Visualization of the Intrinsic Reaction Coordinate and Global Reaction Route Map by Classical Multidimensional Scaling

Theoretical Insights into Ultrafast-Decaying and Long-Lived States of ortho-Nitrophenol upon Photoexcitation in the Gas Phase

Nitrophenols in the atmosphere are chromophore pollutants that absorb sunlight. Among them, ortho-nitrophenol (o-NP) stands out due to its strong intramolecular hydrogen bond which facilitates excited-state intramolecular proton transfer (ESIPT) and influences its photoisomerization and dissociation. Time-resolved experiments have captured both ultrafast-decaying and long-lived signals. Here, we employ non-adiabatic molecular dynamics simulations and the reaction space projector method to elucidate the photoinduced reactions of o-NP. Our simulations show that photoexcited o-NP in the S1(ππ*) state undergoes ultrafast ESIPT followed by rapid decay through one of two non-adiabatic pathways: ultrafast internal conversion to the S0 state and intersystem crossing (ISC) to the triplet states. Furthermore, trajectories undergoing ISC remain trapped in triplet states, with reverse ISC to the singlet states rarely observed. These trajectories are clearly linked to the long-lived excited-state signal, providing more conclusive computational evidence of the origin.

Acceleration of Reaction Space Projector Analysis Using Combinatorial Optimization: Application to Organic Chemical Reactions

In recent years, automated reaction path search methods have established the concept of a reaction route network. The Reaction Space Projector (ReSPer) visualizes the potential energy hypersurface into a lower-dimensional subspace using principal coordinates. The main time-consuming process in ReSPer is calculating the structural distance matrix, making it impractical for complex organic reaction route networks. We implemented the Alternate Optimization (AO) algorithm, one of the combinatorial optimizations, in ReSPer to reduce computational costs. Evaluations using gold clusters and the Au5 several reaction route networks showed that ReSPer-AO accurately computes distances with lower computational costs. Applying ReSPer-AO to the C5H8O reaction route network clarified dynamic conformation changes in its potential energy landscape. The ReSPer-AO method enables analysis of chemical reactions and dynamic conformations in a low-dimensional reaction space that accurately represents hydrocarbon reaction route networks.

Investigation on the combustion mechanism for NF3/H2 in DF/HF chemical lasers: a new perspective based on deep potential molecular dynamics simulations

Combustion-driven deuterium fluoride/hydrogen fluoride (DF/HF) lasers are a crucial type of chemical lasers. Their chemical efficiency mainly depends on the production efficiency of atomic fluorine in the combustion chamber, where NF3 serves as the fluorine resource, and H2 acts as the reducing agent. However, due to the complex combustion process, high reaction temperatures, and potent corrosiveness of the products, the combustion mechanism of NF3/H2 in the combustion chamber is still not fully revealed, including the chemical details of F atom generation. In this work, we firstly employed the molecular dynamics (MD) method to simulate the combustion reaction for combustion-driven DF/HF chemical lasers. Additionally, for the first time, a high-accuracy neural network potential (NNP) for the NF3/H2 system was constructed using machine learning methodologies. The simulation results reveal that the combustion process of the NF3/H2 system comprises three stages: the initiation of combustion, the generation of HF, and the formation of N2. The fluorine atoms in the system primarily originate from the cleavage of the N-F bond in N2F4, which is formed via the dimerization of NF2. Temperature and molar ratios of reactants are two important factors influencing the F atom formation. Higher temperatures and an excess number of NF3 favor the generation of F atoms. Besides, we found that the initial HF production stems from H-abstraction reaction between the F radical and H2, rather than the previously proposed reaction between NF3 and H2. The NNP-based MD simulations unveil the atomic-scale reaction mechanisms for NF3/H2 combustion in combustion-driven DF/HF chemical lasers, indicating its potential as an effective tool for the studies in the field of chemical lasers. The results also offer theoretical insights for enhancing the performance of the combustion-driven DF/HF chemical lasers.

Benchmark ab initio characterization of the complex potential energy surfaces of the HOO- + CH3Y [Y = F, Cl, Br, I] reactions

The α-effect is a well-known phenomenon in organic chemistry, and is related to the enhanced reactivity of nucleophiles involving one or more lone-pair electrons adjacent to the nucleophilic center. The gas-phase bimolecular nucleophilic substitution (SN2) reactions of α-nucleophile HOO- with methyl halides have been thoroughly investigated experimentally and theoretically; however, these investigations have mainly focused on identifying and characterizing the α-effect of HOO-. Here, we perform the first comprehensive high-level ab initio mapping for the HOO- + CH3Y [Y = F, Cl, Br and I] reactions utilizing the modern explicitly-correlated CCSD(T)-F12b method with the aug-cc-pVnZ [n = 2-4] basis sets. The present ab initio characterization considers five distinct product channels of SN2: (CH3OOH + Y-), proton abstraction (CH2Y- + H2O2), peroxide ion substitution (CH3OO- + HY), SN2-induced elimination (CH2O + HY + HO-) and SN2-induced rearrangement (CH2(OH)O- + HY). Moreover, besides the traditional back-side attack Walden inversion, the pathways of front-side attack, double inversion and halogen-bond complex formation have also been explored for SN2. With regard to the Walden inversion of HOO- + CH3Cl, the previously unaddressed discrepancies concerning the geometry of the corresponding transition state are clarified. For the HOO- + CH3F reaction, the recently identified SN2-induced elimination is found to be more exothermic than the SN2 channel, submerged by ∼36 kcal mol-1. The accuracy of our high-level ab initio calculations performed in the present study is validated by the fact that our new benchmark 0 K reaction enthalpies show excellent agreement with the experimental data in nearly all cases.

Biomimetic Frustrated Lewis Pair Catalysts for Hydrogenation of CO to Methanol at Low Temperatures

The industrial production of methanol through CO hydrogenation using the Cu/ZnO/Al2O3 catalyst requires harsh conditions, and the development of new catalysts with low operating temperatures is highly desirable. In this study, organic biomimetic FLP catalysts with good tolerance to CO poison are theoretically designed. The base-free catalytic reaction contains the 1,1-addition of CO into a formic acid intermediate and the hydrogenation of the formic acid intermediate into methanol. Low-energy spans (25.6, 22.1, and 20.6 kcal/mol) are achieved, indicating that CO can be hydrogenated into methanol at low temperatures. The new extended aromatization-dearomatization effect involving multiple rings is proposed to effectively facilitate the rate-determining CO 1,1-addition step, and a new CO activation model is proposed for organic catalysts.

Unveiling Pre-Transmetalation Intermediates in Base-Free Suzuki-Miyaura Cross-Couplings: A Computational Study

The pre-transmetalation intermediates are critically important in Suzuki-Miyaura cross-coupling (SMC) reactions and have become a hot spot of the current research. However, the pre-transmetalation intermediates under base-free conditions have not been clear. Herein, a comprehensive theoretical study is performed on the base-free Pd-catalyzed desulfonative SMC reaction. The fragile coordination feature and the acceleration role of the RuPhos chelate ligand are revealed. The hydrogen-bond complex between the Pd-F complex and aryl boronic acid is identified as an important pre-transmetalation intermediate, which increases the energy span to 32.5 kcal/mol. The controlling factor for the formation of the hydrogen-bond complexes is attributed to the electronegativities of halogen atoms in the metal halide complexes. What is more, other reported SMC reaction systems involving metal halide complexes and aryl boronic acids are reconsidered and suggest that the hydrogen-bond complexes widely exist as stable pre-transmetalation intermediates with influencing the catalytic activities. The earth-abundant Ni-catalyzed desulfonative SMC reaction is further designed and predicted to have a higher activity than the original Pd-catalyzed SMC reaction.

Vibrational mode-specificity in the dynamics of the OH- + CH3I multi-channel reaction

We report a comprehensive characterization of the vibrational mode-specific dynamics of the OH- + CH3I reaction. Quasi-classical trajectory simulations are performed at four different collision energies on our previously-developed full-dimensional high-level ab initio potential energy surface in order to examine the impact of four different normal-mode excitations in the reactants. Considering the 11 possible pathways of OH- + CH3I, pronounced mode-specificity is observed in reactivity: In general, the excitations of the OH- stretching and CH stretching exert the greatest influence on the channels. For the SN2 and proton-abstraction products, the reactant initial attack angle and the product scattering angle distributions do not show major mode-specific features, except for SN2 at higher collision energies, where forward scattering is promoted by the CI stretching and CH stretching excitations. The post-reaction energy flow is also examined for SN2 and proton abstraction, and it is unveiled that the excess vibrational excitation energies rather transfer into the product vibrational energy because the translational and rotational energy distributions of the products do not represent significant mode-specificity. Moreover, in the course of proton abstraction, the surplus vibrational energy in the OH- reactant mostly remains in the H2O product owing to the prevailing dominance of the direct stripping mechanism.

Hydrogen-migration governed dynamic magnetic coupling characteristics in nitrogen-vacancy-hydrogen nanodiamonds

The nitrogen-vacancy center doped with hydrogen (NVH) is one of the most common defects in diamonds, and the doping of hydrogen is known to enable mobility among three equivalent C-radicals in the defect, which noticeably affects the spin coupling among the radicals. Here, we for the first time uncover the dynamic nature of magnetic coupling induced by H-migration in the NVH center of nanodiamonds, using spin-polarized density functional theory calculations and enhanced sampling metadynamics simulations. The mobility of doping H enables the interior NVH region to become a variable magnetic space (antiferromagnetic/AFM versus ferromagnetic/FM). That is, the dynamic H has three frequently reachable binding C sites where H enables the center to exhibit variable AFM coupling (high up to J = -1282 cm-1) and that in other H-reachable regions including N sites, it enables the center to exhibit FM coupling (high up to J = 598 cm-1). The magnetic switching (AFM ↔ FM) and strength fluctuation strongly depend on the H-position which can adjust the ratio of the C radical orbitals in their mixing orbitals for a special three-electron three-center covalent C⋯H⋯C H-bonding and radical orbital distributions. Clearly, this work provides insights into the dynamic switching of magnetic coupling in such multi-radical centers of defect nanodiamonds.

Reaction mechanism - explored with the unified reaction valley approach

One of the ultimate goals of chemistry is to understand and manipulate chemical reactions, which implies the ability to monitor the reaction and its underlying mechanism at an atomic scale. In this article, we introduce the Unified Reaction Valley Approach (URVA) as a tool for elucidating reaction mechanisms, complementing existing computational procedures. URVA combines the concept of the potential energy surface with vibrational spectroscopy and describes a chemical reaction via the reaction path and the surrounding reaction valley traced out by the reacting species on the potential energy surface on their way from the entrance to the exit channel, where the products are located. The key feature of URVA is the focus on the curving of the reaction path. Moving along the reaction path, any electronic structure change of the reacting species is registered by a change in the normal vibrational modes spanning the reaction valley and their coupling with the path, which recovers the curvature of the reaction path. This leads to a unique curvature profile for each chemical reaction, with curvature minima reflecting minimal change and curvature maxima indicating the location of important chemical events such as bond breaking/formation, charge polarization and transfer, rehybridization, etc. A decomposition of the path curvature into internal coordinate components or other coordinates of relevance for the reaction under consideration, provides comprehensive insight into the origin of the chemical changes taking place. After giving an overview of current experimental and computational efforts to gain insight into the mechanism of a chemical reaction and presenting the theoretical background of URVA, we illustrate how URVA works for three diverse processes, (i) [1,3] hydrogen transfer reactions; (ii) α-keto-amino inhibitor for SARS-CoV-2 Mpro; (iii) Rh-catalyzed cyanation. We hope that this article will inspire our computational colleagues to add URVA to their repertoire and will serve as an incubator for new reaction mechanisms to be studied in collaboration with our experimental experts in the field.

Challenges for Kinetics Predictions via Neural Network Potentials: A Wilkinson's Catalyst Case

Ab initio kinetic studies are important to understand and design novel chemical reactions. While the Artificial Force Induced Reaction (AFIR) method provides a convenient and efficient framework for kinetic studies, accurate explorations of reaction path networks incur high computational costs. In this article, we are investigating the applicability of Neural Network Potentials (NNP) to accelerate such studies. For this purpose, we are reporting a novel theoretical study of ethylene hydrogenation with a transition metal complex inspired by Wilkinson's catalyst, using the AFIR method. The resulting reaction path network was analyzed by the Generative Topographic Mapping method. The network's geometries were then used to train a state-of-the-art NNP model, to replace expensive ab initio calculations with fast NNP predictions during the search. This procedure was applied to run the first NNP-powered reaction path network exploration using the AFIR method. We discovered that such explorations are particularly challenging for general purpose NNP models, and we identified the underlying limitations. In addition, we are proposing to overcome these challenges by complementing NNP models with fast semiempirical predictions. The proposed solution offers a generally applicable framework, laying the foundations to further accelerate ab initio kinetic studies with Machine Learning Force Fields, and ultimately explore larger systems that are currently inaccessible.

A comparable DFT study on reaction of CHCl•- with O3 and S2O

CONTEXT

In this discussion, we began building two model, S₂O + CHCl^•- and O₃ + CHCl^•-, using DFT-BHandHLYP method, to study their reactions mechanisms on singlet PES. For this purpose, we hope to explore the effects of the difference between sulfur and oxygen atoms on the CHCl^•- anion. Experimentalists and computer scientists may utilize the collected data to generate a wide range of hypotheses for experimental phenomena and predictions, allowing them to realize their full potential.

METHODS

The ion-molecule reaction mechanism of CHCl^•- with S₂O and O₃ was studied using the DFT-BHandHLYP level of theory with the aug-cc-pVDZ basis set. Our theoretical findings show that Path 6 is the favored reaction pathway for CHCl^•- + O₃ reaction as identified by the O-abstraction reaction pattern. Comparing to the direct H- and Cl-abstraction mechanisms, the reaction (CHCl^•- + S₂O) prefers the intramolecular S_N2 reaction pattern. Moreover, the calculated results demonstrated that the CHCl^•- + S₂O reaction is thermodynamically more favorable than the CHCl^•- + O₃ reaction, which is kinetically more advantageous. As a result, if the required reaction condition in the atmospheric process is met, the O₃ reaction will happen more effectively. In terms of kinetics and thermodynamics viewpoints, the CHCl^•- anion was very effective in eliminating S₂O and O₃.

Quasi-classical trajectory study of the OH- + CH3I reaction: theory meets experiment

Regarding OH^- + CH₃I, several studies have focused on the dynamics of the reaction. Here, high-level quasi-classical trajectory simulations are carried out at four different collision energies on our recently developed potential energy surface. In all, more than half a million trajectories are performed, and for the first time, the detailed quasi-classical trajectory results are compared with the reanalysed crossed-beam ion imaging experiments. Concerning the previously reported direct dynamics study of OH^- + CH₃I, a better agreement can be obtained between the revised experiment and our novel theoretical results. Furthermore, in the present work, the benchmark geometries, frequencies and relative energies of the stationary points are also determined for the OH^- + CH₃I proton-abstraction channel along with the earlier characterized S_N2 channel.

Multi-state Energy Landscape for Photoreaction of Stilbene and Dimethyl-stilbene

We have recently developed the reaction space projector (ReSPer) method, which constructs a reduced-dimensionality reaction space uniquely determined from reference reaction paths for a polyatomic molecular system and projects classical trajectories into the same reaction space. In this paper, we extend ReSPer to the analysis of photoreaction dynamics and relaxation processes of stilbene and present the concept of a "multi-state energy landscape," incorporating the ground- and excited-state reaction subspaces. The multi-state energy landscape successfully explains the previously established photoreaction processes of cis-stilbene, such as the cis-trans photoisomerization and photocyclization. In addition, we discuss the difference in the excited-state reaction dynamics between stilbene and 1,1'-dimethyl stilbene based on a common reaction subspace determined from the framework part of reference structures with different number of atoms. This approach allows us to target any molecule with a common framework, greatly expanding the applicability of the ReSPer analysis. The multi-state energy landscape provides fruitful insight into photochemical reactions, exploring the excited- and ground-state potential energy surfaces, as well as comprehensive reaction processes with nonradiative transitions between adiabatic states, within the stage of a reduced-dimensionality reaction space.

Isomerization Reactions of the Cu15V+ Cluster: A Density Functional Theory Study

The investigation of the chemical reactivity of complex systems such as transition metal clusters is a very complicated task because often the structures of the corresponding transition states are far from being intuitive. Bimetallic transition metal clusters represent a particular class of complex systems. In this work, density functional theory (DFT) is applied to study the isomerization reactions of the Cu₁₅V⁺ cluster. Full geometry optimizations of dozens of initial structures taken along Born-Oppenheimer molecular dynamics (BOMD) trajectories were performed using a quasi-Newton method in a reduced space Cartesian coordinate system that works considering the internal degrees of freedom. Harmonic frequencies calculations were performed at the optimized structures. To study the isomerization reactions between the obtained stable isomers, a hierarchical transition state algorithm has been applied to locate the transition states of this cluster. The found transition states were than connected with the corresponding minimum structures by calculating the intrinsic reaction coordinates. This work demonstrates the capability of the applied method to study non-intuitive rearrangement mechanisms in complex finite systems and to create networks between minima and transition state structures on their potential energy surface.

Reaction Space Projector (ReSPer) for Visualizing Dynamic Reaction Routes Based on Reduced-Dimension Space

To analyze chemical reaction dynamics based on a reaction path network, we have developed the "Reaction Space Projector" (ReSPer) method with the aid of the dimensionality reduction method. This program has two functions: the construction of a reduced-dimensionality reaction space from a molecular structure dataset, and the projection of dynamic trajectories into the low-dimensional reaction space. In this paper, we apply ReSPer to isomerization and bifurcation reactions of the Au₅ cluster and succeed in analyzing dynamic reaction routes involved in multiple elementary reaction processes, constructing complicated networks (called "closed islands") of nuclear permutation-inversion (NPI) isomerization reactions, and elucidating dynamic behaviors in bifurcation reactions with reference to bundles of trajectories. Interestingly, in the second application, we find a correspondence between the contribution ratios in the ability to visualize and the symmetry of the morphology of closed islands. In addition, the third application suggests the existence of boundaries that determine the selectivity in bifurcation reactions, which was discussed in the phase space. The ReSPer program is a versatile and robust tool to clarify dynamic reaction mechanisms based on the reduced-dimensionality reaction space without prior knowledge of target reactions.

Acceleration Effect of Bases on Mn Pincer Complex-Catalyzed CO2 Hydroboration

Herein, we report a comprehensive study of CO₂ hydroboration catalyzed by Mn pincer complexes. The traditional metal-ligand cooperation (MLC) mechanism based on the H-Mn-N-Bpin pincer complex is not viable due to the competing abstraction of the Bpin group from the H-Mn-N-Bpin complex by NaO^tBu. Instead, we propose an ionic mechanism based on the H-Mn-N-Na species with a low energy span (22.5 kcal/mol) and unveil the acceleration effect of bases. The X groups in the H-Mn-N-X catalyst models are further modulated, and the steric hindrance and H→B donor-acceptor interactions of the X group increase the energy barrier of the hydride transfer. The hydrogen bond and electrostatic interactions of the X group can accelerate the hydride transfer to HCOOBpin and HCHO molecules except for the nonpolar CO₂ molecule. Based on these discoveries, we designed a pyridine-based Mn pincer catalyst system, which could achieve CO₂ hydroboration in low-temperature and base-free conditions through a metal-ligand cooperation mechanism.

Uncovering an oxide ion substitution for the OH- + CH3F reaction

Theoretical investigations on chemical reactions allow us to understand the dynamics of the possible pathways and identify new unexpected routes. Here, we develop a global analytical potential energy surface (PES) for the OH⁻ + CH₃F reaction in order to perform high-level dynamics simulations. Besides bimolecular nucleophilic substitution (S_N2) and proton abstraction, our quasi-classical trajectory computations reveal a novel oxide ion substitution leading to the HF + CH₃O⁻ products. This exothermic reaction pathway occurs via the CH₃OH⋯F⁻ deep potential well of the S_N2 product channel as a result of a proton abstraction from the hydroxyl group by the fluoride ion. The present detailed dynamics study of the OH⁻ + CH₃F reaction focusing on the surprising oxide ion substitution demonstrates how incomplete our knowledge is of fundamental chemical reactions.

Reaction dynamics simulations on a high-level ab initio analytical potential energy surface reveal a novel oxide ion substitution channel for the OH⁻ + CH₃F reaction.

Visualization of reaction route map and dynamical trajectory in reduced dimension

In the quantum chemical approach, chemical reaction mechanisms are investigated based on a potential energy surface (PES). Automated reaction path search methods enable us to construct a global reaction route map containing multiple reaction paths corresponding to a series of elementary reaction processes. The on-the-fly molecular dynamics (MD) method provides a classical trajectory exploring the full-dimensional PES based on electronic structure calculations. We have developed two reaction analysis methods, the on-the-fly trajectory mapping method and the reaction space projector (ReSPer) method, by introducing a structural similarity to a pair of geometric structures and revealed dynamic aspects affecting chemical reaction mechanisms. In this review, we will present the details of these analysis methods and discuss the dynamics effects of reaction path curvature and reaction path bifurcation with applications to the CH₃OH + OH^- collision reaction and the Au₅ cluster branching and isomerization reactions.

Exploring the Mechanism of Catalysis with the Unified Reaction Valley Approach (URVA)—A Review

The unified reaction valley approach (URVA) differs from mainstream mechanistic studies, as it describes a chemical reaction via the reaction path and the surrounding reaction valley on the potential energy surface from the van der Waals region to the transition state and far out into the exit channel, where the products are located. The key feature of URVA is the focus on the curving of the reaction path. Moving along the reaction path, any electronic structure change of the reacting molecules is registered by a change in their normal vibrational modes and their coupling with the path, which recovers the curvature of the reaction path. This leads to a unique curvature profile for each chemical reaction with curvature minima reflecting minimal change and curvature maxima, the location of important chemical events such as bond breaking/forming, charge polarization and transfer, rehybridization, etc. A unique decomposition of the path curvature into internal coordinate components provides comprehensive insights into the origins of the chemical changes taking place. After presenting the theoretical background of URVA, we discuss its application to four diverse catalytic processes: (i) the Rh catalyzed methanol carbonylation—the Monsanto process; (ii) the Sharpless epoxidation of allylic alcohols—transition to heterogenous catalysis; (iii) Au(I) assisted [3,3]-sigmatropic rearrangement of allyl acetate; and (iv) the Bacillus subtilis chorismate mutase catalyzed Claisen rearrangement—and show how URVA leads to a new protocol for fine-tuning of existing catalysts and the design of new efficient and eco-friendly catalysts. At the end of this article the pURVA software is introduced. The overall goal of this article is to introduce to the chemical community a new protocol for fine-tuning existing catalytic reactions while aiding in the design of modern and environmentally friendly catalysts.

Construction of Two-Dimensional Potential Energy Surfaces of Reactions with Post-Transition-State Bifurcations

Reactions with post-transition-state bifurcations (PTSBs) involve initial ambimodal transition-state structures followed by an unstable region leading to two possible products. PTSBs are seen in many organic, organometallic, and biosynthetic reactions, but analyzing the origins of selectivity for these reactions is challenging, in large part due to the complex nature of the potential energy surfaces involved, which precludes analyses based on single intrinsic reaction coordinate (IRC; steepest-descent path in mass-weighted coordinate). While selectivity can be predicted using molecular dynamics simulation, connecting results from such calculations to the topography of potential energy surfaces is difficult. In the present work, a method for generating two-dimensional potential energy surfaces for PTSBs is described. The first dimension starts with the IRC for the first transition-state structure, followed by a modified reaction coordinate that reaches the second transition-state structure, which interconverts the two products of a bifurcating reaction path. The IRC for the second transition-state structure constitutes the second dimension. In addition, a method for mapping trajectories from Born-Oppenheimer molecular dynamics simulations onto these surfaces is described. Both approaches are illustrated with representative examples from the field of organic chemistry. The 2D-PESs for five asymmetric cases tested have clear tilted topography after the first transition-state structure, and the tilted direction correlates well with the selectivity observed from previous dynamic simulation. Instead of selecting reaction coordinates by chemical intuition, our method provides a general means to construct two-dimensional potential energy surfaces for reactions with post-transition-state bifurcations.

Quasi-classical trajectory analysis with isometric feature mapping and locally linear embedding: deep insights into the multichannel reaction on an NH3+(4A) potential energy surface

Two manifold learning methods, isometric feature mapping and locally linear embedding, are applied to the analysis of quasi-classical trajectories for multi-channel reaction NH⁺ + H₂ → N + H₃⁺/NH₂⁺ + H.

Exploring free energy profile of petroleum thermal cracking mechanisms

Understanding the mechanisms of petroleum thermal cracking is critical to develop more efficient and eco-friendly petroleum cracking processes. Asphaltenes are the main component of petroleum subjected to cracking processes. Thermal cracking mechanisms of petroleum were explored by computational methods using 1,2-diphenylethane (DPE) as a model molecule in this study. The overall mechanisms were divided into four steps including initiation, H-transfer reaction, H-ipso reaction, and termination represented by seven reactions. We carried out extensive quantum chemistry calculations at high levels of theory to accurately explore the minimum energy pathways as the mechanisms of the proposed reactions. The reaction energy and barriers in terms of enthalpy and free energy and their temperature dependence were calculated in the vacuum and in both polar and nonpolar solvents using the polarizable continuum model (PCM) method. The temperature dependence of the target reaction barriers are characterized in different environments and provides computational guidance for future development for petroleum thermal cracking. As the first reported systematic investigation of petroleum cracking mechanisms, this study provided a comprehensive theoretical description of petroleum cracking processes with valuable information about temperature and solvent dependence. Graphical abstract.

Low dimensional representations along intrinsic reaction coordinates and molecular dynamics trajectories using interatomic distance matrices

Most chemical transformations (reactions or conformational changes) that are of interest to researchers have many degrees of freedom, usually too many to visualize without reducing the dimensionality of the system to include only the most important atomic motions. In this article, we describe a method of using Principal Component Analysis (PCA) for analyzing a series of molecular geometries (e.g., a reaction pathway or molecular dynamics trajectory) and determining the reduced dimensional space that captures the most structural variance in the fewest dimensions. The software written to carry out this method is called PathReducer, which permits (1) visualizing the geometries in a reduced dimensional space, (2) determining the axes that make up the reduced dimensional space, and (3) projecting the series of geometries into the low-dimensional space for visualization. We investigated two options to represent molecular structures within PathReducer: aligned Cartesian coordinates and matrices of interatomic distances. We found that interatomic distance matrices better captured non-linear motions in a smaller number of dimensions. To demonstrate the utility of PathReducer, we have carried out a number of applications where we have projected molecular dynamics trajectories into a reduced dimensional space defined by an intrinsic reaction coordinate. The visualizations provided by this analysis show that dynamic paths can differ greatly from the minimum energy pathway on a potential energy surface. Viewing intrinsic reaction coordinates and trajectories in this way provides a quick way to gather qualitative information about the pathways trajectories take relative to a minimum energy path. Given that the outputs from PCA are linear combinations of the input molecular structure coordinates (i.e., Cartesian coordinates or interatomic distances), they can be easily transferred to other types of calculations that require the definition of a reduced dimensional space (e.g., biased molecular dynamics simulations).

Combined Automated Reaction Pathway Searches and Sparse Modeling Analysis for Catalytic Properties of Lowest Energy Twins of Cu13

In nanocatalysis, growing attention has recently been given to investigation of energetically low-lying structural isomers of atomic clusters, because some isomers can demonstrate better catalytic activity than the most stable structures. In this study, we present a comparative investigation of catalytic activity for NO dissociation of a pair of the energetically degenerated isomers of Cu₁₃ cluster having C₂ and C _s symmetries. It is shown that although these isomers have similar structural, electronic, and optical properties, they can possess very different catalytic activities. The effect of isomerization between cluster isomers is considered using state-of-the-art automated reaction pathway search techniques such as an artificial force induced reaction (AFIR) method as a part of a global reaction route mapping (GRRM) strategy. This method allows effectively to locate a large number of possible reaction pathways and transition states (TSs). In total, 12 TSs for NO dissociation were obtained for Cu₁₃, of C₂, C _s, as well as I _h isomers. Sparse modeling analysis shows that LUMO is strongly negatively correlated with total energy of TSs. For most TSs, LUMO has the antibonding character of NO, consisting of the interaction between π* of NO and SOMO of Cu₁₃. Therefore, an increase in the strength of interaction between NO molecule and Cu₁₃ cluster causes the rise in energy of the LUMO, resulting in lowering of the TS energy for NO dissociation. The combination of the automated reaction pathway search technique and sparse modeling represents a powerful tool for analysis and prediction of the physicochemical properties of atomic clusters, especially in the regime of structural fluxionality, where traditional methods based on random geometry search analyses are difficult.