Search

Graph-based machine learning models for materials properties show great potential to accelerate virtual high-throughput screening of large chemical spaces. However, in their simplest forms, graph-based models do not include any 3D information and are unable to distinguish stereoisomers such as those arising from different orderings of ligands around a metal center in coordination complexes. In this work we present a modification to revised autocorrelation descriptors, our molecular graph featurization method for machine learning various spin state dependent properties of octahedral transition metal complexes (TMCs). Inspired by analytical semi-empirical models for TMCs, the new modeling strategy is based on the many-body expansion (MBE) and allows one to tune the captured stereoisomer information by changing the truncation order of the MBE. We present the necessary modifications to include this approach in two commonly used machine learning methods, kernel ridge regression and feed-forward neural networks. On a test set composed of all possible isomers of binary transition metal complexes, the best MBE models achieve mean absolute errors of 2.75 kcal/mol on spin-splitting energies and 0.26 eV on frontier orbital energy gaps, a 30-40% reduction in error compared to models based on our previous approach. We also observe improved generalization to previously unseen ligands where the best-performing models exhibit mean absolute errors of 4.00 kcal/mol (i.e., a 0.73 kcal/mol reduction) on the spin-splitting energies and 0.53 eV (i.e., a 0.10 eV reduction) on the frontier orbital energy gaps. Because the new approach incorporates insights from electronic structure theory, such as ligand additivity relationships, these models exhibit systematic generalization from homoleptic to heteroleptic complexes, allowing for efficient screening of TMC search spaces.

Transition states (TSs) are transient structures that are key in understanding reaction mechanisms and designing catalysts but challenging to be captured in experiments. Alternatively, many optimization algorithms have been developed to search for TSs computationally. Yet the cost of these algorithms driven by quantum chemistry methods (usually density functional theory) is still high, posing challenges for their applications in building large reaction networks for reaction exploration. Here we developed React-OT, an optimal transport approach for generating unique TS structures from reactants and products. React-OT generates highly accurate TS structures with a median structural root mean square deviation (RMSD) of 0.053{\AA} and median barrier height error of 1.06 kcal/mol requiring only 0.4 second per reaction. The RMSD and barrier height error is further improved by roughly 25\% through pretraining React-OT on a large reaction dataset obtained with a lower level of theory, GFN2-xTB. We envision that the remarkable accuracy and rapid inference of React-OT will be highly useful when integrated with the current high-throughput TS search workflow. This integration will facilitate the exploration of chemical reactions with unknown mechanisms.

Metal-organic frameworks (MOFs) are promising materials for gas sensing but are often limited to single-use detection. We demonstrate a hybridization strategy synergistically deploying conductive MOFs (cMOFs) and conductive polymers (cPs) as two complementary mixed ionic-electronic conductors in high-performing stand-alone chemiresistors. Our work presents significant improvement in i) sensor recovery kinetics, ii) cycling stability, and iii) dynamic range at room temperature. We demonstrate the effect of hybridization across well-studied cMOFs based on 2,3,6,7,10,11-hexahydroxytriphenylene (HHTP) and 2,3,6,7,10,11-hexaiminotripphenylene (HITP) ligands with varied metal nodes (Co, Cu, Ni). We conduct a comprehensive mechanistic study to relate energy band alignments at the heterojunctions between the MOFs and the polymer with sensing thermodynamics and binding kinetics. Our findings reveal that hole enrichment of the cMOF component upon hybridization leads to selective enhancement in desorption kinetics, enabling significantly improved sensor recovery at room temperature, and thus long-term response retention. This mechanism was further supported by density functional theory calculations on sorbate-analyte interactions. We also find that alloying cPs and cMOFs enables facile thin film co-processing and device integration, potentially unlocking the use of these hybrid conductors in diverse electronic applications.

Transition state (TS) search is key in chemistry for elucidating reaction mechanisms and exploring reaction networks. The search for accurate 3D TS structures, however, requires numerous computationally intensive quantum chemistry calculations due to the complexity of potential energy surfaces. Here, we developed an object-aware SE(3) equivariant diffusion model that satisfies all physical symmetries and constraints for generating sets of structures - reactant, TS, and product - in an elementary reaction. Provided reactant and product, this model generates a TS structure in seconds instead of hours required when performing quantum chemistry-based optimizations. The generated TS structures achieve a median of 0.08 {\AA} root mean square deviation compared to the true TS. With a confidence scoring model for uncertainty quantification, we approach an accuracy required for reaction rate estimation (2.6 kcal/mol) by only performing quantum chemistry-based optimizations on 14\% of the most challenging reactions. We envision the proposed approach useful in constructing large reaction networks with unknown mechanisms., Comment: 5 figures and 1 table

High-throughput screening of large hypothetical databases of metal-organic frameworks (MOFs) can uncover new materials, but their stability in real-world applications is often unknown. We leverage community knowledge and machine learning (ML) models to identify MOFs that are thermally stable and stable upon activation. We separate these MOFs into their building blocks and recombine them to make a new hypothetical MOF database of over 50,000 structures that samples orders of magnitude more connectivity nets and inorganic building blocks than prior databases. This database shows an order of magnitude enrichment of ultrastable MOF structures that are stable upon activation and more than one standard deviation more thermally stable than the average experimentally characterized MOF. For the nearly 10,000 ultrastable MOFs, we compute bulk elastic moduli to confirm these materials have good mechanical stability, and we report methane deliverable capacities. Our work identifies privileged metal nodes in ultrastable MOFs that optimize gas storage and mechanical stability simultaneously.

Photoactive iridium complexes are of broad interest due to their applications ranging from lighting to photocatalysis. However, the excited state property prediction of these complexes challenges ab initio methods such as time-dependent density functional theory (TDDFT) both from an accuracy and a computational cost perspective, complicating high throughput virtual screening (HTVS). We instead leverage low-cost machine learning (ML) models to predict the excited state properties of photoactive iridium complexes. We use experimental data of 1,380 iridium complexes to train and evaluate the ML models and identify the best-performing and most transferable models to be those trained on electronic structure features from low-cost density functional theory tight binding calculations. Using these models, we predict the three excited state properties considered, mean emission energy of phosphorescence, excited state lifetime, and emission spectral integral, with accuracy competitive with or superseding TDDFT. We conduct feature importance analysis to identify which iridium complex attributes govern excited state properties and we validate these trends with explicit examples. As a demonstration of how our ML models can be used for HTVS and the acceleration of chemical discovery, we curate a set of novel hypothetical iridium complexes and identify promising ligands for the design of new phosphors.

To accelerate exploration of chemical space, it is necessary to identify the compounds that will provide the most additional information or value. A large-scale analysis of mononuclear octahedral transition metal complexes deposited in an experimental database confirms an under-representation of lower-symmetry complexes. From a set of around 1000 previously studied Fe(II) complexes, we show that the theoretical space of synthetically accessible complexes formed from the relatively small number of unique ligands is significantly (ca. 816k) larger. For the properties of these complexes, we validate the concept of ligand additivity by inferring heteroleptic properties from a stoichiometric combination of homoleptic complexes. An improved interpolation scheme that incorporates information about cis and trans isomer effects predicts the adiabatic spin-splitting energy to around 2 kcal/mol and the HOMO level to less than 0.2 eV. We demonstrate a multi-stage strategy to discover leads from the 816k Fe(II) complexes within a targeted property region. We carry out a coarse interpolation from homoleptic complexes that we refine over a subspace of ligands based on the likelihood of generating complexes with targeted properties. We validate our approach on 9 new binary and ternary complexes predicted to be in a targeted zone of discovery, suggesting opportunities for efficient transition metal complex discovery.

Transition metal chromophores with earth-abundant transition metals are an important design target for their applications in lighting and non-toxic bioimaging, but their design is challenged by the scarcity of complexes that simultaneously have optimal target absorption energies in the visible region as well as well-defined ground states. Machine learning (ML) accelerated discovery could overcome such challenges by enabling screening of a larger space, but is limited by the fidelity of the data used in ML model training, which is typically from a single approximate density functional. To address this limitation, we search for consensus in predictions among 23 density functional approximations across multiple rungs of Jacobs ladder. To accelerate the discovery of complexes with absorption energies in the visible region while minimizing MR character, we use 2D efficient global optimization to sample candidate low-spin chromophores from multi-million complex spaces. Despite the scarcity (i.e., approx. 0.01\%) of potential chromophores in this large chemical space, we identify candidates with high likelihood (i.e., > 10\%) of computational validation as the ML models improve during active learning, representing a 1,000-fold acceleration in discovery. Absorption spectra of promising chromophores from time-dependent density functional theory verify that 2/3 of candidates have the desired excited state properties. The observation that constituent ligands from our leads have demonstrated interesting optical properties in the literature exemplifies the effectiveness of our construction of a realistic design space and active learning approach.

Approximate density functional theory (DFT) has become indispensable owing to its cost-accuracy trade-off in comparison to more computationally demanding but accurate correlated wavefunction theory. To date, however, no single density functional approximation (DFA) with universal accuracy has been identified, leading to uncertainty in the quality of data generated from DFT. With electron density fitting and transfer learning, we build a DFA recommender that selects the DFA with the lowest expected error with respect to gold standard but cost-prohibitive coupled cluster theory in a system-specific manner. We demonstrate this recommender approach on vertical spin-splitting energy evaluation for challenging transition metal complexes. Our recommender predicts top-performing DFAs and yields excellent accuracy (ca. 2 kcal/mol) for chemical discovery, outperforming both individual transfer learning models and the single best functional in a set of 48 DFAs. We demonstrate the transferability of the DFA recommender to experimentally synthesized compounds with distinct chemistry.

Accelerated discovery with machine learning (ML) has begun to provide the advances in efficiency needed to overcome the combinatorial challenge of computational materials design. Nevertheless, ML-accelerated discovery both inherits the biases of training data derived from density functional theory (DFT) and leads to many attempted calculations that are doomed to fail. Many compelling functional materials and catalytic processes involve strained chemical bonds, open-shell radicals and diradicals, or metal-organic bonds to open-shell transition-metal centers. Although promising targets, these materials present unique challenges for electronic structure methods and combinatorial challenges for their discovery. In this Perspective, we describe the advances needed in accuracy, efficiency, and approach beyond what is typical in conventional DFT-based ML workflows. These challenges have begun to be addressed through ML models trained to predict the results of multiple methods or the differences between them, enabling quantitative sensitivity analysis. For DFT to be trusted for a given data point in a high-throughput screen, it must pass a series of tests. ML models that predict the likelihood of calculation success and detect the presence of strong correlation will enable rapid diagnoses and adaptation strategies. These "decision engines" represent the first steps toward autonomous workflows that avoid the need for expert determination of the robustness of DFT-based materials discoveries.

Accurate virtual high-throughput screening (VHTS) of transition metal complexes (TMCs) remains challenging due to the possibility of high multi-reference (MR) character that complicates property evaluation. We compute MR diagnostics for over 5,000 ligands present in previously synthesized 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 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 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.

Despite its widespread use, the predictive accuracy of density functional theory (DFT) is hampered by delocalization errors, especially for correlated systems such as transition-metal complexes. Two complementary tuning strategies have been developed to reduce delocalization error: eliminating the global curvature with respect to charge addition or removal, and computing a linear response Hubbard U as a measure of local curvature at the metal center at fixed charge and applying it to the transition-metal complex in a DFT+U framework. We investigate the relationship between the two measures of delocalization error as we manipulate the ligand field strength by varying the number of strong-field ligands in a series of heteroleptic complexes or by geometrically constraining the metal-ligand bond length in homoleptic octahedral complexes. We show that across these sets of complexes with varying ligand fields, an inverse relationship generally exists between global and local curvatures. We find that effects of ligand substitution on both measures of delocalization are typically additive, but the two quantities seldom coincide. The observation of ligand additivity suggests opportunities for evaluating errors on homoleptic complexes to infer corrections for lower-symmetry complexes.

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 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 optimization on the fly, and exploit its good performance and transferability 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 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 to the use of on-the-fly electronic structure and geometric information generated from density functional theory calculations and the convolutional layer in the dynamic classifier. Combined with model 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.

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). Nevertheless, most VHTS is carried out with approximate density functional theory (DFT) using a single functional. Despite development of numerous MR diagnostics, the extent to which a single value of such a diagnostic indicates MR effect on chemical property prediction is not well established. We evaluate MR diagnostics of over 10,000 transition metal complexes (TMCs) and compare to those in organic molecules. We reveal that only some MR diagnostics are transferable across these materials spaces. By studying the influence of MR character on chemical properties (i.e., MR effect) that involves multiple potential energy surfaces (i.e., adiabatic spin splitting, $\Delta E_\mathrm{H-L}$, and ionization potential, IP), we observe that cancellation in MR effect outweighs accumulation. Differences in MR character are more important than the total degree of MR character in predicting MR effect in property prediction. Motivated by this observation, we build transfer learning models to directly predict CCSD(T)-level adiabatic $\Delta E_\mathrm{H-L}$ 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 chemical accuracy (i.e., 1 kcal/mol) for robust VHTS.

Low-cost, non-empirical corrections to semi-local density functional theory are essential for accurately modeling transition metal chemistry. Here, we demonstrate the judiciously-modified density functional theory (jmDFT) approach with non-empirical U and J parameters obtained directly from frontier orbital energetics on a series of transition metal complexes. We curate a set of nine representative Ti(III) and V(IV) $d^1$ transition metal complexes and evaluate their flat plane errors along the fractional spin and charge lines. We demonstrate that while jmDFT improves upon both DFT+U and semi-local DFT with the standard atomic orbital projectors (AOPs), it does so inefficiently. We rationalize these inefficiencies by quantifying hybridization in the relevant frontier orbitals for both the case of fractional spins and fractional charges. To overcome these limitations, we introduce a procedure for computing a molecular orbital projector (MOP) basis for use with jmDFT. We demonstrate this single set of $d^1$ MOPs to be suitable for nearly eliminating all energetic delocalization error and static correlation error. In all cases, the MOP jmDFT outperforms AOP jmDFT, and it eliminates most flat plane errors at non-empirical values. Unlike widely employed DFT+U or hybrid functionals, jmDFT nearly eliminates energetic delocalization error and static correlation error within a non-empirical framework.

Approximate semi-local density functional theory (DFT) is known to underestimate surface formation energies yet paradoxically overbind adsorbates on catalytic transition-metal oxide surfaces due to delocalization error. The low-cost DFT+U approach only improves surface formation energies for early transition-metal oxides or adsorption energies for late transition-metal oxides. In this work, we demonstrate that this inefficacy arises due to the conventional usage of metal-centered atomic orbitals as projectors within DFT+U. We analyze electron density rearrangement during surface formation and O atom adsorption on rutile transition-metal oxides to highlight that a standard DFT+U correction fails to tune properties when the corresponding density rearrangement is highly delocalized across both metal and oxygen sites. To improve both surface properties simultaneously while retaining the simplicity of a single-site DFT+U correction, we systematically construct multi-atom-centered molecular-orbital-like projectors for DFT+U. We demonstrate this molecular DFT+U approach for tuning adsorption energies and surface formation energies of minimal two-dimensional models of representative early (i.e., TiO2) and late (i.e., PtO2) transition-metal oxides. Molecular DFT+U simultaneously corrects adsorption energies and surface formation energies of multi-layer models of rutile TiO2(110) and PtO2(110) to resolve the paradoxical description of surface stability and surface reactivity of semi-local DFT.

Machine learning (ML)-accelerated discovery requires large amounts of high-fidelity data to reveal predictive structure-property relationships. For many properties of interest in materials discovery, the challenging nature and high cost of data generation has resulted in a data landscape that is both scarcely populated and of dubious quality. Data-driven techniques starting to overcome these limitations include the use of consensus across functionals in density functional theory, the development of new functionals or accelerated electronic structure theories, and the detection of where computationally demanding methods are most necessary. When properties cannot be reliably simulated, large experimental data sets can be used to train ML models. In the absence of manual curation, increasingly sophisticated natural language processing and automated image analysis are making it possible to learn structure-property relationships from the literature. Models trained on these data sets will improve as they incorporate community feedback.

The rational tailoring of transition metal complexes is necessary to address outstanding challenges in energy utilization and storage. Heterobimetallic transition metal complexes that exhibit metal-metal bonding in stacked "double decker" ligand structures are an emerging, attractive platform for catalysis, but their properties are challenging to predict prior to laborious synthetic efforts. We demonstrate an alternative, data-driven approach to uncovering structure-property relationships for rational bimetallic complex design. We tailor graph-based representations of the metal-local environment for these heterobimetallic complexes for use in training of multiple linear regression and kernel ridge regression (KRR) models. Focusing on oxidation potentials, we obtain a set of 28 experimentally characterized complexes to develop a multiple linear regression model. On this training set, we achieve good accuracy (mean absolute error, MAE, of 0.25 V) and preserve transferability to unseen experimental data with a new ligand structure. We trained 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 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.

Modifying the optoelectronic properties of nanostructured materials through introduction of dopant atoms has attracted intense interest. Nevertheless, the approaches employed are often trial and error, preventing rational design. We demonstrate the power of large-scale electronic structure calculations with density functional theory (DFT) to build an atlas of preferential dopant sites for a range of M(II) and M(III) dopants in the representative III-V InP magic sized cluster (MSC). We quantify the thermodynamic favorability of dopants, which we identify to be both specific to the sites within the MSC (i.e., interior vs surface) and to the nature of the dopant atom (i.e., smaller Ga(III) vs larger Y(III) or Sc(III)). These observations motivate development of maps of the most and least favorable doping sites, which are consistent with some known experimental expectations but also yield unexpected observations. For isovalent doping (i.e., Y(III)/Sc(III) or Ga(III), we observed stronger sensitivity of the predicted energetics to the type of ligand orientation on the surface than to the dopant type, but divergent behavior is observed for whether interior doping is favorable. For charge balancing with M(II) (i.e., Zn or Cd) dopants, we show that the type of ligand removed during the doping reaction is critical. We show that limited cooperativity with dopants up to moderate concentrations occurs, indicating rapid single-dopant estimations of favorability from DFT can efficiently guide rational design. Our work emphasizes the strong importance of ligand chemistry and surface heterogeneity in determining paths to favorable doping in quantum dots, an observation that will be general to other III-V and II-VI quantum dot systems generally synthesized with carboxylate ligands.

Although the tailored metal active sites and porous architectures of MOFs hold great promise for engineering challenges ranging from gas separations to catalysis, a lack of understanding of how to improve their stability limits their use in practice. To overcome this limitation, we extract thousands of published reports of the key aspects of MOF stability necessary for their practical application: the ability to withstand high temperatures without degrading and the capacity to be activated by removal of solvent molecules. From nearly 4,000 manuscripts, we use natural language processing and automated image analysis to obtain over 2,000 solvent-removal stability measures and 3,000 thermal degradation temperatures. We analyze the relationships between stability properties and the chemical and geometric structures in this set to identify limits of prior heuristics derived from smaller sets of MOFs. By training predictive machine learning (ML, i.e., Gaussian process and artificial neural network) models to encode the structure-property relationships with graph- and pore-structure-based representations, we are able to make predictions of stability orders of magnitude faster than conventional physics-based modeling or experiment. Interpretation of important features in ML models provides insights that we use to identify strategies to engineer increased stability into typically unstable 3d-containing MOFs that are frequently targeted for catalytic applications. We expect our approach to accelerate the time to discovery of stable, practical MOF materials for a wide range of applications.

Computational 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 the 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 and "rungs" (e.g., semi-local to double hybrid) and basis sets on over 2,000 TMCs. Although computed properties (e.g., spin-state ordering and frontier orbital gap) naturally 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; these features thus provide DFA-invariant, universal design rules. We devise a strategy to train ML models informed by all 23 DFAs and use them to predict properties (e.g., spin-splitting energy) of over 182k TMCs. By requiring consensus of the ANN-predicted DFA properties, we improve correspondence of these computational lead compounds with literature-mined, experimental compounds over the single-DFA approach typically employed. Both feature analysis and consensus-based ML provide efficient, alternative paths to overcome accuracy limitations of practical DFT.

Strategies for machine-learning(ML)-accelerated discovery that are general across materials composition spaces are essential, but demonstrations of ML have been primarily limited to narrow composition variations. By addressing the scarcity of data in promising regions of chemical space for challenging targets like open-shell transition-metal complexes, general representations and transferable ML models that leverage known relationships in existing data will accelerate discovery. Over a large set (ca. 1000) of isovalent transition-metal complexes, we quantify evident relationships for different properties (i.e., spin-splitting and ligand dissociation) between rows of the periodic table (i.e., 3d/4d metals and 2p/3p ligands). We demonstrate an extension to graph-based revised autocorrelation (RAC) representation (i.e., eRAC) that incorporates the effective nuclear charge alongside the nuclear charge heuristic that otherwise overestimates dissimilarity of isovalent complexes. To address the common challenge of discovery in a new space where data is limited, we introduce a transfer learning approach in which we seed models trained on a large amount of data from one row of the periodic table with a small number of data points from the additional row. We demonstrate the synergistic value of the eRACs alongside this transfer learning strategy to consistently improve model performance. Analysis of these models highlights how the approach succeeds by reordering the distances between complexes to be more consistent with the periodic table, a property we expect to be broadly useful for other materials domains.

Computational prediction of enzyme mechanism and protein function requires accurate physics-based models and suitable sampling. We discuss recent advances in large-scale quantum mechanical (QM) modeling of biochemical systems that have reduced the cost of high-accuracy models. Trade-offs between sampling and accuracy have motivated modeling with molecular mechanics (MM) in a multi-scale QM/MM or iterative approach. Limitations to both conventional density functional theory (DFT) and classical MM force fields remain for describing non-covalent interactions in comparison to experiment or wavefunction theory. Because predictions of enzyme action (i.e., electrostatics), free energy barriers, and mechanisms are sensitive to the protocol and embedding method in QM/MM, convergence tests and systematic methods for quantifying QM-level interactions are a needed, active area of development.

Polymers that extend covalently in two dimensions have attracted recent attention as a means of combining the mechanical strength and in-plane energy conduction of conventional two-dimensional (2D) materials with the low densities, synthetic processability, and organic composition of their one-dimensional counterparts. Efforts to date have proven successful in forms that do not allow full realization of these properties, such as polymerization at flat interfaces or fixation of monomers in immobilized lattices. A frequently employed synthetic approach is to introduce microscopic reversibility, at the cost of bond stability, to achieve 2D crystals after extensive error correction. Herein we demonstrate a synthetic route to 2D irreversible polycondensation directly in the solution phase, resulting in covalently bonded 2D polymer platelets that are chemically stable and highly processable. Further fabrication offers highly oriented, free-standing films which exhibit exceptional 2D elastic modulus and yield strength at 50.9 +- 15.0 GPa and 0.976 +- 0.113 GPa, respectively. Platelet alignment is evidenced by polarized photoluminescence centered at 580 and 680 nm from different dipole transitions. This new synthetic route provides opportunities for 2D polymers in applications ranging from composite structures to molecular sieving membranes., Comment: 13 pages, 4 figures

While density functional theory (DFT) is widely applied for its combination of cost and accuracy, corrections (e.g., DFT+U) that improve it are often needed to tackle correlated transition-metal chemistry. In principle, the functional form of DFT+U, consisting of a set of localized atomic orbitals (AO) and a quadratic energy penalty for deviation from integer occupations of those AOs, enables the recovery of the exact conditions of piecewise linearity and the derivative discontinuity. Nevertheless, for practical transition-metal complexes, where both atomic states and ligand orbitals participate in bonding, standard DFT+U can fail to eliminate delocalization error (DE). Here, we show that by introducing an alternative valence-state (i.e., molecular orbital or MO) basis to the DFT+U approach, we recover exact conditions in cases where standard DFT+U corrections have no error-reducing effect. This MO-based DFT+U also eliminates DE where standard AO-based DFT+U is already successful. We demonstrate the transferability of our approach on a range of ligand field strengths (i.e., from H_2O to CO), electron configurations (i.e., from Sc to Fe to Zn), and spin states (i.e., low-spin and high-spin) in representative transition-metal complexes., Comment: 16 double-spaced pages, 5 figures

The flat plane condition is the union of two exact constraints in electronic structure theory: i) energetic piecewise linearity with fractional electron removal or addition and ii) invariant energetics with change in electron spin in a half filled orbital. Semi-local density functional theory (DFT) fails to recover the flat plane, exhibiting convex fractional charge errors (FCE) and concave fractional spin errors (FSE) that are related to delocalization and static correlation errors. We previously showed that DFT+U eliminates FCE but now demonstrate that, like other widely employed corrections (i.e., Hartree Fock exchange), it worsens FSE. To find an alternative strategy, we examine the shape of semi-local DFT deviations from the exact flat plane, and we find this shape to be remarkably consistent across ions and molecules. We introduce the jmDFT approach, wherein corrections are constructed from few-parameter, low- order, functional forms that fit the shape of semi-local DFT errors. We select one such physically intuitive form and incorporate it self-consistently to correct semi-local DFT. We demonstrate on model systems that this jmDFT approach represents the first easy-to-implement, no-overhead approach to recovering the flat plane from semi-local DFT., Comment: 18 pages, 4 figures

Machine learning (ML) of quantum mechanical properties shows promise for accelerating chemical discovery. For transition metal chemistry where accurate calculations are computationally costly and available training data sets are small, the molecular representation becomes a critical ingredient in ML model predictive accuracy. We introduce a series of revised autocorrelation functions (RACs) that encode relationships between the heuristic atomic properties (e.g., size, connectivity, and electronegativity) on a molecular graph. We alter the starting point, scope, and nature of the quantities evaluated in standard ACs to make these RACs amenable to inorganic chemistry. On an organic molecule set, we first demonstrate superior standard AC performance to other presently-available topological descriptors for ML model training, with mean unsigned errors (MUEs) for atomization energies on set-aside test molecules as low as 6 kcal/mol. For inorganic chemistry, our RACs yield 1 kcal/mol ML MUEs on set-aside test molecules in spin-state splitting in comparison to 15-20x higher errors from feature sets that encode whole-molecule structural information. Systematic feature selection methods including univariate filtering, recursive feature elimination, and direct optimization (e.g., random forest and LASSO) are compared. Random-forest- or LASSO-selected subsets 4-5x smaller than RAC-155 produce sub- to 1-kcal/mol spin-splitting MUEs, with good transferability to metal-ligand bond length prediction (0.004-5 {\AA} MUE) and redox potential on a smaller data set (0.2-0.3 eV MUE). Evaluation of feature selection results across property sets reveals the relative importance of local, electronic descriptors (e.g., electronegativity, atomic number) in spin-splitting and distal, steric effects in redox potential and bond lengths., Comment: 43 double spaced pages, 11 figures, 4 tables

High-throughput computational screening has emerged as a critical component of materials discovery. Direct density functional theory (DFT) simulation of inorganic materials and molecular transition metal complexes is often used to describe subtle trends in inorganic bonding and spin-state ordering, but these calculations are computationally costly and properties are sensitive to the exchange-correlation functional employed. To begin to overcome these challenges, we trained artificial neural networks (ANNs) to predict quantum-mechanically-derived properties, including spin-state ordering, sensitivity to Hartree-Fock exchange, and spin- state specific bond lengths in transition metal complexes. Our ANN is trained on a small set of inorganic-chemistry-appropriate empirical inputs that are both maximally transferable and do not require precise three-dimensional structural information for prediction. Using these descriptors, our ANN predicts spin-state splittings of single-site transition metal complexes (i.e., Cr-Ni) at arbitrary amounts of Hartree-Fock exchange to within 3 kcal/mol accuracy of DFT calculations. Our exchange-sensitivity ANN enables improved predictions on a diverse test set of experimentally-characterized transition metal complexes by extrapolation from semi-local DFT to hybrid DFT. The ANN also outperforms other machine learning models (i.e., support vector regression and kernel ridge regression), demonstrating particularly improved performance in transferability, as measured by prediction errors on the diverse test set. We establish the value of new uncertainty quantification tools to estimate ANN prediction uncertainty in computational chemistry, and we provide additional heuristics for identification of when a compound of interest is likely to be poorly predicted by the ANN., Comment: 26 pages of text, 13 figures, 4 tables

Hybrid quantum mechanical-molecular mechanical (QM/MM) simulations are widely used in enzyme simulation. Over ten convergence studies of QM/MM methods have revealed over the past several years that key energetic and structural properties approach asymptotic limits with only very large (ca. 500-1000 atom) QM regions. This slow convergence has been observed to be due in part to significant charge transfer between the core active site and surrounding protein environment, which cannot be addressed by improvement of MM force fields or the embedding method employed within QM/MM. Given this slow convergence, it becomes essential to identify strategies for the most atom-economical determination of optimal QM regions and to gain insight into the crucial interactions captured only in large QM regions. Here, we extend and develop two methods for quantitative determination of QM regions. First, in the charge shift analysis (CSA) method, we probe the reorganization of electron density when core active site residues are removed completely, as determined by large-QM region QM/MM calculations. Second, we introduce the highly-parallelizable Fukui shift analysis (FSA), which identifies how core/substrate frontier states are altered by the presence of an additional QM residue on smaller initial QM regions. We demonstrate that the FSA and CSA approaches are complementary and consistent on three test case enzymes: catechol O-methyltransferase, cytochrome P450cam, and hen eggwhite lysozyme. We also introduce validation strategies and test sensitivities of the two methods to geometric structure, basis set size, and electronic structure methodology. Both methods represent promising approaches for the systematic, unbiased determination of quantum mechanical effects in enzymes and large systems that necessitate multi-scale modeling., Comment: 44 pages, 13 figures, submitted