Informing geometric deep learning with electronic interactions to accelerate quantum chemistry.

Predicting electronic energies, densities, and related chemical properties can facilitate the discovery of novel catalysts, medicines, and battery materials. However, existing machine learning techniques are challenged by the scarcity of training data when exploring unknown chemical spaces. We overcome this barrier by systematically incorporating knowledge of molecular electronic structure into deep learning. By developing a physics-inspired equivariant neural network, we introduce a method to learn molecular representations based on the electronic interactions among atomic orbitals. Our method, OrbNet-Equi, leverages efficient tight-binding simulations and learned mappings to recover high-fidelity physical quantities. OrbNet-Equi accurately models a wide spectrum of target properties while being several orders of magnitude faster than density functional theory. Despite only using training samples collected from readily available small-molecule libraries, OrbNet-Equi outperforms traditional semiempirical and machine learning-based methods on comprehensive downstream benchmarks that encompass diverse main-group chemical processes. Our method also describes interactions in challenging charge-transfer complexes and open-shell systems. We anticipate that the strategy presented here will help to expand opportunities for studies in chemistry and materials science, where the acquisition of experimental or reference training data is costly.

Coordination of -1 programmed ribosomal frameshifting by transcript and nascent chain features revealed by deep mutational scanning.

Programmed ribosomal frameshifting (PRF) is a translational recoding mechanism that enables the synthesis of multiple polypeptides from a single transcript. During translation of the alphavirus structural polyprotein, the efficiency of -1PRF is coordinated by a 'slippery' sequence in the transcript, an adjacent RNA stem-loop, and a conformational transition in the nascent polypeptide chain. To characterize each of these effectors, we measured the effects of 4530 mutations on -1PRF by deep mutational scanning. While most mutations within the slip-site and stem-loop reduce the efficiency of -1PRF, the effects of mutations upstream of the slip-site are far more variable. We identify several regions where modifications of the amino acid sequence of the nascent polypeptide impact the efficiency of -1PRF. Molecular dynamics simulations of polyprotein biogenesis suggest the effects of these mutations primarily arise from their impacts on the mechanical forces that are generated by the translocon-mediated cotranslational folding of the nascent polypeptide chain. Finally, we provide evidence suggesting that the coupling between cotranslational folding and -1PRF depends on the translation kinetics upstream of the slip-site. These findings demonstrate how -1PRF is coordinated by features within both the transcript and nascent chain.

Solution-Phase Conformational/Vibrational Anharmonicity in Comonomer Incorporation Polyolefin Catalysis.

The prediction of comonomer incorporation statistics in polyolefin catalysis necessitates an accurate calculation of free energies corresponding to monomer binding and insertion, often requiring sub-kcal/mol resolution to resolve experimental free energies. Batch reactor experiments are used to probe incorporation statistics of ethene and larger α-olefins for three constrained geometry complexes which are employed as model systems. Herein, over 6 ns of quantum mechanics/molecular mechanics (QM/MM) molecular dynamics is performed in combination with the zero-temperature string method to characterize the solution-phase insertion barrier and to analyze the contributions from conformational and vibrational anharmonicity arising both in vacuum and in solution. Conformational sampling in the solution-phase results in 0-2 kcal/mol corrections to the insertion barrier which are on the same scale necessary to resolve experimental free energies. Anharmonic contributions from conformational sampling in the solution phase are crucial energy contributions missing from static density functional theory calculations and implicit solvation models, and the accurate calculation of these contributions is a key step toward the quantitative prediction of comonomer incorporation statistics.

Fast Near Ab Initio Potential Energy Surfaces Using Machine Learning.

A machine-learning based approach for evaluating potential energies for quantum mechanical studies of properties of the ground and excited vibrational states of small molecules is developed. This approach uses the molecular-orbital-based machine learning (MOB-ML) method to generate electronic energies with the accuracy of CCSD(T) calculations at the same cost as a Hartree-Fock calculation. To further reduce the computational cost of the potential energy evaluations without sacrificing the CCSD(T) level accuracy, GPU-accelerated Neural Network Potential Energy Surfaces (NN-PES) are trained to geometries and energies that are collected from small-scale Diffusion Monte Carlo (DMC) simulations, which are run using energies evaluated using the MOB-ML model. The combined NN+(MOB-ML) approach is used in variational calculations of the ground and low-lying vibrational excited states of water and in DMC calculations of the ground states of water, CH5+, and its deuterated analogues. For both of these molecules, comparisons are made to the results obtained using potentials that were fit to much larger sets of electronic energies than were required to train the MOB-ML models. The NN+(MOB-ML) approach is also used to obtain a potential surface for C2H5+, which is a carbocation with a nonclassical equilibrium structure for which there is currently no available potential surface. This potential is used to explore the CH stretching vibrations, focusing on those of the bridging hydrogen atom. For both CH5+ and C2H5+ the MOB-ML model is trained using geometries that were sampled from an AIMD trajectory, which was run at 350 K. By comparison, the structures sampled in the ground state calculations can have energies that are as much as ten times larger than those used to train the MOB-ML model. For water a higher temperature AIMD trajectory is needed to obtain accurate results due to the smaller thermal energy. A second MOB-ML model for C2H5+ was developed with additional higher energy structures in the training set. The two models are found to provide nearly identical descriptions of the ground state of C2H5+.

Molecular dipole moment learning via rotationally equivariant derivative kernels in molecular-orbital-based machine learning.

This study extends the accurate and transferable molecular-orbital-based machine learning (MOB-ML) approach to modeling the contribution of electron correlation to dipole moments at the cost of Hartree-Fock computations. A MOB pairwise decomposition of the correlation part of the dipole moment is applied, and these pair dipole moments could be further regressed as a universal function of MOs. The dipole MOB features consist of the energy MOB features and their responses to electric fields. An interpretable and rotationally equivariant derivative kernel for Gaussian process regression (GPR) is introduced to learn the dipole moment more efficiently. The proposed problem setup, feature design, and ML algorithm are shown to provide highly accurate models for both dipole moments and energies on water and 14 small molecules. To demonstrate the ability of MOB-ML to function as generalized density-matrix functionals for molecular dipole moments and energies of organic molecules, we further apply the proposed MOB-ML approach to train and test the molecules from the QM9 dataset. The application of local scalable GPR with Gaussian mixture model unsupervised clustering GPR scales up MOB-ML to a large-data regime while retaining the prediction accuracy. In addition, compared with the literature results, MOB-ML provides the best test mean absolute errors of 4.21 mD and 0.045 kcal/mol for dipole moment and energy models, respectively, when training on 110 000 QM9 molecules. The excellent transferability of the resulting QM9 models is also illustrated by the accurate predictions for four different series of peptides.

Equilibrium-nonequilibrium ring-polymer molecular dynamics for nonlinear spectroscopy.

Two-dimensional Raman and hybrid terahertz-Raman spectroscopic techniques provide invaluable insight into molecular structures and dynamics of condensed-phase systems. However, corroborating experimental results with theory is difficult due to the high computational cost of incorporating quantum-mechanical effects in the simulations. Here, we present the equilibrium-nonequilibrium ring-polymer molecular dynamics (RPMD), a practical computational method that can account for nuclear quantum effects on the two-time response function of nonlinear optical spectroscopy. Unlike a recently developed approach based on the double Kubo transformed (DKT) correlation function, our method is exact in the classical limit, where it reduces to the established equilibrium-nonequilibrium classical molecular dynamics method. Using benchmark model calculations, we demonstrate the advantages of the equilibrium-nonequilibrium RPMD over classical and DKT-based approaches. Importantly, its derivation, which is based on the nonequilibrium RPMD, obviates the need for identifying an appropriate Kubo transformed correlation function and paves the way for applying real-time path-integral techniques to multidimensional spectroscopy.

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.

Energy conversion via metal nanolayers.

Current approaches for electric power generation from nanoscale conducting or semiconducting layers in contact with moving aqueous droplets are promising as they show efficiencies of around 30%, yet even the most successful ones pose challenges regarding fabrication and scaling. Here, we report stable, all-inorganic single-element structures synthesized in a single step that generate electrical current when alternating salinity gradients flow along its surface in a liquid flow cell. Nanolayers of iron, vanadium, or nickel, 10 to 30 nm thin, produce open-circuit potentials of several tens of millivolt and current densities of several microA cm-2 at aqueous flow velocities of just a few cm s-1 The principle of operation is strongly sensitive to charge-carrier motion in the thermal oxide nanooverlayer that forms spontaneously in air and then self-terminates. Indeed, experiments suggest a role for intraoxide electron transfer for Fe, V, and Ni nanolayers, as their thermal oxides contain several metal-oxidation states, whereas controls using Al or Cr nanolayers, which self-terminate with oxides that are redox inactive under the experimental conditions, exhibit dramatically diminished performance. The nanolayers are shown to generate electrical current in various modes of application with moving liquids, including sliding liquid droplets, salinity gradients in a flowing liquid, and in the oscillatory motion of a liquid without a salinity gradient.

Force transduction creates long-ranged coupling in ribosomes stalled by arrest peptides.

Force-sensitive arrest peptides regulate protein biosynthesis by stalling the ribosome as they are translated. Synthesis can be resumed when the nascent arrest peptide experiences a pulling force of sufficient magnitude to break the stall. Efficient stalling is dependent on the specific identity of a large number of amino acids, including amino acids that are tens of angstroms away from the peptidyl transferase center (PTC). The mechanism of force-induced restart and the role of these essential amino acids far from the PTC is currently unknown. We use hundreds of independent molecular dynamics trajectories spanning over 120 µs in combination with kinetic analysis to characterize multiple barriers along the force-induced restart pathway for the arrest peptide SecM. We find that the essential amino acids far from the PTC play a major role in controlling the transduction of applied force. In successive states along the stall-breaking pathway, the applied force propagates up the nascent chain until it reaches the C-terminus of SecM and the PTC, inducing conformational changes that allow for restart of translation. A similar mechanism of force propagation through multiple states is observed in the VemP stall-breaking pathway, but secondary structure in VemP allows for heterogeneity in the order of transitions through intermediate states. Results from both arrest peptides explain how residues that are tens of angstroms away from the catalytic center of the ribosome impact stalling efficiency by mediating the response to an applied force and shielding the amino acids responsible for maintaining the stalled state of the PTC.

Cotranslational folding stimulates programmed ribosomal frameshifting in the alphavirus structural polyprotein.

Viruses maximize their genetic coding capacity through a variety of biochemical mechanisms, including programmed ribosomal frameshifting (PRF), which facilitates the production of multiple proteins from a single mRNA transcript. PRF is typically stimulated by structural elements within the mRNA that generate mechanical tension between the transcript and ribosome. However, in this work, we show that the forces generated by the cotranslational folding of the nascent polypeptide chain can also enhance PRF. Using an array of biochemical, cellular, and computational techniques, we first demonstrate that the Sindbis virus structural polyprotein forms two competing topological isomers during its biosynthesis at the ribosome-translocon complex. We then show that the formation of one of these topological isomers is linked to PRF. Coarse-grained molecular dynamics simulations reveal that the translocon-mediated membrane integration of a transmembrane domain upstream from the ribosomal slip site generates a force on the nascent polypeptide chain that scales with observed frameshifting. Together, our results indicate that cotranslational folding of this viral protein generates a tension that stimulates PRF. To our knowledge, this constitutes the first example in which the conformational state of the nascent polypeptide chain has been linked to PRF. These findings raise the possibility that, in addition to RNA-mediated translational recoding, a variety of cotranslational folding or binding events may also stimulate PRF.

Efficient Copolymerization of Acrylate and Ethylene with Neutral P, O-Chelated Nickel Catalysts: Mechanistic Investigations of Monomer Insertion and Chelate Formation.

The efficient copolymerization of acrylates with ethylene using Ni catalysts remains a challenge. Herein, we report two neutral Ni(II) catalysts (POP-Ni-py (1) and PONap-Ni-py (2)) that exhibit high thermal stability and significantly higher incorporation of polar monomer (for 1) or improved resistance to tert-butylacrylate (tBA)-induced chain transfer (for 2), in comparison to previously reported catalysts. Nickel alkyl complexes generated after tBA insertion, POP-Ni-CCO(py) (3) and PONap-Ni-CCO(py) (4), were isolated and, for the first time, characterized by crystallography. Weakened lutidine vs pyridine coordination in 2-lut facilitated the isolation of a N-donor-free adduct after acrylate insertion PONap-Ni-CCO (5) which represents a novel example of a four-membered chelate relevant to acrylate polymerization catalysis. Experimental kinetic studies of six cases of monomer insertion with aforementioned nickel complexes indicate that pyridine dissociation and monomer coordination are fast relative to monomer migratory insertion and that monomer enchainment after tBA insertion is the rate limiting step of copolymerization. Further evaluation of monomer insertion using density functional theory studies identified a cis-trans isomerization via Berry-pseudorotation involving one of the pendant ether groups as the rate-limiting step for propagation, in the absence of a polar group at the chain end. The energy profiles for ethylene and tBA enchainments are in qualitative agreement with experimental measurements.

Electronic Structure of Superoxidized Radical Cationic Dodecaborate-Based Clusters.

The expanding field of boron clusters has attracted continuous theoretical efforts to understand their diverse structures and unique bonding. We recently discovered a new reversible redox event of B12(O-3-methylbutyl)12 in which the superoxidized radical cationic form [B12(O-3-methylbutyl)12]•+ was identified and isolated for the first time. Herein, comprehensive (TD-)DFT studies in tandem with electrochemical experiments were employed to demonstrate the generality of the reported behavior across perfunctionalized B12(OR)12 clusters (R = aryl or alkyl). While the spin density of radical cationic clusters is delocalized in the core region, the oxidation brings about notable gains of positive partial charges on the supporting groups whose electronics can readily tune the redox potential of the 0/•+ couple. The underlying changes of frontier orbitals were elucidated, and the resulting [B12(OR)12]•+ species manifest a general diagnostic absorption as a consequence of mixed local/charge-transfer excitations.

A generalized class of strongly stable and dimension-free T-RPMD integrators.

Recent work shows that strong stability and dimensionality freedom are essential for robust numerical integration of thermostatted ring-polymer molecular dynamics (T-RPMD) and path-integral molecular dynamics, without which standard integrators exhibit non-ergodicity and other pathologies [R. Korol et al., J. Chem. Phys. 151, 124103 (2019) and R. Korol et al., J. Chem. Phys. 152, 104102 (2020)]. In particular, the BCOCB scheme, obtained via Cayley modification of the standard BAOAB scheme, features a simple reparametrization of the free ring-polymer sub-step that confers strong stability and dimensionality freedom and has been shown to yield excellent numerical accuracy in condensed-phase systems with large time steps. Here, we introduce a broader class of T-RPMD numerical integrators that exhibit strong stability and dimensionality freedom, irrespective of the Ornstein-Uhlenbeck friction schedule. In addition to considering equilibrium accuracy and time step stability as in previous work, we evaluate the integrators on the basis of their rates of convergence to equilibrium and their efficiency at evaluating equilibrium expectation values. Within the generalized class, we find BCOCB to be superior with respect to accuracy and efficiency for various configuration-dependent observables, although other integrators within the generalized class perform better for velocity-dependent quantities. Extensive numerical evidence indicates that the stated performance guarantees hold for the strongly anharmonic case of liquid water. Both analytical and numerical results indicate that BCOCB excels over other known integrators in terms of accuracy, efficiency, and stability with respect to time step for practical applications.

Analytical gradients for molecular-orbital-based machine learning.

Molecular-orbital-based machine learning (MOB-ML) enables the prediction of accurate correlation energies at the cost of obtaining molecular orbitals. Here, we present the derivation, implementation, and numerical demonstration of MOB-ML analytical nuclear gradients, which are formulated in a general Lagrangian framework to enforce orthogonality, localization, and Brillouin constraints on the molecular orbitals. The MOB-ML gradient framework is general with respect to the regression technique (e.g., Gaussian process regression or neural networks) and the MOB feature design. We show that MOB-ML gradients are highly accurate compared to other ML methods on the ISO17 dataset while only being trained on energies for hundreds of molecules compared to energies and gradients for hundreds of thousands of molecules for the other ML methods. The MOB-ML gradients are also shown to yield accurate optimized structures at a computational cost for the gradient evaluation that is comparable to a density-corrected density functional theory calculation.

Improved accuracy and transferability of molecular-orbital-based machine learning: Organics, transition-metal complexes, non-covalent interactions, and transition states.

Molecular-orbital-based machine learning (MOB-ML) provides a general framework for the prediction of accurate correlation energies at the cost of obtaining molecular orbitals. The application of Nesbet's theorem makes it possible to recast a typical extrapolation task, training on correlation energies for small molecules and predicting correlation energies for large molecules, into an interpolation task based on the properties of orbital pairs. We demonstrate the importance of preserving physical constraints, including invariance conditions and size consistency, when generating the input for the machine learning model. Numerical improvements are demonstrated for different datasets covering total and relative energies for thermally accessible organic and transition-metal containing molecules, non-covalent interactions, and transition-state energies. MOB-ML requires training data from only 1% of the QM7b-T dataset (i.e., only 70 organic molecules with seven and fewer heavy atoms) to predict the total energy of the remaining 99% of this dataset with sub-kcal/mol accuracy. This MOB-ML model is significantly more accurate than other methods when transferred to a dataset comprising of 13 heavy atom molecules, exhibiting no loss of accuracy on a size intensive (i.e., per-electron) basis. It is shown that MOB-ML also works well for extrapolating to transition-state structures, predicting the barrier region for malonaldehyde intramolecular proton-transfer to within 0.35 kcal/mol when only trained on reactant/product-like structures. Finally, the use of the Gaussian process variance enables an active learning strategy for extending the MOB-ML model to new regions of chemical space with minimal effort. We demonstrate this active learning strategy by extending a QM7b-T model to describe non-covalent interactions in the protein backbone-backbone interaction dataset to an accuracy of 0.28 kcal/mol.

OrbNet Denali: A machine learning potential for biological and organic chemistry with semi-empirical cost and DFT accuracy.

We present OrbNet Denali, a machine learning model for an electronic structure that is designed as a drop-in replacement for ground-state density functional theory (DFT) energy calculations. The model is a message-passing graph neural network that uses symmetry-adapted atomic orbital features from a low-cost quantum calculation to predict the energy of a molecule. OrbNet Denali is trained on a vast dataset of 2.3 × 106 DFT calculations on molecules and geometries. This dataset covers the most common elements in biochemistry and organic chemistry (H, Li, B, C, N, O, F, Na, Mg, Si, P, S, Cl, K, Ca, Br, and I) and charged molecules. OrbNet Denali is demonstrated on several well-established benchmark datasets, and we find that it provides accuracy that is on par with modern DFT methods while offering a speedup of up to three orders of magnitude. For the GMTKN55 benchmark set, OrbNet Denali achieves WTMAD-1 and WTMAD-2 scores of 7.19 and 9.84, on par with modern DFT functionals. For several GMTKN55 subsets, which contain chemical problems that are not present in the training set, OrbNet Denali produces a mean absolute error comparable to those of DFT methods. For the Hutchison conformer benchmark set, OrbNet Denali has a median correlation coefficient of R2 = 0.90 compared to the reference DLPNO-CCSD(T) calculation and R2 = 0.97 compared to the method used to generate the training data (ωB97X-D3/def2-TZVP), exceeding the performance of any other method with a similar cost. Similarly, the model reaches chemical accuracy for non-covalent interactions in the S66x10 dataset. For torsional profiles, OrbNet Denali reproduces the torsion profiles of ωB97X-D3/def2-TZVP with an average mean absolute error of 0.12 kcal/mol for the potential energy surfaces of the diverse fragments in the TorsionNet500 dataset.

Fluctuating hydrogen-bond networks govern anomalous electron transfer kinetics in a blue copper protein.

We combine experimental and computational methods to address the anomalous kinetics of long-range electron transfer (ET) in mutants of Pseudomonas aeruginosa azurin. ET rates and driving forces for wild type (WT) and three N47X mutants (X = L, S, and D) of Ru(2,2'-bipyridine)2 (imidazole)(His83) azurin are reported. An enhanced ET rate for the N47L mutant suggests either an increase of the donor-acceptor (DA) electronic coupling or a decrease in the reorganization energy for the reaction. The underlying atomistic features are investigated using a recently developed nonadiabatic molecular dynamics method to simulate ET in each of the azurin mutants, revealing unexpected aspects of DA electronic coupling. In particular, WT azurin and all studied mutants exhibit more DA compression during ET (>2 Å) than previously recognized. Moreover, it is found that DA compression involves an extended network of hydrogen bonds, the fluctuations of which gate the ET reaction, such that DA compression is facilitated by transiently rupturing hydrogen bonds. It is found that the N47L mutant intrinsically disrupts this hydrogen-bond network, enabling particularly facile DA compression. This work, which reveals the surprisingly fluctional nature of ET in azurin, suggests that hydrogen-bond networks can modulate the efficiency of long-range biological ET.

Dynamics of Co-translational Membrane Protein Integration and Translocation via the Sec Translocon.

An important aspect of cellular function is the correct targeting and delivery of newly synthesized proteins. Central to this task is the machinery of the Sec translocon, a transmembrane channel that is involved in both the translocation of nascent proteins across cell membranes and the integration of proteins into the membrane. Considerable experimental and computational effort has focused on the Sec translocon and its role in nascent protein biosynthesis, including the correct folding and expression of integral membrane proteins. However, the use of molecular simulation methods to explore Sec-facilitated protein biosynthesis is hindered by the large system sizes and long (i.e., minute) time scales involved. In this work, we describe the development and application of a coarse-grained simulation approach that addresses these challenges and allows for direct comparison with both in vivo and in vitro experiments. The method reproduces a wide range of experimental observations, providing new insights into the underlying molecular mechanisms, predictions for new experiments, and a strategy for the rational enhancement of membrane protein expression levels.

A Super-Oxidized Radical Cationic Icosahedral Boron Cluster.

While the icosahedral closo-[B12H12]2- cluster does not display reversible electrochemical behavior, perfunctionalization of this species via substitution of all 12 B-H vertices with alkoxy or benzyloxy (OR) substituents engenders reversible redox chemistry, providing access to clusters in the dianionic, monoanionic, and neutral forms. Here, we evaluated the electrochemical behavior of the electron-rich B12(O-3-methylbutyl)12 (1) cluster and discovered that a new reversible redox event that gives rise to a fourth electronic state is accessible through one-electron oxidation of the neutral species. Chemical oxidation of 1 with [N(2,4-Br2C6H3)3]•+ afforded the isolable [1]•+ cluster, which is the first example of an open-shell cationic B12 cluster in which the unpaired electron is proposed to be delocalized throughout the boron cluster core. The oxidation of 1 is also chemically reversible, where treatment of [1]•+ with ferrocene resulted in its reduction back to 1. The identity of [1]•+ is supported by EPR, UV-vis, multinuclear NMR (1H, 11B), and X-ray photoelectron spectroscopic characterization.

Projection-Based Wavefunction-in-DFT Embedding.

Complex chemical systems present challenges to electronic structure theory stemming from large system sizes, subtle interactions, coupled dynamical time scales, and electronically nonadiabatic effects. New methods are needed to perform reliable, rigorous, and affordable electronic structure calculations for simulating the properties and dynamics of such systems. This Account reviews projection-based quantum embedding for electronic structure, which provides a formally exact method for density functional theory (DFT) embedding. The method also provides a rigorous and accurate approach for describing a small part of a chemical system at the level of a correlated wavefunction (WF) method while the remainder of the system is described at the level of DFT. A key advantage of projection-based embedding is that it can be formulated in terms of an extremely simple level-shift projection operator, which eliminates the need for any optimized effective potential calculation or kinetic energy functional approximation while simultaneously ensuring that no extra programming is needed to perform WF-in-DFT embedding with an arbitrary WF method. The current work presents the theoretical underpinnings of projection-based embedding, describes use of the method for combining wavefunction and density functional theories, and discusses technical refinements that have improved the applicability and robustness of the method. Applications of projection-based WF-in-DFT embedding are also reviewed, with particular focus on recent work on transition-metal catalysis, enzyme reactivity, and battery electrolyte decomposition. In particular, we review the application of projection-based embedding for the prediction of electrochemical potentials and reaction pathways in a Co-centered hydrogen evolution catalyst. Projection-based WF-in-DFT calculations are shown to provide quantitative accuracy while greatly reducing the computational cost compared with a reference coupled cluster calculation on the full system. Additionally, projection-based WF-in-DFT embedding is used to study the mechanism of citrate synthase; it is shown that projection-based WF-in-DFT largely eliminates the sensitivity of the potential energy landscape to the employed DFT exchange-correlation functional. Finally, we demonstrate the use of projection-based WF-in-DFT to study electron transfer reactions associated with battery electrolyte decomposition. Projection-based WF-in-DFT embedding is used to calculate the oxidation potentials of neat ethylene carbonate (EC), neat dimethyl carbonate (DMC), and 1:1 mixtures of EC and DMC in order to overcome qualitative inaccuracies in the electron densities and ionization energies obtained from conventional DFT methods. By further embedding the WF-in-DFT description in a molecular mechanics point-charge environment, this work enables an explicit description of the solvent and ensemble averaging of the solvent configurations. Looking forward, we anticipate continued refinement of the projection-based embedding methodology as well as its increasingly widespread application in diverse areas of chemistry, biology, and materials science.