A Trajectory-Based Method to Explore Reaction Mechanisms

SCINE-Software for chemical interaction networks

The software for chemical interaction networks (SCINE) project aims at pushing the frontier of quantum chemical calculations on molecular structures to a new level. While calculations on individual structures as well as on simple relations between them have become routine in chemistry, new developments have pushed the frontier in the field to high-throughput calculations. Chemical relations may be created by a search for specific molecular properties in a molecular design attempt, or they can be defined by a set of elementary reaction steps that form a chemical reaction network. The software modules of SCINE have been designed to facilitate such studies. The features of the modules are (i) general applicability of the applied methodologies ranging from electronic structure (no restriction to specific elements of the periodic table) to microkinetic modeling (with little restrictions on molecularity), full modularity so that SCINE modules can also be applied as stand-alone programs or be exchanged for external software packages that fulfill a similar purpose (to increase options for computational campaigns and to provide alternatives in case of tasks that are hard or impossible to accomplish with certain programs), (ii) high stability and autonomous operations so that control and steering by an operator are as easy as possible, and (iii) easy embedding into complex heterogeneous environments for molecular structures taken individually or in the context of a reaction network. A graphical user interface unites all modules and ensures interoperability. All components of the software have been made available as open source and free of charge.

Quantum chemical data generation as fill-in for reliability enhancement of machine-learning reaction and retrosynthesis planning

Data-driven synthesis planning has seen remarkable successes in recent years by virtue of modern approaches of artificial intelligence that efficiently exploit vast databases with experimental data on chemical reactions. However, this success story is intimately connected to the availability of existing experimental data. It may well occur in retrosynthetic and synthesis design tasks that predictions in individual steps of a reaction cascade are affected by large uncertainties. In such cases, it will, in general, not be easily possible to provide missing data from autonomously conducted experiments on demand. However, first-principles calculations can, in principle, provide missing data to enhance the confidence of an individual prediction or for model retraining. Here, we demonstrate the feasibility of such an ansatz and examine resource requirements for conducting autonomous first-principles calculations on demand.

Accelerating Reaction Network Explorations with Automated Reaction Template Extraction and Application

Autonomously exploring chemical reaction networks with first-principles methods can generate vast data. Especially autonomous explorations without tight constraints risk getting trapped in regions of reaction networks that are not of interest. In many cases, these regions of the networks are only exited once fully searched. Consequently, the required human time for analysis and computer time for data generation can make these investigations unfeasible. Here, we show how simple reaction templates can facilitate the transfer of chemical knowledge from expert input or existing data into new explorations. This process significantly accelerates reaction network explorations and improves cost-effectiveness. We discuss the definition of the reaction templates and their generation based on molecular graphs. The resulting simple filtering mechanism for autonomous reaction network investigations is exemplified with a polymerization reaction.

Barrier Height Prediction by Machine Learning Correction of Semiempirical Calculations

Different machine learning (ML) models are proposed in the present work to predict density functional theory-quality barrier heights (BHs) from semiempirical quantum mechanical (SQM) calculations. The ML models include a multitask deep neural network, gradient-boosted trees by means of the XGBoost interface, and Gaussian process regression. The obtained mean absolute errors are similar to those of previous models considering the same number of data points. The ML corrections proposed in this paper could be useful for rapid screening of the large reaction networks that appear in combustion chemistry or in astrochemistry. Finally, our results show that 70% of the features with the highest impact on model output are bespoke predictors. This custom-made set of predictors could be employed by future Δ-ML models to improve the quantitative prediction of other reaction properties.

Chemoton 2.0: Autonomous Exploration of Chemical Reaction Networks

Fueled by advances in hardware and algorithm design, large-scale automated explorations of chemical reaction space have become possible. Here, we present our approach to an open-source, extensible framework for explorations of chemical reaction mechanisms based on the first-principles of quantum mechanics. It is intended to facilitate reaction network explorations for diverse chemical problems with a wide range of goals such as mechanism elucidation, reaction path optimization, retrosynthetic path validation, reagent design, and microkinetic modeling. The stringent first-principles basis of all algorithms in our framework is key for the general applicability that avoids any restrictions to specific chemical systems. Such an agile framework requires multiple specialized software components of which we present three modules in this work. The key module, Chemoton, drives the exploration of reaction networks. For the exploration itself, we introduce two new algorithms for elementary-step searches that are based on Newton trajectories. The performance of these algorithms is assessed for a variety of reactions characterized by a broad chemical diversity in terms of bonding patterns and chemical elements. Chemoton successfully recovers the vast majority of these. We provide the resulting data, including large numbers of reactions that were not included in our reference set, to be used as a starting point for further explorations and for future reference.

New Tools for Taming Complex Reaction Networks: The Unimolecular Decomposition of Indole Revisited

The level of detail attained in the computational description of reaction mechanisms can be vastly improved through tools for automated chemical space exploration, particularly for systems of small to medium size. Under this approach, the unimolecular decomposition landscape for indole was explored through the automated reaction mechanism discovery program AutoMeKin. Nevertheless, the sheer complexity of the obtained mechanisms might be a hindrance regarding their chemical interpretation. In this spirit, the new Python library amk-tools has been designed to read and manipulate complex reaction networks, greatly simplifying their overall analysis. The package provides interactive dashboards featuring visualizations of the network, the three-dimensional (3D) molecular structures and vibrational normal modes of all chemical species, and the corresponding energy profiles for selected pathways. The combination of the joined mechanism generation and postprocessing workflow with the rich chemistry of indole decomposition enabled us to find new details of the reaction (obtained at the CCSD(T)/aug-cc-pVTZ//M06-2X/MG3S level of theory) that were not reported before: (i) 16 pathways leading to the formation of HCN and NH₃ (via amino radical); (ii) a barrierless reaction between methylene radical and phenyl isocyanide, which might be an operative mechanism under the conditions of the interstellar medium; and (iii) reaction channels leading to both hydrogen cyanide and hydrogen isocyanide, of potential astrochemical interest as the computed HNC/HCN ratios greatly exceed the calculated equilibrium value at very low temperatures. The reported reaction networks can be very valuable to supplement databases of kinetic data, which is of remarkable interest for pyrolysis and astrochemical studies.

Autonomous Reaction Network Exploration in Homogeneous and Heterogeneous Catalysis

Autonomous computations that rely on automated reaction network elucidation algorithms may pave the way to make computational catalysis on a par with experimental research in the field. Several advantages of this approach are key to catalysis: (i) automation allows one to consider orders of magnitude more structures in a systematic and open-ended fashion than what would be accessible by manual inspection. Eventually, full resolution in terms of structural varieties and conformations as well as with respect to the type and number of potentially important elementary reaction steps (including decomposition reactions that determine turnover numbers) may be achieved. (ii) Fast electronic structure methods with uncertainty quantification warrant high efficiency and reliability in order to not only deliver results quickly, but also to allow for predictive work. (iii) A high degree of autonomy reduces the amount of manual human work, processing errors, and human bias. Although being inherently unbiased, it is still steerable with respect to specific regions of an emerging network and with respect to the addition of new reactant species. This allows for a high fidelity of the formalization of some catalytic process and for surprising in silico discoveries. In this work, we first review the state of the art in computational catalysis to embed autonomous explorations into the general field from which it draws its ingredients. We then elaborate on the specific conceptual issues that arise in the context of autonomous computational procedures, some of which we discuss at an example catalytic system.

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SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s11244-021-01543-9.

Expansive Quantum Mechanical Exploration of Chemical Reaction Paths

Quantum mechanical methods have been well-established for the elucidation of reaction paths of chemical processes and for the explicit dynamics of molecular systems. While they are usually deployed in routine manual calculations on reactions for which some insights are already available (typically from experiment), new algorithms and continuously increasing capabilities of modern computer hardware allow for exploratory open-ended computational campaigns that are unbiased and therefore enable unexpected discoveries. Highly efficient and even automated procedures facilitate systematic approaches toward the exploration of uncharted territory in molecular transformations and dynamics. In this work, we elaborate on such explorative approaches that range from reaction network explorations with (stationary) quantum chemical methods to explorative molecular dynamics and migrant wave packet dynamics. The focus is on recent developments that cover the following strategies. (i) Pruning search options for elementary reaction steps by heuristic rules based on the first-principles of quantum mechanics: Rules are required for reducing the combinatorial explosion of potentially reactive atom pairings, and rooting them in concepts derived from the electronic wave function makes them applicable to any molecular system. (ii) Enforcing reactive events by external biases: Inducing a reaction requires constraints that steer and direct elementary-step searches, which can be formulated in terms of forces, velocities, or supplementary potentials. (iii) Manual steering facilitated by interactive quantum mechanics: As ultrafast quantum chemical methods allow for real-time manual interactions with molecular systems, human-intuition-guided paths can be easily explored with suitable human-machine interfaces. (iv) New approaches for transition-state optimization with continuous curve representations can provide stable schemes to be driven in an automated way by allowing for an efficient tuning of the curve's parameters (instead of a manipulation of a collection of structures along the path), and (v) reactive molecular dynamics and direct wave packet propagation exploit the equations of motion of an underlying mechanical theory (usually, classical Newtonian mechanics or Schrödinger quantum mechanics). Explorative approaches are likely to replace the current state of the art in computational chemistry, because they reduce the human effort to be invested in reaction path elucidations, they are less prone to errors and bias-free, and they cover more extensive regions of the relevant configuration space. As a result, computational investigations that rely on these techniques are more likely to deliver surprising discoveries.

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 Effects of Methylation on the CID of Protonated Lysine: A Combined Experimental and Computational Approach

We report the results of experiments, simulations, and DFT calculations that focus on describing the reaction dynamics observed within the collision-induced dissociation of l-lysine-H⁺ and its side-chain methylated analogues, N_ε-methyl-l-lysine-H⁺ (Me₁-lysine-H⁺), N_ε,N_ε-dimethyl-l-lysine-H⁺ (Me₂-lysine-H⁺), and N_ε,N_ε,N_ε-trimethyl-l-lysine-H⁺ (Me₃-lysine-H⁺). The major pathways observed in the experimental measurements were m/z 130 and 84, with the former dominant at low collision energies and the latter at intermediate to high collision energies. The m/z 130 peak corresponds to loss of N(CH₃)_nH_3-n, while m/z 84 has the additional loss of H₂CO₂ likely in the form of H₂O + CO. Within the time frame of the direct dynamics simulations, m/z 130 and 101 were the most populous peaks, with the latter identified as an intermediate to m/z 84. The simulations allowed for the determination of several reaction pathways that result in these products. A graph theory analysis enabled the elucidation of the significant structures that compose each peak. Methylation results in the preferential loss of the side-chain amide group and a reduction of cyclic structures within the m/z 84 peak population in simulations.

Determination of kinetic properties in unimolecular dissociation of complex systems from graph theory based analysis of an ensemble of reactive trajectories

In this paper, we report how graph theory can be used to analyze an ensemble of independent molecular trajectories, which can react during the simulation time-length, and obtain structural and kinetic information. This method is totally general and here is applied to the prototypical case of gas phase fragmentation of protonated cyclo-di-glycine. This methodology allows us to analyze the whole set of trajectories in an automatic computer-based way without the need of visual inspection but by getting all the needed information. In particular, we not only determine the appearance of different products and intermediates but also characterize the corresponding kinetics. The use of colored graph and canonical labeling allows for the correct characterization of the chemical species involved. In the present case, the simulations consist of an ensemble of unimolecular fragmentation trajectories at constant energy such that from the rate constants at different energies, the threshold energy can also be obtained for both global and specific pathways. This approach allows for the characterization of ion-molecule complexes, likely through a roaming mechanism, by properly taking into account the elusive nature of such species. Finally, it is possible to directly obtain the theoretical mass spectrum of the fragmenting species if the reacting system is an ion as in the specific example.

AutoMeKin2021: An open-source program for automated reaction discovery

AutoMeKin2021 is an updated version of tsscds2018, a program for the automated discovery of reaction mechanisms (J. Comput. Chem. 2018, 39, 1922). This release features a number of new capabilities: rare-event molecular dynamics simulations to enhance reaction discovery, extension of the original search algorithm to study van der Waals complexes, use of chemical knowledge, a new search algorithm based on bond-order time series analysis, statistics of the chemical reaction networks, a web application to submit jobs, and other features. The source code, manual, installation instructions and the website link are available at: https://rxnkin.usc.es/index.php/AutoMeKin.

Quantum Chemistry Calculations for Metabolomics

A primary goal of metabolomics studies is to fully characterize the small-molecule composition of complex biological and environmental samples. However, despite advances in analytical technologies over the past two decades, the majority of small molecules in complex samples are not readily identifiable due to the immense structural and chemical diversity present within the metabolome. Current gold-standard identification methods rely on reference libraries built using authentic chemical materials ("standards"), which are not available for most molecules. Computational quantum chemistry methods, which can be used to calculate chemical properties that are then measured by analytical platforms, offer an alternative route for building reference libraries, i.e., in silico libraries for "standards-free" identification. In this review, we cover the major roadblocks currently facing metabolomics and discuss applications where quantum chemistry calculations offer a solution. Several successful examples for nuclear magnetic resonance spectroscopy, ion mobility spectrometry, infrared spectroscopy, and mass spectrometry methods are reviewed. Finally, we consider current best practices, sources of error, and provide an outlook for quantum chemistry calculations in metabolomics studies. We expect this review will inspire researchers in the field of small-molecule identification to accelerate adoption of in silico methods for generation of reference libraries and to add quantum chemistry calculations as another tool at their disposal to characterize complex samples.

A map of mass spectrometry-based in silico fragmentation prediction and compound identification in metabolomics

Metabolomics, the comprehensive study of the metabolome, and lipidomics-the large-scale study of pathways and networks of cellular lipids-are major driving forces in enabling personalized medicine. Complicated and error-prone data analysis still remains a bottleneck, however, especially for identifying novel metabolites. Comparing experimental mass spectra to curated databases containing reference spectra has been the gold standard for identification of compounds, but constructing such databases is a costly and time-demanding task. Many software applications try to circumvent this process by utilizing cutting-edge advances in computational methods-including quantum chemistry and machine learning-and simulate mass spectra by performing theoretical, so called in silico fragmentations of compounds. Other solutions concentrate directly on experimental spectra and try to identify structural properties by investigating reoccurring patterns and the relationships between them. The considerable progress made in the field allows recent approaches to provide valuable clues to expedite annotation of experimental mass spectra. This review sheds light on individual strengths and weaknesses of these tools, and attempts to evaluate them-especially in view of lipidomics, when considering complex mixtures found in biological samples as well as mass spectrometer inter-instrument variability.

Modeling the Effects of O-Sulfonation on the CID of Serine

We present the results of direct dynamics simulations and DFT calculations aimed at elucidating the effect of O-sulfonation on the collision-induced dissociation for serine. Toward this end, direct dynamics simulations of both serine and sulfoserine were performed at multiple collision energies and theoretical mass spectra obtained. Comparisons to experimental results are favorable for both systems. Peaks related to the sulfo group are identified and the reaction dynamics explored. In particular, three significant peaks (m/z 106, 88, and 81) seen in the theoretical mass spectrum directly related to the sulfo group are analyzed as well as major peaks shared by both systems. Our analysis shows that the m/z 106 peaks result from intramolecular rearrangements, intermolecular proton transfer among complexes composed of initial fragmentation products, and at high energy side-chain fragmentation. The m/z 88 peak was found to contain multiple constitutional isomers, including a previously unconsidered, low energy structure. It was also observed that the RM1 semiempirical method was not able to obtain all of the major peaks seen in experimens for sulfoserine. In contrast, PM6 did obtain all major experimental peaks.

Some Mathematical Reasoning on the Artificial Force Induced Reaction Method

There are works of the Maeda-Morokuma group, which propose the artificial force induced reaction (AFIR) method (Maeda et al., J. Comput. Chem. 2014, 35, 166 and 2018, 39, 233). We study this important method from a theoretical point of view. The understanding of the proposers does not use the barrier breakdown point of the AFIR parameter, which usually is half of the reaction path between the minimum and the transition state which is searched for. Based on a comparison with the theory of Newton trajectories, we could better understand the method. It allows us to follow along some reaction pathways from minimum to saddle point, or vice versa. We discuss some well-known two-dimensional test surfaces where we calculate full AFIR pathways. If one has special AFIR curves at hand, one can also study the behavior of the ansatz. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.

When classical trajectories get to quantum accuracy: II. The scattering of rotationally excited H2 on Pd(111)

The classical trajectory method in a quantum spirit assigns statistical weights to classical paths on the basis of two semiclassical corrections: Gaussian binning and the adiabaticity correction.

When Classical Trajectories Get to Quantum Accuracy: The Scattering of H2 on Pd(111)

When elementary reactive processes occur at such low energies that only a few states of reactants and/or products are available, quantum effects strongly manifest and the standard description of the dynamics within the classical framework fails. We show here, for H₂ scattering on Pd(111), that by pseudoquantizing in the spirit of Bohr the relevant final actions of the system, along with adequately treating the diffraction-mediated trapping of the incoming wave, classical simulations achieve an unprecedented agreement with state-of-the-art quantum dynamics calculations.

Finding Reaction Pathways with Optimal Atomic Index Mappings

Finding complex reaction and transformation pathways involving many intermediate states is, in general, not possible on the density-functional theory level with existing simulation methods, due to the very large number of required energy and force evaluations. For complex reactions, it is not possible to determine which atom in the reactant is mapped onto which atom in the product. Trying out all possible atomic index mappings is not feasible because of the factorial increase in the number of possible mappings. We use a penalty function that is invariant under index permutations to bias the potential energy surface in such a way that it obtains the characteristics of a structure seeker, whose global minimum is the reaction product. By performing a minima-hopping-based global optimization on this biased potential energy surface, we rapidly find intermediate states that lead into the global minimum and allow us to then extract entire reaction pathways. We first demonstrate for a benchmark system, namely, the Lennard-Jones cluster LJ_{38}, that our method finds intermediate states relevant to the lowest energy reaction pathway, and hence we need to consider much fewer intermediate states than previous methods to find the lowest energy reaction pathway. Finally, we apply the method to two real systems, C_{60} and C_{20}H_{20}, and show that the reaction pathways found contain valuable information on how these molecules can be synthesized.

Theoretical Study of Barrierless Chemical Reactions Involving Nearly Elastic Rebound: The Case of S(1D) + X2, X = H, D

For some values of the total angular momentum consistent with reaction, the title processes involve nonreactive trajectories proceeding through a single rebound mechanism during which the internal motion of the reagent diatom is nearly unperturbed. When such paths are in a significant amount, the classical reaction probability is found to be markedly lower than the quantum mechanical one. This finding was recently attributed to an unusual quantum effect called diffraction-mediated trapping, and a semiclassical correction was proposed in order to take into account this effect in the classical trajectory method. In the present work, we apply the resulting approach to the calculation of opacity functions as well as total and state-resolved integral cross sections (ICSs) and compare the values obtained with exact quantum ones, most of which are new. As the title reactions proceed through a deep insertion well, mean potential statistical calculations are also presented. Seven values of the collision energy, ranging from 30 to 1127 K, are considered. Two remarkable facts stand out: (i) The corrected classical treatment strongly improves the accuracy of the opacity function as compared to the usual classical treatment. When the entrance transition state is tight, however, those trajectories crossing it with a bending vibrational energy below the zero point energy must be discarded. (ii) The quantum opacity function, particularly its cutoff, is finely reproduced by the statistical approach. Consequently, the total ICS is also very well described by the two previous approximate methods. These, however, do not predict state-resolved ICSs with the same accuracy, proving thereby that (i) one or several genuine quantum effects involved in the dynamics are missed by the corrected classical treatment and (ii) the dynamics are not fully statistical.

Fully versus constrained statistical fragmentation of carbon clusters and their heteronuclear derivatives

The Microcanonical Metropolis Monte Carlo (MMMC) method has been shown to describe reasonably well fragmentation of clusters composed of identical atomic species. However, this is not so clear in the case of heteronuclear clusters as some regions of phase space might be inaccessible due to the different mobility of the different atomic species, the existence of large isomerization barriers, or the quite different chemical nature of the possible intermediate species. In this paper, we introduce a constrained statistical model that extends the range of applicability of the MMMC method to such mixed clusters. The method is applied to describe fragmentation of isolated clusters with high, moderate, and no heteronuclear character, namely, C_nH_m, C_nN, and C_n clusters for which experimental fragmentation branching ratios are available in the literature. We show that the constrained statistical model describes fairly well fragmentation of C_nH_m clusters in contrast with the poor description provided by the fully statistical model. The latter model, however, works pretty well for both C_n and C_nN clusters, thus showing that the ultimate reason for this discrepancy is the inability of the MMMC method to selectively explore the whole phase space. This conclusion has driven us to predict the fragmentation patterns of the C₄N cluster for which experiments are not yet available.