NONSTATISTICAL DYNAMICS IN THERMAL REACTIONS OF POLYATOMIC MOLECULES

A Maze of Dyotropic Rearrangements and Triple Shifts: Carbocation Rearrangements Connecting Stemarene, Stemodene, Betaerdene, Aphidicolene, and Scopadulanol

Results of quantum chemical investigations shed new light on the mechanisms of formation of the stemarene, stemodene, betaerdene, aphidicolene, and scopadulanol diterpenes from syn-copalyl diphosphate ( syn-CPP). These terpenes are shown to be connected by a complex network of reaction pathways involving concerted but asynchronous dyotropic rearrangements and triple shift rearrangements. The interconnection of these pathways leads to multiple routes for formation of each diterpene, which could lead to different origins for some carbon atoms in a given diterpenes under different conditions.

Mode-Selective Laser Control of Palladium Catalyst Decomposition

It is generally assumed that molecules behave ergodically during chemical reactions, that is, reactivities depend only on the total energy content and not on the initial state of the molecule. While there are a few examples of nonergodic behavior in small (usually electronically excited) species, to date there have been no reports of such behavior in larger covalently bound species composed of several tens of atoms. Here, we demonstrate vibrational mode-selective behavior in a series of palladium catalysts. When we excite solvent-tagged gas-phase Pd catalysts with an infrared laser that is tuned to be resonant with specific molecular vibrations, depending on which vibration we excite, we can select different reaction pathways. We also demonstrate that this behavior can be "turned off" via chemical substitution.

Empirical Classification of Trajectory Data: An Opportunity for the Use of Machine Learning in Molecular Dynamics

Classical Hamiltonian trajectories are initiated at random points in phase space on a fixed energy shell of a model two degrees of freedom potential, consisting of two interacting minima in an otherwise flat energy plane of infinite extent. Below the energy of the plane, the dynamics are demonstrably chaotic. However, most of the work in this paper involves trajectories at a fixed energy that is 1% above that of the plane, in which regime the dynamics exhibit behavior characteristic of chaotic scattering. The trajectories are analyzed without reference to the potential, as if they had been generated in a typical direct molecular dynamics simulation. The questions addressed are whether one can recover useful information about the structures controlling the dynamics in phase space from the trajectory data alone, and whether, despite the at least partially chaotic nature of the dynamics, one can make statistically meaningful predictions of trajectory outcomes from initial conditions. It is found that key unstable periodic orbits, which can be identified on the analytical potential, appear by simple classification of the trajectories, and that the specific roles of these periodic orbits in controlling the dynamics are also readily discerned from the trajectory data alone. Two different approaches to predicting trajectory outcomes from initial conditions are evaluated, and it is shown that the more successful of them has ∼90% success. The results are compared with those from a simple neural network, which has higher predictive success (97%) but requires the information obtained from the "by-hand" analysis to achieve that level. Finally, the dynamics, which occur partly on the very flat region of the potential, show characteristics of the much-studied phenomenon called "roaming." On this potential, it is found that roaming trajectories are effectively "failed" periodic orbits and that angular momentum can be identified as a key controlling factor, despite the fact that it is not a strictly conserved quantity. It is also noteworthy that roaming on this potential occurs in the absence of a "roaming saddle," which has previously been hypothesized to be a necessary feature for roaming to occur.

Lagrangian descriptors of driven chemical reaction manifolds

The persistence of a transition state structure in systems driven by time-dependent environments allows the application of modern reaction rate theories to solution-phase and nonequilibrium chemical reactions. However, identifying this structure is problematic in driven systems and has been limited by theories built on series expansion about a saddle point. Recently, it has been shown that to obtain formally exact rates for reactions in thermal environments, a transition state trajectory must be constructed. Here, using optimized Lagrangian descriptors [G. T. Craven and R. Hernandez, Phys. Rev. Lett. 115, 148301 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.148301], we obtain this so-called distinguished trajectory and the associated moving reaction manifolds on model energy surfaces subject to various driving and dissipative conditions. In particular, we demonstrate that this is exact for harmonic barriers in one dimension and this verification gives impetus to the application of Lagrangian descriptor-based methods in diverse classes of chemical reactions. The development of these objects is paramount in the theory of reaction dynamics as the transition state structure and its underlying network of manifolds directly dictate reactivity and selectivity.

Post-transition state bifurcations gain momentum – current state of the field

The existence of post-transition state bifurcations on potential energy surfaces for organic and biological reaction mechanisms has been known for decades, but recently, new reports of bifurcations have been occurring at a much higher rate. Beyond simply discovering bifurcations, computational chemists are developing techniques to understand what aspects of molecular structure and vibrations control the product selectivity in systems containing bifurcations. For example, the distribution of products seen in simulations has been found to be extremely sensitive to the local environment of the reacting system (i.e. the presence of a catalyst, enzyme, or explicit solvent molecules). The outlook for the future of this field is discussed, with an eye towards the application of the principles discussed here by experimental chemists to design a reaction setup to efficiently generate desired products.

Perspective: chemical dynamics simulations of non-statistical reaction dynamics

Non-statistical chemical dynamics are exemplified by disagreements with the transition state (TS), RRKM and phase space theories of chemical kinetics and dynamics. The intrinsic reaction coordinate (IRC) is often used for the former two theories, and non-statistical dynamics arising from non-IRC dynamics are often important. In this perspective, non-statistical dynamics are discussed for chemical reactions, with results primarily obtained from chemical dynamics simulations and to a lesser extent from experiment. The non-statistical dynamical properties discussed are: post-TS dynamics, including potential energy surface bifurcations, product energy partitioning in unimolecular dissociation and avoiding exit-channel potential energy minima; non-RRKM unimolecular decomposition; non-IRC dynamics; direct mechanisms for bimolecular reactions with pre- and/or post-reaction potential energy minima; non-TS theory barrier recrossings; and roaming dynamics.This article is part of the themed issue 'Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces'.

Sequential Gas-Phase Activation of Carbon Dioxide and Methane by [Re(CO)2]+: The Sequence of Events Matters!

The potential of carbonyl rhenium complexes in activating and coupling carbon dioxide and methane has been explored by using a combination of gas-phase experiments (FT-ICR mass spectrometry) and high-level quantum chemical calculations. While the complexes [Re(CO)_x]⁺ (x = 0, 1, 3) are thermally unreactive toward CO₂, [Re(CO)₂]⁺ abstracts one oxygen atom from this substrate spontaneously at ambient conditions. Based on ¹³C and ¹⁸O labeling experiments, the newly generated CO ligand is preferentially eliminated, and two mechanistic scenarios are considered to account for this unexpected finding. The oxo complex [ORe(CO)₂]⁺ reacts further with CH₄ to produce the dihydridomethylene complex [ORe(CO)(CH₂)(H)₂]⁺. However, coupling of the CO and CH₂ ligands to form CH₂═C═O does not take place. Further, the complexes [Re(CO)_x(CH₂)]⁺ (x = 1, 2), generated in the thermal reaction of [Re(CO)_x]⁺ (x = 1, 2) with CH₄, are inert toward CO₂. Mechanistic insight on the origin of this remarkable reactivity pattern has been derived from detailed quantum chemical calculations.

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.

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.

Beyond static structures: Putting forth REMD as a tool to solve problems in computational organic chemistry

Computational studies of organic systems are frequently limited to static pictures that closely align with textbook style presentations of reaction mechanisms and isomerization processes. Of course, in reality chemical systems are dynamic entities where a multitude of molecular conformations exists on incredibly complex potential energy surfaces (PES). Here, we borrow a computational technique originally conceived to be used in the context of biological simulations, together with empirical force fields, and apply it to organic chemical problems. Replica-exchange molecular dynamics (REMD) permits thorough exploration of the PES. We combined REMD with density functional tight binding (DFTB), thereby establishing the level of accuracy necessary to analyze small molecular systems. Through the study of four prototypical problems: isomer identification, reaction mechanisms, temperature-dependent rotational processes, and catalysis, we reveal new insights and chemistry that likely would be missed using static electronic structure computations. The REMD-DFTB methodology at the heart of this study is powered by i-PI, which efficiently handles the interface between the DFTB and REMD codes.

Structural and relative energy assessments of DFT functionals and the MP2 method to describe the gas phase methylation of nitronates: [R1R2CNO2]− + CH3I

The structures and energetics of CH₃I + [R¹R²CNO²]⁻ gas phase C- and O-methylation reactions were computed with several functionals and ECP/basis sets and compared to CCSD(T)/CBS.

Nonstatistical dynamics on the caldera

We explore both classical and quantum dynamics of a model potential exhibiting a caldera: that is, a shallow potential well with two pairs of symmetry related index one saddles associated with entrance/exit channels. Classical trajectory simulations at several different energies confirm the existence of the "dynamical matching" phenomenon originally proposed by Carpenter, where the momentum direction associated with an incoming trajectory initiated at a high energy saddle point determines to a considerable extent the outcome of the reaction (passage through the diametrically opposing exit channel). By studying a "stretched" version of the caldera model, we have uncovered a generalized dynamical matching: bundles of trajectories can reflect off a hard potential wall so as to end up exiting predominantly through the transition state opposite the reflection point. We also investigate the effects of dissipation on the classical dynamics. In addition to classical trajectory studies, we examine the dynamics of quantum wave packets on the caldera potential (stretched and unstretched). These computations reveal a quantum mechanical analogue of the "dynamical matching" phenomenon, where the initial expectation value of the momentum direction for the wave packet determines the exit channel through which most of the probability density passes to product.

Assessment of density-functionals for describing the X(-) + CH3ONO2 gas-phase reactions with X = F, OH, CH2CN

The energetics of the ECO2, SN2@C and SN2@N channels of X(-) + CH3ONO2 (X = F, OH, CH2CN) gas-phase reactions were computed using the CCSD(T)/CBS method. This benchmark extends a previous study with X = OH [M. A. F. de Souza et al., J. Am. Chem. Soc., 2012, 134, 19004] and was used to ascertain the accuracy and robustness of nineteen density-functionals for describing these potential energy profiles (PEP) as well as the kinetic product distributions obtained from RRKM calculations. Assessments were based on the mean unsigned error (MUE), the mean signed error (MSE), the #best : #worst (BW) criterion and the statistical confidence interval (CI) for the MSE. In general, double-hybrid (DH) functionals perform better than the range-separated ones, and both are better than the global-hybrid functionals. Based on the MUE and CI criteria the B2GPPLYP, B2PLYP, M08-SO, BMK, ωB97X-D, CAM-B3LYP, M06, M08-HX, ωB97X and B97-K functionals show the best performance in the description of these PEPs. Within this set, the B2GPPLYP functional is the most accurate and robust. The RRKM results indicate that the DHs are the best for describing the selectivities of these reactions. Compared to CCSD(T), the B2PLYP method has a relative error of only ca. 1% for the selectivity and the accuracy to provide the correct conclusion concerning the nonstatistical behavior of these reactions.

Mechanistic studies of copper(I)-catalyzed 1,3-halogen migration

An ongoing challenge in modern catalysis is to identify and understand new modes of reactivity promoted by earth-abundant and inexpensive first-row transition metals. Herein, we report a mechanistic study of an unusual copper(I)-catalyzed 1,3-migration of 2-bromostyrenes that reincorporates the bromine activating group into the final product with concomitant borylation of the aryl halide bond. A combination of experimental and computational studies indicated this reaction does not involve any oxidation state changes at copper; rather, migration occurs through a series of formal sigmatropic shifts. Insight provided from these studies will be used to expand the utility of aryl copper species in synthesis and develop new ligands for enantioselective copper-catalyzed halogenation.

Dynamic effects dictate the mechanism and selectivity of dehydration-rearrangement reactions of protonated alcohols [Me2 (R)CCH(OH2 )Me](+) (R=Me, Et, iPr) in the gas phase

The gas-phase dehydration-rearrangement (DR) reactions of protonated alcohols [Me2 (R)CCH(OH2 )Me](+) [R=Me (ME), Et (ET), and iPr (I-PR)] were studied by using static approaches (intrinsic reaction coordinate (IRC), Rice-Ramsperger-Kassel-Marcus theory) and dynamics (quasiclassical trajectory) simulations at the B3LYP/6-31G(d) level of theory. The concerted mechanism involves simultaneous water dissociation and alkyl migration, whereas in the stepwise reaction pathway the dehydration step leads to a secondary carbocation intermediate followed by alkyl migration. Internal rotation (IR) can change the relative position of the migrating alkyl group and the leaving group (water), so distinct products may be obtained: [Me(R)CCH(Me)Me⋅⋅⋅OH2 ](+) and [Me(Me)CCH(R)Me⋅⋅⋅OH2 ](+) . The static approach predicts that these reactions are concerted, with the selectivity towards these different products determined by the proportion of the conformers of the initial protonated alcohols. These selectivities are explained by the DR processes being much faster than IR. These results are in direct contradiction with the dynamics simulations, which indicate a predominantly stepwise mechanism and selectivities that depend on the alkyl groups and dynamics effects. Indeed, despite the lifetimes of the secondary carbocations being short (<0.5 ps), IR can take place and thus provide a rich selectivity. These different selectivities, particularly for ET and I-PR, are amenable to experimental observation and provide evidence for the minor role played by potential-energy surface and the relevance of the dynamics effects (non-IRC pathways, IR) in determining the reaction mechanisms and product distribution (selectivity).

Uncovering the role of intra- and intermolecular motion in frustrated Lewis acid/base chemistry: ab initio molecular dynamics study of CO2 binding by phosphorus/boron frustrated Lewis pair [tBu3P/B(C6F5)3]

The role of the intra- and intermolecular motion, i.e., molecular vibrations and the relative motion of reactants, remains largely unexplored in the frustrated Lewis acid/base chemistry. Here, we address the issue with the ab initio molecular dynamics (AIMD) study of CO2 binding by a Lewis acid (LA) and a Lewis base (LB), i.e., tBu3P + CO2 + B(C6F5)3 → tBu3P-C(O)O-B(C6F5)3 ([1]). Reasonably large ensemble of AIMD trajectories propagated at 300 K from structures in the saddle region as well as trajectories propagated directly from the reactants region revealed an effect arising from significant recrossing of the saddle area. The effect is that transient complexes composed of weakly interacting reactants nearly cease to progress along the segment of the minimum energy pathway (MEP) at the saddle region for a (subpicosecond) period of time during which the dominant factor is the light-to-heavy type of relative motion of the vibrating reactants, i.e., the "bouncing"-like movement of CO2 with respect to much heavier phosphine and borane as main contributor to the mode that is perpendicular to the MEP-direction. In terms of how P···C and B···O distances change with time, the roaming-like patterns of typical AIMD trajectories, reactive and nonreactive alike, extend far beyond the saddle region. In addition to the dynamical portrayal of [1], we provide the energy-landscape perspective that takes into account the hierarchy of time scales. The verifiable implication of the effect found here is that the isotopically substituted (heavier) LB/LA "pair" should be less reactive that the "normal" and thus lighter counterpart.

A cytochrome P450 serves as an unexpected terpene cyclase during fungal meroterpenoid biosynthesis

Viridicatumtoxin (1) is a tetracycline-like fungal meroterpenoid with a unique, fused spirobicyclic ring system. Puzzlingly, no dedicated terpene cyclase is found in the gene cluster identified in Penicillium aethiopicum. Cytochrome P450 enzymes VrtE and VrtK in the vrt gene cluster were shown to catalyze C5-hydroxylation and spirobicyclic ring formation, respectively. Feeding acyclic previridicatumtoxin to Saccharomyces cerevisiae expressing VrtK confirmed that VrtK is the sole enzyme required for cyclizing the geranyl moiety. Thus, VrtK is the first example of a P450 that can catalyze terpene cyclization, most likely via initial oxidation of C17 to an allylic carbocation. Quantum chemical modeling revealed a possible new tertiary carbocation intermediate E that forms after allylic carbocation formation. Intermediate E can readily undergo concerted 1,2-alkyl shift/1,3-hydride shift, either spontaneously or further aided by VrtK, followed by C7 Friedel-Crafts alkylation to afford 1. The most likely stereochemical course of the reaction was proposed on the basis of the results of our computations.

Inherent dynamical preferences in carbocation rearrangements leading to terpene natural products

An introduction to the application of quantum chemical dynamics calculations to mechanistic problems in the field of terpene biosynthesis is provided. A bare bones introduction to the fundamentals of chemical dynamics is followed by a brief account of previous applications to terpene-forming carbocation reactions, a discussion of questions in this field that dynamics calculations may help answer, and a description of current problems to which dynamics calculations are being applied.

Theory of divalent main group H2 activation: electronics and quasiclassical trajectories

Density functional theory (DFT), absolutely localized molecular orbital (ALMO) analysis, and quasiclassical trajectories (QCTs) were used to study the structure, barrier heights, thermodynamics, electronic properties, and dynamics of dihydrogen (H2) activation by singlet divalent main group compounds (ER2; E = C, Si, Ge). ALMO energy and charge decomposition calculations reveal that in the transition state CR2 acts as an ambiphile toward H2 because of equal forward-bonding and back-bonding orbital stabilization while SiR2 and GeR2 act as nucleophiles with dominant orbital energy stabilization arising from ER2 to H2 donation. Frontier molecular orbital (FMO) energy gaps do not provide a reasonable estimate of energy stabilization gained between the ER2 and H2 in the transition state or an accurate description of the nucleophilic versus electrophilic character because of electron repulsion and orbital overlap influences that are neglected. In CR2 transition states, forward-bonding and back-bonding are maximized in the nonleast motion geometry. In contrast, SiR2/GeR2 transition states have side-on geometries to avoid electron-electron repulsion. Electron repulsion, rather than orbital interactions, also determines the relative barrier heights of CR2 versus SiR2/GeR2 reactions. Examination of barrier heights and reaction energies shows a clear kinetic-thermodynamic relationship for ER2 activation of H2. A computational survey of R groups on ER2 divalent atom centers was performed to explore the possibility for H2 activation to occur with a low barrier and thermodynamically reversible. QCTs show that dihydrogen approach and reaction with CR2 may involve geometries significantly different than the static transition-state structure. In contrast, trajectories for dihydrogen addition to SiR2 involve geometries close to the side-on approach suggested by the static transition-state structure. QCTs also demonstrate that addition of H2 to CR2 and SiR2 is dynamically concerted with the average time gap of bond formation between E-H bonds of approximately 11 and 21 fs, respectively.