation rearrangements are included throughout.