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

Unsupervised Machine Learning in the Analysis of Nonadiabatic Molecular Dynamics Simulation

The all-atomic full-dimensional-level simulations of nonadiabatic molecular dynamics (NAMD) in large realistic systems has received high research interest in recent years. However, such NAMD simulations normally generate an enormous amount of time-dependent high-dimensional data, leading to a significant challenge in result analyses. Based on unsupervised machine learning (ML) methods, considerable efforts were devoted to developing novel and easy-to-use analysis tools for the identification of photoinduced reaction channels and the comprehensive understanding of complicated molecular motions in NAMD simulations. Here, we tried to survey recent advances in this field, particularly to focus on how to use unsupervised ML methods to analyze the trajectory-based NAMD simulation results. Our purpose is to offer a comprehensive discussion on several essential components of this analysis protocol, including the selection of ML methods, the construction of molecular descriptors, the establishment of analytical frameworks, their advantages and limitations, and persistent challenges.

Boosting the Modeling of Infrared and Raman Spectra of Bulk Phase Chromophores with Machine Learning

In the field of vibrational spectroscopy simulation, hybrid approximations to Kohn-Sham density-functional theory (KS-DFT) are often considered computationally prohibitive due to the significant effort required to evaluate the exchange-correlation potential in planewave codes. In this Letter, we show that by leveraging the porting of KS-DFT on GPU and incorporating machine-learning techniques, simulating IR and Raman spectra of real-life chromophores in bulk aqueous solution becomes a routine application at this level of theory.

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.

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.

A 21st Century View of Allowed and Forbidden Electrocyclic Reactions

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

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.

The essential role of GSTP1 I105V polymorphism in the prediction of CDNB metabolism and toxicity: In silico and in vitro insights

Humans are continuously exposed to toxic chemicals such as nitro-chlorobenzene (CDNB) through occupation, water, and even the air we breathe. Due to the severe toxicity caused by the high electrophilicity of CDNB, occupational and environmental exposure to CDNB can produce toxic effects that ultimately lead to cell damage. CDNB can be eliminated from organisms by binding to GSH, the catalytic product of glutathione S-transferase P1 (GSTP1). Therefore, GSTP1 plays an important role in the detoxification of CDNB. However, subtle variations in GSTP1 can result in single nucleotide polymorphisms (SNPs). Indeed, the correlation between the clinical outcome of the disease and certain genotypes of GSTP1 has been extensively studied, however, their impact on the metabolic detoxification of toxicants such as CDNB remains to be elucidated. Among the various SNPs of GSTP1, I105V has a significant effect on the catalytic activity of GSTP1. In this paper, a GSTP1 I105V polymorphism model was successfully established, and its effect on CDNB metabolism and toxicity was studied by computer analysis including molecular docking and molecular dynamics simulation. The result demonstrated that the binding capacity of CDNB decreases with the I105V mutation of GSTP1(p < 0.001), indicating the changes in its detoxification efficacy in CDNB-induced cell damage. Organisms expressing GSTP1 V105 are more susceptible to cell damage caused by CDNB than individuals expressing GSTP1 I105 (p < 0.001). In sum, the data in this study provide prospective insights into the mechanism and capacity of CDNB detoxification in the GSTP1 allele, extending the CDNB-mediated toxicological profile. In addition, the heterogeneity of the GSTP1 allele should be included in toxicological studies of individuals exposed to CDNB.

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.

E-Z Isomerization in Guanidine: Second-order Saddle Dynamics, Non-statisticality, and Time-frequency Analysis

Our recent work on the E-Z isomerization reaction of guanidine using ab initio chemical dynamics simulations [Rashmi et al., Regul. Chaotic Dyn. 2021, 26, 119] emphasized the role of second-order saddle (SOS) in the isomerization reaction; however, we could not unequivocally establish the non-statistical nature of the dynamics followed in the reaction. In the present study, we performed thousands of on-the-fly trajectories using forces computed at the MNDO level to investigate the influence of second-order saddle in the E-Z isomerization reaction of guanidine and the role of intramolecular vibrational energy redistribution (IVR) on the reaction dynamics. The simulations reveal that while majority of the trajectories follow the traditional transition state pathways, 15 % of the trajectories follow the SOS path. The dynamics was found to be highly non-statistical with the survival probabilities of the reactants showing large deviations from those obtained within the RRKM assumptions. In addition, a detailed analysis of the dynamics using time-dependent frequencies and the frequency ratio spaces reveal the existence of multiple resonance junctions that indicate the existence of regular dynamics and long-lived quasi-periodic trajectories in the phase space associated with non-RRKM behavior.

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.

The principal component analysis of the ring deformation in the nonadiabatic surface hopping dynamics

The analysis of the leading active molecular motions in the on-the-fly trajectory surface hopping simulation provides the essential information to understand the geometric evolution in nonadiabatic dynamics. When the ring deformation is involved, the identification of the key active coordinates becomes challenging. A "hierarchical" protocol based on the dimensionality reduction and clustering approaches is proposed for the automatic analysis of the ring deformation in the nonadiabatic molecular dynamics. The representative system keto isocytosine is taken as the prototype to illustrate this protocol. The results indicate that the current hierarchical analysis protocol is a powerful way to clearly clarify both the major and minor active molecular motions of the ring distortion in nonadiabatic dynamics.

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

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

Portable Models for Entropy Effects on Kinetic Selectivity

Differences in entropies of competing transition states can direct kinetic selectivity. Understanding and modeling such entropy differences at the molecular level is complicated by the fact that entropy is statistical in nature; i.e., it depends on multiple vibrational states of transition structures, the existence of multiple dynamically accessible pathways past these transition structures, and contributions from multiple transition structures differing in conformation/configuration. The difficulties associated with modeling each of these contributors are discussed here, along with possible solutions, all with an eye toward the development of portable qualitative models of use to experimentalists aiming to design reactions that make use of entropy to control kinetic selectivity.

Influence of an Oriented External Electric Field on the Mechanism of Double Proton Transfer between Pyrazole and Guanidine: from an Asynchronous Plateau Transition State to a Synchronous or Stepwise Mechanism

The double proton transfer (DPT) reaction between pyrazole and guanidine, a concerted reaction but strongly asynchronous and presenting a "plateau transition region", has been theoretically reinvestigated in the presence of an external uniform electric field. First, we computed the reaction path by DFT and proposed a very detailed description of the constitutive electronic events, based on the ELF topology and the bond evolution theory. Then, we studied the effect of an oriented external electric field (OEEF) on the reaction mechanism, for an OEEF oriented along the proton transfer axis. We observe that in one direction, the DPT reaction can be transformed into a stepwise reaction, going through a stabilized single proton transferred intermediate. Contrarily, the two proton transfers occur simultaneously when the electric field is applied in the opposite direction. In the latter case, the order in which the two protons are transferred in the same elementary step can even be reversed if the OEEF is intense enough. Finally, it has been shown that the evolution of the double proton transfer reaction in the presence of an electric field could be quantitatively anticipated by analyzing the ELF value at the bifurcation point between V(A, H) proton donor and V(B) proton acceptor of the double hydrogen bonded complex in the entrance channel.

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.

Behavior of Linear and Nonlinear Dimensionality Reduction for Collective Variable Identification of Small Molecule Solution-Phase Reactions

Identifying collective variables (CVs) for chemical reactions is essential to reduce the 3N-dimensional energy landscape into lower dimensional basins and barriers of interest. However, in condensed phase processes, the nonmeaningful motions of bulk solvent often overpower the ability of dimensionality reduction methods to identify correlated motions that underpin collective variables. Yet solvent can play important indirect or direct roles in reactivity, and much can be lost through treatments that remove or dampen solvent motion. This has been amply demonstrated within principal component analysis (PCA), although less is known about the behavior of nonlinear dimensionality reduction methods, e.g., uniform manifold approximation and projection (UMAP), that have become recently utilized. The latter presents an interesting alternative to linear methods though often at the expense of interpretability. This work presents distance-attenuated projection methods of atomic coordinates that facilitate the application of both PCA and UMAP to identify collective variables in the presence of explicit solvent and further the specific identity of solvent molecules that participate in chemical reactions. The performance of both methods is examined in detail for two reactions where the explicit solvent plays very different roles within the collective variables. When applied to raw molecular dynamics data in solution, both PCA and UMAP representations are dominated by bulk solvent motions. On the other hand, when applied to data preprocessed by our attenuated projection methods, both PCA and UMAP identify the appropriate collective variables (though varying sensitivity is observed due to the presence of explicit solvent that results from the projection method). Importantly, this approach allows identification of specific solvent molecules that are relevant to the CVs and their importance.

Influence of Water and Enzyme on the Post-Transition State Bifurcation of NgnD-Catalyzed Ambimodal [6+4]/[4+2] Cycloaddition

The enzyme NgnD catalyzes an ambimodal cycloaddition that bifurcates to [6+4]- and [4+2]-adducts. Both products have been isolated in experiments, but it remains unknown how enzyme and water influence the bifurcation selectivity at the femtosecond time scale. Here, we study the impact of water and enzyme on the post-transition state bifurcation of NgnD-catalyzed [6+4]/[4+2] cycloaddition by integrating quantum mechanics/molecular mechanics quasiclassical dynamics simulations and biochemical assays. The ratio of [6+4]/[4+2] products significantly differs in the gas phase, water, and enzyme. Biochemical assays were employed to validate computational predictions. The study informs how water and enzyme affect the bifurcation selectivity through perturbation of the reaction dynamics in the femtosecond time scale, revealing the fundamental roles of condensed media in dynamically controlling the chemical selectivity for biosynthetic reactions.

Interpolation Methods for Molecular Potential Energy Surface Construction

The concept of a potential energy surface (PES) is one of the most important concepts in modern chemistry. A PES represents the relationship between the chemical system's energy and its geometry (i.e., atom positions) and can provide useful information about the system's chemical properties and reactivity. Construction of accurate PESs with high-level theoretical methodologies, such as density functional theory, is still challenging due to a steep increase in the computational cost with the increase of the system size. Thus, over the past few decades, many different mathematical approaches have been applied to the problem of the cost-efficient PES construction. This article serves as a short overview of interpolative methods for the PES construction, including global polynomial interpolation, trigonometric interpolation, modified Shepard interpolation, interpolative moving least-squares, and the automated PES construction derived from these.

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 human-guided strategies for reaction network exploration: Interactive molecular dynamics in virtual reality as a tool for citizen scientists

The emerging fields of citizen science and gamification reformulate scientific problems as games or puzzles to be solved. Through engaging the wider non-scientific community, significant breakthroughs may be made by analyzing citizen-gathered data. In parallel, recent advances in virtual reality (VR) technology are increasingly being used within a scientific context and the burgeoning field of interactive molecular dynamics in VR (iMD-VR) allows users to interact with dynamical chemistry simulations in real time. Here, we demonstrate the utility of iMD-VR as a medium for gamification of chemistry research tasks. An iMD-VR "game" was designed to encourage users to explore the reactivity of a particular chemical system, and a cohort of 18 participants was recruited to playtest this game as part of a user study. The reaction game encouraged users to experiment with making chemical reactions between a propyne molecule and an OH radical, and "molecular snapshots" from each game session were then compiled and used to map out reaction pathways. The reaction network generated by users was compared to existing literature networks demonstrating that users in VR capture almost all the important reaction pathways. Further comparisons between humans and an algorithmic method for guiding molecular dynamics show that through using citizen science to explore these kinds of chemical problems, new approaches and strategies start to emerge.

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

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

1 Introduction

2 Mechanistic Models

3 Theoretical Approaches and Caveats

3.1 Recommended Computational Tools

3.2 Choice of Functional and Basis Set

3.3 Conformations and Ligand-Binding Modes

3.4 Solvation

4 Synergy of Experiment and Theory – Case Studies

4.1 Metal-Bound or Free Ylides?

4.2 Conformations and Ligand-Binding Modes of Paddlewheel Complexes

4.3 No Metal, Just Light

4.4 How To ‘Cope’ with Nonstatistical Dynamic Effects

5 Outlook

Mode-specific dynamics in multichannel reaction NH+ + H2

The vibrational- and rotational-mode specificity of the multichannel NH⁺ + H₂ reaction is studied on a recently constructed ab initio-based global potential energy surface using an initial state selected quasi-classical trajectory method, and the trajectories are analyzed using an isometric feature mapping and k-means approach. All excitation modes promote two reactions (R1: NH'⁺ + H₂ → NH⁺ + HH' and R4: NH'⁺ + H₂ → NH₂⁺ + H') where both NH and HH bonds are broken, but reduce the reactivity of the proton-transfer reaction R2 (NH'⁺ + H₂ → N + H'H₂⁺) at low collision energies. For the hydrogen-transfer reaction R3 (NH'⁺ + H₂ → HNH'⁺ + H), the rotational excitation of NH⁺ enhances the reactivity remarkably, while its vibrational excitation has an inhibiting effect on the reaction. The trajectory analyses show that the vibrational and rotational excitations of NH⁺ make R3 tend to go over a submerged saddle point instead of extracting hydrogen atoms directly. On the other hand, the motions of the H₂ reactant facilitate the enhancement of the reactivity but they do not affect the mechanism of R3. In addition, the results suggest that the coupling of the isometric feature mapping and the k-means approach in the trajectory analysis is an appropriate tool for reaction-dynamics studies.

Reduced-dimensional surface hopping with offline-online computations

Molecular dynamics simulations often classically evolve the nuclear geometry on adiabatic potential energy surfaces (PESs), punctuated by random hops between energy levels in regions of strong coupling, in an algorithm known as surface hopping. However, the computational expense of integrating the geometry on a full-dimensional PES and computing the required couplings can quickly become prohibitive as the number of atoms increases. In this work, we describe a method for surface hopping that uses only important reaction coordinates, performs all expensive evaluations of the true PESs and couplings only once before simulating dynamics (offline), and then queries the stored values during the surface hopping simulation (online). Our Python codes are freely available on GitHub. Using photodissociation of azomethane as a test case, this method is able to reproduce experimental results that have thus far eluded ab initio surface hopping studies.

Efficient Approximation of Potential Energy Surfaces with Mixed-Basis Interpolation

The potential energy surface (PES) describes the energy of a chemical system as a function of its geometry and is a fundamental concept in modern chemistry. A PES provides much useful information about the system, including the structures and energies of various stationary points, such as stable conformers (local minima) and transition states (first-order saddle points) connected by a minimum-energy path. Our group has previously produced surrogate reduced-dimensional PESs using sparse interpolation along chemically significant reaction coordinates, such as bond lengths, bond angles, and torsion angles. These surrogates used a single interpolation basis, either polynomials or trigonometric functions, in every dimension. However, relevant molecular dynamics (MD) simulations often involve some combination of both periodic and nonperiodic coordinates. Using a trigonometric basis on nonperiodic coordinates, such as bond lengths, leads to inaccuracies near the domain boundary. Conversely, polynomial interpolation on the periodic coordinates does not enforce the periodicity of the surrogate PES gradient, leading to nonconservation of total energy even in a microcanonical ensemble. In this work, we present an interpolation method that uses trigonometric interpolation on the periodic reaction coordinates and polynomial interpolation on the nonperiodic coordinates. We apply this method to MD simulations of possible isomerization pathways of azomethane between cis and trans conformers. This method is the only known interpolative method that appropriately conserves total energy in systems with both periodic and nonperiodic reaction coordinates. In addition, compared to all-polynomial interpolation, the mixed basis requires fewer electronic structure calculations to obtain a given level of accuracy, is an order of magnitude faster, and is freely available on GitHub.

Dissociation of hydrogen peroxide in water and methanol through a biased molecular dynamics investigation

The two dissociation channels of HOOH, namely, HOOH and HOOH, in water and methanol are investigated using umbrella-sampling ab initio molecular dynamics. Our potential of mean force calculations reveals the HOOH dissociation to be more favorable in methanol with a free energy barrier of 7.56 kcal/mol, while the HOOH dissociation possesses a free energy barrier of 11.46 kcal/mol. In water, the HOOH dissociation channel is more favorable (8.25 kcal/mol), while the HOOH dissociation process requires a higher free energy (11.28 kcal/mol). Such reaction favorability can be explained by inspecting the formation of secondary radical species during the course of multiple hydrogen donating-accepting processes in each reaction channel. The radical species, that is, H₃ O^• (observed in water) and CH₃ OH₂ ^• (observed in methanol), are the first subordinate species upon the HOOH dissociation. For the HOOH dissociation channel in methanol, the secondary species such as water and formaldehyde can be observed, while the re-generation of HOOH in water can be spotted.

Analysis of bath motion in MM-SQC dynamics via dimensionality reduction approach: Principal component analysis

The system-plus-bath model is an important tool to understand the nonadiabatic dynamics of large molecular systems. Understanding the collective motion of a large number of bath modes is essential for revealing their key roles in the overall dynamics. Here, we applied principal component analysis (PCA) to investigate the bath motion in the basis of a large dataset generated from the symmetrical quasi-classical dynamics method based on the Meyer-Miller mapping Hamiltonian nonadiabatic dynamics for the excited-state energy transfer in the Frenkel-exciton model. The PCA method clearly elucidated that two types of bath modes, which either display strong vibronic coupling or have frequencies close to that of the electronic transition, are important to the nonadiabatic dynamics. These observations were fully consistent with the physical insights. The conclusions were based on the PCA of the trajectory data and did not involve significant pre-defined physical knowledge. The results show that the PCA approach, which is one of the simplest unsupervised machine learning dimensionality reduction methods, is a powerful one for analyzing complicated nonadiabatic dynamics in the condensed phase with many degrees of freedom.

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

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

Reaction probability and kinetics of water splitting on the penta-NiAs2 monolayer from an ab initio molecular dynamics investigation

The reaction probability and kinetics of the water splitting process on the penta-NiAs2 monolayer are studied using ab initio molecular dynamics simulations. A total of 100 trajectories are investigated, in which a H2O molecule is set to strike the surface with a translational energy of 1 eV or 2 eV. The results show that the NiAs2 monolayer is an excellent candidate for the activation of water splitting with a reaction probability of 94% for both energy levels. Interestingly, the kinetics of two O-H dissociation stages varies greatly with respect to the inletting translational energy. Interpreting the reaction data for the 1 eV case, we conclude that O-H1 and O-H2 dissociations are first-order processes. However, such dissociation steps become pseudo-zeroth order in the 2 eV case. At the time of the dissociation, the force acting on atoms and the principal component analysis suggest that the two OH breaking stages behave like harmonic springs until reaching the dissociation.

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.

An approach to calculate the free energy changes of surface reactions using free energy decomposition on ab initio brute-force molecular dynamics trajectories

To understand the mechanisms and kinetics of catalytic reactions in heterogeneous catalysis, ab initio molecular dynamics is one of the powerful methods used to explore the free energy surface (FES) of surface elementary steps.

Interactive molecular dynamics in virtual reality for accurate flexible protein-ligand docking

Simulating drug binding and unbinding is a challenge, as the rugged energy landscapes that separate bound and unbound states require extensive sampling that consumes significant computational resources. Here, we describe the use of interactive molecular dynamics in virtual reality (iMD-VR) as an accurate low-cost strategy for flexible protein-ligand docking. We outline an experimental protocol which enables expert iMD-VR users to guide ligands into and out of the binding pockets of trypsin, neuraminidase, and HIV-1 protease, and recreate their respective crystallographic protein-ligand binding poses within 5-10 minutes. Following a brief training phase, our studies shown that iMD-VR novices were able to generate unbinding and rebinding pathways on similar timescales as iMD-VR experts, with the majority able to recover binding poses within 2.15 Å RMSD of the crystallographic binding pose. These results indicate that iMD-VR affords sufficient control for users to carry out the detailed atomic manipulations required to dock flexible ligands into dynamic enzyme active sites and recover crystallographic poses, offering an interesting new approach for simulating drug docking and generating binding hypotheses.