Putting Density Functional Theory to the Test in Machine-Learning-Accelerated Materials Discovery

Machine Learning Mapping Approach for Computing Spin Relaxation Dynamics

In this work, a machine learning mapping approach for predicting the properties of atomistic systems is reported. Within this approach, the atomic orbital overlap, density, or Kohn-Sham (KS) Fock matrix elements obtained at a low level of theory such as extended tight-binding have been used as input features to predict the electric field gradient (EFG) tensors at a higher level of theory such as those obtained with hybrid functionals. It is shown that the machine-learning-predicted EFG tensors can be used to compute spin relaxation rates of several ions in aqueous solutions. From only a fraction of data used in direct calculation, one can predict the quadrupolar isotropic spin relaxation rates with good accuracy, achieving relative errors between about 2-8% for different ions.

Applications of metal nanoclusters supported on the two-dimensional material graphene in electrocatalytic carbon dioxide reduction

Metal nanoclusters (MNCs) have been demonstrated to exhibit superior catalytic performance compared to single nanoparticles. This is attributed to their quantized electronic structure, unique geometrical stacking and abundant active sites. While the exposed metal atoms can markedly enhance the efficiency of catalysis, unfortunately, MNCs are susceptible to agglomeration, which impairs their catalytic activity and stability. Graphene is a two-dimensional material consisting of a single atomic layer formed by the hybridization of the s and p orbitals of carbon atoms. It exhibits stable physical and chemical properties and has an easily controllable structure, making it an ideal carrier for MNCs. When metal nanoclusters (MNCs) are loaded on a graphene substrate, the MNCs can form a stable binding site on the graphene substrate. Furthermore, the construction of a defective structure on the graphene substrate enables the formation of robust interactions between the metal atoms of the MNCs and the substrate, facilitating the rapid establishment of electron conduction pathways and markedly enhancing the electrocatalytic performance. This paper presents a review of the applications of metal nanoclusters supported on graphene skeletons in the field of the electrocatalytic CO2 reduction reaction (CO2RR). Firstly, we briefly introduce the reaction mechanism of the CO2RR, then we systematically discuss the synthesis strategies, properties and applications of metal nanoclusters in electrocatalytic carbon dioxide reduction from both experimental and theoretical perspectives, and lastly, we discuss the opportunities and challenges of metal nanocluster catalysts supported on carbon materials.

A semi-automated quantum-mechanical workflow for the generation of molecular monolayers and aggregates

Organic electronics (OE) such as organic light-emitting diodes or organic solar cells represent an important and innovative research area to achieve global goals like environmentally friendly energy production. To accelerate OE material discovery, various computational methods are employed. For the initial generation of structures, a molecular cluster approach is employed. Here, we present a semi-automated workflow for the generation of monolayers and aggregates using the GFNn-xTB methods and composite density functional theory (DFT-3c). Furthermore, we present the novel D11A8MERO dye interaction energy benchmark with high-level coupled cluster reference interaction energies for the assessment of efficient quantum chemical and force-field methods. GFN2-xTB performs similar to low-cost DFT, reaching DFT/mGGA accuracy at two orders of magnitude lower computational cost. As an example application, we investigate the influence of the dye aggregate size on the optical and electrical properties and show that at least four molecules in a cluster model are needed for a qualitatively reasonable description.

Challenges Reconciling Theory and Experiments in the Prediction of Lattice Thermal Conductivity: The Case of Cu-Based Sulvanites

The exploration of large chemical spaces in search of new thermoelectric materials requires the integration of experiments, theory, simulations, and data science. The development of high-throughput strategies that combine DFT calculations with machine learning has emerged as a powerful approach to discovering new materials. However, experimental validation is crucial to confirm the accuracy of these workflows. This validation becomes especially important in understanding the transport properties that govern the thermoelectric performance of materials since they are highly influenced by synthetic, processing, and operating conditions. In this work, we explore the thermal conductivity of Cu-based sulvanites by using a combination of theoretical and experimental methods. Previous discrepancies and significant variations in reported data for Cu3VS4 and Cu3VSe4 are explained using the Boltzmann Transport Equation for phonons and by synthesizing well-characterized defect-free samples. The use of machine learning approaches for extracting high-order force constants opens doors to charting the lattice thermal conductivity across the entire Cu-based sulvanite family-finding not only materials with κ l values below 2 W m-1 K-1 at moderate temperatures but also rationalizing their thermal transport properties based on chemical composition.

Deep Mind 21 functional does not extrapolate to transition metal chemistry

The development of density functional approximations stands at a crossroads: while machine-learned functionals show potential to surpass their human-designed counterparts, their extrapolation to unseen chemistry lags behind. Here we assess how well the recent Deep Mind 21 (DM21) machine-learned functional [Science, 2021, 374, 1385-1389], trained on main-group chemistry, extrapolates to transition metal chemistry (TMC). We show that DM21 demonstrates comparable or occasionally superior accuracy to B3LYP for TMC, but consistently struggles with achieving self-consistent field convergence for TMC molecules. We also compare main-group and TMC machine-learning DM21 features to shed light on DM21's challenges in TMC. We finally propose strategies to overcome limitations in the extrapolative capabilities of machine-learned functionals in TMC.

Efficient Exploration of Chemical Compound Space Using Active Learning for Prediction of Thermodynamic Properties of Alkane Molecules

We introduce an exploratory active learning (AL) algorithm using Gaussian process regression and marginalized graph kernel (GPR-MGK) to sample chemical compound space (CCS) at minimal cost. Targeting 251,728 enumerated alkane molecules with 4-19 carbon atoms, we applied the AL algorithm to select a diverse and representative set of molecules and then conducted high-throughput molecular simulations on these selected molecules. To demonstrate the power of the AL algorithm, we built directed message-passing neural networks (D-MPNN) using simulation data as the training set to predict liquid densities, heat capacities, and vaporization enthalpies of the CCS. Validations show that D-MPNN models built on the smallest training set considered in this work, which consists of 313 molecules or 0.124% of the original CCS, predict the properties with R2 > 0.99 against the computational data and R2 > 0.94 against the experimental data. The advantage of the presented AL algorithm is that the predicted uncertainty of GPR depends on only the molecular structures, which renders it compatible with high-throughput data generation.

Performance of the r2SCAN Functional in Transition Metal Oxides

We assess the accuracy and computational efficiency of the recently developed meta-generalized gradient approximation (metaGGA) functional, restored regularized strongly constrained and appropriately normed (r²SCAN), in transition metal oxide (TMO) systems and compare its performance against SCAN. Specifically, we benchmark the r²SCAN-calculated oxidation enthalpies, lattice parameters, on-site magnetic moments, and band gaps of binary 3d TMOs against the SCAN-calculated and experimental values. Additionally, we evaluate the optimal Hubbard U correction required for each transition metal (TM) to improve the accuracy of the r²SCAN functional, based on experimental oxidation enthalpies, and verify the transferability of the U values by comparing against experimental properties on other TM-containing oxides. Notably, including the U-correction with r²SCAN increases the lattice parameters, on-site magnetic moments, and band gaps of TMOs, apart from an improved description of the ground state electronic state in narrow band gap TMOs. The r²SCAN and r²SCAN+U calculated oxidation enthalpies follow the qualitative trends of SCAN and SCAN+U, with r²SCAN and r²SCAN+U predicting marginally larger lattice parameters, smaller magnetic moments, and lower band gaps compared to SCAN and SCAN+U, respectively. We observe the overall computational time (i.e., for all ionic+electronic steps) required for r²SCAN(+U) to be lower than SCAN(+U). Thus, the r²SCAN(+U) framework can offer a reasonably accurate description of the ground state properties of TMOs with better computational efficiency than SCAN(+U).

Insights into the deviation from piecewise linearity in transition metal complexes from supervised machine learning models

Virtual high-throughput screening (VHTS) and machine learning (ML) with density functional theory (DFT) suffer from inaccuracies from the underlying density functional approximation (DFA). Many of these inaccuracies can be traced to the lack of derivative discontinuity that leads to a curvature in the energy with electron addition or removal. Over a dataset of nearly one thousand transition metal complexes typical of VHTS applications, we computed and analyzed the average curvature (i.e., deviation from piecewise linearity) for 23 density functional approximations spanning multiple rungs of "Jacob's ladder". While we observe the expected dependence of the curvatures on Hartree-Fock exchange, we note limited correlation of curvature values between different rungs of "Jacob's ladder". We train ML models (i.e., artificial neural networks or ANNs) to predict the curvature and the associated frontier orbital energies for each of these 23 functionals and then interpret differences in curvature among the different DFAs through analysis of the ML models. Notably, we observe spin to play a much more important role in determining the curvature of range-separated and double hybrids in comparison to semi-local functionals, explaining why curvature values are weakly correlated between these and other families of functionals. Over a space of 187.2k hypothetical compounds, we use our ANNs to pinpoint DFAs for which representative transition metal complexes have near-zero curvature with low uncertainty, demonstrating an approach to accelerate screening of complexes with targeted optical gaps.

Large Data Set-Driven Machine Learning Models for Accurate Prediction of the Thermoelectric Figure of Merit

The figure of merit (zT) is a key parameter to measure the performance of thermoelectric materials. At present, the prediction of zT values via machine leaning has emerged as a promising method for exploring high-performance materials. However, the machine learning-based predictions still suffer from unsatisfactory accuracy, and this is related to the size of the data set, the hyperparameters of models, and the quality of the data. In this work, 5038 pieces of data of thermoelectric materials were selected, and several regression models were generated to predict zT values. This large data set-driven light gradient boosting (LGB) model with 57 features performed with an excellent accuracy, achieving a coefficient of determination (R²) value of 0.959, a root mean squared error (RMSE) of 0.094, a mean absolute error (MAE) of 0.057, and a correlation coefficient (R) of 0.979. Owing to the large size of the data set, the prediction accuracy exceeds that of most reported zT predictions via machine learning. The "M_E Lattice Parameter" was verified as the most important feature in the zT prediction. Furthermore, nine potential candidates were screened out from among one million pieces of data. This study solves the problem of the data set size, adjusts the hyperparameters of the models, uses feature engineering to improve data quality, and provides an efficient strategy to perform wide-ranging screening for promising materials.

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.

Exploiting Ligand Additivity for Transferable Machine Learning of Multireference Character across Known Transition Metal Complex Ligands

Accurate virtual high-throughput screening (VHTS) of transition metal complexes (TMCs) remains challenging due to the possibility of high multireference (MR) character that complicates property evaluation. We compute MR diagnostics for over 5,000 ligands present in previously synthesized octahedral mononuclear transition metal complexes in the Cambridge Structural Database (CSD). To accomplish this task, we introduce an iterative approach for consistent ligand charge assignment for ligands in the CSD. Across this set, we observe that the MR character correlates linearly with the inverse value of the averaged bond order over all bonds in the molecule. We then demonstrate that ligand additivity of the MR character holds in TMCs, which suggests that the TMC MR character can be inferred from the sum of the MR character of the ligands. Encouraged by this observation, we leverage ligand additivity and develop a ligand-derived machine learning representation to train neural networks to predict the MR character of TMCs from properties of the constituent ligands. This approach yields models with excellent performance and superior transferability to unseen ligand chemistry and compositions.

Machine Learning Models Predict Calculation Outcomes with the Transferability Necessary for Computational Catalysis

Virtual high-throughput screening (VHTS) and machine learning (ML) have greatly accelerated the design of single-site transition-metal catalysts. VHTS of catalysts, however, is often accompanied with a high calculation failure rate and wasted computational resources due to the difficulty of simultaneously converging all mechanistically relevant reactive intermediates to expected geometries and electronic states. We demonstrate a dynamic classifier approach, i.e., a convolutional neural network that monitors geometry optimizations on the fly, and exploit its good performance and transferability in identifying geometry optimization failures for catalyst design. We show that the dynamic classifier performs well on all reactive intermediates in the representative catalytic cycle of the radical rebound mechanism for the conversion of methane to methanol despite being trained on only one reactive intermediate. The dynamic classifier also generalizes to chemically distinct intermediates and metal centers absent from the training data without loss of accuracy or model confidence. We rationalize this superior model transferability as arising from the use of electronic structure and geometric information generated on-the-fly from density functional theory calculations and the convolutional layer in the dynamic classifier. When used in combination with uncertainty quantification, the dynamic classifier saves more than half of the computational resources that would have been wasted on unsuccessful calculations for all reactive intermediates being considered.

New Strategies for Direct Methane-to-Methanol Conversion from Active Learning Exploration of 16 Million Catalysts

Despite decades of effort, no earth-abundant homogeneous catalysts have been discovered that can selectively oxidize methane to methanol. We exploit active learning to simultaneously optimize methane activation and methanol release calculated with machine learning-accelerated density functional theory in a space of 16 M candidate catalysts including novel macrocycles. By constructing macrocycles from fragments inspired by synthesized compounds, we ensure synthetic realism in our computational search. Our large-scale search reveals that low-spin Fe(II) compounds paired with strong-field (e.g., P or S-coordinating) ligands have among the best energetic tradeoffs between hydrogen atom transfer (HAT) and methanol release. This observation contrasts with prior efforts that have focused on high-spin Fe(II) with weak-field ligands. By decoupling equatorial and axial ligand effects, we determine that negatively charged axial ligands are critical for more rapid release of methanol and that higher-valency metals [i.e., M(III) vs M(II)] are likely to be rate-limited by slow methanol release. With full characterization of barrier heights, we confirm that optimizing for HAT does not lead to large oxo formation barriers. Energetic span analysis reveals designs for an intermediate-spin Mn(II) catalyst and a low-spin Fe(II) catalyst that are predicted to have good turnover frequencies. Our active learning approach to optimize two distinct reaction energies with efficient global optimization is expected to be beneficial for the search of large catalyst spaces where no prior designs have been identified and where linear scaling relationships between reaction energies or barriers may be limited or unknown.

Detection of multi-reference character imbalances enables a transfer learning approach for virtual high throughput screening with coupled cluster accuracy at DFT cost

Appropriately identifying and treating molecules and materials with significant multi-reference (MR) character is crucial for achieving high data fidelity in virtual high-throughput screening (VHTS). Despite development of numerous MR diagnostics, the extent to which a single value of such a diagnostic indicates the MR effect on a chemical property prediction is not well established. We evaluate MR diagnostics for over 10 000 transition-metal complexes (TMCs) and compare to those for organic molecules. We observe that only some MR diagnostics are transferable from one chemical space to another. By studying the influence of MR character on chemical properties (i.e., MR effect) that involve multiple potential energy surfaces (i.e., adiabatic spin splitting, ΔE H-L, and ionization potential, IP), we show that differences in MR character are more important than the cumulative degree of MR character in predicting the magnitude of an MR effect. Motivated by this observation, we build transfer learning models to predict CCSD(T)-level adiabatic ΔE H-L and IP from lower levels of theory. By combining these models with uncertainty quantification and multi-level modeling, we introduce a multi-pronged strategy that accelerates data acquisition by at least a factor of three while achieving coupled cluster accuracy (i.e., to within 1 kcal mol-1 MAE) for robust VHTS.

Multiscale molecular modelling: from electronic structure to dynamics of nanosystems and beyond

Important contemporary biological and materials problems often depend on interactions that span orders of magnitude differences in spatial and temporal dimensions. This Tutorial Review attempts to provide an introduction to such fascinating problems through a series of case studies, aimed at beginning researchers, graduate students, postdocs and more senior colleagues who are changing direction to focus on multiscale aspects of their research. The choice of specific examples is highly personal, with examples either chosen from our own work or outstanding multiscale efforts from the literature. I start with various embedding schemes, as exemplified by polarizable continuum models, 3-D RISM, molecular DFT and frozen-density embedding. Next, QM/MM (quantum mechanical/molecular mechanical) techniques are the workhorse of pm-to-nm/ps-to-ns simulations; examples are drawn from enzymes and from nanocatalysis for oil-sands upgrading. Using polarizable force-fields in the QM/MM framework represents a burgeoning subfield; with examples from ion channels and electron dynamics in molecules subject to strong external fields, probing the atto-second dynamics of the electrons with RT-TDDFT (real-time - time-dependent density functional theory) eventually coupled with nuclear motion through the Ehrenfest approximation. This is followed by a section on coarse graining, bridging dimensions from atoms to cells. The penultimate chapter gives a quick overview of multiscale approaches that extend into the meso- and macro-scales, building on atomistic and coarse-grained techniques to enter the world of materials engineering, on the one hand, and cell biology, on the other. A final chapter gives just a glimpse of the burgeoning impact of machine learning on the structure-dynamics front. I aim to capture the excitement of contemporary leading-edge breakthroughs in the description of physico-chemical systems and processes in complex environments, with only enough historical content to provide context and aid the next generation of methodological development. While I aim also for a clear description of the essence of methodological breakthroughs, equations are kept to a minimum and detailed formalism and implementation details are left to the references. My approach is very selective (case studies) rather than exhaustive. I think that these case studies should provide fodder to build as complete a reference tree on multiscale modelling as the reader may wish, through forward and backward citation analysis. I hope that my choices of cases will excite interest in newcomers and help to fuel the growth of multiscale modelling in general.

The long road to calibrated prediction uncertainty in computational chemistry

Uncertainty quantification (UQ) in computational chemistry (CC) is still in its infancy. Very few CC methods are designed to provide a confidence level on their predictions, and most users still rely improperly on the mean absolute error as an accuracy metric. The development of reliable UQ methods is essential, notably for CC to be used confidently in industrial processes. A review of the CC-UQ literature shows that there is no common standard procedure to report or validate prediction uncertainty. I consider here analysis tools using concepts (calibration and sharpness) developed in meteorology and machine learning for the validation of probabilistic forecasters. These tools are adapted to CC-UQ and applied to datasets of prediction uncertainties provided by composite methods, Bayesian ensembles methods, and machine learning and a posteriori statistical methods.

Catalytic properties of the ferryl ion in the solid state: a computational review

This review summarises the last findings in the emerging field of heterogeneous catalytic oxidation of light alkanes by ferryl species supported on solid-state systems such as the conversion of methane into methanol by FeO-MOF74.

Machine learning to tame divergent density functional approximations: a new path to consensus materials design principles

Virtual high-throughput screening (VHTS) with density functional theory (DFT) and machine-learning (ML)-acceleration is essential in rapid materials discovery. By necessity, efficient DFT-based workflows are carried out with a single density functional approximation (DFA). Nevertheless, properties evaluated with different DFAs can be expected to disagree for cases with challenging electronic structure (e.g., open-shell transition-metal complexes, TMCs) for which rapid screening is most needed and accurate benchmarks are often unavailable. To quantify the effect of DFA bias, we introduce an approach to rapidly obtain property predictions from 23 representative DFAs spanning multiple families, “rungs” (e.g., semi-local to double hybrid) and basis sets on over 2000 TMCs. Although computed property values (e.g., spin state splitting and frontier orbital gap) differ by DFA, high linear correlations persist across all DFAs. We train independent ML models for each DFA and observe convergent trends in feature importance, providing DFA-invariant, universal design rules. We devise a strategy to train artificial neural network (ANN) models informed by all 23 DFAs and use them to predict properties (e.g., spin-splitting energy) of over 187k TMCs. By requiring consensus of the ANN-predicted DFA properties, we improve correspondence of computational lead compounds with literature-mined, experimental compounds over the typically employed single-DFA approach.

Machine learning (ML)-based feature analysis reveals universal design rules regardless of density functional choices. Using the consensus among multiple functionals, we identify robust lead complexes in ML-accelerated chemical discovery.

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.

Trends in computational molecular catalyst design

Computational methods have emerged as a powerful tool to augment traditional experimental molecular catalyst design by providing useful predictions of catalyst performance and decreasing the time needed for catalyst screening. In this perspective, we discuss three approaches for computational molecular catalyst design: (i) the reaction mechanism-based approach that calculates all relevant elementary steps, finds the rate and selectivity determining steps, and ultimately makes predictions on catalyst performance based on kinetic analysis, (ii) the descriptor-based approach where physical/chemical considerations are used to find molecular properties as predictors of catalyst performance, and (iii) the data-driven approach where statistical analysis as well as machine learning (ML) methods are used to obtain relationships between available data/features and catalyst performance. Following an introduction to these approaches, we cover their strengths and weaknesses and highlight some recent key applications. Furthermore, we present an outlook on how the currently applied approaches may evolve in the near future by addressing how recent developments in building automated computational workflows and implementing advanced ML models hold promise for reducing human workload, eliminating human bias, and speeding up computational catalyst design at the same time. Finally, we provide our viewpoint on how some of the challenges associated with the up-and-coming approaches driven by automation and ML may be resolved.