Exchange Spin Coupling from Gaussian Process Regression

Machine Learning Isotropic g Values of Radical Polymers

Methods for electronic structure computations, such as density functional theory (DFT), are routinely used for the calculation of spectroscopic parameters to establish and validate structure-parameter correlations. DFT calculations, however, are computationally expensive for large systems such as polymers. This work explores the machine learning (ML) of isotropic g values, giso, obtained from electron paramagnetic resonance (EPR) experiments of an organic radical polymer. An ML model based on regression trees is trained on DFT-calculated g values of poly(2,2,6,6-tetramethylpiperidinyloxy-4-yl methacrylate) (PTMA) polymer structures extracted from different time frames of a molecular dynamics trajectory. The DFT-derived g values, gisocalc, for different radical densities of PTMA, are compared against experimentally derived g values obtained from in operando EPR measurements of a PTMA-based organic radical battery. The ML-predicted giso values, gisopred, were compared with gisocalc to evaluate the performance of the model. Mean deviations of gisopred from gisocalc were found to be on the order of 0.0001. Furthermore, a performance evaluation on test structures from a separate MD trajectory indicated that the model is sensitive to the radical density and efficiently learns to predict giso values even for radical densities that were not part of the training data set. Since our trained model can reproduce the changes in giso along the MD trajectory and is sensitive to the extent of equilibration of the polymer structure, it is a promising alternative to computationally more expensive DFT methods, particularly for large systems that cannot be easily represented by a smaller model system.

Developing Cheap but Useful Machine Learning-Based Models for Investigating High-Entropy Alloy Catalysts

This work aims to address the challenge of developing interpretable ML-based models when access to large-scale computational resources is limited. Using CoMoFeNiCu high-entropy alloy catalysts as an example, we present a cost-effective workflow that synergistically combines descriptor-based approaches, machine learning-based force fields, and low-cost density functional theory (DFT) calculations to predict high-quality adsorption energies for H, N, and NHx (x = 1, 2, and 3) adsorbates. This is achieved using three specific modifications to typical DFT workflows including: (1) using a sequential optimization protocol, (2) developing a new geometry-based descriptor, and (3) repurposing the already-available low-cost DFT optimization trajectories to develop a ML-FF. Taken together, this study illustrates how cost-effective DFT calculations and appropriately designed descriptors can be used to develop cheap but useful models for predicting high-quality adsorption energies at significantly lower computational costs. We anticipate that this resource-efficient philosophy may be broadly relevant to the larger surface catalysis community.

Quantitative Structure-Reactivity Relationships for Synthesis Planning: The Benzhydrylium Case

Selective and feasible reactions are among the top targets in synthesis planning. Mayr's approach to quantifying chemical reactivity has greatly facilitated the planning process, but reactivity parameters for new compounds require time-consuming experiments. In the past decade, data-driven modeling has been gaining momentum in the field, as it shows promise in terms of efficient reactivity prediction. However, state-of-the-art models use quantum chemical data as input, which prevent access to real-time planning in organic synthesis. Here, we present a novel data-driven workflow for predicting reactivity parameters of molecules that takes only structural information as input, enabling de facto real-time reactivity predictions. We use the well-understood chemical space of benzhydrylium ions as an example to demonstrate the functionality of our approach and the performance of the resulting quantitative structure-reactivity relationships (QSRRs). Our results suggest that it is straightforward to build low-cost QSRR models that are accurate, interpretable, and transferable to unexplored systems within a given scope of application. Moreover, our QSRR approach suggests that Hammett σ parameters are only approximately additive.

Learning Conductance: Gaussian Process Regression for Molecular Electronics

Experimental studies of charge transport through single molecules often rely on break junction setups, where molecular junctions are repeatedly formed and broken while measuring the conductance, leading to a statistical distribution of conductance values. Modeling this experimental situation and the resulting conductance histograms is challenging for theoretical methods, as computations need to capture structural changes in experiments, including the statistics of junction formation and rupture. This type of extensive structural sampling implies that even when evaluating conductance from computationally efficient electronic structure methods, which typically are of reduced accuracy, the evaluation of conductance histograms is too expensive to be a routine task. Highly accurate quantum transport computations are only computationally feasible for a few selected conformations and thus necessarily ignore the rich conformational space probed in experiments. To overcome these limitations, we investigate the potential of machine learning for modeling conductance histograms, in particular by Gaussian process regression. We show that by selecting specific structural parameters as features, Gaussian process regression can be used to efficiently predict the zero-bias conductance from molecular structures, reducing the computational cost of simulating conductance histograms by an order of magnitude. This enables the efficient calculation of conductance histograms even on the basis of computationally expensive first-principles approaches by effectively reducing the number of necessary charge transport calculations, paving the way toward their routine evaluation.

Machine learning, artificial intelligence, and chemistry: how smart algorithms are reshaping simulation and the laboratory

Machine learning and artificial intelligence are increasingly gaining in prominence through image analysis, language processing, and automation, to name a few applications. Machine learning is also making profound changes in chemistry. From revisiting decades-old analytical techniques for the purpose of creating better calibration curves, to assisting and accelerating traditional in silico simulations, to automating entire scientific workflows, to being used as an approach to deduce underlying physics of unexplained chemical phenomena, machine learning and artificial intelligence are reshaping chemistry, accelerating scientific discovery, and yielding new insights. This review provides an overview of machine learning and artificial intelligence from a chemist’s perspective and focuses on a number of examples of the use of these approaches in computational chemistry and in the laboratory.

Validation of the Green's Function Approximation for the Calculation of Magnetic Exchange Couplings

In this work, we assess the potential of the Green's function approximation to predict isotropic magnetic exchange couplings and to reproduce the standard broken-symmetry energy difference approach for transition metal complexes. To this end, we have selected a variety of heterodinuclear, homodinuclear, and polynuclear systems containing 3d transition metal centers and computed the couplings using both the Green's function and energy difference methods. The Green's function approach is shown to have mixed results for the cases tested. For dinuclear complexes with large strength couplings (≳50 cm^-1), the Green's function method is unable to reliably reproduce the energy difference values. However, for weaker dinuclear couplings, the Green's function approach acceptably reproduces broken-symmetry energy difference couplings. In polynuclear cases, the Green's function approximation worked remarkably well, especially for Fe^III complexes. On the other hand, for a Ni^II polynuclear complex, qualitatively wrong couplings are predicted. Overall, the evaluation of exchange couplings from local rigid magnetization rotations offers a powerful alternative to time-consuming energy differences methods for large polynuclear transition metal complexes, but to achieve a quantitative agreement, some improvements to the method are needed.

Machine learning for a finite size correction in periodic coupled cluster theory calculations

We introduce a straightforward Gaussian process regression (GPR) model for the transition structure factor of metal periodic coupled cluster singles and doubles (CCSD) calculations. This is inspired by the method introduced by Liao and Gr\"uneis for interpolating over the transition structure factor to obtain a finite size correction for CCSD [J. Chem. Phys. 145, 141102 (2016)], and by our own prior work using the transition structure factor to efficiently converge CCSD for metals to the thermodynamic limit [Nat. Comput. Sci. 1, 801 (2021)]. In our CCSD-FS-GPR method to correct for finite size errors, we fit the structure factor to a 1D function in the momentum transfer, $G$.We then integrate over this function by projecting it onto a k-point mesh to obtain comparisons with extrapolated results. Results are shown for lithium, sodium, and the uniform electron gas.

Uncertainty Quantification of Reactivity Scales

According to Mayr, polar organic synthesis can be rationalized by a simple empirical relationship linking bimolecular rate constants to as few as three reactivity parameters. Here, we propose an extension to Mayr's reactivity method that is rooted in uncertainty quantification and transforms the reactivity parameters into probability distributions. Through uncertainty propagation, these distributions can be transformed into uncertainty estimates for bimolecular rate constants. Chemists can exploit these virtual error bars to enhance synthesis planning and to decrease the ambiguity of conclusions drawn from experimental data. We demonstrate the above at the example of the reference data set released by Mayr and co-workers [J. Am. Chem. Soc. 2001, 123, 9500; J. Am. Chem. Soc. 2012, 134, 13902]. As by-product of the new approach, we obtain revised reactivity parameters for 36 π-nucleophiles and 32 benzhydrylium ions.

Learning the Use of Artificial Intelligence in Heterogeneous Catalysis

We describe the use of artificial intelligence techniques in heterogeneous catalysis. This description is intended to give readers some clues for the use of these techniques in their research or industrial processes related to hydrodesulfurization. Since the description corresponds to supervised learning, first of all, we give a brief introduction to this type of learning, emphasizing the variables X and Y that define it. For each description, there is a particular emphasis on highlighting these variables. This emphasis will help define them when one works on a new application. The descriptions that we present relate to the construction of learning machines that infer adsorption energies, surface areas, adsorption isotherms of nanoporous materials, novel catalysts, and the sulfur content after hydrodesulfurization. These learning machines can predict adsorption energies with mean absolute errors of 0.15 eV for a diverse chemical space. They predict more precise surface areas of porous materials than the BET technique and can calculate their isotherms much faster than the Monte Carlo method. These machines can also predict new catalysts by learning from the catalytic behavior of materials generated through atomic substitutions. When the machines learn from the variables associated with a hydrodesulfurization process, they can predict the sulfur content in the final product.

Deciphering Cryptic Behavior in Bimetallic Transition-Metal Complexes with Machine Learning

We demonstrate an alternative, data-driven approach to uncovering structure-property relationships for the rational design of heterobimetallic transition-metal complexes that exhibit metal-metal bonding. We tailor graph-based representations of the metal-local environment for these complexes for use in multiple linear regression and kernel ridge regression (KRR) models. We curate a set of 28 experimentally characterized complexes to develop a multiple linear regression model for oxidation potentials. We achieve good accuracy (mean absolute error of 0.25 V) and preserve transferability to unseen experimental data with a new ligand structure. We also train a KRR model on a subset of 330 structurally characterized heterobimetallics to predict the degree of metal-metal bonding. This KRR model predicts relative metal-metal bond lengths in the test set to within 5%, and analysis of key features reveals the fundamental atomic contributions (e.g., the valence electron configuration) that most strongly influence the behavior of these complexes. Our work provides guidance for rational bimetallic design, suggesting that properties, including the formal shortness ratio, should be transferable from one period to another.

Computational Discovery of Transition-metal Complexes: From High-throughput Screening to Machine Learning

Transition-metal complexes are attractive targets for the design of catalysts and functional materials. The behavior of the metal-organic bond, while very tunable for achieving target properties, is challenging to predict and necessitates searching a wide and complex space to identify needles in haystacks for target applications. This review will focus on the techniques that make high-throughput search of transition-metal chemical space feasible for the discovery of complexes with desirable properties. The review will cover the development, promise, and limitations of "traditional" computational chemistry (i.e., force field, semiempirical, and density functional theory methods) as it pertains to data generation for inorganic molecular discovery. The review will also discuss the opportunities and limitations in leveraging experimental data sources. We will focus on how advances in statistical modeling, artificial intelligence, multiobjective optimization, and automation accelerate discovery of lead compounds and design rules. The overall objective of this review is to showcase how bringing together advances from diverse areas of computational chemistry and computer science have enabled the rapid uncovering of structure-property relationships in transition-metal chemistry. We aim to highlight how unique considerations in motifs of metal-organic bonding (e.g., variable spin and oxidation state, and bonding strength/nature) set them and their discovery apart from more commonly considered organic molecules. We will also highlight how uncertainty and relative data scarcity in transition-metal chemistry motivate specific developments in machine learning representations, model training, and in computational chemistry. Finally, we will conclude with an outlook of areas of opportunity for the accelerated discovery of transition-metal complexes.