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.

Generative Models as an Emerging Paradigm in the Chemical Sciences.

Traditional computational approaches to design chemical species are limited by the need to compute properties for a vast number of candidates, e.g., by discriminative modeling. Therefore, inverse design methods aim to start from the desired property and optimize a corresponding chemical structure. From a machine learning viewpoint, the inverse design problem can be addressed through so-called generative modeling. Mathematically, discriminative models are defined by learning the probability distribution function of properties given the molecular or material structure. In contrast, a generative model seeks to exploit the joint probability of a chemical species with target characteristics. The overarching idea of generative modeling is to implement a system that produces novel compounds that are expected to have a desired set of chemical features, effectively sidestepping issues found in the forward design process. In this contribution, we overview and critically analyze popular generative algorithms like generative adversarial networks, variational autoencoders, flow, and diffusion models. We highlight key differences between each of the models, provide insights into recent success stories, and discuss outstanding challenges for realizing generative modeling discovered solutions in chemical applications.

Two-Dimensional Energy Histograms as Features for Machine Learning to Predict Adsorption in Diverse Nanoporous Materials.

A major obstacle for machine learning (ML) in chemical science is the lack of physically informed feature representations that provide both accurate prediction and easy interpretability of the ML model. In this work, we describe adsorption systems using novel two-dimensional energy histogram (2D-EH) features, which are obtained from the probe-adsorbent energies and energy gradients at grid points located throughout the adsorbent. The 2D-EH features encode both energetic and structural information of the material and lead to highly accurate ML models (coefficient of determination R2 ∼ 0.94-0.99) for predicting single-component adsorption capacity in metal-organic frameworks (MOFs). We consider the adsorption of spherical molecules (Kr and Xe), linear alkanes with a wide range of aspect ratios (ethane, propane, n-butane, and n-hexane), and a branched alkane (2,2-dimethylbutane) over a wide range of temperatures and pressures. The interpretable 2D-EH features enable the ML model to learn the basic physics of adsorption in pores from the training data. We show that these MOF-data-trained ML models are transferrable to different families of amorphous nanoporous materials. We also identify several adsorption systems where capillary condensation occurs, and ML predictions are more challenging. Nevertheless, our 2D-EH features still outperform structural features including those derived from persistent homology. The novel 2D-EH features may help accelerate the discovery and design of advanced nanoporous materials using ML for gas storage and separation in the future.

Machine Learning Interatomic Potentials and Long-Range Physics.

Advances in machine learned interatomic potentials (MLIPs), such as those using neural networks, have resulted in short-range models that can infer interaction energies with near ab initio accuracy and orders of magnitude reduced computational cost. For many atom systems, including macromolecules, biomolecules, and condensed matter, model accuracy can become reliant on the description of short- and long-range physical interactions. The latter terms can be difficult to incorporate into an MLIP framework. Recent research has produced numerous models with considerations for nonlocal electrostatic and dispersion interactions, leading to a large range of applications that can be addressed using MLIPs. In light of this, we present a Perspective focused on key methodologies and models being used where the presence of nonlocal physics and chemistry are crucial for describing system properties. The strategies covered include MLIPs augmented with dispersion corrections, electrostatics calculated with charges predicted from atomic environment descriptors, the use of self-consistency and message passing iterations to propagated nonlocal system information, and charges obtained via equilibration schemes. We aim to provide a pointed discussion to support the development of machine learning-based interatomic potentials for systems where contributions from only nearsighted terms are deficient.

Temperature Effects in Flexible Adsorption Processes for Amorphous Microporous Polymers.

A collection of atomistic molecular simulations is reported that illustrate the impact of adsorption temperature on species uptake and adsorbate-induced structural rearrangement for amorphous polymers of intrinsic microporosity. Temperature-sensitive structural rearrangement is evaluated by contrasting two methods: standard grand canonical Monte Carlo simulations using a rigid framework approximation and a combined Monte Carlo/molecular dynamics approach that fully incorporates framework flexibility. We report single-component gas phase adsorption isotherms for CH4, C2H4, C2H6, C3H6, C3H8, and CO2 across a temperature range of 250-400 K for models of an archetypal polymer of intrinsic microporosity, PIM-1. A quadratic model is presented that captures two main mechanisms of temperature-dependent adsorption-induced deformation of PIM-1 up to a relative swelling of 1.15: thermal expansion and an increased propensity to swell as a function of species uptake. Two case studies are reported that highlight the critical role of operating temperature in industrial storage and separation applications. The first study focuses on methane storage and delivery applications using a pressure-temperature swing adsorption application (PTSA). We demonstrate that larger working capacities are accompanied by increased volumetric strain between adsorption-desorption steps. The second case study considers PIM-1 as an adsorbent to separate an exemplar ternary syngas mixture at operating temperatures ranging 300-550 K. A temperature threshold of ∼400 K is identified, beyond which adsorption-induced PIM-1 swelling is negligible and the solubility selectivity-loading curve transitions to exhibiting a nearly linear relationship.

PEGDA hydrogel structure from semi-dilute concentrations: insights from experiments and molecular simulations.

The efficacy of hydrogel materials used in biomedical applications is dependent on polymer network topology and the structure of water-laden pore space. Hydrogel microstructure can be tuned by adjusting synthesis parameters such as macromer molar mass and concentration. Moreover, hydrogels beyond dilute conditions are needed to produce mechanically robust and dense networks for tissue engineering and/or drug delivery systems. Thus, this study utilizes a combined experimental and molecular simulation approach to characterize structural features for 4.8 and 10 kDa poly (ethylene glycol) diacrylate (PEGDA) hydrogels formed from a range of semi-dilute solution concentrations. The connection between chain-chain interactions in polymer solutions, hydrogel structure, and equilibrium swelling behavior is presented. Bulk rheology analysis revealed an entanglement concentration for PEGDA pre-gel solutions around 28 wt% for both macromers studied. A similar transition in swelling behavior was revealed around the same concentration where hydrogel capacity to retain water was drastically reduced. To understand this transition, the hydrogel structure was characterized using the swollen polymer network hypothesis and compared to pore size distributions from molecular dynamics simulations. We find in both approaches a structural transition concentration at the hydrogel swelling inflection point that is comparable to the entanglement concentration. Calculated mesh sizes from theory are compared with computationally determined average maximum pore diameters; mesh sizes from theory yielded greater feature sizes across all concentrations considered. Molecular simulations are further used to assess pore dynamics, which are shown to vary in distribution shape and number of modes compared to the time-averaged hydrogel pore features. Altogether, this work provides insights into hydrogel network features and their dynamic behavior at physiological conditions (37 °C) as a basis for hydrogel design beyond dilute conditions for biomedical applications.

Incorporating Flexibility Effects into Metal-Organic Framework Adsorption Simulations Using Different Models.

High-throughput calculations based on molecular simulations to predict the adsorption of molecules inside metal-organic frameworks (MOFs) have become a useful complement to experimental efforts to identify promising adsorbents for chemical separations and storage. For computational convenience, all existing efforts of this kind have relied on simulations in which the MOF is approximated as rigid. In this paper, we use extensive adsorption-relaxation simulations that fully include MOF flexibility effects to explore the validity of the rigid framework approximation. We also examine the accuracy of several approximate methods to incorporate framework flexibility that are more computationally efficient than adsorption-relaxation calculations. We first benchmark various models of MOF flexibility for four MOFs with well-established CO2 experimental consensus isotherms. We then consider a range of adsorption properties, including Henry's constants, nondilute loadings, and adsorption selectivity, for seven adsorbates in 15 MOFs randomly selected from the CoRE MOF database. Our results indicate that in many MOFs adsorption-relaxation simulations are necessary to make quantitative predictions of adsorption, particularly for adsorption at dilute concentrations, although more standard calculations based on rigid structures can provide useful information. Finally, we investigate whether a correlation exists between the elastic properties of empty MOFs and the importance of including framework flexibility in making accurate predictions of molecular adsorption. Our results did not identify a simple correlation of this type.

New Pd(II) hemichelates devoid of incipient bridging COPd interactions.

In organometallic chemistry the commonly known Sidgwick-Langmuir 18 electron rule is constantly being probed for further discovery of molecular compounds that arise as exceptions. The present study examines the formation and the structure of three novel hemichelates of Pd(ii) derived from the reaction of in situ-formed indene and hydrophenanthrene-based organometallic anions with three different µ-chloro-bridged palladacycles. Electronic structure and interaction behavior have been calculated with methods of the density functional theory at the (ZORA) MetaGGA-D TPSS-D3(BJ), GGA-D PBE-D3(BJ), and hybrid PBE0-dDsC dispersion corrected levels, all with the implementation of all electron triple zeta single polarization basis set. A particular focus of the theoretical investigation was made on the nature of the interaction between the [Cr(CO)3] moiety and the Pd(ii) centers, which according to X-ray diffraction analyses lack significant incipient bridging COPd character. Structures were further assessed - Natural Bonding Orbitals (NBO), Quantum Theory of Atoms in Molecules (QTAIM), and Extended Transition State with Natural Orbitals for Chemical Valence (ETS-NOCV) analysis methods. As a result, intramolecular interactions of interest, primarily around the Pd atom, were analyzed as a measure of natural atomic orbital (NAO) contributions to the natural bonding orbital (NBO) formation, QTAIM analysis with special attention to the bonding critical points (BCPs), as well as energetic analysis of intramolecular interaction forces by Energy Decomposition Analysis (EDA). Theoretical analyses confirm that attractive electrostatics dominate the stabilization of Pd(ii) hemichelates. In the case of complexes , and we expand the known amount of 14 electron transition metal complexes that can be synthesized via reliable synthetic methods. However, complex presented some means of stability but was more reactive to moisture and air under laboratory conditions and escaped thorough analytical characterization.