Exploration of Reaction Pathways and Chemical Transformation Networks

Real-time observation of a metal complex-driven reaction intermediate using a porous protein crystal and serial femtosecond crystallography

Determining short-lived intermediate structures in chemical reactions is challenging. Although ultrafast spectroscopic methods can detect the formation of transient intermediates, real-space structures cannot be determined directly from such studies. Time-resolved serial femtosecond crystallography (TR-SFX) has recently proven to be a powerful method for capturing molecular changes in proteins on femtosecond timescales. However, the methodology has been mostly applied to natural proteins/enzymes and limited to reactions promoted by synthetic molecules due to structure determination challenges. This work demonstrates the applicability of TR-SFX for investigations of chemical reaction mechanisms of synthetic metal complexes. We fix a light-induced CO-releasing Mn(CO)3 reaction center in porous hen egg white lysozyme (HEWL) microcrystals. By controlling light exposure and time, we capture the real-time formation of Mn-carbonyl intermediates during the CO release reaction. The asymmetric protein environment is found to influence the order of CO release. The experimentally-observed reaction path agrees with quantum mechanical calculations. Therefore, our demonstration offers a new approach to visualize atomic-level reactions of small molecules using TR-SFX with real-space structure determination. This advance holds the potential to facilitate design of artificial metalloenzymes with precise mechanisms, empowering design, control and development of innovative reactions.

Nanoscale chemical reaction exploration with a quantum magnifying glass

Nanoscopic systems exhibit diverse molecular substructures by which they facilitate specific functions. Theoretical models of them, which aim at describing, understanding, and predicting these capabilities, are difficult to build. Viable quantum-classical hybrid models come with specific challenges regarding atomistic structure construction and quantum region selection. Moreover, if their dynamics are mapped onto a state-to-state mechanism such as a chemical reaction network, its exhaustive exploration will be impossible due to the combinatorial explosion of the reaction space. Here, we introduce a "quantum magnifying glass" that allows one to interactively manipulate nanoscale structures at the quantum level. The quantum magnifying glass seamlessly combines autonomous model parametrization, ultra-fast quantum mechanical calculations, and automated reaction exploration. It represents an approach to investigate complex reaction sequences in a physically consistent manner with unprecedented effortlessness in real time. We demonstrate these features for reactions in bio-macromolecules and metal-organic frameworks, diverse systems that highlight general applicability.

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.

Identification of Reaction Network Hypotheses for Complex Feedstocks from Spectroscopic Measurements with Minimal Human Intervention

In this work, we detail an automated reaction network hypothesis generation protocol for processes involving complex feedstocks where information about the species and reactions involved is unknown. Our methodology is process agnostic and can be utilized in any reactive process with spectroscopic measurements that provide information on the evolution of the components in the mixture. We decompose the mixture spectra to obtain spectroscopic signatures of the individual components and use a 1-D convolutional neural network to automatically identify functional groups indicated by them. We employ atom-atom mapping to automatically recover reaction rules that are applied on candidate molecules identified from chemistry databases through fingerprint similarity. The method is tested on synthetic data and on spectroscopic measurements of lab-scale batch hydrothermal liquefaction (HTL) of biomass to determine the accuracy of prediction across datasets of varying complexities. Our methodology is able to identify reaction network hypotheses containing reaction networks close to the ground truth in the case of synthetic data, and we are also able to recover candidate molecules and reaction networks close to the ones reported in the previous literature studies for biomass pyrolysis.

TS-tools: Rapid and automated localization of transition states based on a textual reaction SMILES input

Here, TS-tools is presented, a Python package facilitating the automated localization of transition states (TS) based on a textual reaction SMILES input. TS searches can either be performed at xTB or DFT level of theory, with the former yielding guesses at marginal computational cost, and the latter directly yielding accurate structures at greater expense. On a benchmarking dataset of mono- and bimolecular reactions, TS-tools reaches an excellent success rate of 95% already at xTB level of theory. For tri- and multimolecular reaction pathways - which are typically not benchmarked when developing new automated TS search approaches, yet are relevant for various types of reactivity, cf. solvent- and autocatalysis and enzymatic reactivity - TS-tools retains its ability to identify TS geometries, though a DFT treatment becomes essential in many cases. Throughout the presented applications, a particular emphasis is placed on solvation-induced mechanistic changes, another issue that received limited attention in the automated TS search literature so far.

Uncertainty-Aware First-Principles Exploration of Chemical Reaction Networks

Exploring large chemical reaction networks with automated exploration approaches and accurate quantum chemical methods can require prohibitively large computational resources. Here, we present an automated exploration approach that focuses on the kinetically relevant part of the reaction network by interweaving (i) large-scale exploration of chemical reactions, (ii) identification of kinetically relevant parts of the reaction network through microkinetic modeling, (iii) quantification and propagation of uncertainties, and (iv) reaction network refinement. Such an uncertainty-aware exploration of kinetically relevant parts of a reaction network with automated accuracy improvement has not been demonstrated before in a fully quantum mechanical approach. Uncertainties are identified by local or global sensitivity analysis. The network is refined in a rolling fashion during the exploration. Moreover, the uncertainties are considered during kinetically steering of a rolling reaction network exploration. We demonstrate our approach for Eschenmoser-Claisen rearrangement reactions. The sensitivity analysis identifies that only a small number of reactions and compounds are essential for describing the kinetics reliably, resulting in efficient explorations without sacrificing accuracy and without requiring prior knowledge about the chemistry unfolding.

A human-machine interface for automatic exploration of chemical reaction networks

Autonomous reaction network exploration algorithms offer a systematic approach to explore mechanisms of complex chemical processes. However, the resulting reaction networks are so vast that an exploration of all potentially accessible intermediates is computationally too demanding. This renders brute-force explorations unfeasible, while explorations with completely pre-defined intermediates or hard-wired chemical constraints, such as element-specific coordination numbers, are not flexible enough for complex chemical systems. Here, we introduce a STEERING WHEEL to guide an otherwise unbiased automated exploration. The STEERING WHEEL algorithm is intuitive, generally applicable, and enables one to focus on specific regions of an emerging network. It also allows for guiding automated data generation in the context of mechanism exploration, catalyst design, and other chemical optimization challenges. The algorithm is demonstrated for reaction mechanism elucidation of transition metal catalysts. We highlight how to explore catalytic cycles in a systematic and reproducible way. The exploration objectives are fully adjustable, allowing one to harness the STEERING WHEEL for both structure-specific (accurate) calculations as well as for broad high-throughput screening of possible reaction intermediates.

Exploring Chemical Reaction Space with Machine Learning Models: Representation and Feature Perspective

Chemical reactions serve as foundational building blocks for organic chemistry and drug design. In the era of large AI models, data-driven approaches have emerged to innovate the design of novel reactions, optimize existing ones for higher yields, and discover new pathways for synthesizing chemical structures comprehensively. To effectively address these challenges with machine learning models, it is imperative to derive robust and informative representations or engage in feature engineering using extensive data sets of reactions. This work aims to provide a comprehensive review of established reaction featurization approaches, offering insights into the selection of representations and the design of features for a wide array of tasks. The advantages and limitations of employing SMILES, molecular fingerprints, molecular graphs, and physics-based properties are meticulously elaborated. Solutions to bridge the gap between different representations will also be critically evaluated. Additionally, we introduce a new frontier in chemical reaction pretraining, holding promise as an innovative yet unexplored avenue.

Differentiating the Yield of Chemical Reactions Using Parameters in First-Order Kinetic Equations to Identify Elementary Steps That Control the Reactivity from Complicated Reaction Path Networks

The yield of a chemical reaction is obtained by solving its rate equation. This study introduces an approach for differentiating yields by utilizing the parameters of the rate equation, which is expressed as a first-order linear differential equation. The yield derivative for a specific pair of reactants and products is derived by mathematically expressing the rate constant matrix contraction method, which is a simple kinetic analysis method. The parameters of the rate equation are the Gibbs energies of the intermediates and transition states in the reaction path network used to formulate the rate equation. Thus, our approach for differentiating the yield allows a numerical evaluation of the contribution of energy variation to the yield for each intermediate and transition state in the reaction path network. In other words, a comparison of these values automatically extracts the factors affecting the yield from a complicated reaction path network consisting of numerous reaction paths and intermediates. This study verifies the behavior of the proposed approach through numerical experiments on the reaction path networks of a model system and the Rh-catalyzed hydroformylation reaction. Moreover, the possibility of using this approach for designing ligands in organometallic catalysts is discussed.

A Computational Perspective on the Reactivity of π-spacers in Self-Immolative Elimination Reactions

The controlled release of chemicals, especially in drug delivery, is crucial, often employing "self-immolative" spacers to enhance reliability. These spacers separate the payload from the protecting group, ensuring a more controlled release. Over the years, design rules have been proposed to improve the elimination process's reaction rate by modifying spacers with electron-donating groups or reducing their aromaticity. The spacer design is critical for determining the range of functional groups released during this process. This study explores various strategies from the literature aimed at improving release rates, focusing on the electronic nature of the spacer, its aromaticity, the electronic nature of its substituents, and the leaving groups involved in the elimination reaction. Through computational analysis, I investigate activation free energies by identifying transition states for model reactions. My calculations align qualitatively with experimental results, demonstrating the feasibility and reliability of computationally pre-screening model self-immolative eliminations. This approach allows proposing optimal combinations of spacer and leaving group for achieving the highest possible release rate.

Density functional theory methods applied to homogeneous and heterogeneous catalysis: a short review and a practical user guide

The application of density functional theory (DFT) methods in catalysis has been growing fast in the last few decades thanks to both the availability of more powerful high computing resources and the development of new efficient approximations and approaches. DFT calculations allow for the understanding of crucial catalytic aspects that are difficult or even impossible to access by experiments, thus contributing to faster development of more efficient and selective catalysts. Depending on the catalytic system and properties under investigation, different approaches should be used. Moreover, the reliability of the obtained results deeply depends on the approximations involved in both the selected method and model. This review addresses chemists, physicists and materials scientists whose interest deals with the application of DFT-based computational tools in both homogeneous catalysis and heterogeneous catalysis. First, a brief introduction to DFT is presented. Then, the main approaches based on atomic centered basis sets and plane waves are discussed, underlining the main differences, advantages and limitations. Eventually, guidance towards the selection of the catalytic model is given, with a final focus on the evaluation of the energy barriers, which represents a crucial step in all catalytic processes. Overall, the review represents a rational and practical guide for both beginners and more experienced users involved in the wide field of catalysis.

Diffusion-based generative AI for exploring transition states from 2D molecular graphs

The exploration of transition state (TS) geometries is crucial for elucidating chemical reaction mechanisms and modeling their kinetics. Recently, machine learning (ML) models have shown remarkable performance for prediction of TS geometries. However, they require 3D conformations of reactants and products often with their appropriate orientations as input, which demands substantial efforts and computational cost. Here, we propose a generative approach based on the stochastic diffusion method, namely TSDiff, for prediction of TS geometries just from 2D molecular graphs. TSDiff outperforms the existing ML models with 3D geometries in terms of both accuracy and efficiency. Moreover, it enables to sample various TS conformations, because it learns the distribution of TS geometries for diverse reactions in training. Thus, TSDiff finds more favorable reaction pathways with lower barrier heights than those in the reference database. These results demonstrate that TSDiff shows promising potential for an efficient and reliable TS exploration.

Accurate transition state generation with an object-aware equivariant elementary reaction diffusion model

Transition state search is key in chemistry for elucidating reaction mechanisms and exploring reaction networks. The search for accurate 3D transition state structures, however, requires numerous computationally intensive quantum chemistry calculations due to the complexity of potential energy surfaces. Here we developed an object-aware SE(3) equivariant diffusion model that satisfies all physical symmetries and constraints for generating sets of structures-reactant, transition state and product-in an elementary reaction. Provided reactant and product, this model generates a transition state structure in seconds instead of hours, which is typically required when performing quantum-chemistry-based optimizations. The generated transition state structures achieve a median of 0.08 Å root mean square deviation compared to the true transition state. With a confidence scoring model for uncertainty quantification, we approach an accuracy required for reaction barrier estimation (2.6 kcal mol-1) by only performing quantum chemistry-based optimizations on 14% of the most challenging reactions. We envision usefulness for our approach in constructing large reaction networks with unknown mechanisms.

Automated Exploration of Reaction Networks and Mechanisms Based on Metadynamics Nanoreactor Simulations

We developed an automated approach to construct a complex reaction network and explore the reaction mechanisms for numerous reactant molecules by integrating several theoretical approaches. Nanoreactor-type molecular dynamics was used to generate possible chemical reactions, in which the metadynamics was used to overcome the reaction barriers, and the semiempirical GFN2-xTB method was used to reduce the computational cost. Reaction events were identified from trajectories using the hidden Markov model based on the evolution of the molecular connectivity. This provided the starting points for further transition-state searches at the electronic structure levels of density functional theory to obtain the reaction mechanism. Finally, the entire reaction network containing multiple pathways was built. The feasibility and efficiency of the automated construction of the reaction network were investigated using the HCHO and NH3 biomolecular reaction and the reaction network for a multispecies system comprising dozens of HCN and H2O molecules. The results indicated that the proposed approach provides a valuable and effective tool for the automated exploration of the reaction networks.

Quantum chemical calculations for reaction prediction in the development of synthetic methodologies

Quantum chemical calculations have been used in the development of synthetic methodologies to analyze the reaction mechanisms of the developed reactions. Their ability to estimate chemical reaction pathways, including transition state energies and connected equilibria, has led researchers to embrace their use in predicting unknown reactions. This perspective highlights strategies that leverage quantum chemical calculations for the prediction of reactions in the discovery of new methodologies. Selected examples demonstrate how computation has driven the development of unknown reactions, catalyst design, and the exploration of synthetic routes to complex molecules prior to often laborious, costly, and time-consuming experimental investigations.

A Combined Reaction Path Search and Hybrid Solvation Method for the Systematic Exploration of Elementary Reactions at the Solid-Liquid Interface

We present a combined simulation method of single-component artificial force induced reaction (SC-AFIR) and effective screening medium combined with the reference interaction site model (ESM-RISM), termed SC-AFIR+ESM-RISM. SC-AFIR automatically and systematically explores the chemical reaction pathway, and ESM-RISM directly simulates the precise electronic structure at the solid-liquid interface. Hence, SC-AFIR+ESM-RISM enables us to explore reliable reaction pathways at the solid-liquid interface. We applied it to explore the dissociation pathway of an H2O molecule at the Cu(111)/water interface. The reaction path networks of the whole reaction and the minimum energy paths from H2O to H2 + O depend on the interfacial environment. The qualitative difference in the energy diagrams and the resulting change in the kinematically favored dissociation pathway upon changing the solvation environments are discussed. We believe that SC-AFIR+ESM-RISM will be a powerful tool to reveal the details of chemical reactions in surface catalysis and electrochemistry.

Integrated data-driven cross-disciplinary framework to prevent chemical water pollution

Access to a clean and healthy environment is a human right and a prerequisite for maintaining a sustainable ecosystem. Experts across domains along the chemical life cycle have traditionally operated in isolation, leading to limited connectivity between upstream chemical innovation to downstream development of water-treatment technologies. This fragmented and historically reactive approach to managing emerging contaminants has resulted in significant externalized societal costs. Herein, we propose an integrated data-driven framework to foster proactive action across domains to effectively address chemical water pollution. By implementing this integrated framework, it will not only enhance the capabilities of experts in their respective fields but also create opportunities for novel approaches that yield co-benefits across multiple domains. To successfully operationalize the integrated framework, several concerted efforts are warranted, including adopting open and FAIR (findable, accessible, interoperable, and reusable) data practices, developing common knowledge bases/platforms, and staying vigilant against new substance "properties" of concern.

First principles reaction discovery: from the Schrodinger equation to experimental prediction for methane pyrolysis

Our recent success in exploiting graphical processing units (GPUs) to accelerate quantum chemistry computations led to the development of the ab initio nanoreactor, a computational framework for automatic reaction discovery and kinetic model construction. In this work, we apply the ab initio nanoreactor to methane pyrolysis, from automatic reaction discovery to path refinement and kinetic modeling. Elementary reactions occurring during methane pyrolysis are revealed using GPU-accelerated ab initio molecular dynamics simulations. Subsequently, these reaction paths are refined at a higher level of theory with optimized reactant, product, and transition state geometries. Reaction rate coefficients are calculated by transition state theory based on the optimized reaction paths. The discovered reactions lead to a kinetic model with 53 species and 134 reactions, which is validated against experimental data and simulations using literature kinetic models. We highlight the advantage of leveraging local brute force and Monte Carlo sensitivity analysis approaches for efficient identification of important reactions. Both sensitivity approaches can further improve the accuracy of the methane pyrolysis kinetic model. The results in this work demonstrate the power of the ab initio nanoreactor framework for computationally affordable systematic reaction discovery and accurate kinetic modeling.

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.

High-throughput ab initio reaction mechanism exploration in the cloud with automated multi-reference validation

Quantum chemical calculations on atomistic systems have evolved into a standard approach to studying molecular matter. These calculations often involve a significant amount of manual input and expertise, although most of this effort could be automated, which would alleviate the need for expertise in software and hardware accessibility. Here, we present the AutoRXN workflow, an automated workflow for exploratory high-throughput electronic structure calculations of molecular systems, in which (i) density functional theory methods are exploited to deliver minimum and transition-state structures and corresponding energies and properties, (ii) coupled cluster calculations are then launched for optimized structures to provide more accurate energy and property estimates, and (iii) multi-reference diagnostics are evaluated to back check the coupled cluster results and subject them to automated multi-configurational calculations for potential multi-configurational cases. All calculations are carried out in a cloud environment and support massive computational campaigns. Key features of all components of the AutoRXN workflow are autonomy, stability, and minimum operator interference. We highlight the AutoRXN workflow with the example of an autonomous reaction mechanism exploration of the mode of action of a homogeneous catalyst for the asymmetric reduction of ketones.

Molecular Understanding and Practical In Silico Catalyst Design in Computational Organocatalysis and Phase Transfer Catalysis-Challenges and Opportunities

Through the lens of organocatalysis and phase transfer catalysis, we will examine the key components to calculate or predict catalysis-performance metrics, such as turnover frequency and measurement of stereoselectivity, via computational chemistry. The state-of-the-art tools available to calculate potential energy and, consequently, free energy, together with their caveats, will be discussed via examples from the literature. Through various examples from organocatalysis and phase transfer catalysis, we will highlight the challenges related to the mechanism, transition state theory, and solvation involved in translating calculated barriers to the turnover frequency or a metric of stereoselectivity. Examples in the literature that validated their theoretical models will be showcased. Lastly, the relevance and opportunity afforded by machine learning will be discussed.

Species-selective nanoreactor molecular dynamics simulations based on linear-scaling tight-binding quantum chemical calculations

Here, extensions to quantum chemical nanoreactor molecular dynamics simulations for discovering complex reactive events are presented. The species-selective algorithm, where the nanoreactor effectively works for the selected desired reactants, was introduced to the original scheme. Moreover, for efficient simulations of large model systems with the modified approach, the divide-and-conquer linear-scaling density functional tight-binding method was exploited. Two illustrative applications of the polymerization of propylene and cyclopropane mixtures and the aggregation of sodium chloride from aqueous solutions indicate that species-selective quantum chemical nanoreactor molecular dynamics is a promising method to accelerate the sampling of multicomponent chemical processes proceeding under relatively mild conditions.

Automated Reaction Kinetics of Gas-Phase Organic Species over Multiwell Potential Energy Surfaces

Automation of rate-coefficient calculations for gas-phase organic species became possible in recent years and has transformed how we explore these complicated systems computationally. Kinetics workflow tools bring rigor and speed and eliminate a large fraction of manual labor and related error sources. In this paper we give an overview of this quickly evolving field and illustrate, through five detailed examples, the capabilities of our own automated tool, KinBot. We bring examples from combustion and atmospheric chemistry of C-, H-, O-, and N-atom-containing species that are relevant to molecular weight growth and autoxidation processes. The examples shed light on the capabilities of automation and also highlight particular challenges associated with the various chemical systems that need to be addressed in future work.

Exploring the Quantum Chemical Energy Landscape with GNN-Guided Artificial Force

Artificial force has been proven useful to get over energy barriers and quickly search a large portion of the energy landscape. This work proposes a method based on graph neural networks to optimize the choice of transformation patterns to examine and accelerate energy landscape exploration. In open search from glutathione, the search efficiency was largely improved in comparison to random selection. We also applied transfer learning from glutathione to tuftsin, resulting in further efficiency gains.

Early-Stage Formation of the SIFSIX-3-Zn Metal-Organic Framework: An Automated Computational Study

Metal-organic frameworks (MOFs) have attracted significant attention over the past 2 decades due to their wide applicability as functional materials. However, targeted synthesis of novel MOFs remains problematic as their formation mechanisms are poorly understood, which forces us to rely on serendipity in the synthesis of novel MOFs. Here, we demonstrate a workflow employing the artificial force induced reaction (AFIR) method to investigate the self-assembly process of the node of the SIFSIX-3-Zn MOF, [Zn(pyz)₄(SiF₆)₂]^2- (pyz = pyrazine), in an automated manner. The workflow encompassing AFIR calculations, generation of extensive reaction path networks, propagation simulations of intermediates, and further refinements of identified formation pathways showed that the nodal structure can form through multiple competing pathways involving interconvertible intermediates. This finding provides a plausible rationale for the stochastic multistage processes believed to be key in MOF formation. Furthermore, this work represents the first application of an automated reaction mechanism discovery method to a MOF system using a general workflow that is applicable to study the formation of other MOF motifs as well.

Pathfinder─Navigating and Analyzing Chemical Reaction Networks with an Efficient Graph-Based Approach

While the field of first-principles explorations into chemical reaction space has been continuously growing, the development of strategies for analyzing resulting chemical reaction networks (CRNs) is lagging behind. A CRN consists of compounds linked by reactions. Analyzing how these compounds are transformed into one another based on kinetic modeling is a nontrivial task. Here, we present the graph-optimization-driven algorithm and program Pathfinder to allow for such an analysis of a CRN. The CRN for this work has been obtained with our open-source Chemoton reaction network exploration software. Chemoton probes reactive combinations of compounds for elementary steps and sorts them into reactions. By encoding these reactions of the CRN as a graph consisting of compound and reaction vertices and adding information about activation barriers as well as required reagents to the edges of the graph yields a complete graph-theoretical representation of the CRN. Since the probabilities of the formation of compounds depend on the starting conditions, the consumption of any compound during a reaction must be accounted for to reflect the availability of reagents. To account for this, we introduce compound costs to reflect compound availability. Simultaneously, the determined compound costs rank the compounds in the CRN in terms of their probability to be formed. This ranking then allows us to probe easily accessible compounds in the CRN first for further explorations into yet unexplored terrain. We first illustrate the working principle on an abstract small CRN. Afterward, Pathfinder is demonstrated in the example of the disproportionation of iodine with water and the comproportionation of iodic acid and hydrogen iodide. Both processes are analyzed within the same CRN, which we construct with our autonomous first-principles CRN exploration software Chemoton [Unsleber, J. P.; J. Chem. Theory Comput. 2022, 18, 5393-5409] guided by Pathfinder.

Predictive chemistry: machine learning for reaction deployment, reaction development, and reaction discovery

The field of predictive chemistry relates to the development of models able to describe how molecules interact and react. It encompasses the long-standing task of computer-aided retrosynthesis, but is far more reaching and ambitious in its goals. In this review, we summarize several areas where predictive chemistry models hold the potential to accelerate the deployment, development, and discovery of organic reactions and advance synthetic chemistry.

Oxidation and Reduction Pathways in the Knowles Hydroamination via a Photoredox-Catalyzed Radical Reaction

Systematic reaction path exploration revealed the entire mechanism of Knowles's light-promoted catalytic intramolecular hydroamination. Bond formation/cleavage competes with single electron transfer (SET) between the catalyst and substrate. These processes are described by adiabatic processes through transition states in an electronic state and non-radiative transitions through the seam of crossings (SX) between different electronic states. This study determined the energetically favorable SET path by introducing a practical computational model representing SET as non-adiabatic transitions via SXs between substrate's potential energy surfaces for different charge states adjusted based on the catalyst's redox potential. Calculations showed that the reduction and proton shuttle process proceeded concertedly. Also, the relative importance of SET paths (giving the product and leading back to the reactant) varies depending on the catalyst's redox potential, affecting the yield.

Chemical reaction networks and opportunities for machine learning

Chemical reaction networks (CRNs), defined by sets of species and possible reactions between them, are widely used to interrogate chemical systems. To capture increasingly complex phenomena, CRNs can be leveraged alongside data-driven methods and machine learning (ML). In this Perspective, we assess the diverse strategies available for CRN construction and analysis in pursuit of a wide range of scientific goals, discuss ML techniques currently being applied to CRNs and outline future CRN-ML approaches, presenting scientific and technical challenges to overcome.

Prediction of High-Yielding Single-Step or Cascade Pericyclic Reactions for the Synthesis of Complex Synthetic Targets

Pericyclic reactions, which involve cyclic concerted transition states without ionic or radical intermediates, have been extensively studied since their definition in the 1960s, and the famous Woodward-Hoffmann rules predict their stereoselectivity and chemoselectivity. Here, we describe the application of a fully automated reaction-path search method, that is, the artificial force induced reaction (AFIR), to trace an input compound back to reasonable starting materials through thermally allowed pericyclic reactions via product-based quantum-chemistry-aided retrosynthetic analysis (QCaRA) without using any a priori experimental knowledge. All categories of pericyclic reactions, including cycloadditions, ene reactions, group-transfer, cheletropic, electrocyclic, and sigmatropic reactions, were successfully traced back via concerted reaction pathways, and starting materials were computationally obtained with the correct stereochemistry. Furthermore, AFIR was used to predict whether the identified reaction pathway can be expected to occur in good yield relative to other possible reactions of the identified starting material. In order to showcase its practical utility, this state-of-the-art technology was also applied to the retrosynthetic analysis of a natural product with a relatively high number of atoms (52 atoms: endiandric acid C methyl ester), which was first synthesized by Nicolaou in 1982 and provided the corresponding starting polyenes with the correct stereospecificity via three pericyclic reaction cascades (one Diels-Alder reaction as well as 6π and 8π electrocyclic reactions). Moreover, not only systems that obey the Woodward-Hoffmann rules but also systems that violate these rules, such as those recently calculated by Houk, can be retrosynthesized accurately.

A Reactive Molecular Dynamics Study of Chlorinated Organic Compounds. Part II: A ChemTraYzer Study of Chlorinated Dibenzofuran Formation and Decomposition Processes

In our two-paper series, we first present the development of ReaxFF CHOCl parameters using the recently published ParAMS parametrization tool. In this second part, we update the reactive Molecular Dynamics - Quantum Mechanics coupling scheme ChemTraYzer and combine it with our new ReaxFF parameters from Part I to study formation and decomposition processes of chlorinated dibenzofurans. We introduce a self-learning method for recovering failed transition-state searches that improves the overall ChemTraYzer transition-state search success rate by 10 percentage points to a total of 48 %. With ChemTraYzer, we automatically find and quantify more than 500 reactions using transition state theory and DFT. Among the discovered chlorinated dibenzofuran reactions are numerous reactions that are new to the literature. In three case studies, we discuss the set of reactions that are most relevant to the dibenzofuran literature: (i) bimolecular reactions of the chlorinated-dibenzofuran precursors phenoxy radical and 1,3,5-trichlorobenzene, (ii) dibenzofuran chlorination and pyrolysis, and (iii) oxidation of chlorinated dibenzofurans.

Guided discovery of chemical reaction pathways with imposed activation

Computational power and quantum chemical methods have improved immensely since computers were first applied to the study of reactivity, but the de novo prediction of chemical reactions has remained challenging. We show that complex reaction pathways can be efficiently predicted in a guided manner using chemical activation imposed by geometrical constraints of specific reactive modes, which we term imposed activation (IACTA). Our approach is demonstrated on realistic and challenging chemistry, such as a triple cyclization cascade involved in the total synthesis of a natural product, a water-mediated Michael addition, and several oxidative addition reactions of complex drug-like molecules. Notably and in contrast with traditional hand-guided computational chemistry calculations, our method requires minimal human involvement and no prior knowledge of the products or the associated mechanisms. We believe that IACTA will be a transformational tool to screen for chemical reactivity and to study both by-product formation and decomposition pathways in a guided way.

Fully Automated Generation of Prebiotically Relevant Reaction Networks from Optimized Nanoreactor Simulations

The nanoreactor approach first introduced by the group of Martı́nez [Wang et al. Nat. Chem. 2014, 6, 1044-1048] has recently attracted much attention because of its ability to accelerate the discovery of reaction pathways. Here, we provide a comprehensive study of various simulation parameters and present an alternative implementation for the reactivity-enhancing spherical constraint function, as well as for the detection of reaction events. In this context, a fully automated postsimulation evaluation procedure based on RDKit and NetworkX analysis is introduced. The chemical and physical robustness of the procedure is examined by investigating the reactivity of selected homogeneous systems. The optimized procedure is applied at the GFN2-xTB level of theory to a system composed of HCN molecules and argon atoms, acting as a buffer, yielding prebiotically plausible primary and secondary precursors for the synthesis of RNA. Furthermore, the formose reaction network is explored leading to numerous sugar precursors. The discovered compounds reflect experimental findings; however, new synthetic routes and a large collection of exotic, highly reactive molecules are observed, highlighting the predictive power of the nanoreactor approach for unraveling the reactive manifold.

An automated method for graph-based chemical space exploration and transition state finding

Algorithms that automatically explore the chemical space have been limited to chemical systems with a low number of atoms due to expensive involved quantum calculations and the large amount of possible reaction pathways. The method described here presents a novel solution to the problem of chemical exploration by generating reaction networks with heuristics based on chemical theory. First, a second version of the reaction network is determined through molecular graph transformations acting upon functional groups of the reacting. Only transformations that break two chemical bonds and form two new ones are considered, leading to a significant performance enhancement compared to previously presented algorithm. Second, energy barriers for this reaction network are estimated through quantum chemical calculations by a growing string method, which can also identify non-octet species missed during the previous step and further define the reaction network. The proposed algorithm has been successfully applied to five different chemical reactions, in all cases identifying the most important reaction pathways.

Enhanced Sampling Aided Design of Molecular Photoswitches

Advances in the evolving field of atomistic simulations promise important insights for the design and fundamental understanding of novel molecular photoswitches. Here, we use state-of-the-art enhanced simulation techniques to unravel the complex, multistep chemistry of donor-acceptor Stenhouse adducts (DASAs). Our reaction discovery workflow consists of enhanced sampling for efficient chemical space exploration, refinement of newly observed pathways with more accurate ab initio electronic structure calculations, and structural modifications to introduce design principles within future generations of DASAs. We showcase our discovery workflow by not only recovering the full photoswitching mechanism of DASA but also predicting a plethora of new plausible thermal pathways and suggesting a way for their experimental validation. Furthermore, we illustrate the tunability of these newly discovered reactions, leading to a potential avenue for controlling DASA dynamics through multiple external stimuli. Overall, these insights could offer alternative routes to increase the efficiency and control of DASA's photoswitching mechanism, providing new elements to design more complex light-responsive materials.

Quantum Chemical Roots of Machine-Learning Molecular Similarity Descriptors

In this work, we explore the quantum chemical foundations of descriptors for molecular similarity. Such descriptors are key for traversing chemical compound space with machine learning. Our focus is on the Coulomb matrix and on the smooth overlap of atomic positions (SOAP). We adopt a basic framework that allows us to connect both descriptors to electronic structure theory. This framework enables us to then define two new descriptors that are more closely related to electronic structure theory, which we call Coulomb lists and smooth overlap of electron densities (SOED). By investigating their usefulness as molecular similarity descriptors, we gain new insights into how and why Coulomb matrix and SOAP work. Moreover, Coulomb lists avoid the somewhat mysterious diagonalization step of the Coulomb matrix and might provide a direct means to extract subsystem information that can be compared across Born-Oppenheimer surfaces of varying dimension. For the electron density, we derive the necessary formalism to create the SOED measure in close analogy to SOAP. Because this formalism is more involved than that of SOAP, we review the essential theory as well as introduce a set of approximations that eventually allow us to work with SOED in terms of the same implementation available for the evaluation of SOAP. We focus our analysis on elementary reaction steps, where transition state structures are more similar to either reactant or product structures than the latter two are with respect to one another. The prediction of electronic energies of transition state structures can, however, be more difficult than that of stable intermediates due to multi-configurational effects. The question arises to what extent molecular similarity descriptors rooted in electronic structure theory can resolve these intricate effects.

Graph-Driven Reaction Discovery: Progress, Challenges, and Future Opportunities

Graph-based descriptors, such as bond-order matrices and adjacency matrices, offer a simple and compact way of categorizing molecular structures; furthermore, such descriptors can be readily used to catalog chemical reactions (i.e., bond-making and -breaking). As such, a number of graph-based methodologies have been developed with the goal of automating the process of generating chemical reaction network models describing the possible mechanistic chemistry in a given set of reactant species. Here, we outline the evolution of these graph-based reaction discovery schemes, with particular emphasis on more recent methods incorporating graph-based methods with semiempirical and ab initio electronic structure calculations, minimum-energy path refinements, and transition state searches. Using representative examples from homogeneous catalysis and interstellar chemistry, we highlight how these schemes increasingly act as "virtual reaction vessels" for interrogating mechanistic questions. Finally, we highlight where challenges remain, including issues of chemical accuracy and calculation speeds, as well as the inherent challenge of dealing with the vast size of accessible chemical reaction space.

Fast Screening of Minimum Energy Crossing Points with Semiempirical Tight-Binding Methods

The investigation of photochemical processes is a highly active field in computational chemistry. One research direction is the automated exploration and identification of minimum energy conical intersection (MECI) geometries. However, due to the immense technical effort required to calculate nonadiabatic potential energy landscapes, the routine application of such computational protocols is severely limited. In this study, we will discuss the prospect of combining adiabatic potential energy surfaces from semiempirical quantum mechanical calculations with specialized confinement potential and metadynamics simulations to identify S₀/T₁ minimum energy crossing point (MECP) geometries. It is shown that MECPs calculated at the GFN2-xTB level can provide suitable approximations to high-level S₀/S₁ab initio conical intersection geometries at a fraction of the computational cost. Reference MECIs of benzene are studied to illustrate the basic concept. An example application of the presented protocol is demonstrated for a set of photoswitch molecules.

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.

The chemistry of AlF and CaF production in buffer gas sources

In this work, we explore the role of chemical reactions on the properties of buffer gas cooled molecular beams. In particular, we focus on scenarios relevant to the formation of AlF and CaF via chemical reactions between the Ca and Al atoms ablated from a solid target in an atmosphere of a fluorine-containing gas, in this case, SF6 and NF3. Reactions are studied following an ab initio molecular dynamics approach, and the results are rationalized following a tree-shaped reaction model based on Bayesian inference. We find that NF3 reacts more efficiently with hot metal atoms to form monofluoride molecules than SF6. In addition, when using NF3, the reaction products have lower kinetic energy, requiring fewer collisions to thermalize with the cryogenic helium. Furthermore, we find that the reaction probability for AlF formation is much higher than for CaF across a broad range of temperatures.

Multistructural microiteration combined with QM/MM-ONIOM electrostatic embedding

Multistructural microiteration (MSM) is a method to take account of contributions of multiple surrounding structures in a geometrical optimization or reaction path calculation using the quantum mechanics/molecular mechanics (QM/MM) ONIOM method. In this study, we combined MSM with the electrostatic embedding (EE) scheme of the QM/MM-ONIOM method by extending its original formulation for mechanical embedding (ME). MSM-EE takes account of the polarization in the QM region induced by point charges assigned to atoms in the multiple surrounding structures, where the point charges are scaled by the weight factor of each surrounding structure determined through MSM. The performance of MSM-EE was compared with that of the other methods, i.e., ONIOM-ME, ONIOM-EE, and MSM-ME, by applying them to three chemical processes: (1) chorismate-to-prephenate transformation in aqueous solution, (2) the same transformation as (1) in an enzyme, and (3) hydroxylation in p-hydroxybenzoate hydroxylase. These numerical tests of MSM-EE yielded barriers and reaction energies close to experimental values with computational costs comparable to those of the other three methods.

Experimental and Computational Mechanistic Study of Carbonazidate-Initiated Cascade Reactions

A variety of Huisgen cyclization or nitrene/carbene alkyne cascade reactions with different types of termination were investigated. Accessible nitrene precursors were assessed, and carbonazidates were found to be the only effective initiators. Solvents, terminal alkynyl substituents, and catalysts can all impact the reaction outcome. Study of the mechanism both computationally (by density functional theory) and experimentally revealed relevant intermediates and plausible reaction pathways.

Successes and challenges in using machine-learned activation energies in kinetic simulations

The prediction of the thermodynamic and kinetic properties of chemical reactions is increasingly being addressed by machine-learning (ML) methods such as artificial neural networks (ANNs). While a number of recent studies have reported success in predicting chemical reaction activation energies, less attention has focused on how the accuracy of ML predictions filter through to predictions of macroscopic observables. Here, we consider the impact of the uncertainty associated with ML prediction of activation energies on observable properties of chemical reaction networks, as given by microkinetics simulations based on ML-predicted reaction rates. After training an ANN to predict activation energies given standard molecular descriptors for reactants and products alone, we performed microkinetics simulations of three different prototypical reaction networks: formamide decomposition, aldol reactions and decomposition of 3-hydroperoxypropanal. We find that the kinetic modelling predictions can be in excellent agreement with corresponding simulations performed with ab initio calculations, but this is dependent on the inherent energetic landscape of the networks. We use these simulations to suggest some guidelines for when ML-based activation energies can be reliable, and when one should take more care in applications to kinetics modelling.

Quantum Chemical Calculations to Trace Back Reaction Paths for the Prediction of Reactants

The long-due development of a computational method for the ab initio prediction of chemical reactants that provide a target compound has been hampered by the combinatorial explosion that occurs when reactions consist of multiple elementary reaction processes. To address this challenge, we have developed a quantum chemical calculation method that can enumerate the reactant candidates from a given target compound by combining an exhaustive automated reaction path search method with a kinetics method for narrowing down the possibilities. Two conventional name reactions were then assessed by tracing back the reaction paths using this new method to determine whether the known reactants could be identified. Our method is expected to be a powerful tool for the prediction of reactants and the discovery of new reactions.

Leveraging algorithmic search in quantum chemical reaction path finding

Reaction path finding methods construct a graph connecting reactants and products in a quantum chemical energy landscape. They are useful in elucidating various reactions and provide footsteps for designing new reactions. Their enormous computational cost, however, limits their application to relatively simple reactions. This paper engages in accelerating reaction path finding by introducing the principles of algorithmic search. A new method called RRT/SC-AFIR is devised by combining rapidly exploring random tree (RRT) and single component artificial force induced reaction (SC-AFIR). Using 96 cores, our method succeeded in constructing a reaction graph for Fritsch-Buttenberg-Wiechell rearrangement within a time limit of 3 days, while the conventional methods could not. Our results illustrate that the algorithm theory provides refreshing and beneficial viewpoints on quantum chemical methodologies.

Community Reaction Network Reduction for Constructing a Coarse-Grained Representation of Combustion Reaction Mechanisms

A community-reaction network reduction (CNR) approach is presented for mechanism reduction on the basis of a network-based community detection technique, a concept related to pre-equilibrium in chemical kinetics. In this method, the detailed combustion mechanism is first transformed into a weighted network, in which communities of species that have dense inner connections under the critical ignition conditions are identified. By analyzing the community partitions in different regions, we determine the effective functional groups and driving processes. Then, a skeletal model for the overall mechanism is deduced according to the network centrality data, including transition pathway identification and reaction-path flux. The CNR method is illustrated on the hydrogen autoignition system which has been extensively investigated, and a new reduced mechanism involving seven processes is proposed. Dynamics simulations employing the present CNR model show that the computed ignition time and distribution of major species on a wide range of temperature and pressure conditions are in accord with the experiments and results from other methods.