Transition State Region Research Articles

Non-covalent interactions and charge transfer in the CO activation by low-valent group 14 complexes.

The CO activation by low-valent group 14 catalysts encompasses the rupture of varied covalent bonds in a single transition state through a concerted pathway. The bond between the central main group atom and the hydride in the complex is elongated to trigger the formation of the C-H bond with CO accompanied by the concomitant formation of the E-O bond between the complex and CO to lead the corresponding formate product. Prior studies have established that besides the apolar nature of CO , its initial interaction with the complex is primarily governed by electrostatic interactions. Notably, other stabilizing interactions and the transfer of charge between catalysts and CO during the initial phases of the reaction have been ignored. In this study, we have quantified the non-covalent interactions and charge transfer that facilitate the activation of CO by group 14 main group complex. Our findings indicate that electrostatic interactions predominantly stabilize the complex and CO in the reactant region. However, induction energy becomes the main stabilizing force as the reaction progresses towards the transition state, surpassing electrostatics. Induction contributes about 50% to the stabilization at the transition state, followed by electrostatics (40%) and dispersion interactions (10%). Atomic charges calculated with the minimal basis iterative stockholder (MBIS) method reveal larger charge transfer for the back-side reaction path in which CO approaches the catalysts in contrast to the front-side approach. Notably, it was discovered that a minor initial bending of CO to approximately initiates the charge transfer process for all systems. Furthermore, our investigation of group 14 elements demonstrates a systematic reduction in both activation energies and charge transfer to CO while descending in group 14. All studied reactions were characterized along the reaction coordinate obtained with the intrinsic reaction coordinate (IRC) methodology at the M06-2X/6-31g(d,p) level of theory. Gibbs free energy in toluene was computed using electronic energies at the DLPNO-CCSD(T)/cc-pVTZ-SSD(E) level of theory. Vibrational and translational entropy corrections were applied to provide a more accurate description of the obtained Gibbs free energies. To better characterize the changes in the reaction coordinate for all reactions, the reaction force analysis (RFA) has been employed. It enables the partition of the reaction coordinate into the reactant, transition state, and product regions where different stages of the mechanism occur. A detailed characterization of the main non-covalent driving forces in the initial stages of the activation of CO by low-valent group 14 complexes was performed using symmetry-adapted perturbation theory (SAPT). The SAPT0-CT/def2-SVP method was employed for these computations. Charge transfer descriptors based on atomic population using the MBIS scheme were also obtained to complement the SAPT analyses.

Multi-Level Protocol for Mechanistic Reaction Studies Using Semi-Local Fitted Potential Energy Surfaces.

In this work, we propose a multi-level protocol for routine theoretical studies of chemical reaction mechanisms. The initial reaction paths of our investigated systems are sampled using the Nudged Elastic Band (NEB) method driven by a cheap electronic structure method. Forces recalculated at the more accurate electronic structure theory for a set of points on the path are fitted with a machine learning technique (in our case symmetric gradient domain machine learning or sGDML) to produce a semi-local reactive potential energy surface (PES), embracing reactants, products and transition state (TS) regions. This approach has been successfully applied to a unimolecular (Bergman cyclization of enediyne) and a bimolecular (SN2 substitution) reaction. In particular, we demonstrate that with only 50 to 150 energy-force evaluations with the accurate reference methods (here complete-active-space self-consistent field, CASSCF, and coupled-cluster singles and doubles, CCSD) it is possible to construct a semi-local PES giving qualitative agreement for stationary-point geometries, intrinsic reaction coordinates and barriers. Furthermore, we find a qualitative agreement in vibrational frequencies and reaction rate coefficients. The key aspect of the method's performance is its multi-level nature, which not only saves computational effort but also allows extracting meaningful information along the reaction path, characterized by zero gradients in all but one direction. Agnostic to the nature of the TS and computationally economic, the protocol can be readily automated and routinely used for mechanistic reaction studies.

Steric Effect and Intrinsic Electrophilicity and Nucleophilicity from Conceptual Density Functional Theory and Information-Theoretic Approach as Quantitative Probes of Chemical Reactions.

Appreciating reactivity in terms of physicochemical effects for chemical processes is one of the most important undertakings in chemistry. While transition state (TS) theory provides the framework enabling the reliable calculation of the barrier height for a given elementary step, analytical tools are necessary to gain insight into key factors governing the different processes during chemical reactions. In this contribution, we partition the potential energy surface of an elementary step along the intrinsic coordinate into three segments, the so-called Pre-TS, TS, and Post-TS regions, and then determine the most important factors dictating each segment. This analysis is based on the use of both reactivity descriptors from conceptual density functional theory and concepts from the information-theoretic approach in density functional theory. We found that in both Pre-TS and Post-TS regions, steric effects are the dominant factors, whereas in the TS region, it is the intrinsic electrophilic and nucleophilic propensity of the transition state structure that governs the reactivity. The wide applicability of our approach is shown by a validation for a total of 37 organic and inorganic reactions. Different partition approaches from density functional theory, energy decomposition analysis and wavefunction-based resonance theory are employed to support our main conclusions.

Understanding the coupling of non-metallic heteroatoms to CO2 from a Conceptual DFT perspective

ContextA Conceptual DFT (CDFT) study has been carry out to analyse the coupling reactions of the simplest amine (CH3NH2), alcohol (CH3OH), and thiol (CH3SH) compounds with CO2 to form the corresponding adducts CH3NHCO2H, CH3OCO2H, and CH3SCO2H. The reaction mechanism takes place in a single step comprising two chemical events: nucleophilic attack of the non-metallic heteroatoms to CO2 followed by hydrogen atom transfer (HAT). According to our calculations, the participation of an additional nucleophilic molecule as HAT assistant entails important decreases in activation electronic energies. In such cases, the formation of a six-membered ring in the transition state (TS) reduces the angular stress with respect to the non-assisted paths, characterised by four-membered ring TSs. Through the analysis of the energy and reaction force profiles along the intrinsic reaction coordinate (IRC), the ratio of structural reorganisation and electronic rearrangement for both activation and relaxation energies has been computed. In addition, the analysis of the electronic chemical potential and reaction electronic flux profiles confirms that the highest electronic activity as well as their changes take place in the TS region. Finally, the distortion/interaction model using an energy decomposition scheme based on the electron density along the reaction coordinate has been carried out and the relative energy gradient (REG) method has been applied to identify the most important components associated to the barriers.MethodsThe theoretical calculation were performed with Gaussian-16 scientific program. The B3LYP-D3(BJ)/aug-cc-pVDZ level was used for optimization of the minima and TSs. IRC calculations has also been carried out connecting the TS with the associated minima. Conceptual-DFT (CDFT) calculations have been carried out with the Eyringpy program and in-house code. The distortion/interaction model along the reaction coordinate have used the decomposition scheme of Mandado et al. and the analysis of the importance of each components have been done with the relative energy gradient (REG) method.

Probing the activated complex of the F + NH3 reaction via a dipole-bound state

Experimental characterization of the transition state poses a significant challenge due to its fleeting nature. Negative ion photodetachment offers a unique tool for probing transition states and their vicinity. However, this approach is usually limited to Franck-Condon regions. For example, high-lying Feshbach resonances with an excited HF stretching mode (vHF = 2-4) were recently identified in the transition-state region of the F + NH3 → HF + NH2 reaction through photo-detaching FNH3− anions, but the direct photodetachment failed to observe the lower-lying vHF = 0,1 resonances and bound states due apparently to negligible Franck-Condon factors. Indeed, these weak transitions can be resonantly enhanced via a dipole-bound state (DBS) formed between an electron and the polar FNH3 species. In this study, we unveil a series of Feshbach resonances and bound states along the F + NH3 reaction path via a DBS by combining high-resolution photoelectron spectroscopy with high-level quantum dynamical computations. This study presents an approach for probing the activated complex in a reaction by negative ion photodetachment through a DBS.

Why Do Empirical Valence Bond Simulations Yield Accurate Arrhenius Plots?

Computer simulations of the temperature dependence of enzyme reactions using the empirical valence bond (EVB) method have proven to give very accurate results in terms of the thermodynamic activation parameters. Here, we analyze the reasons for why such simulations are able to correctly capture activation enthalpies and entropies and how sensitive these quantities are to parametrization of the reactive potential energy function. We examine first the solution reference reaction for the enzyme ketosteroid isomerase, which corresponds to the acetate catalyzed deprotonation of the steroid in water. The experimentally determined activation parameters for this reaction turn out to be remarkably well reproduced by the calculations. By modifying the EVB potential so that the activation and reaction free energies become significantly shifted, we show that the activation entropy is basically invariant to such changes and that ΔS⧧ is instead determined by the specific mixture of the underlying force fields in the transition state region. The coefficients of this mixture do not change appreciably when the EVB potential is modified within reasonable limits, and hence, the estimate of ΔS⧧ becomes very robust. This is further verified by examining a more complex concerted hydride and proton transfer reaction in the enzyme hydroxybutyrate dehydrogenase.

Quantum dynamics study of C—H stretching vibrational excitation in the F+CHD<sub>3</sub> → HF+CD<sub>3</sub> reaction

In recent decades, significant progress has been made in the precise theoretical investigation of gas-phase chemical reactions. Presently, a major challenge in the field of quantum dynamics is to develop the precise methodologies for studying chemical reactions involving more than four atoms. As a typical multi-atomic reaction system, the F+CH<sub>4</sub> reaction and its isotopic substitution reactions have attracted widespread attention from both experimental and theoretical perspectives in recent years. Experimental studies on the reaction of F+CHD<sub>3</sub> have revealed that the stretching vibration excitation of the C—H bond inhibits the bond dissociation, favoring the formation of DF+CHD<sub>2</sub> product channels. In this study, we use a seven-dimensional quantum time-dependent wave packet method to investigate the dynamics of the F+CHD<sub>3</sub> reaction in both the reactant vibrational ground state and the first stretching excited state of the C—H bond. In this work, the reaction probabilities under different vibrational conditions are analyzed, showing that when the collision energy is below 0.06 eV, the reaction probability curves exhibit numerous fast-oscillating peaks, supporting the experimentally suggested phenomena of dynamic resonance. In a collision energy range from 0.06 eV to 0.3 eV, the reaction probability for the HF product channel in the vibrational excited state is lower than that in the ground state, which is consistent with experimental observation. Through the analysis of the time-independent wave functions of product channels under low-energy collision conditions, it is found that for reactions involving vibrational ground states, the HF products in the product asymptotic region and the reaction transition state region are in the <i>v'</i> = 2 excited state and <i>v'</i> = 3 excited state of stretching vibration, respectively, which are consistent with previous experimental observations and six-dimensional quantum wave packet simulations. For reactions involving the first excited state of C—H stretching vibration, the HF products in the product asymptotic region and the reaction transition state region are both in the <i>v'</i> = 3 excited state of stretching vibration, which are consistent with the results obtained based on energy analysis. Simulation results indicate that in the case of low-energy collisions, the time-independent wave function for the C—H stretching vibrational excited state tends to be closer to the D atom side in the transition state region. This phenomenon is attributed to the more significant energy advantage of the vibrational excited state potential energy surface in the large collision angle region, explaining the inhibitory effect of stretching vibration excitation on the HF product channel. This study offers important theoretical support for explaining experimental results and contributes to a more in-depth understanding of the influence of vibrational mode excitations on the dynamical processes in poly-atomic reactions.

On committor functions in milestoning.

As an optimal one-dimensional reaction coordinate, the committor function not only describes the probability of a trajectory initiated at a phase space point first reaching the product state before reaching the reactant state but also preserves the kinetics when utilized to run a reduced dynamics model. However, calculating the committor function in high-dimensional systems poses significant challenges. In this paper, within the framework of milestoning, exact expressions for committor functions at two levels of coarse graining are given, including committor functions of phase space point to point (CFPP) and milestone to milestone (CFMM). When combined with transition kernels obtained from trajectory analysis, these expressions can be utilized to accurately and efficiently compute the committor functions. Furthermore, based on the calculated committor functions, an adaptive algorithm is developed to gradually refine the transition state region. Finally, two model examples are employed to assess the accuracy of these different formulations of committor functions.

Accelerating Kinetics with Time-Reversal Path Sampling.

In comparison to numerous enhanced sampling methods for equilibrium thermodynamics, accelerating simulations for kinetics and nonequilibrium statistics are relatively rare and less effective. Here, we derive a time-reversal path sampling (tRPS) method based on time reversibility to accelerate simulations for determining the transition rates between free-energy basins. It converts the difficult uphill path sampling into an easy downhill problem. This method is easy to implement, i.e., forward and backward shooting simulations with opposite initial velocities are conducted from random initial conformations within a transition-state region until they reach the basin minima, which are then assembled to give the distribution of transition paths efficiently. The effects of tRPS are demonstrated using a comparison with direct simulations of protein folding and unfolding, where tRPS is shown to give results consistent with direct simulations and increase the efficiency by up to five orders of magnitude. This approach is generally applicable to stochastic processes with microscopic reversibility, regardless of whether the variables are continuous or discrete.

Multiple Dissociation Pathways in HNCO Decomposition Governed by Potential Energy Surface Topography.

The exquisite features of molecular photochemistry are key to any complete understanding of the chemical processes governed by potential energy surfaces (PESs). It is well established that multiple dissociation pathways relate to nonadiabatic transitions between multiple coupled PESs. However, little detail is known about how the single PES determines reaction outcomes. Here we perform detailed experiments on HNCO photodissociation, acquiring the state-specific correlations of the NH (a1Δ) and CO (X1Σ+) products. The experiments reveal a trimodal CO rotational distribution. Dynamics simulations based on a full-dimensional machine-learning-based PES of HNCO unveil three dissociation pathways exclusively occurring on the S1 excited electronic state. One pathway, following the minimum energy path (MEP) via the transition state, contributes to mild rotational excitation in CO, while the other two pathways deviating substantially from the MEP account for relatively cold and hot CO rotational state populations. These peculiar dynamics are unambiguously governed by the S1 state PES topography, i.e., a narrow acceptance cone in the vicinity of the transition state region. The dynamical picture shown in this work will serve as a textbook example illustrating the importance of the PES topography in molecular photochemistry.

Characterizing the Folding Transition-State Ensembles in the Energy Landscape of an RNA Tetraloop.

Molecular dynamics (MD) simulations have become increasingly powerful and can now describe the folding/unfolding of small biomolecules in atomic detail. However, a major challenge in MD simulations is to represent the complex energy landscape of biomolecules using a small number of reaction coordinates. In this study, we investigate the folding pathways of an RNA tetraloop, gcGCAAgc, using five classical MD simulations with a combined simulation time of approximately 120 μs. Our approach involves analyzing the tetraloop dynamics, including the folding transition state ensembles, using the energy landscape visualization method (ELViM). The ELViM is an approach that uses internal distances to compare any two conformations, allowing for a detailed description of the folding process without requiring root mean square alignment of structures. This method has previously been applied to describe the energy landscape of disordered β-amyloid peptides and other proteins. The ELViM results in a non-linear projection of the multidimensional space, providing a comprehensive representation of the tetraloop's energy landscape. Our results reveal four distinct transition-state regions and establish the paths that lead to the folded tetraloop structure. This detailed analysis of the tetraloop's folding process has important implications for understanding RNA folding, and the ELViM approach can be used to study other biomolecules.

Operando Modeling of Zeolite-Catalyzed Reactions Using First-Principles Molecular Dynamics Simulations.

Within this Perspective, we critically reflect on the role of first-principles molecular dynamics (MD) simulations in unraveling the catalytic function within zeolites under operating conditions. First-principles MD simulations refer to methods where the dynamics of the nuclei is followed in time by integrating the Newtonian equations of motion on a potential energy surface that is determined by solving the quantum-mechanical many-body problem for the electrons. Catalytic solids used in industrial applications show an intriguing high degree of complexity, with phenomena taking place at a broad range of length and time scales. Additionally, the state and function of a catalyst critically depend on the operating conditions, such as temperature, moisture, presence of water, etc. Herein we show by means of a series of exemplary cases how first-principles MD simulations are instrumental to unravel the catalyst complexity at the molecular scale. Examples show how the nature of reactive species at higher catalytic temperatures may drastically change compared to species at lower temperatures and how the nature of active sites may dynamically change upon exposure to water. To simulate rare events, first-principles MD simulations need to be used in combination with enhanced sampling techniques to efficiently sample low-probability regions of phase space. Using these techniques, it is shown how competitive pathways at operating conditions can be discovered and how broad transition state regions can be explored. Interestingly, such simulations can also be used to study hindered diffusion under operating conditions. The cases shown clearly illustrate how first-principles MD simulations reveal insights into the catalytic function at operating conditions, which could not be discovered using static or local approaches where only a few points are considered on the potential energy surface (PES). Despite these advantages, some major hurdles still exist to fully integrate first-principles MD methods in a standard computational catalytic workflow or to use the output of MD simulations as input for multiple length/time scale methods that aim to bridge to the reactor scale. First of all, methods are needed that allow us to evaluate the interatomic forces with quantum-mechanical accuracy, albeit at a much lower computational cost compared to currently used density functional theory (DFT) methods. The use of DFT limits the currently attainable length/time scales to hundreds of picoseconds and a few nanometers, which are much smaller than realistic catalyst particle dimensions and time scales encountered in the catalysis process. One solution could be to construct machine learning potentials (MLPs), where a numerical potential is derived from underlying quantum-mechanical data, which could be used in subsequent MD simulations. As such, much longer length and time scales could be reached; however, quite some research is still necessary to construct MLPs for the complex systems encountered in industrially used catalysts. Second, most currently used enhanced sampling techniques in catalysis make use of collective variables (CVs), which are mostly determined based on chemical intuition. To explore complex reactive networks with MD simulations, methods are needed that allow the automatic discovery of CVs or methods that do not rely on a priori definition of CVs. Recently, various data-driven methods have been proposed, which could be explored for complex catalytic systems. Lastly, first-principles MD methods are currently mostly used to investigate local reactive events. We hope that with the rise of data-driven methods and more efficient methods to describe the PES, first-principles MD methods will in the future also be able to describe longer length/time scale processes in catalysis. This might lead to a consistent dynamic description of all steps-diffusion, adsorption, and reaction-as they take place at the catalyst particle level.

Dynamic Effects on the Ionization-Induced Reactions of Methyl Halides: Quantum Mechanical and Molecular Dynamics Studies.

The mechanisms of the ionization-induced fragmentation and H migration of methyl halides CH3X (X = F, Cl, Br) have been examined by quantum mechanical and molecular dynamics methods. When CH3X (X = F, Cl, Br) is vertically ionized into a divalent cation, it can obtain enough excess energy to overcome the energy barrier of subsequent reaction channels for the formation of H+, H2+, and H3+ species and intramolecular H migration. The product distributions of these species greatly depend on the halogen atoms. The H+ formation decreases in the order of F > Cl > Br, which is inversely proportional to the increase in the magnitude of the energy barrier in the order of Br > Cl > F. This is attributable to the change in the charge distribution of the entire molecule by the halogen atoms. Meanwhile, the small H migration ratio for Cl and Br, despite their low energy barriers, was explained by the small sum of states at the transition state based on the Rice-Ramsperger-Kassel-Marcus (RRKM) theory. The H3+ formation ratio is unexpectedly smaller despite its low energy barrier. This is attributed to the dynamic effects of the H2 roaming that always occur prior to the reaction in question. Molecular dynamics simulations showed that the H2 roaming was restricted in a certain area due to an initially produced driving force on the hydrogen atoms in a certain direction by vertical ionization; this phenomenon suppresses the formation of H3+, which requires the hydrogen atoms to be in motion over a relatively wide range to enter the transition state region. Thus, the low proportion of the observed H3+ can be explained by the dynamical probability of the transition state structure formation.

The transition state region in nonsynchronous concerted reactions.

The critical and vanishing points of the reaction force F(ξ) = -dV(ξ)/dξ yield five important coordinates (ξR, ξR* , ξTS, ξP* , ξP) along the intrinsic reaction coordinate (IRC) for a given concerted reaction or reaction step. These points partition the IRC into three well-defined regions, reactants (ξR→ξR* ), transition state (ξR* →ξP* ), and products (ξP* →ξP), with traditional roles of mostly structural changes associated with the reactants and products regions and mostly electronic activity associated with the transition state (TS) region. Following the evolution of chemical bonding along the IRC using formal descriptors of synchronicity, reaction electron flux, Wiberg bond orders, and their derivatives (or, more precisely, the intensity of the electron activity) unambiguously indicates that for nonsynchronous reactions, electron activity transcends the TS region and takes place well into the reactants and products regions. Under these circumstances, an extension of the TS region toward the reactants and products regions may occur.

High-level ab initio mapping of the multiple H-abstraction pathways of the OH + glycine reaction.

We perform a systematic search in the transition-state (TS) and product-channel complex (MIN) regions of the multi-channel OH + glycine → H2O + H2N-CH-COOH (CH)/HN-CH2-COOH (NH)/H2N-CH2-COO (COOH) reactions. Geometry optimizations reveal {7, 3, 3} CH-TS, {2, 2, 2} CH-MIN, {17, 10, 5} NH-TS, {35, 19, 19} NH-MIN, and {6, 5, 5} COOH-TS conformers at the {MP2/3-21G, MP2/aug-cc-pVDZ, CCSD(T)-F12b/aug-cc-pVDZ} levels of theory as well as 2 additional CH-TSs based on chemical intuition. The benchmark relative energies of the TS, MIN, and product conformers are obtained by considering basis set effects up to aug-cc-pVQZ using the explicitly-correlated CCSD(T)-F12b method, post-(T) correlation up to CCSDT(Q), core correlation, scalar relativistic effects, spin-orbit coupling, and zero-point energy corrections. All the CH [ΔEe(ΔH0) = -38.54(-38.61) kcal mol-1], NH [ΔEe(ΔH0) = -16.72(-17.98) kcal mol-1], and COOH [ΔEe = -4.98 kcal mol-1] reactions are exothermic and proceed via shallow, usually negative, classical(adiabatic) barriers of -0.37(-0.95), -1.91(-2.48), and 1.02(-0.57) kcal mol-1, respectively. In the entrance channel MRCI/aug-cc-pVTZ computations reveal several complexes with reactive(non-reactive) arrangements and binding energies of 1.0, 1.6, 3.3, (5.2 and 5.9) kcal mol-1, stabilized by CH⋯OH, NH⋯OH, COOH⋯OH, (OH⋯OC and OH⋯N) hydrogen bonds, respectively.

Transition1x - a dataset for building generalizable reactive machine learning potentials

Machine Learning (ML) models have, in contrast to their usefulness in molecular dynamics studies, had limited success as surrogate potentials for reaction barrier search. This is primarily because available datasets for training ML models on small molecular systems almost exclusively contain configurations at or near equilibrium. In this work, we present the dataset Transition1x containing 9.6 million Density Functional Theory (DFT) calculations of forces and energies of molecular configurations on and around reaction pathways at the ωB97x/6–31 G(d) level of theory. The data was generated by running Nudged Elastic Band (NEB) with DFT on 10k organic reactions of various types while saving intermediate calculations. We train equivariant graph message-passing neural network models on Transition1x and cross-validate on the popular ANI1x and QM9 datasets. We show that ML models cannot learn features in transition state regions solely by training on hitherto popular benchmark datasets. Transition1x is a new challenging benchmark that will provide an important step towards developing next-generation ML force fields that also work far away from equilibrium configurations and reactive systems.

Quantum dynamics reveal different ligand effects by vibrational excitation in the dissociative chemisorption of HCl on the Au/Ag(111) surface.

The reactivity and selectivity of bimetallic surfaces are of fundamental importance in industrial applications. Here, we report the first six-dimensional (6D) quantum dynamics study for the role of surface strain and ligand effects on the reactivity of HCl on a strained pseudomorphic monolayer of Au deposited onto a Ag(111) substrate, with the aid of accurate machine learning-based potential energy surfaces. The substitute of Au into Ag changes the location of the transition state; however, the static barrier height remains roughly the same as pure Au(111). The 6D quantum dynamics calculations reveal that the surface strain due to lattice expansion slightly enhances the reactivity. The ligand effect due to electronic structure interactions between Au and Ag substantially suppresses the reactivity of HCl in the ground vibrational state but promotes the reactivity via vibrational excitation at high kinetic energies. This finding can be attributed to more close interaction with Ag atoms at the transition state close to the fcc site, as well as the tight transition-state region, making the vibrational excitation highly efficient in enhancing the reactivity. Our study quantitatively unravels the dynamical origin of reactivity control by two metals, which will ultimately provide valuable insight into the selectivity of the catalyst.

Observation of resonances in the transition state region of the F + NH3 reaction using anion photoelectron spectroscopy.

The transition state of a chemical reaction is a dividing surface on the reaction potential energy surface (PES) between reactants and products and is thus of fundamental interest in understanding chemical reactivity. The transient nature of the transition state presents challenges to its experimental characterization. Transition-state spectroscopy experiments based on negative-ion photodetachment can provide a direct probe of this region of the PES, revealing the detailed vibrational structure associated with the transition state. Here we study the F + NH3 → HF + NH2 reaction using slow photoelectron velocity-map imaging spectroscopy of cryogenically cooled FNH3- anions. Reduced-dimensionality quantum dynamical simulations performed on a global PES show excellent agreement with the experimental results, enabling the assignment of spectral structure. Our combined experimental-theoretical study reveals a manifold of vibrational Feshbach resonances in the product well of the F + NH3 PES. At higher energies, the spectra identify features attributed to resonances localized across the transition state and into the reactant complex that may impact the bimolecular reaction dynamics.

Energy Decomposition along Reaction Coordinate: Theory and Applications to Nonequilibrium Ensembles of Trajectories.

A theoretical framework is proposed for an energy decomposition scheme along the reaction coordinate, in which the ensemble average of the potential energy weighted with reactive flux intensity is decomposed into energy components at the per-coordinate level. The decomposed energy quantity is demonstrated to be closely related to the free energy along the reaction coordinate, and its connection to the emergent potential energy is provided. In the application to alanine dipeptide under vacuum, illustrative calculations were performed in three nonequilibrium ensembles of trajectories: (1) transition path ensemble sampled with transition path sampling; (2) ensemble of short trajectories initiated from configurations around the transition-state region; and (3) ensemble of short trajectories shooting from configurations in several transition paths. The energy components on each coordinate were found to be consistent among the three ensembles of trajectories, indicating a broad applicability of the approach in biomolecular studies. In addition, the free energies along an optimized reaction coordinate obtained with these nonequilibrium ensembles were largely overlapped with a reference free energy calculated from a long equilibrium trajectory.

Domino Effect in Allosteric Signaling of Peptide Binding

While being a thoroughly studied model of dynamic allostery in a small protein, the pathway of signal transduction in the PDZ3 domain has not been fully determined. Here, we investigate peptide binding to the PDZ3 domain by conventional and fully data-driven analyses of molecular dynamics simulations. First, we identify isoleucine 37 as a key residue by widely used computational procedures such as cross-correlation and community network analysis. Simulations of the Ile37Ala mutant show disruption of the coordinated movements of spatially close regular elements of secondary structure. Then, we employ a recently developed unsupervised, data-driven procedure to determine an optimized reaction coordinate (slowest-relaxation eigenvector) of peptide binding. We use this reaction coordinate to improve sampling by restarting additional simulations from the transition state region. Significant differences in the distributions of some of the pairwise residue distances in the bound and unbound states emerge from the projection onto the optimized reaction coordinate. The unsupervised analysis shows that allosteric signaling is transduced from the β2 strand, which forms part of the peptide binding site, to the spatially adjacent β3 and β4 strands, and from there to the α3 helix. The domino-like transmission of a (peptide binding) signal along β strands and α helices that are close in three-dimensional space is likely to be a general mechanism of allostery in single-domain proteins.