Making machine learning a useful tool in the accelerated discovery of transition metal complexes

Paving the road towards automated homogeneous catalyst design

In the past decade, computational tools have become integral to catalyst design. They continue to offer significant support to experimental organic synthesis and catalysis researchers aiming for optimal reaction outcomes. More recently, data-driven approaches utilizing machine learning have garnered considerable attention for their expansive capabilities. This Perspective provides an overview of diverse initiatives in the realm of computational catalyst design and introduces our automated tools tailored for high-throughput in silico exploration of the chemical space. While valuable insights are gained through methods for high-throughput in silico exploration and analysis of chemical space, their degree of automation and modularity are key. We argue that the integration of data-driven, automated and modular workflows is key to enhancing homogeneous catalyst design on an unprecedented scale, contributing to the advancement of catalysis research.

Interoperable workflows by exchanging grid-based data between quantum-chemical program packages

Quantum-chemical subsystem and embedding methods require complex workflows that may involve multiple quantum-chemical program packages. Moreover, such workflows require the exchange of voluminous data that go beyond simple quantities, such as molecular structures and energies. Here, we describe our approach for addressing this interoperability challenge by exchanging electron densities and embedding potentials as grid-based data. We describe the approach that we have implemented to this end in a dedicated code, PyEmbed, currently part of a Python scripting framework. We discuss how it has facilitated the development of quantum-chemical subsystem and embedding methods and highlight several applications that have been enabled by PyEmbed, including wave-function theory (WFT) in density-functional theory (DFT) embedding schemes mixing non-relativistic and relativistic electronic structure methods, real-time time-dependent DFT-in-DFT approaches, the density-based many-body expansion, and workflows including real-space data analysis and visualization. Our approach demonstrates, in particular, the merits of exchanging (complex) grid-based data and, in general, the potential of modular software development in quantum chemistry, which hinges upon libraries that facilitate interoperability.

Modeling Zinc Complexes Using Neural Networks

Understanding the energetic landscapes of large molecules is necessary for the study of chemical and biological systems. Recently, deep learning has greatly accelerated the development of models based on quantum chemistry, making it possible to build potential energy surfaces and explore chemical space. However, most of this work has focused on organic molecules due to the simplicity of their electronic structures as well as the availability of data sets. In this work, we build a deep learning architecture to model the energetics of zinc organometallic complexes. To achieve this, we have compiled a configurationally and conformationally diverse data set of zinc complexes using metadynamics to overcome the limitations of traditional sampling methods. In terms of the neural network potentials, our results indicate that for zinc complexes, partial charges play an important role in modeling the long-range interactions with a neural network. Our developed model outperforms semiempirical methods in predicting the relative energy of zinc conformers, yielding a mean absolute error (MAE) of 1.32 kcal/mol with reference to the double-hybrid PWPB95 method.

MetalHawk: Enhanced Classification of Metal Coordination Geometries by Artificial Neural Networks

The chemical properties of metal complexes are strongly dependent on the number and geometrical arrangement of ligands coordinated to the metal center. Existing methods for determining either coordination number or geometry rely on a trade-off between accuracy and computational costs, which hinders their application to the study of large structure data sets. Here, we propose MetalHawk (https://github.com/vrettasm/MetalHawk), a machine learning-based approach to perform simultaneous classification of metal site coordination number and geometry through artificial neural networks (ANNs), which were trained using the Cambridge Structural Database (CSD) and Metal Protein Data Bank (MetalPDB). We demonstrate that the CSD-trained model can be used to classify sites belonging to the most common coordination numbers and geometry classes with balanced accuracy equal to 96.51% for CSD-deposited metal sites. The CSD-trained model was also found to be capable of classifying bioinorganic metal sites from the MetalPDB database, with balanced accuracy equal to 84.29% on the whole PDB data set and to 91.66% on manually reviewed sites in the PDB validation set. Moreover, we report evidence that the output vectors of the CSD-trained model can be considered as a proxy indicator of metal-site distortions, showing that these can be interpreted as a low-dimensional representation of subtle geometrical features present in metal site structures.

Spin-state gaps and self-interaction-corrected density functional approximations: Octahedral Fe(II) complexes as case study

Accurate prediction of a spin-state energy difference is crucial for understanding the spin crossover phenomena and is very challenging for density functional approximations, especially for local and semi-local approximations due to delocalization errors. Here, we investigate the effect of the self-interaction error removal from the local spin density approximation (LSDA) and Perdew-Burke-Ernzerhof generalized gradient approximation on the spin-state gaps of Fe(II) complexes with various ligands using recently developed locally scaled self-interaction correction (LSIC) by Zope et al. [J. Chem. Phys. 151, 214108 (2019)]. The LSIC method is exact for one-electron density, recovers the uniform electron gas limit of the underlying functional, and approaches the well-known Perdew-Zunger self-interaction correction (PZSIC) as a particular case when the scaling factor is set to unity. Our results, when compared with reference diffusion Monte Carlo results, show that the PZSIC method significantly overestimates spin-state gaps favoring low spin states for all ligands and does not improve upon density functional approximations. The perturbative LSIC-LSDA using PZSIC densities significantly improves the gaps with a mean absolute error of 0.51 eV but slightly overcorrects for the stronger CO ligands. The quasi-self-consistent LSIC-LSDA, such as coupled-cluster single double and perturbative triple [CCSD(T)], gives a correct sign of spin-state gaps for all ligands with a mean absolute error of 0.56 eV, comparable to that of CCSD(T) (0.49 eV).

Molecular-orbital-based machine learning for open-shell and multi-reference systems with kernel addition Gaussian process regression

We introduce a novel machine learning strategy, kernel addition Gaussian process regression (KA-GPR), in molecular-orbital-based machine learning (MOB-ML) to learn the total correlation energies of general electronic structure theories for closed- and open-shell systems by introducing a machine learning strategy. The learning efficiency of MOB-ML(KA-GPR) is the same as the original MOB-ML method for the smallest criegee molecule, which is a closed-shell molecule with multi-reference characters. In addition, the prediction accuracies of different small free radicals could reach the chemical accuracy of 1 kcal/mol by training on one example structure. Accurate potential energy surfaces for the H₁₀ chain (closed-shell) and water OH bond dissociation (open-shell) could also be generated by MOB-ML(KA-GPR). To explore the breadth of chemical systems that KA-GPR can describe, we further apply MOB-ML to accurately predict the large benchmark datasets for closed- (QM9, QM7b-T, and GDB-13-T) and open-shell (QMSpin) molecules.

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.

Interplay of Electronic and Geometric Structure Tunes Organic Biradical Character in Bimetallic Tetrathiafulvalene Tetrathiolate Complexes

The synthesis and design of organic biradicals with tunable singlet-triplet gaps have become the subject of significant research interest, owing to their possible photochemical applications and use in the development of molecular switches and conductors. Recently, tetrathiafulvalene tetrathiolate (TTFtt) has been demonstrated to exhibit such organic biradical character in doubly ionized bimetallic complexes. In this article we use high-level ab initio calculations to interrogate the electronic structure of a series of TTFtt-bridged metal complexes, resolving the factors governing their biradical character and singlet-triplet gaps. We show that the degree of biradical character correlates with a readily measured experimental predictor, the central TTFtt C-C bond length, and that it may be described by a one-parameter model, providing valuable insight for the future rational design of TTFtt based biradical compounds and materials.

Machine Learning for Electronically Excited States of Molecules

Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

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.

Machine Learning for Electronically Excited States of Molecules

Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

The Impact of Computational Uncertainties on the Enantioselectivity Predictions: A Microkinetic Modeling of Ketone Transfer Hydrogenation with a Noyori-type Mn-diamine Catalyst

Selectivity control is one of the most important functions of a catalyst. In asymmetric catalysis the enantiomeric excess (e.e.) is a property of major interest, with a lot of effort dedicated to developing the most enantioselective catalyst, understanding the origin of selectivity, and predicting stereoselectivity. Herein, we investigate the relationship between predicted selectivity and the uncertainties in the computed energetics of the catalytic reaction mechanism obtained by DFT calculations in a case study of catalytic asymmetric transfer hydrogenation (ATH) of ketones with an Mn-diamine catalyst. Data obtained from our analysis of DFT data by microkinetic modeling is compared to results from experiment. We discuss the limitations of the conventional reductionist approach of e.e. estimation from assessing the enantiodetermining steps only. Our analysis shows that the energetics of other reaction steps in the reaction mechanism have a substantial impact on the predicted reaction selectivity. The uncertainty of DFT calculations within the commonly accepted energy ranges of chemical accuracy may reverse the predicted e.e. with the non-enantiodetermining steps contributing to e.e. deviations of up to 25 %.

Representations of energy landscapes by sublevelset persistent homology: An example with n-alkanes

Encoding the complex features of an energy landscape is a challenging task, and often, chemists pursue the most salient features (minima and barriers) along a highly reduced space, i.e., two- or three-dimensions. Even though disconnectivity graphs or merge trees summarize the connectivity of the local minima of an energy landscape via the lowest-barrier pathways, there is much information to be gained by also considering the topology of each connected component at different energy thresholds (or sublevelsets). We propose sublevelset persistent homology as an appropriate tool for this purpose. Our computations on the configuration phase space of n-alkanes from butane to octane allow us to conjecture, and then prove, a complete characterization of the sublevelset persistent homology of the alkane C_mH_2m+2 Potential Energy Landscapes (PELs), for all m, in all homological dimensions. We further compare both the analytical configurational PELs and sampled data from molecular dynamics simulation using the united and all-atom descriptions of the intramolecular interactions. In turn, this supports the application of distance metrics to quantify sampling fidelity and lays the foundation for future work regarding new metrics that quantify differences between the topological features of high-dimensional energy landscapes.

Navigating Transition-Metal Chemical Space: Artificial Intelligence for First-Principles Design

The variability of chemical bonding in open-shell transition-metal complexes not only motivates their study as functional materials and catalysts but also challenges conventional computational modeling tools. Here, tailoring ligand chemistry can alter preferred spin or oxidation states as well as electronic structure properties and reactivity, creating vast regions of chemical space to explore when designing new materials atom by atom. Although first-principles density functional theory (DFT) remains the workhorse of computational chemistry in mechanism deduction and property prediction, it is of limited use here. DFT is both far too computationally costly for widespread exploration of transition-metal chemical space and also prone to inaccuracies that limit its predictive performance for localized d electrons in transition-metal complexes. These challenges starkly contrast with the well-trodden regions of small-organic-molecule chemical space, where the analytical forms of molecular mechanics force fields and semiempirical theories have for decades accelerated the discovery of new molecules, accurate DFT functional performance has been demonstrated, and gold-standard methods from correlated wavefunction theory can predict experimental results to chemical accuracy.The combined promise of transition-metal chemical space exploration and lack of established tools has mandated a distinct approach. In this Account, we outline the path we charted in exploration of transition-metal chemical space starting from the first machine learning (ML) models (i.e., artificial neural network and kernel ridge regression) and representations for the prediction of open-shell transition-metal complex properties. The distinct importance of the immediate coordination environment of the metal center as well as the lack of low-level methods to accurately predict structural properties in this coordination environment first motivated and then benefited from these ML models and representations. Once developed, the recipe for prediction of geometric, spin state, and redox potential properties was straightforwardly extended to a diverse range of other properties, including in catalysis, computational "feasibility", and the gas separation properties of periodic metal-organic frameworks. Interpretation of selected features most important for model prediction revealed new ways to encapsulate design rules and confirmed that models were robustly mapping essential structure-property relationships. Encountering the special challenge of ensuring that good model performance could generalize to new discovery targets motivated investigation of how to best carry out model uncertainty quantification. Distance-based approaches, whether in model latent space or in carefully engineered feature space, provided intuitive measures of the domain of applicability. With all of these pieces together, ML can be harnessed as an engine to tackle the large-scale exploration of transition-metal chemical space needed to satisfy multiple objectives using efficient global optimization methods. In practical terms, bringing these artificial intelligence tools to bear on the problems of transition-metal chemical space exploration has resulted in ML-model assessments of large, multimillion compound spaces in minutes and validated new design leads in weeks instead of decades.

SSnet: A Deep Learning Approach for Protein-Ligand Interaction Prediction

Computational prediction of Protein-Ligand Interaction (PLI) is an important step in the modern drug discovery pipeline as it mitigates the cost, time, and resources required to screen novel therapeutics. Deep Neural Networks (DNN) have recently shown excellent performance in PLI prediction. However, the performance is highly dependent on protein and ligand features utilized for the DNN model. Moreover, in current models, the deciphering of how protein features determine the underlying principles that govern PLI is not trivial. In this work, we developed a DNN framework named SSnet that utilizes secondary structure information of proteins extracted as the curvature and torsion of the protein backbone to predict PLI. We demonstrate the performance of SSnet by comparing against a variety of currently popular machine and non-Machine Learning (ML) models using various metrics. We visualize the intermediate layers of SSnet to show a potential latent space for proteins, in particular to extract structural elements in a protein that the model finds influential for ligand binding, which is one of the key features of SSnet. We observed in our study that SSnet learns information about locations in a protein where a ligand can bind, including binding sites, allosteric sites and cryptic sites, regardless of the conformation used. We further observed that SSnet is not biased to any specific molecular interaction and extracts the protein fold information critical for PLI prediction. Our work forms an important gateway to the general exploration of secondary structure-based Deep Learning (DL), which is not just confined to protein-ligand interactions, and as such will have a large impact on protein research, while being readily accessible for de novo drug designers as a standalone package.

Machine Learning in Computational Surface Science and Catalysis: Case Studies on Water and Metal-Oxide Interfaces

The goal of many computational physicists and chemists is the ability to bridge the gap between atomistic length scales of about a few multiples of an Ångström (Å), i. e., 10⁻¹⁰ m, and meso- or macroscopic length scales by virtue of simulations. The same applies to timescales. Machine learning techniques appear to bring this goal into reach. This work applies the recently published on-the-fly machine-learned force field techniques using a variant of the Gaussian approximation potentials combined with Bayesian regression and molecular dynamics as efficiently implemented in the Vienna ab initio simulation package, VASP. The generation of these force fields follows active-learning schemes. We apply these force fields to simple oxides such as MgO and more complex reducible oxides such as iron oxide, examine their generalizability, and further increase complexity by studying water adsorption on these metal oxide surfaces. We successfully examined surface properties of pristine and reconstructed MgO and Fe₃O₄ surfaces. However, the accurate description of water–oxide interfaces by machine-learned force fields, especially for iron oxides, remains a field offering plenty of research opportunities.

Composition- and Condition-Dependent Kinetics of Homogeneous Ester Hydrogenation by a Mn-Based Catalyst

The reaction medium and conditions are the key parameters defining the efficiency and performance of a homogeneous catalyst. In the state-of-the-art molecular descriptions of catalytic systems by density functional theory (DFT) calculations, the reaction medium is commonly reduced to an infinitely diluted ideal solution model. In this work, we carry out a detailed operando computational modeling analysis of the condition dependencies and nonideal solution effects on the mechanism and kinetics of a model ester hydrogenation reaction by a homogeneous Mn(I)-P,N catalyst. By combining DFT calculations, COSMO-RS solvent model, and the microkinetic modeling approach, the kinetic behavior of the multicomponent homogeneous catalyst system under realistic reaction conditions was investigated in detail. The effects of the reaction medium and its dynamic evolution in the course of the reaction were analyzed by comparing the results obtained for the model methyl acetate hydrogenation reaction in a THF solution and under solvent-free neat reaction conditions. The dynamic representations of the reaction medium give rise to strongly nonlinear effects in the kinetic models. The nonideal representation of the reaction medium results in pronounced condition dependencies of the computed energetics of the elementary reaction steps and the computed kinetic profiles but affects only slightly such experimentally accessible kinetic descriptors as the apparent activation energy and the degree of rate control.

Describing Polytopal Rearrangements of Fluxional Molecules with Curvilinear Coordinates Derived from Normal Vibrational Modes: A Conceptual Extension of Cremer-Pople Puckering Coordinates

In this work a new curvilinear coordinate system is presented for the comprehensive description of polytopal rearrangements of N-coordinate compounds (N = 4-7) and systems containing an N-coordinate subunit. It is based on normal vibrational modes and a natural extension of the Cremer-Pople puckering coordinates ( J. Am. Chem. Soc. 1975, 97, 1354) together with the Zou-Izotov-Cremer deformation coordinates ( J. Phys. Chem. A 2011, 115, 8731) for ring structures to N-coordinate systems. We demonstrate that the new curvilinear coordinates are ideal reaction coordinates describing fluxional rearrangement pathways by revisiting the Berry pseudorotation and the lever mechanism in sulfur tetrafluoride, the Berry pseudorotation and two Muetterties' mechanisms in pentavalent compounds, the chimeric pseudorotation in iodine pentafluoride, Bailar and Ray-Dutt twists in hexacoordinate tris-chelates as well as the Bartell mechanism in iodine heptafluoride. The results of our study reveal that this dedicated curvilinear coordinate system can be applied to most coordination compounds opening new ways for the systematic modeling of fluxional processes.

Seeing Is Believing: Experimental Spin States from Machine Learning Model Structure Predictions

Determination of ground-state spins of open-shell transition-metal complexes is critical to understanding catalytic and materials properties but also challenging with approximate electronic structure methods. As an alternative approach, we demonstrate how structure alone can be used to guide assignment of ground-state spin from experimentally determined crystal structures of transition-metal complexes. We first identify the limits of distance-based heuristics from distributions of metal–ligand bond lengths of over 2000 unique mononuclear Fe(II)/Fe(III) transition-metal complexes. To overcome these limits, we employ artificial neural networks (ANNs) to predict spin-state-dependent metal–ligand bond lengths and classify experimental ground-state spins based on agreement of experimental structures with the ANN predictions. Although the ANN is trained on hybrid density functional theory data, we exploit the method-insensitivity of geometric properties to enable assignment of ground states for the majority (ca. 80–90%) of structures. We demonstrate the utility of the ANN by data-mining the literature for spin-crossover (SCO) complexes, which have experimentally observed temperature-dependent geometric structure changes, by correctly assigning almost all (>95%) spin states in the 46 Fe(II) SCO complex set. This approach represents a promising complement to more conventional energy-based spin-state assignment from electronic structure theory at the low cost of a machine learning model.