Energy Disposition in Reactive Intermediates

Predicting Selectivity with a Bifurcating Surface: Inaccurate Model or Inaccurate Statistics of Dynamics?

Reactions on post-transition-state bifurcation (PTSB) energy surfaces are an important class of reaction in which classical rate theories, such as the transition state theory, fail to account for the selectivity. Quasiclassical trajectory molecular dynamic (QCT-MD) simulation is an important computational approach to understanding reactions mechanisms, especially for reactions that cannot be predicted from conventional rate theories. However, the applicability of direct dynamic simulations is hampered by huge computational costs for collecting a statistically meaningful set of trajectories, making it difficult to compare simulation results with theoretical or physical insights-based predictions (non-MD predictions). In this work, we examine the PTSB of Schmidt-Aubé reactions studied by Tantillo and co-workers. With machine-learning using kernel-ridge regression (KRR) to predict atomic forces, statistical reliability was enhanced by significantly increasing the number of trajectories. With KRR, the bottleneck of simulating dynamics (atomic forces in QCT-MD with density functional theory) was accelerated more than 100-fold. We found that this KRR-aided QCT-MD approach is successful in predicting branching ratios with a much larger number of trajectories. With our approach, statistical errors are greatly reduced, and hypothetical non-MD models for predicting selectivity are tested with much higher confidence. By comparison with non-MD models, dynamical properties that affect branching ratios become more clearly described.

Rearrangement, Elimination, and Ring-Opening Reactions of Cyclopropyl-Substituted Nitrenium Ions: A Computational and Experimental Investigation

N-(4-Biphenylyl)-N-cyclopropyl nitrenium ion 5 and N-benzyl-N-cyclopropyl nitrenium ion (6) were generated through photolysis of their corresponding N-aminopyridinium ion photoprecursors. In the case of 5, stable products result from a combination of cyclopropyl ring expansion (N-biphenylazetium ion) and ethylene elimination (biphenylisonitrilium ion). When present in high concentrations, methanol can add to the cyclopropyl ring-forming N-3-methoxypropyl-N-biphenyl iminium ion. In contrast, the only detectable product from the N-benzyl-N-cyclopropyl nitrenium ion (6) is benzylisonitrile, resulting from the elimination of ethylene. Density functional theory (DFT) calculations predict the product distributions from the more stable biphenyl system 5 with reasonable accuracy. However, product distributions from the less stable benzyl system 6 are forecast with less accuracy.

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.

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.

Can Twisted Double Bonds Facilitate Stepwise [2 + 2] Cycloadditions?

Computational studies for a series of low to high strain anti-Bredt alkenes suggest that those with highly twisted bridgehead double bonds and a small singlet-triplet energy gap may undergo facile stepwise [2 + 2] cycloadditions to furnish four membered rings. A selection of reaction substrates, including ethylene, acetylene, perfluoroethylene, and cyclooctyne are considered.

Analogies between photochemical reactions and ground-state post-transition-state bifurcations shed light on dynamical origins of selectivity

Revealing the origins of kinetic selectivity is one of the premier tasks of applied theoretical organic chemistry, and for many reactions, doing so involves comparing competing transition states. For some reactions, however, a single transition state leads directly to multiple products, in which case non-statistical dynamic effects influence selectivity control. The selectivity of photochemical reactions-where crossing between excited-state and ground-state surfaces occurs near ground-state transition structures that interconvert competing products-also should be controlled by the momentum of the reacting molecules as they return to the ground state in addition to the shape of the potential energy surfaces involved. Now, using machine-learning-assisted non-adiabatic molecular dynamics and multiconfiguration pair-density functional theory, these factors are examined for a classic photochemical reaction-the deazetization of 2,3-diazabicyclo[2.2.2]oct-2-ene-for which we demonstrate that momentum dominates the selectivity for hexadiene versus [2.2.2] bicyclohexane products.

Running Wild through Dirhodium Tetracarboxylate-Catalyzed Combined CH(C)-Functionalization/Cope Rearrangement Landscapes: Does Post-Transition-State Dynamic Mismatching Influence Product Distributions?

A special type of C-H functionalization can be achieved through C-H insertion combined with Cope rearrangement (CHCR) in the presence of dirhodium catalysts. This type of reaction was studied using density functional theory and ab initio molecular dynamics simulations, the results of which pointed to the dynamic origins of low yields observed in some experiments. These studies not only reveal intimate details of the complex reaction network underpinning CHCR reactions but also further cement the generality of the importance of nonstatistical dynamic effects in controlling Rh2L4-promoted reactions.

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.

Post-Transition-State Dynamic Effects in the Transmetalation of Pd(II)-F to Pd(II)-CF3

The observation of post-transition-state dynamic effects in the context of metal-based transformation is rare. To date, there has been no reported case of a dynamic effect for the widely employed class of palladium-mediated coupling reactions. We performed an experimental and computational study of the trifluoromethylation of Pd(II)F, which is a key step in the Pd(0)/Pd(II)-catalyzed trifluoromethylation of aryl halides or acid fluorides. Our experiments show that the cis/trans speciation of the formed Pd(II)CF3 is highly solvent- and transmetalation reagent-dependent. We employed GFN2-xTB- and B3LYP-D3-based molecular dynamics trajectory calculations (with and without explicit solvation) along with high-level QM calculations and found that depending on the medium, different transmetalation mechanisms appear to be operative. A statistically representative number of Born-Oppenheimer molecular dynamics (MD) simulations suggest that in benzene, a difluorocarbene is generated in the transmetalation with R3SiCF3, which subsequently recombines with the Pd via two distinct pathways, leading to either the cis- or trans-Pd(II)CF3. Conversely, GFN2-xTB simulations in MeCN suggest that in polar/coordinating solvents an ion-pair mechanism is dominant. A CF3 anion is initially liberated and then rebinds with the Pd(II) cation to give a cis- or trans-Pd(II). In both scenarios, a single transmetalation transition state gives rise to both cis- and trans-species directly, owing to bifurcation after the transition state. The potential subsequent cis- to trans isomerization of the Pd(II)CF3 was also studied and found to be strongly inhibited by free phosphine, which in turn was experimentally identified to be liberated through displacement by a polar/coordinating solvent from the cis-Pd(II)CF3 complex. The simulations also revealed how the variation of the Pd-coordination sphere results in divergent product selectivities.

A 21st Century View of Allowed and Forbidden Electrocyclic Reactions

In 1965, Woodward and Hoffmann proposed a theory to predict the stereochemistry of electrocyclic reactions, which, after expansion and generalization, became known as the Woodward-Hoffmann Rules. Subsequently, Longuet-Higgins and Abrahamson used correlation diagrams to propose that the stereoselectivity of electrocyclizations could be explained by the correlation of reactant and product orbitals with the same symmetry. Immediately thereafter, Hoffmann and Woodward applied correlation diagrams to explain the mechanism of cycloadditions. We describe these discoveries and their evolution. We now report an investigation of various electrocyclic reactions using DFT and CASSCF. We track the frontier molecular orbitals along the intrinsic reaction coordinate and modeled trajectories and examine the correlation between HOMO and LUMO for thermally forbidden systems. We also investigate the electrocyclizations of several highly polarized systems for which the Houk group had predicted that donor-acceptor substitution can induce zwitterionic character, thereby providing low-energy pathways for formally forbidden reactions. We conclude with perspectives on the field of pericyclic reactions, including a refinement as the meaning of Woodward and Hoffmann's "Violations. There are none!" Lastly, we comment on the burgeoning influence of computations on all fields of chemistry.

The Intrinsic Barrier Width and Its Role in Chemical Reactivity

Chemical reactions are in virtually all cases understood and explained on the basis of depicting the molecular potential energy landscape, i.e., the change in atomic positions vs the free-energy change. With such landscapes, the features of the reaction barriers solely determine chemical reactivities. The Marcus dissection of the barrier height (activation energy) on such a potential into the thermodynamically independent (intrinsic) and the thermodynamically dependent (Bell-Evans-Polanyi) contributions successfully models the interplay of reaction rate and driving force. This has led to the well-known and ubiquitously used reactivity paradigm of "kinetic versus thermodynamic control". However, an analogous dissection concept regarding the barrier width is absent. Here we define and outline the concept of intrinsic barrier width and the driving force effect on the barrier width and report experimental as well as theoretical studies to demonstrate their distinct roles. We present the idea of changing the barrier widths of conformational isomerizations of some simple aromatic carboxylic acids as models and use quantum mechanical tunneling (QMT) half-lives as a read-out for these changes because QMT is particularly sensitive to barrier widths. We demonstrate the distinct roles of the intrinsic and the thermodynamic contributions of the barrier width on QMT half-lives. This sheds light on resolving conflicting trends in chemical reactivities where barrier widths are relevant and allows us to draw some important conclusions about the general relevance of barrier widths, their qualitative definition, and the consequences for more complete descriptions of chemical reactions.

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.

First principles reaction discovery: from the Schrodinger equation to experimental prediction for methane pyrolysis

Our recent success in exploiting graphical processing units (GPUs) to accelerate quantum chemistry computations led to the development of the ab initio nanoreactor, a computational framework for automatic reaction discovery and kinetic model construction. In this work, we apply the ab initio nanoreactor to methane pyrolysis, from automatic reaction discovery to path refinement and kinetic modeling. Elementary reactions occurring during methane pyrolysis are revealed using GPU-accelerated ab initio molecular dynamics simulations. Subsequently, these reaction paths are refined at a higher level of theory with optimized reactant, product, and transition state geometries. Reaction rate coefficients are calculated by transition state theory based on the optimized reaction paths. The discovered reactions lead to a kinetic model with 53 species and 134 reactions, which is validated against experimental data and simulations using literature kinetic models. We highlight the advantage of leveraging local brute force and Monte Carlo sensitivity analysis approaches for efficient identification of important reactions. Both sensitivity approaches can further improve the accuracy of the methane pyrolysis kinetic model. The results in this work demonstrate the power of the ab initio nanoreactor framework for computationally affordable systematic reaction discovery and accurate kinetic modeling.

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.

Molecular Understanding and Practical In Silico Catalyst Design in Computational Organocatalysis and Phase Transfer Catalysis-Challenges and Opportunities

Through the lens of organocatalysis and phase transfer catalysis, we will examine the key components to calculate or predict catalysis-performance metrics, such as turnover frequency and measurement of stereoselectivity, via computational chemistry. The state-of-the-art tools available to calculate potential energy and, consequently, free energy, together with their caveats, will be discussed via examples from the literature. Through various examples from organocatalysis and phase transfer catalysis, we will highlight the challenges related to the mechanism, transition state theory, and solvation involved in translating calculated barriers to the turnover frequency or a metric of stereoselectivity. Examples in the literature that validated their theoretical models will be showcased. Lastly, the relevance and opportunity afforded by machine learning will be discussed.

Phosphine Reactivity and Its Implications for Pyrolysis Experiments and Astrochemistry

Despite the importance of phosphorus-bearing molecules for life and their abundance outside Earth, the chemistry of those compounds still is poorly described. The present study investigates phosphine (PH₃) decomposition and formation pathways. The reactions studied include phosphine thermal dissociation, conversion into PO(²Π), PN(¹Σ₊), and reactions in the presence of H₂O⁺. The thermodynamic and rate coefficients of all reactions are calculated in the range of 50-2000 K considering the CCSD(T)/6-311G(3df,3pd)//ωB97xD/6-311G(3df,3pd) electronic structure data. The rate coefficients were calculated by RRKM and semiclassical transition-state theory (SCTST). According to our results, PH₃ is stable to thermal decomposition at T < 100 K and can be formed promptly by a reaction network involving PH(³Σ_-), PO(²Π), and PN(¹Σ₊). In the presence of radiation or ions, PH₃ is readily decomposed. For this reason, it should be mainly associated with dust grains or icy mantles to be observed under the physical conditions prevailing in the interstellar medium (ISM). The intersystem crossing associated with the dissociation of the isomers PON, NPO, and PNO is accessed by multireference methods, and its importance for the gas-phase PH₃ formation/destruction is discussed. Also, the implications of the present outcomes on phosphorus astrochemistry are highlighted.

Electronic Character of α,3-Dehydrotoluene Intermediates Generated from Isolable Allenyne-Containing Substrates

We report here the generation of α,3-dehydrotoluenes, a relatively rare subset of reactive intermediates of the dehydroaromatic family, from isolable allenynes. The substructure motif in the allenyne substrates is distinct from, and complementary to, those found in Myers-Saito/Schmittel-type cycloisomerizations. The reactions reported here give rise to product profiles that provide insight about the electronic nature (i.e., diradical vs. zwitterion vs. cyclic allene) of the particular isomeric DHT(s) that is(are) produced under different reaction conditions differing most significantly in the polarity of the reaction solvent. One example also revealed previously unobserved carbene-like reactivity of the DHT.

C-H Insertion in Dirhodium Tetracarboxylate-Catalyzed Reactions despite Dynamical Tendencies toward Fragmentation: Implications for Reaction Efficiency and Catalyst Design

Rh-catalyzed C-H insertion reactions to form β-lactones suffer from post-transition state bifurcations, with the same transition states leading to ketones and ketenes via fragmentation in addition to β-lactones. In such a circumstance, traditional transition state theory cannot predict product selectivity, so we employed ab initio molecular dynamics simulations to do so and provide a framework for rationalizing the origins of said selectivity. Weak interactions between the catalyst and substrate were studied using energy decomposition and noncovalent interaction analyses, which unmasked an important role of the 2-bromophenyl substituent that has been used in multiple β-lactone-forming C-H insertion reactions. Small and large catalysts were shown to behave differently, with the latter providing a means of overcoming dynamically preferred fragmentation by lowering the barrier for the recombination of the product fragments in the grip of the large catalyst active site cavity.

Divergent stereochemical outcomes in the insertion of donor/donor carbenes into the C-H bonds of stereogenic centers

Intramolecular C-H insertions with donor/donor dirhodium carbenes provide a concise and highly stereoselective method to set two contiguous stereocenters in a single step. Herein, we report the insertion of donor/donor carbenes into stereogenic carbon centers allowing access to trisubstituted benzodihydrofurans in a single step. This study illuminates, for the first time, the stereochemical impact on the carbene center and delineates the structural factors that enable control over both stereogenic centers. Sterically bulky, highly activated C-H insertion centers exhibit high substrate control yielding a single diastereomer and a single enantiomer of product regardless of the catalyst used. Less bulky, less activated C-H insertion centers exhibit catalyst control over the diastereomeric ratio (dr), where a single enantiomer of each diastereomer is observed with high selectivity. A combination of experimental studies and DFT calculations was used to elucidate the origin of these results. First, hydride transfer from the stereogenic insertion site proceeds with high stereoselectivity to the carbene center, thus determining the absolute configuration of the product. Second, the short lived zwitterionic intermediate can diaster-eoselectively ring-close by a hitherto unreported SE2 mechanism that is either controlled by the substrate or the catalyst. These results demonstrate that donor/donor carbenes undergo uniquely stereoselective reactions that originate from a stepwise reaction mechanism, in contrast to the analogous concerted reactions of carbenes with one or more electron-withdrawing groups attached.

Heavy-Atom Kinetic Isotope Effects: Primary Interest or Zero Point?

Chemists have many options for elucidating reaction mechanisms. Global kinetic analysis and classic transition-state probes (e.g., LFERs, Eyring) inevitably form the cornerstone of any strategy, yet their application to increasingly sophisticated synthetic methodologies often leads to a wide range of indistinguishable mechanistic proposals. Computational chemistry provides powerful tools for narrowing the field in such cases, yet wholly simulated mechanisms must be interpreted with great caution. Heavy-atom kinetic isotope effects (KIEs) offer an exquisite but underutilized method for reconciling the two approaches, anchoring the theoretician in the world of calculable observables and providing the experimentalist with atomistic insights. This Perspective provides a personal outlook on this synergy. It surveys the computation of heavy-atom KIEs and their measurement by NMR spectroscopy, discusses recent case studies, highlights the intellectual reward that lies in alignment of experiment and theory, and reflects on the changes required in chemical education in the area.

Effect of solvent motions on the dynamics of the Diels-Alder reaction

How solvent motions affect the dynamics of chemical reactions in which the solute undergoes a substantial shape change is a fundamental but elusive issue. This work utilizes reactive simulation and Grote-Hynes theory to explore the effect of solvent motions on the dynamics of the Diels-Alder reaction (in the reverse direction, this reaction involves very substantial solute expansion) in aprotic solvents. The results reveal that the solvent environment is not sufficiently constraining to influence transition state passage dynamics, with the calculated transmission coefficients being close to unity. Even when solvent motions are suppressed or artificially slowed down, the solvent only affects the reaction dynamics in the transition state region to a very small extent. The only notable effect of solvent occurs far from the transition state region and corresponds to caging of the reactants within the reactant well.

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.

Melding of Experiment and Theory Illuminates Mechanisms of Metal-Catalyzed Rearrangements: Computational Approaches and Caveats

This review summarizes approaches and caveats in computational modeling of transition-metal-catalyzed sigmatropic rearrangements involving carbene transfer. We highlight contemporary examples of combined synthetic and theoretical investigations that showcase the synergy achievable by integrating experiment and theory.

1 Introduction

2 Mechanistic Models

3 Theoretical Approaches and Caveats

3.1 Recommended Computational Tools

3.2 Choice of Functional and Basis Set

3.3 Conformations and Ligand-Binding Modes

3.4 Solvation

4 Synergy of Experiment and Theory – Case Studies

4.1 Metal-Bound or Free Ylides?

4.2 Conformations and Ligand-Binding Modes of Paddlewheel Complexes

4.3 No Metal, Just Light

4.4 How To ‘Cope’ with Nonstatistical Dynamic Effects

5 Outlook

Highs and Lows of Bond Lengths: Is There Any Limit?

Two distinct points on the potential energy curve (PEC) of a pairwise interaction, the zero-energy crossing point and the point where the stretching force constant vanishes, allow us to anticipate the range of possible distances between two atoms in diatomic, molecular moieties and crystalline systems. We show that these bond-stability boundaries are unambiguously defined and correlate with topological descriptors of electron-density-based scalar fields, and can be calculated using generic PECs. Chemical databases and quantum-mechanical calculations are used to analyze a full set of diatomic bonds of atoms from the s-p main block. Emphasis is placed on the effect of substituents in C-C covalent bonds, concluding that distances shorter than 1.14 Å or longer than 2.0 Å are unlikely to be achieved, in agreement with ultra-high-pressure data and transition-state distances, respectively. Presumed exceptions are used to place our model in the correct framework and to formulate a conjecture for chained interactions, which offers an explanation for the multimodal histogram of O-H distances reported for hundreds of chemical systems.

Flyby reaction trajectories: Chemical dynamics under extrinsic force

Dynamic effects are an important determinant of chemical reactivity and selectivity, but the deliberate manipulation of atomic motions during a chemical transformation is not straightforward. Here, we demonstrate that extrinsic force exerted upon cyclobutanes by stretching pendant polymer chains influences product selectivity through force-imparted nonstatistical dynamic effects on the stepwise ring-opening reaction. The high product stereoselectivity is quantified by carbon-13 labeling and shown to depend on external force, reactant stereochemistry, and intermediate stability. Computational modeling and simulations show that, besides altering energy barriers, the mechanical force activates reactive intramolecular motions nonstatistically, setting up "flyby trajectories" that advance directly to product without isomerization excursions. A mechanistic model incorporating nonstatistical dynamic effects accounts for isomer-dependent mechanochemical stereoselectivity.

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.

VRAI-selectivity: calculation of selectivity beyond transition state theory

In recent years, a growing number of organic reactions in the literature have shown selectivity controlled by reaction dynamics rather than by transition state theory. Such reactions are difficult to analyse because the transition state theory approach often does not capture the subtlety of the energy landscapes the compounds traverse and, therefore, cannot accurately predict the selectivity. We present an algorithm that can predict the major product and selectivity for a wide range of potential energy surfaces where the product distribution is influenced by reaction dynamics. The method requires as input calculation of the transition states, the intermediate (if present) and the product geometries. The algorithm is quick and simple to run and, except for two reactions with long alkyl chains, calculates selectivity more accurately than transition state theory alone.

Energy Read-out as a Probe of Kinetically Hidden Transition States

The initial energy in a reactive intermediate is derived from the transition state before the intermediate but can affect selectivity after the intermediate. In this way an observable selectivity can report on a prior, kinetically hidden mechanistic step. This new type of mechanistic probe is demonstrated here for the oxidation of 1-methylcyclobutanol by phthaloyl peroxide/Bu₄N⁺Br^-, and it supports a hypobromite chain mechanism in place of the previously proposed hydrogen atom transfer mechanism.

Nonequilibrium effects of cavity leakage and vibrational dissipation in thermally activated polariton chemistry

In vibrational strong coupling (VSC), molecular vibrations strongly interact with the modes of an optical cavity to form hybrid light-matter states known as vibrational polaritons. Experiments show that the kinetics of thermally activated chemical reactions can be modified by VSC. Transition-state theory, which assumes that internal thermalization is fast compared to reactive transitions, has been unable to explain the observed findings. Here, we carry out kinetic simulations to understand how dissipative processes, namely, those introduced by VSC to the chemical system, affect reactions where internal thermalization and reactive transitions occur on similar timescales. Using the Marcus-Levich-Jortner type of electron transfer as a model reaction, we show that such dissipation can change reactivity by accelerating internal thermalization, thereby suppressing nonequilibrium effects that occur in the reaction outside the cavity. This phenomenon is attributed mainly to cavity decay (i.e., photon leakage), but a supporting role is played by the relaxation between polaritons and dark states. When nonequilibrium effects are already suppressed in the bare reaction (the reactive species are essentially at internal thermal equilibrium throughout the reaction), we find that reactivity does not change significantly under VSC. Connections are made between our results and experimental observations.

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.

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.

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.

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.

The full dynamics of energy relaxation in large organic molecules: from photo-excitation to solvent heating

In some molecular systems, such as nucleobases, polyenes or sunscreens, substantial amounts of photo-excitation energy are dissipated on a sub-picosecond time scale. Where does this energy go or among which degrees of freedom it is being distributed at such early times?

In some molecular systems, such as nucleobases, polyenes or the active ingredients of sunscreens, substantial amounts of photo-excitation energy are dissipated on a sub-picosecond time scale, raising questions such as: where does this energy go or among which degrees of freedom it is being distributed at such early times? Here we use transient absorption spectroscopy to track excitation energy dispersing from the optically accessible vibronic subsystem into the remaining vibrational subsystem of the solute and solvent. Monitoring the flow of energy during vibrational redistribution enables quantification of local molecular heating. Subsequent heat dissipation away from the solute molecule is characterized by classical thermodynamics and molecular dynamics simulations. Hence, we present a holistic approach that tracks the internal temperature and vibronic distribution from the act of photo-excitation to the restoration of the global equilibrium. Within this framework internal vibrational redistribution and vibrational cooling are emergent phenomena. We demonstrate the validity of the framework by examining a highly controversial example, carotenoids. We show that correctly accounting for the local temperature unambiguously explains their energetically and temporally congested spectral dynamics without the ad hoc postulation of additional ‘dark’ states. An immediate further application of this approach would be to monitor the excitation and thermal dynamics of pigment–protein systems.

Unified Mechanism of Oxygen Atom Transfer and Hydrogen Atom Transfer Reactions with a Triflic Acid-Bound Nonheme Manganese(IV)-Oxo Complex via Outer-Sphere Electron Transfer

Outer-sphere electron transfer from styrene, thioanisole, and toluene derivatives to a triflic acid (HOTf)-bound nonheme Mn(IV)-oxo complex, [(N4Py)Mn^IV(O)]²⁺-(HOTf)₂ (N4Py = N, N-bis(2-pyridylmethyl)- N-bis(2-pyridyl)methylamine), has been shown to be the rate-determining step of different types of redox reactions such as epoxidation, sulfoxidation, and hydroxylation of styrene, thioanisole, and toluene derivatives, respectively, by [(N4Py)Mn^IV(O)]²⁺-(HOTf)₂. The rate constants of HOTf-promoted epoxidation of all styrene derivatives with [(N4Py)Mn^IV(O)]²⁺ and electron transfer from electron donors to [(N4Py)Mn^V(O)]²⁺ exhibit a remarkably unified correlation with the driving force of outer-sphere electron transfer in light of the Marcus theory of electron transfer. The same electron-transfer driving force dependence is observed in the oxygen atom transfer from [(N4Py)Mn^IV(O)]²⁺-(HOTf)₂ to thioanisole derivatives as well as in the hydrogen atom transfer from toluene derivatives to [(N4Py)Mn^IV(O)]²⁺-(HOTf)₂. Thus, mechanisms of oxygen atom transfer (epoxidation and sulfoxidation) reactions of styrene and thioanisole derivatives and hydrogen atom transfer (hydroxylation) reactions of toluene derivatives by [(N4Py)Mn^IV(O)]²⁺-(HOTf)₂ have been unified for the first time as the same reaction pathway via outer-sphere electron transfer, followed by the fast bond-forming step, which exhibits the singly unified electron-transfer driving force dependence of the rate constants as outer-sphere electron-transfer reactions. In the case of the epoxidation of cis-stilbene by [(N4Py)Mn^IV(O)]²⁺-(HOTf)₂, the isomerization of cis-stilbene radical cation to trans-stilbene radical cation occurs after outer-sphere electron transfer from cis-stilbene to [(N4Py)Mn^IV(O)]²⁺-(HOTf)₂ to yield trans-stilbene oxide selectively, which is also taken as evidence for the occurrence of electron transfer in the acid-catalyzed epoxidation.

Relevance of the Resonance Junctions on the Arnold Web to Dynamical Tunneling and Eigenstate Delocalization

We study the competition and correspondence between the classical and quantum routes to intramolecular vibrational energy redistribution (IVR) in a three degrees of freedom model effective Hamiltonian. Specifically, we focus on the classical and the quantum dynamics near the resonance junctions on the Arnold web that are formed by an intersection of independent resonances. The regime of interest models the IVR dynamics from highly excited initial states near dissociation thresholds of molecular systems wherein both classical and purely quantum, involving dynamical tunneling, routes to IVR coexist. In the vicinity of a resonance junction, classical chaos is inevitably present, and hence one expects the quantum IVR pathways to have a strong classical component as well. We show that with increasing resonant coupling strengths the classical component of IVR leads to a transition from coherent dynamical tunneling to incoherent dynamical tunneling. Furthermore, we establish that the quantum IVR dynamics can be predicted based on the structures on the classical Arnold web. In addition, we investigate the nature of the highly excited eigenstates to identify the quantum signatures of the multiplicity-2 junctions. For the parameter regimes studies herein, by projecting the eigenstates onto the Arnold web, we find that eigenstates in the vicinity of the junctions are primarily delocalized due to dynamical tunneling.