A growing string method for determining transition states: Comparison to the nudged elastic band and string methods

Comparative Analysis of Reinforcement Learning Algorithms for Finding Reaction Pathways: Insights from a Large Benchmark Data Set

The identification of kinetically feasible reaction pathways that connect a reactant to its product, including numerous intermediates and transition states, is crucial for predicting chemical reactions and elucidating reaction mechanisms. However, as molecular systems become increasingly complex or larger, the number of local minimum structures and transition states grows, which makes this task challenging, even with advanced computational approaches. We introduced a reinforcement learning algorithm to efficiently identify a kinetically feasible reaction pathway between a given local minimum structure for the reactant and a given one for the product, starting from the reactant. The performance of the algorithm was validated using a benchmark data set of large-scale chemical reaction path networks. Several search policies were proposed, using metrics based on energetic or structural similarity to the product's goal structure, for each local minimum structure candidate found during the search. The performances of baseline greedy, random, and uniform search policies varied substantially depending on the system. In contrast, exploration-exploitation balanced policies such as Thompson sampling, probability of improvement, and expected improvement consistently demonstrated stable and high performance. Furthermore, we characterized the search mechanisms that depend on different policies in detail. This study also addressed potential avenues for further research, such as hierarchical reinforcement learning and multiobjective optimization, which could deepen the problem setting explored in this study.

Correlated Flat-Bottom Elastic Network Model for Improved Bond Rearrangement in Reaction Paths

This study introduces correlated flat-bottom elastic network model (CFB-ENM), an extension of our recently developed flat-bottom elastic network model (FB-ENM) for generating plausible reaction paths, i.e., collision-free paths preserving nonreactive parts. While FB-ENM improved upon the widely used image-dependent pair potential (IDPP) by addressing unintended structural distortion and bond breaking, it still struggled with regulating the timing of series of bond breaking and formation. CFB-ENM overcomes this limitation by incorporating structure-based correlation terms. These terms impose constraints on pairs of atom pairs, ensuring immediate formation of new bonds after breaking of existing bonds. Using the direct MaxFlux method, we generated paths for 121 reactions involving main group elements and 35 reactions involving transition metals. We found that CFB-ENM significantly improves reaction paths compared to FB-ENM. CFB-ENM paths exhibited lower maximum DFT energies along the paths in most reactions, with nearly half showing significant energy reductions of several tens of kcal/mol. In the few cases where CFB-ENM yielded higher energy paths, most increases were below 10 kcal/mol. We also confirmed that CFB-ENM reduces computational costs in subsequent precise reaction path or transition state searches compared to FB-ENM. An implementation of CFB-ENM based on the Atomic Simulation Environment is available on GitHub for use in computational chemistry research.

Computational framework for discovery of degradation mechanisms of organic flow battery electrolytes

The stability of organic redox-active molecules is a key challenge for the long-term viability of organic redox flow batteries (ORFBs). Electrolyte degradation leads to capacity fade, reducing the efficiency and lifespan of ORFBs. To systematically investigate degradation mechanisms, we present a computational framework that automates the exploration of degradation pathways. The approach integrates local reactivity descriptors to generate reactive complexes and employs a single-ended process search to discover elementary reaction steps, including transition states and intermediates. The resulting reaction network is iteratively refined with heuristics and human-guided validation. The framework is applied to study the degradation mechanisms of quinone- and quinoxaline-based electrolytes under acidic and basic aqueous conditions. The predicted reaction pathways and degradation products align with experimental observations, highlighting key degradation modes such as Michael addition, disproportionation, dimerization, and electrochemical transformation. The framework provides a valuable tool for in silico screening of stable electrolyte candidates and guiding the molecular design of next-generation ORFBs.

Facilitating Transition State Search with Minimal Conformational Sampling Using Reaction Graph

Elucidating transition states (TSs) is crucial for understanding chemical reactions. The reliability of traditional TS search approaches depends on input conformations that require significant effort to prepare. Previous automated methods for generating input reaction conformations typically involve extensive exploration of a large conformational space. Such exhaustive search can be complicated by the rapid growth of the conformational space, especially for reactions involving many rotatable bonds, multiple reacting molecules, and numerous bond formations and dissociations. To address this problem, we propose a new approach that generates reaction conformations for TS searches with minimal reliance on sampling. This method constructs a pseudo-TS structure based on a reaction graph containing bond formation and dissociation information and modifies it to produce reactant and product conformations. Tested on three different benchmarks, our method consistently generated suitable conformations without necessitating extensive sampling, demonstrating its potential to significantly improve the applicability of automated TS searches. This approach offers a valuable tool for a broad range of applications such as reaction mechanism analysis and network exploration.

Transition State Searching Accelerated by Neural Network Potential

Understanding transition states is pivotal in the design of efficient chemical processes and catalysts. However, identifying transition states is challenging due to the resource-intensive and iterative nature of current computational methods. This study integrates neural network potentials with physical models to enhance the transition state prediction. Different neural network potentials and transition states locating algorithms are benchmarked. By combining NequIP with the energy-weighted Climbing Image-Nudged Elastic Band (EW-CI-NEB) method, we achieved highly accurate transition state predictions, significantly surpassing semiempirical methods in accuracy and greatly outpacing density functional theory in efficiency. Additionally, the transferability of the model was evaluated using a NequIP model trained on a refined subset of the dataset, and the model's performance was further improved through active learning. This method can directly search for transition states in given reactions or serve as an efficient tool for generating initial guesses of transition state structures, significantly reducing manual effort.

Accessing Numerical Energy Hessians with Graph Neural Network Potentials and Their Application in Heterogeneous Catalysis

Access to the potential energy Hessian enables determination of the Gibbs free energy and certain approaches to transition state search and optimization. Here, we demonstrate that off-the-shelf pretrained Open Catalyst Project (OCP) machine learned potentials (MLPs) determine the Hessian with great success (58 cm-1 mean absolute error (MAE)) for intermediates adsorbed to heterogeneous catalyst surfaces. This enables the use of OCP models for the aforementioned applications. The top performing model, with a simple offset correction, gives good estimations of the vibrational entropy contribution to the Gibbs free energy with an MAE of 0.042 eV at 300 K. The ability to leverage models to capture the translational entropy was also explored. It was determined that 94% of randomly sampled systems had a translational entropy greater than 0.1 eV at 300 K. This underscores the need to go beyond the harmonic approximation to consider the entropy introduced by adsorbate translation, which increases with temperature. Lastly, we used MLP-determined Hessian information for transition state search and found we were able to reduce the number of unconverged systems by 65 to 93% overall convergence, improving on the baseline established by CatTSunami.

Chemical Reaction Networks from Scratch with Reaction Prediction and Kinetics-Guided Exploration

Algorithmic reaction explorations based on transition state searches can now routinely predict relatively short reaction sequences involving small molecules. However, applying these algorithms to deeper chemical reaction network (CRN) exploration still requires the development of more efficient and accurate exploration policies. Here, an exploration algorithm, which we name yet another kinetic strategy (YAKS), is demonstrated that uses microkinetic simulations of the nascent network to achieve cost-effective, deep network exploration. Key features of the algorithm are the automatic incorporation of bimolecular reactions between network intermediates, compatibility with short-lived but kinetically important species, and incorporation of rate uncertainty into the exploration policy. In validation case studies of glucose pyrolysis, the algorithm rediscovers reaction pathways previously discovered by heuristic exploration policies and elucidates new reaction pathways for experimentally obtained products. The resulting CRN is the first to connect all major experimental pyrolysis products to glucose. Additional case studies are presented that investigate the role of reaction rules, rate uncertainty, and bimolecular reactions. These case studies show that naïve exponential growth estimates can vastly overestimate the actual number of kinetically relevant pathways in the physical reaction networks. In light of this, further improvements in exploration policies and reaction prediction algorithms make it feasible that CRNs might soon be routinely predictable in some contexts.

Precise Large-Scale Chemical Transformations on Surfaces: Deep Learning Meets Scanning Probe Microscopy with Interpretability

Scanning probe microscopy (SPM) techniques have shown great potential in fabricating nanoscale structures endowed with exotic quantum properties achieved through various manipulations of atoms and molecules. However, precise control requires extensive domain knowledge, which is not necessarily transferable to new systems and cannot be readily extended to large-scale operations. Therefore, efficient and autonomous SPM techniques are needed to learn optimal strategies for new systems, in particular for the challenge of controlling chemical reactions and hence offering a route to precise atomic and molecular construction. In this paper, we developed a software infrastructure named AutoOSS (Autonomous On-Surface Synthesis) to automate bromine removal from hundreds of Zn(II)-5,15-bis(4-bromo-2,6-dimethylphenyl)porphyrin (ZnBr2Me4DPP) on Au(111), using neural network models to interpret STM outputs and deep reinforcement learning models to optimize manipulation parameters. This is further supported by Bayesian optimization structure search (BOSS) and density functional theory (DFT) computations to explore 3D structures and reaction mechanisms based on STM images.

Data Generation for Machine Learning Interatomic Potentials and Beyond

The field of data-driven chemistry is undergoing an evolution, driven by innovations in machine learning models for predicting molecular properties and behavior. Recent strides in ML-based interatomic potentials have paved the way for accurate modeling of diverse chemical and structural properties at the atomic level. The key determinant defining MLIP reliability remains the quality of the training data. A paramount challenge lies in constructing training sets that capture specific domains in the vast chemical and structural space. This Review navigates the intricate landscape of essential components and integrity of training data that ensure the extensibility and transferability of the resulting models. We delve into the details of active learning, discussing its various facets and implementations. We outline different types of uncertainty quantification applied to atomistic data acquisition and the correlations between estimated uncertainty and true error. The role of atomistic data samplers in generating diverse and informative structures is highlighted. Furthermore, we discuss data acquisition via modified and surrogate potential energy surfaces as an innovative approach to diversify training data. The Review also provides a list of publicly available data sets that cover essential domains of chemical space.

Size-Increased All-Phenylene Molecular Spoked Wheels - A Combined Theoretical and Experimental Approach

A lateral expansion of molecular spoked wheels (MSWs) based on an all-phenylene backbone is described. The MSWs contain a central hub, six spokes, and a rim that is formed by a sixfold Yamamoto coupling of the respective non-cyclized dodecabromo precursor yielding MSWs with up to 30 phenylene rings in the perimeter. Attempts to prepare compounds of such size without flexible side groups at the spokes were unsuccessful, most probably due to an aggregation and accompanying oligomerization of the precursors during the cyclization. To overcome these problems, fluorene units are inserted into the spokes. These contain additional alkyl chains and lead to a curvature of the wheels. Quantum chemical calculations on the mechanism of the Yamamoto coupling lead to geometry and strain-related criteria for the successful rim closure to the respective MSW. Subsequently, MSWs are prepared with four and even six phenylene units at each edge of the hexagonal wheels. The resulting MSWs are characterized by spectroscopic methods, and additionally some of them are visualized via scanning tunneling microscopy (STM).

Analytical ab initio hessian from a deep learning potential for transition state optimization

Identifying transition states-saddle points on the potential energy surface connecting reactant and product minima-is central to predicting kinetic barriers and understanding chemical reaction mechanisms. In this work, we train a fully differentiable equivariant neural network potential, NewtonNet, on thousands of organic reactions and derive the analytical Hessians. By reducing the computational cost by several orders of magnitude relative to the density functional theory (DFT) ab initio source, we can afford to use the learned Hessians at every step for the saddle point optimizations. We show that the full machine learned (ML) Hessian robustly finds the transition states of 240 unseen organic reactions, even when the quality of the initial guess structures are degraded, while reducing the number of optimization steps to convergence by 2-3× compared to the quasi-Newton DFT and ML methods. All data generation, NewtonNet model, and ML transition state finding methods are available in an automated workflow.

A Mode Evolution Metric to Extract Reaction Coordinates for Biomolecular Conformational Transitions

The complex, multidimensional energy landscape of biomolecules makes the extraction of suitable, nonintuitive collective variables (CVs) that describe their conformational transitions challenging. At present, dimensionality reduction approaches and machine learning (ML) schemes are employed to obtain CVs from molecular dynamics (MD)/Monte Carlo (MC) trajectories or structural databanks for biomolecules. However, minimum sampling conditions to generate reliable CVs that accurately describe the underlying energy landscape remain unclear. Here, we address this issue by developing a Mode evolution Metric (MeM) to extract CVs that can pinpoint new states and describe local transitions in the vicinity of a reference minimum from nonequilibrated MD/MC trajectories. We present a general mathematical formulation of MeM for both statistical dimensionality reduction and machine learning approaches. Application of MeM to MC trajectories of model potential energy landscapes and MD trajectories of solvated alanine dipeptide reveals that the principal components which locate new states in the vicinity of a reference minimum emerge well before the trajectories locally equilibrate between the associated states. Finally, we demonstrate a possible application of MeM in designing efficient biased sampling schemes to construct accurate energy landscape slices that link transitions between states. MeM can help speed up the search for new minima around a biomolecular conformational state and enable the accurate estimation of thermodynamics for states lying on the energy landscape and the description of associated transitions.

Contact-Map-Driven Exploration of Heterogeneous Protein-Folding Paths

We have recently shown how physically realizable protein-folding pathways can be generated using directed walks in the space of inter-residue contact-maps; combined with a back-transformation to move from protein contact-maps to Cartesian coordinates, we have demonstrated how this approach can generate protein-folding trajectory ensembles without recourse to molecular dynamics. In this article, we demonstrate that this framework can be used to study a challenging protein-folding problem that is known to exhibit two different folding paths which were previously identified through molecular dynamics simulation at several different temperatures. From the viewpoint of protein-folding mechanism prediction, this particular problem is extremely challenging to address, specifically involving folding to an identical nontrivial compact native structure along distinct pathways defined by heterogeneous secondary structural elements. Here, we show how our previously reported contact-map-based protein-folding strategy can be significantly enhanced to enable accurate and robust prediction of heterogeneous folding paths by (i) introducing a novel topologically informed metric for comparing two protein contact maps, (ii) reformulating our graph-represented folding path generation, and (iii) introducing a new and more reliable structural back-mapping algorithm. These changes improve the reliability of generating structurally sound folding intermediates and dramatically decrease the number of physically irrelevant folding intermediates generated by our previous simulation strategy. Most importantly, we demonstrate how our enhanced folding algorithm can successfully identify the alternative folding mechanisms of a multifolding-pathway protein, in line with direct molecular dynamics simulations.

Gate-Switchable Molecular Diffusion on a Graphene Field-Effect Transistor

Controlling the surface diffusion of particles on 2D devices creates opportunities for advancing microscopic processes such as nanoassembly, thin-film growth, and catalysis. Here, we demonstrate the ability to control the diffusion of F4TCNQ molecules at the surface of clean graphene field-effect transistors (FETs) via electrostatic gating. Tuning the back-gate voltage (VG) of a graphene FET switches molecular adsorbates between negative and neutral charge states, leading to dramatic changes in their diffusion properties. Scanning tunneling microscopy measurements reveal that the diffusivity of neutral molecules decreases rapidly with a decreasing VG and involves rotational diffusion processes. The molecular diffusivity of negatively charged molecules, on the other hand, remains nearly constant over a wide range of applied VG values and is dominated by purely translational processes. First-principles density functional theory calculations confirm that the energy landscapes experienced by neutral vs charged molecules lead to diffusion behavior consistent with experiment. Gate-tunability of the diffusion barrier for F4TCNQ molecules on graphene enables graphene FETs to act as diffusion switches.

Flat-Bottom Elastic Network Model for Generating Improved Plausible Reaction Paths

Rapid generation of a plausible reaction path connecting a given reactant and product in advance is crucial for the efficient computation of precise reaction paths or transition states. We propose a computationally efficient potential energy based on the molecular structure to generate such paths. This potential energy has a flat bottom consisting of structures without atomic collisions while preserving nonreactive chemical bonds, bond angles, and partial planar structures. By combining this potential energy with the direct MaxFlux method, a recently developed reaction-path/transition-state search method, we can find the shortest plausible path passing within the bottom. Numerical results show that this combination yields lower energy paths compared to the paths obtained by the well-known image-dependent pair potential. We also theoretically investigate the differences between these two potential energies. The proposed potential energy and path generation routine are implemented in our Python version of the direct MaxFlux method, available on GitHub.

The orientation dependence of cavity-modified chemistry

Recent theoretical studies have explored how ultra-strong light-matter coupling can be used as a handle to control chemical transformations. Ab initio cavity quantum electrodynamics calculations demonstrate that large changes to reaction energies or barrier heights can be realized by coupling electronic degrees of freedom to vacuum fluctuations associated with an optical cavity mode, provided that large enough coupling strengths can be achieved. In many cases, the cavity effects display a pronounced orientational dependence. Here, we highlight the critical role that geometry relaxation can play in such studies. As an example, we consider a recent work [Pavošević et al., Nat. Commun. 14, 2766 (2023)] that explored the influence of an optical cavity on Diels-Alder cycloaddition reactions and reported large changes to reaction enthalpies and barrier heights, as well as the observation that changes in orientation can inhibit the reaction or select for one reaction product or another. Those calculations used fixed molecular geometries optimized in the absence of the cavity and fixed relative orientations of the molecules and the cavity mode polarization axis. Here, we show that when given a chance to relax in the presence of the cavity, the molecular species reorient in a way that eliminates the orientational dependence. Moreover, in this case, we find that qualitatively different conclusions regarding the impact of the cavity on the thermodynamics of the reaction can be drawn from calculations that consider relaxed vs unrelaxed molecular structures.

Quantum chemical package Jaguar: A survey of recent developments and unique features

This paper is dedicated to the quantum chemical package Jaguar, which is commercial software developed and distributed by Schrödinger, Inc. We discuss Jaguar's scientific features that are relevant to chemical research as well as describe those aspects of the program that are pertinent to the user interface, the organization of the computer code, and its maintenance and testing. Among the scientific topics that feature prominently in this paper are the quantum chemical methods grounded in the pseudospectral approach. A number of multistep workflows dependent on Jaguar are covered: prediction of protonation equilibria in aqueous solutions (particularly calculations of tautomeric stability and pKa), reactivity predictions based on automated transition state search, assembly of Boltzmann-averaged spectra such as vibrational and electronic circular dichroism, as well as nuclear magnetic resonance. Discussed also are quantum chemical calculations that are oriented toward materials science applications, in particular, prediction of properties of optoelectronic materials and organic semiconductors, and molecular catalyst design. The topic of treatment of conformations inevitably comes up in real world research projects and is considered as part of all the workflows mentioned above. In addition, we examine the role of machine learning methods in quantum chemical calculations performed by Jaguar, from auxiliary functions that return the approximate calculation runtime in a user interface, to prediction of actual molecular properties. The current work is second in a series of reviews of Jaguar, the first having been published more than ten years ago. Thus, this paper serves as a rare milestone on the path that is being traversed by Jaguar's development in more than thirty years of its existence.

The Importance of Reaction Energy in Predicting Chemical Reaction Barriers with Machine Learning Models

Improving our fundamental understanding of complex heterocatalytic processes increasingly relies on electronic structure simulations and microkinetic models based on calculated energy differences. In particular, calculation of activation barriers, usually achieved through compute-intensive saddle point search routines, remains a serious bottleneck in understanding trends in catalytic activity for highly branched reaction networks. Although the well-known Brønsted-Evans-Polyani (BEP) scaling - a one-feature linear regression model - has been widely applied in such microkinetic models, they still rely on calculated reaction energies and may not generalize beyond a single facet on a single class of materials, e. g., a terrace sites on transition metals. For highly branched and energetically shallow reaction networks, such as electrochemical CO2 reduction or wastewater remediation, calculating even reaction energies on many surfaces can become computationally intractable due to the combinatorial explosion of states that must be considered. Here, we investigate the feasibility of activation barrier prediction without knowledge of the reaction energy using linear and nonlinear machine learning (ML) models trained on a new database of over 500 dehydrogenation activation barriers. We also find that inclusion of the reaction energy significantly improves both classes of ML models, but complex nonlinear models can achieve performance similar to the simplest BEP scaling when predicting activation barriers on new systems. Additionally, inclusion of the reaction energy significantly improves generalizability to new systems beyond the training set. Our results suggest that the reaction energy is a critical feature to consider when building models to predict activation barriers, indicating that efforts to reliably predict reaction energies through, e. g., the Open Catalyst Project and others, will be an important route to effective model development for more complex systems.

Predicting Long-Time-Scale Kinetics under Variable Experimental Conditions with Kinetica.jl

Predicting the degradation processes of molecules over long time scales is a key aspect of industrial materials design. However, it is made computationally challenging by the need to construct large networks of chemical reactions that are relevant to the experimental conditions that kinetic models must mirror, with every reaction requiring accurate kinetic data. Here, we showcase Kinetica.jl, a new software package for constructing large-scale chemical reaction networks in a fully automated fashion by exploring chemical reaction space with a kinetics-driven algorithm; coupled to efficient machine-learning models of activation energies for sampled elementary reactions, we show how this approach readily enables generation and kinetic characterization of networks containing ∼103 chemical species and ≃104-105 reactions. Symbolic-numeric modeling of the generated reaction networks is used to allow for flexible, efficient computation of kinetic profiles under experimentally realizable conditions such as continuously variable temperature regimes, enabling direct connection between bottom-up reaction networks and experimental observations. Highly efficient propagation of long-time-scale kinetic profiles is required for automated reaction network refinement and is enabled here by a new discrete kinetic approximation. The resulting Kinetica.jl simulation package therefore enables automated generation, characterization, and long-time-scale modeling of complex chemical reaction systems. We demonstrate this for hydrocarbon pyrolysis simulated over time scales of seconds, using transient temperature profiles representing those of tubular flow reactor experiments.

Generating High-Precision Force Fields for Molecular Dynamics Simulations to Study Chemical Reaction Mechanisms Using Molecular Configuration Transformer

Theoretical studies on chemical reaction mechanisms have been crucial in organic chemistry. Traditionally, calculating the manually constructed molecular conformations of transition states for chemical reactions using quantum chemical calculations is the most commonly used method. However, this way is heavily dependent on individual experience and chemical intuition. In our previous study, we proposed a research paradigm that used enhanced sampling in molecular dynamics simulations to study chemical reactions. This approach can directly simulate the entire process of a chemical reaction. However, the computational speed limited the use of high-precision potential energy functions for simulations. To address this issue, we presented a scheme for training high-precision force fields for molecular modeling using a previously developed graph-neural-network-based molecular model, molecular configuration transformer. This potential energy function allowed for highly accurate simulations at a low computational cost, leading to more precise calculations of the mechanism of chemical reactions. We applied this approach to study a Claisen rearrangement reaction and a carbonyl insertion reaction catalyzed by manganese.

High-throughput investigation of stability and Li diffusion of doped solid electrolytes via neural network potential without configurational knowledge

Solid electrolytes hold substantial promise as vital components of all-solid-state batteries. Enhancing their performance necessitates simultaneous improvements in their stability and lithium conductivity. These properties can be calculated using first-principles simulations, provided that the crystal structure of the material and the diffusion pathway through the material are known. However, solid electrolytes typically incorporate dopants to enhance their properties, necessitating the optimization of the dopant configuration for the simulations. Yet, performing such calculations via the first-principles approach is so costly that existing approaches usually rely on predetermined dopant configurations informed by existing knowledge or are limited to systems doped with only a few atoms. The proposed method enables the optimization of the dopant configuration with the support of neural network potential (NNP). Our approach entails the use of molecular dynamics to analyze the diffusion after the optimization of the dopant configuration. The application of our approach to Li10 MP2 S12 - x Ox (M = Ge, Si, or Sn) reproduce the experimental results well. Furthermore, analysis of the lithium diffusion pathways suggests that the activation energy of diffusion undergoes a percolation transition. This study demonstrates the effectiveness of NNPs in the systematic exploration of solid electrolytes.

Massively scalable workflows for quantum chemistry: BigChem and ChemCloud

Electronic structure theory, i.e., quantum chemistry, is the fundamental building block for many problems in computational chemistry. We present a new distributed computing framework (BigChem), which allows for an efficient solution of many quantum chemistry problems in parallel. BigChem is designed to be easily composable and leverages industry-standard middleware (e.g., Celery, RabbitMQ, and Redis) for distributed approaches to large scale problems. BigChem can harness any collection of worker nodes, including ones on cloud providers (such as AWS or Azure), local clusters, or supercomputer centers (and any mixture of these). BigChem builds upon MolSSI packages, such as QCEngine to standardize the operation of numerous computational chemistry programs, demonstrated here with Psi4, xtb, geomeTRIC, and TeraChem. BigChem delivers full utilization of compute resources at scale, offers a programable canvas for designing sophisticated quantum chemistry workflows, and is fault tolerant to node failures and network disruptions. We demonstrate linear scalability of BigChem running computational chemistry workloads on up to 125 GPUs. Finally, we present ChemCloud, a web API to BigChem and successor to TeraChem Cloud. ChemCloud delivers scalable and secure access to BigChem over the Internet.

Locating Transition States by Variational Reaction Path Optimization with an Energy-Derivative-Free Objective Function

Locating transition states is essential for understanding molecular reactions. We propose a double-ended transition state search method by revisiting a variational reaction path optimization method known as the MaxFlux method. Although its original purpose is to add temperature effects to reaction paths, we conversely let the temperature approach zero to obtain an asymptotically exact minimum energy path and its corresponding transition state in variational formalism with an energy-derivative-free objective function. Using several numerical techniques to directly optimize the objective function, the present method reliably finds transition states with low computational cost. In particular, only three force evaluations per iteration are sufficient. This is confirmed on a variety of molecular reactions where the nudged elastic band method often fails. The present method is implemented in Python using the Atomic Simulation Environment and is available on GitHub.

Surface-Accelerated String Method for Locating Minimum Free Energy Paths

We present a surface-accelerated string method (SASM) to efficiently optimize low-dimensional reaction pathways from the sampling performed with expensive quantum mechanical/molecular mechanical (QM/MM) Hamiltonians. The SASM accelerates the convergence of the path using the aggregate sampling obtained from the current and previous string iterations, whereas approaches like the string method in collective variables (SMCV) or the modified string method in collective variables (MSMCV) update the path only from the sampling obtained from the current iteration. Furthermore, the SASM decouples the number of images used to perform sampling from the number of synthetic images used to represent the path. The path is optimized on the current best estimate of the free energy surface obtained from all available sampling, and the proposed set of new simulations is not restricted to being located along the optimized path. Instead, the umbrella potential placement is chosen to extend the range of the free energy surface and improve the quality of the free energy estimates near the path. In this manner, the SASM is shown to improve the exploration for a minimum free energy pathway in regions where the free energy surface is relatively flat. Furthermore, it improves the quality of the free energy profile when the string is discretized with too few images. We compare the SASM, SMCV, and MSMCV using 3 QM/MM applications: a ribozyme methyltransferase reaction using 2 reaction coordinates, the 2'-O-transphosphorylation reaction of Hammerhead ribozyme using 3 reaction coordinates, and a tautomeric reaction in B-DNA using 5 reaction coordinates. We show that SASM converges the paths using roughly 3 times less sampling than the SMCV and MSMCV methods. All three algorithms have been implemented in the FE-ToolKit package made freely available.

Exploration of biochemical reactivity with a QM/MM growing string method

In this work, we have implemented the single-ended growing string method using a hybrid internal/Cartesian coordinate scheme within our in-house QM/MM package, QoMMMa, representing the first implementation of the growing string method in the QM/MM framework. The goal of the implementation was to facilitate generation of QM/MM reaction pathways with minimal user input, and also to improve the quality of the pathways generated as compared to the widely used adiabatic mapping approach. We have validated the algorithm against a reaction which has been studied extensively in previous computational investigations - the Claisen rearrangement catalysed by chorismate mutase. The nature of the transition state and the height of the barrier was predicted well using our algorithm, where more than 88% of the pathways generated were deemed to be of production quality. Directly compared to using adiabatic mapping, we found that while our QM/MM single-ended growing string method is slightly less efficient, it readily produces reaction pathways with fewer discontinuites and thus minimises the need for involved remapping of unsatisfactory energy profiles.

Improved Initialization of Optimal Path Calculations Using Sequential Traversal over the Image-Dependent Pair Potential Surface

In reaction path optimization, such as the calculation of a minimum energy path (MEP) between given reactant and product configurations of atoms, it is advantageous to start with an initial guess where the close proximity of atoms is avoided and bonds are not unnecessarily broken only to be reformed later. When the configurations of the atoms are described with Cartesian coordinates, a linear interpolation between the end points can be problematic, and a better option is provided by the so-called image dependent pair potential (IDPP) approach where interpolated pairwise distances are generated to form an objective function that can be used to construct an improved initial path. When started with a linear interpolation, this method can, however, still lead to unnecessary bond breaking in, for example, reactions in which a molecular subgroup undergoes significant rotation. In the method presented here, this problem is addressed by constructing the path gradually, introducing images sequentially starting from the vicinity of the end points while the distance between images in the central region is larger. The distribution of images is controlled by systematically scaling the tightness of springs acting between the images until the desired number of images is obtained, and they are evenly spaced. This procedure generates an initial path on the IDPP surface, a task that requires negligible computational effort, as no evaluation of the energy of the system is needed. The calculation of the MEP, typically using electronic structure calculations, is then subsequently carried out in a way that makes efficient use of parallel computing with the nudged elastic band method. Several examples of reactions are given where the linear interpolation IDPP (LI-IDPP) method yields problematic paths with unnecessary bond breaking in some of the intermediate images, while the sequential IDPP (S-IDPP) method yields paths that are significantly closer to realistic MEPs.

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.

Δ2 machine learning for reaction property prediction

The emergence of Δ-learning models, whereby machine learning (ML) is used to predict a correction to a low-level energy calculation, provides a versatile route to accelerate high-level energy evaluations at a given geometry. However, Δ-learning models are inapplicable to reaction properties like heats of reaction and activation energies that require both a high-level geometry and energy evaluation. Here, a Δ2-learning model is introduced that can predict high-level activation energies based on low-level critical-point geometries. The Δ2 model uses an atom-wise featurization typical of contemporary ML interatomic potentials (MLIPs) and is trained on a dataset of ∼167 000 reactions, using the GFN2-xTB energy and critical-point geometry as a low-level input and the B3LYP-D3/TZVP energy calculated at the B3LYP-D3/TZVP critical point as a high-level target. The excellent performance of the Δ2 model on unseen reactions demonstrates the surprising ease with which the model implicitly learns the geometric deviations between the low-level and high-level geometries that condition the activation energy prediction. The transferability of the Δ2 model is validated on several external testing sets where it shows near chemical accuracy, illustrating the benefits of combining ML models with readily available physical-based information from semi-empirical quantum chemistry calculations. Fine-tuning of the Δ2 model on a small number of Gaussian-4 calculations produced a 35% accuracy improvement over DFT activation energy predictions while retaining xTB-level cost. The Δ2 model approach proves to be an efficient strategy for accelerating chemical reaction characterization with minimal sacrifice in prediction accuracy.

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.

Comprehensive exploration of graphically defined reaction spaces

Existing reaction transition state (TS) databases are comparatively small and lack chemical diversity. Here, this data gap has been addressed using the concept of a graphically-defined model reaction to comprehensively characterize a reaction space associated with C, H, O, and N containing molecules with up to 10 heavy (non-hydrogen) atoms. The resulting dataset is composed of 176,992 organic reactions possessing at least one validated TS, activation energy, heat of reaction, reactant and product geometries, frequencies, and atom-mapping. For 33,032 reactions, more than one TS was discovered by conformational sampling, allowing conformational errors in TS prediction to be assessed. Data is supplied at the GFN2-xTB and B3LYP-D3/TZVP levels of theory. A subset of reactions were recalculated at the CCSD(T)-F12/cc-pVDZ-F12 and ωB97X-D2/def2-TZVP levels to establish relative errors. The resulting collection of reactions and properties are called the Reaction Graph Depth 1 (RGD1) dataset. RGD1 represents the largest and most chemically diverse TS dataset published to date and should find immediate use in developing novel machine learning models for predicting reaction properties.

Multireference Generalization of the Weighted Thermodynamic Perturbation Method

We describe the generalized weighted thermodynamic perturbation (gwTP) method for estimating the free energy surface of an expensive "high-level" potential energy function from the umbrella sampling performed with multiple inexpensive "low-level" reference potentials. The gwTP method is a generalization of the weighted thermodynamic perturbation (wTP) method developed by Li and co-workers [J. Chem. Theory Comput. 2018, 14, 5583-5596] that uses a single "low-level" reference potential. The gwTP method offers new possibilities in model design whereby the sampling generated from several low-level potentials may be combined (e.g., specific reaction parameter models that might have variable accuracy at different stages of a multistep reaction). The gwTP method is especially well suited for use with machine learning potentials (MLPs) that are trained against computationally expensive ab initio quantum mechanical/molecular mechanical (QM/MM) energies and forces using active learning procedures that naturally produce multiple distinct neural network potentials. Simulations can be performed with greater sampling using the fast MLPs and then corrected to the ab initio level using gwTP. The capabilities of the gwTP method are demonstrated by creating reference potentials based on the MNDO/d and DFTB2/MIO semiempirical models supplemented with the "range-corrected deep potential" (DPRc). The DPRc parameters are trained to ab initio QM/MM data, and the potentials are used to calculate the free energy surface of stepwise mechanisms for nonenzymatic RNA 2'-O-transesterification model reactions. The extended sampling made possible by the reference potentials allows one to identify unequilibrated portions of the simulations that are not always evident from the short time scale commonly used with ab initio QM/MM potentials. We show that the reference potential approach can yield more accurate ab initio free energy predictions than the wTP method or what can be reasonably afforded from explicit ab initio QM/MM sampling.

Engineering Electro-Optic BaTiO3 Nanocrystals via Efficient Doping

Electro-optic (EO) modulators provide electrical-to-optical signal conversion relevant to optical communications. Barium titanate (BaTiO₃ ) is a promising material system for EO modulation in light of its optical ultrafast nonlinearity, low optical loss, and high refractive index. To enhance further its spontaneous polarization, BaTiO₃ can be doped at the Ba and Ti sites; however, doping is often accompanied by ion migration, which diminishes EO performance. Here, donor-acceptor doping and its effect on EO efficiency are investigated, finding that La-doped BaTiO₃ achieves an EO coefficient of 42 pm V^-1 at 1 kHz, fully twice that of the pristine specimen; however, it is also observed that, with this single-element doping, the EO response falls off rapidly with frequency. From impedance spectroscopy, it is found that frequency-dependent EO is correlated with ion migration. Density functional theory calculations predict that the ion-migration barrier decreases with La³⁺ doping but can be recovered with further Mn²⁺ doping, a finding that prompts to prevent ion migration by incorporating Mn²⁺ into the Ti-site to compensate for the charge imbalance.

Automated input structure generation for single-ended reaction path optimizations

The exploration of a reaction network requires highly automated workflows to avoid error-prone and time-consuming manual steps. In this respect, a major bottleneck is the search for transition-state (TS) structures, which frequently fails and, therefore, makes (manual) revision necessary. In this work, we present a technique for obtaining suitable input structures for automated TS searches based on single-ended reaction path optimization algorithms, which makes subsequent TS searches via this method significantly more robust. First, possible input structures are generated based on the spatial alignment of the reactants. The appropriate orientation of reacting groups is achieved via stepwise rotations along selected torsional degrees of freedom. Second, a ranking of the obtained structures is performed according to selected geometric criteria. The main goals are to properly align the reactive atoms, to avoid hindrance within the reaction channel and to resolve steric clashes between the reactants. The developed procedure has been carefully tested on a variety of examples and provides suitable input structures for TS searches within seconds. The method is in daily use in an industrial setting.

Fast Predictions of Reaction Barrier Heights: Toward Coupled-Cluster Accuracy

Quantitative estimates of reaction barriers are essential for developing kinetic mechanisms and predicting reaction outcomes. However, the lack of experimental data and the steep scaling of accurate quantum calculations often hinder the ability to obtain reliable kinetic values. Here, we train a directed message passing neural network on nearly 24,000 diverse gas-phase reactions calculated at CCSD(T)-F12a/cc-pVDZ-F12//ωB97X-D3/def2-TZVP. Our model uses 75% fewer parameters than previous studies, an improved reaction representation, and proper data splits to accurately estimate performance on unseen reactions. Using information from only the reactant and product, our model quickly predicts barrier heights with a testing MAE of 2.6 kcal mol^-1 relative to the coupled-cluster data, making it more accurate than a good density functional theory calculation. Furthermore, our results show that future modeling efforts to estimate reaction properties would significantly benefit from fine-tuning calibration using a transfer learning technique. We anticipate this model will accelerate and improve kinetic predictions for small molecule chemistry.

Elastic Image Pair Method for Finding Transition States on Potential Energy Surfaces Using Only First Derivatives

Herein, an elastic image pair (EIP) method is proposed to search transition states between two potential-energy minima using only first derivatives. In this method, two images are generated, and the spring forces are added to the images to control the distance between the two images. Transition states are reached when the force and the distance of the image pair are both converged. A set of test molecules is optimized using the EIP method, which shows its efficiency in transition state searching compared to other methods. This new method is more stable and reliable in finding transition states with much less computations.

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.

Serine and Cysteine Peptidases: So Similar, Yet Different. How the Active-Site Electrostatics Facilitates Different Reaction Mechanisms

The catalytic mechanisms of serine and cysteine peptidases are similar: the proton of the nucleophile (serine or cysteine) is transferred to the catalytic histidine, and the nucleophile attacks the substrate for cleavage. However, they differ in an important aspect: cysteine peptidases form a stable ion-pair intermediate in a stepwise mechanism, while serine peptidases follow a concerted mechanism. While it is known that a positive electrostatic potential at the active site of cysteine peptidases stabilizes the cysteine anion in the ion-pair state, the physical basis of the concerted mechanism of serine peptidases is poorly understood. In this work, we use continuum electrostatic analysis and quantum mechanical/molecular mechanical (QM/MM) simulations to demonstrate that a destabilization of an anionic serine by a negative electrostatic potential in combination with a compact active site geometry facilitates a concerted mechanism in serine peptidases. Moreover, we show that an anionic serine would destabilize the protein significantly compared to an anionic cysteine in cysteine peptidases, which underlines the necessity of a concerted mechanism for serine peptidases. On the basis of our calculations on an inactive serine mutant of a natural cysteine peptidase, we show that the energy barrier for the catalytic mechanism can be substantially decreased by introducing a negative electrostatic potential and by reducing the relevant distances indicating that these parameters are essential for the activity of serine peptidases. Our work demonstrates that the concerted mechanism of serine peptidases represents an evolutionary innovative way to perform catalysis without the energetically expensive need to stabilize the anionic serine. In contrast in cysteine peptidases, the anionic cysteine is energetically easily accessible and it is a very efficient nucleophile, making these peptidases mechanistically simple. However, a cysteine is highly oxygen sensitive, which is problematic in an aerobic environment. On the basis of the analysis in this work, we suggest that serine peptidases represent an oxygen-insensitive alternative to cysteine peptidases.

Structural and Biophysical Analysis of the Phytochelatin-Synthase-Like Enzyme from Nostoc sp. Shows That Its Protease Activity is Sensitive to the Redox State of the Substrate

Phytochelatins (PCs) are nonribosomal thiol-rich oligopeptides synthetized from glutathione (GSH) in a γ-glutamylcysteinyl transpeptidation reaction catalyzed by PC synthases (PCSs). Ubiquitous in plant and present in some invertebrates, PCSs are involved in metal detoxification and homeostasis. The PCS-like enzyme from the cyanobacterium Nostoc sp. (NsPCS) is considered to be an evolutionary precursor enzyme of genuine PCSs because it shows sufficient sequence similarity for homology to the catalytic domain of the eukaryotic PCSs and shares the peptidase activity consisting in the deglycination of GSH. In this work, we investigate the catalytic mechanism of NsPCS by combining structural, spectroscopic, thermodynamic, and theoretical techniques. We report several crystal structures of NsPCS capturing different states of the catalyzed chemical reaction: (i) the structure of the wild-type enzyme (wt-NsPCS); (ii) the high-resolution structure of the γ-glutamyl-cysteine acyl-enzyme intermediate (acyl-NsPCS); and (iii) the structure of an inactive variant of NsPCS, with the catalytic cysteine mutated into serine (C70S-NsPCS). We characterize NsPCS as a relatively slow enzyme whose activity is sensitive to the redox state of the substrate. Namely, NsPCS is active with reduced glutathione (GSH), but is inhibited by oxidized glutathione (GSSG) because the cleavage product is not released from the enzyme. Our biophysical analysis led us to suggest that the biological function of NsPCS is being a part of a redox sensing system. In addition, we propose a mechanism how PCS-like enzymes may have evolved toward genuine PCS enzymes.

Metals (Al, Fe, Zn) doped in single walled carbon nanotubes for catalytic oxidation of H2O to H2O2: a theoretical investigation

A theoretical study on the reaction mechanism of oxygen reduction of metal (Al, Zn, Fe) supported carbon nanotubes to hydrogen peroxide.

Progress towards machine learning reaction rate constants

Quantum and classical reaction rate constant calculations come at the cost of exploring potential energy surfaces. Due to the "curse of dimensionality", their evaluation quickly becomes unfeasible as the system size grows. Machine learning algorithms can accelerate the calculation of reaction rate constants by predicting them using low cost input features. In this perspective, we briefly introduce supervised machine learning algorithms in the context of reaction rate constant prediction. We discuss existing and recently created kinetic datasets and input feature representations as well as the use and design of machine learning algorithms to predict reaction rate constants or quantities required for their computation. Amongst these, we first describe the use of machine learning to predict activation, reaction, solvation and dissociation energies. We then look at the use of machine learning to predict reactive force field parameters, reaction rate constants as well as to help accelerate the search for minimum energy paths. Lastly, we provide an outlook on areas which have yet to be explored so as to improve and evaluate the use of machine learning algorithms for chemical reaction rate constants.

Machine Learning to Predict Diels-Alder Reaction Barriers from the Reactant State Electron Density

Reaction barriers are key to our understanding of chemical reactivity and catalysis. Certain reactions are so seminal in chemistry that countless variants, with or without catalysts, have been studied, and their barriers have been computed or measured experimentally. This wealth of data represents a perfect opportunity to leverage machine learning models, which could quickly predict barriers without explicit calculations or measurement. Here, we show that the topological descriptors of the quantum mechanical charge density in the reactant state constitute a set that is both rigorous and continuous and can be used effectively for the prediction of reaction barrier energies to a high degree of accuracy. We demonstrate this on the Diels-Alder reaction, highly important in biology and medicinal chemistry, and as such, studied extensively. This reaction exhibits a range of barriers as large as 270 kJ/mol. While we trained our single-objective supervised (labeled) regression algorithms on simpler Diels-Alder reactions in solution, they predict reaction barriers also in significantly more complicated contexts, such a Diels-Alder reaction catalyzed by an artificial enzyme and its evolved variants, in agreement with experimental changes in k_cat. We expect this tool to apply broadly to a variety of reactions in solution or in the presence of a catalyst, for screening and circumventing heavily involved computations or experiments.

A modified nudged elastic band algorithm with adaptive spring lengths

We present a modified version of the nudged elastic band (NEB) algorithm to find minimum energy paths connecting two known configurations. We show that replacing the harmonic band-energy term with a discretized version of the Onsager-Machlup action leads to a NEB algorithm with adaptive spring lengths that automatically increase the resolution of the minimum energy path around the saddle point of the potential energy surface. The method has the same computational cost per optimization step of the standard NEB algorithm and does not introduce additional parameters. We present applications to the isomerization of alanine dipeptide, the elimination of hydrogen from ethane, and the healing of a 5-77-5 defect in graphene.

Nudged Elastic Band Method for Molecular Reactions Using Energy-Weighted Springs Combined with Eigenvector Following

The climbing image nudged elastic band method (CI-NEB) is used to identify reaction coordinates and to find saddle points representing transition states of reactions. It can make efficient use of parallel computing as the calculations of the discretization points, the so-called images, can be carried out simultaneously. In typical implementations, the images are distributed evenly along the path by connecting adjacent images with equally stiff springs. However, for systems with a high degree of flexibility, this can lead to poor resolution near the saddle point. By making the spring constants increase with energy, the resolution near the saddle point is improved. To assess the performance of this energy-weighted CI-NEB method, calculations are carried out for a benchmark set of 121 molecular reactions. The performance of the method is analyzed with respect to the input parameters. Energy-weighted springs are found to greatly improve performance and result in successful location of the saddle points in less than a thousand energy and force evaluations on average (about a hundred per image) using the same set of parameter values for all of the reactions. Even better performance is obtained by stopping the calculation before full convergence and complete the saddle point search using an eigenvector following method starting from the location of the climbing image. This combination of methods, referred to as NEB-TS, turns out to be robust and highly efficient as it reduces the average number of energy and force evaluations down to a third, to 305. An efficient and flexible implementation of these methods has been made available in the ORCA software.