Conformational Sampling for Transition State Searches on a Computational Budget

Graph to Activation Energy Models Easily Reach Irreducible Errors but Show Limited Transferability

Activation energy characterization of competing reactions is a costly but crucial step for understanding the kinetic relevance of distinct reaction pathways, product yields, and myriad other properties of reacting systems. The standard methodology for activation energy characterization has historically been a transition state search using the highest level of theory that can be afforded. However, recently, several groups have popularized the idea of predicting activation energies directly based on nothing more than the reactant and product graphs, a sufficiently complex neural network, and a broad enough data set. Here, we have revisited this task using the recently developed Reaction Graph Depth 1 (RGD1) transition state data set and several newly developed graph attention architectures. All of these new architectures achieve similar state-of-the-art results of ∼4 kcal/mol mean absolute error on withheld testing sets of reactions but poor performance on external testing sets composed of reactions with differing mechanisms, reaction molecularity, or reactant size distribution. Limited transferability is also shown to be shared by other contemporary graph to activation energy architectures through a series of case studies. We conclude that an array of standard graph architectures can already achieve results comparable to the irreducible error of available reaction data sets but that out-of-distribution performance remains poor.

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.

Large Computational Survey of Intrinsic Reactivity of Aromatic Carbon Atoms with Respect to a Model Aldehyde Oxidase

Aldehyde oxidase (AOX) and other related molybdenum-containing enzymes are known to oxidize the C-H bonds of aromatic rings. This process contributes to the metabolism of pharmaceutical compounds and, therefore, is of vital importance to drug pharmacokinetics. The present work describes an automated computational workflow and its use for the prediction of intrinsic reactivity of small aromatic molecules toward a minimal model of the active site of AOX. The workflow is based on quantum chemical transition state searches for the underlying single-step oxidation reaction, where the automated protocol includes identification of unique aromatic C-H bonds, creation of three-dimensional reactant and product complex geometries via a templating approach, search for a transition state, and validation of reaction end points. Conformational search on the reactants, products, and the transition states is performed. The automated procedure has been validated on previously reported transition state barriers and was used to evaluate the intrinsic reactivity of nearly three hundred heterocycles commonly found in approved drug molecules. The intrinsic reactivity of more than 1000 individual aromatic carbon sites is reported. Stereochemical and conformational aspects of the oxidation reaction, which have not been discussed in previous studies, are shown to play important roles in accurate modeling of the oxidation reaction. Observations on structural trends that determine the reactivity are provided and rationalized.

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.

Computational Study Focusing on a Comprehensive Conformational Analysis of Transition States for Aza-Spiro Ring Formations with N-Alkoxyamides

An accurate understanding of conformations in transition states is a critical piece in the theoretical analysis of complex molecular reactions. In this study, we investigated conformationally diverse transition states during intramolecular aza-spiro ring formation with an allylsilane moiety and N-alkoxy iminium ion, a key reaction in the synthesis of fasicularin by Sato and Chida et al., and identified the origins of stereoselectivity of the cyclization. A large number of conformational isomers with forming C-C bonds were comprehensively analyzed using Cremer-Pople puckering parameters. It was found that the conformations of the transition states had different puckering preferences depending on the reactant's double-bond geometry and the product's stereochemical configuration. Furthermore, an asymmetric aza-spiro cyclization with a tolyl group as a chiral auxiliary was investigated, showing that conformational anchoring by both a CH-O hydrogen bond and the CH-π interaction was critical for the asymmetric induction.

Thermally Accessible Prebiotic Pathways for Forming Ribonucleic Acid and Protein Precursors from Aqueous Hydrogen Cyanide

The search for prebiotic chemical pathways to biologically relevant molecules is a long-standing puzzle that has generated a menagerie of competing hypotheses with limited experimental prospects for falsification. However, the advent of computational network exploration methodologies has created the opportunity to compare the kinetic plausibility of various channels and even propose new pathways. Here, the space of organic molecules that can be formed within four polar or pericyclic reactions from water and hydrogen cyanide (HCN), two established prebiotic candidates for generating biological precursors, was comprehensively explored with a state-of-the-art exploration algorithm. A surprisingly diverse reactivity landscape was revealed within just a few steps of these simple molecules. Reaction pathways to several biologically relevant molecules were discovered involving lower activation energies and fewer reaction steps compared with recently proposed alternatives. Accounting for water-catalyzed reactions qualitatively affects the interpretation of the network kinetics. The case-study also highlights omissions of simpler and lower barrier reaction pathways to certain products by other algorithms that qualitatively affect the interpretation of HCN reactivity.

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.

Algorithmic Explorations of Unimolecular and Bimolecular Reaction Spaces

Algorithmic reaction exploration based on transition state searches has already made inroads into many niche applications, but its potential as a general-purpose tool is still largely unrealized. Computational cost and the absence of benchmark problems involving larger molecules remain obstacles to further progress. Here an ultra-low cost exploration algorithm is implemented and used to explore the reactivity of unimolecular and bimolecular reactants, comprising a total of 581 reactions involving 51 distinct reactants. The algorithm discovers all established reaction pathways, where such comparisons are possible, while also revealing a much richer reactivity landscape, including lower barrier reaction pathways and a strong dependence of reaction conformation in the apparent barriers of the reported reactions. The diversity of these benchmarks illustrate that reaction exploration algorithms are approaching general-purpose capability.

Portable Models for Entropy Effects on Kinetic Selectivity

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