Combining Machine Learning and Computational Chemistry for Predictive Insights Into Chemical Systems.

Machine learning models are poised to make a transformative impact on chemical sciences by dramatically accelerating computational algorithms and amplifying insights available from computational chemistry methods. However, achieving this requires a confluence and coaction of expertise in computer science and physical sciences. This Review is written for new and experienced researchers working at the intersection of both fields. We first provide concise tutorials of computational chemistry and machine learning methods, showing how insights involving both can be achieved. We follow with a critical review of noteworthy applications that demonstrate how computational chemistry and machine learning can be used together to provide insightful (and useful) predictions in molecular and materials modeling, retrosyntheses, catalysis, and drug design.

Quantum alchemy beyond singlets: Bonding in diatomic molecules with hydrogen.

Bonding energies play an essential role in describing the relative stability of molecules in chemical space. Therefore, methods employed to search chemical space need to capture the bonding behavior for a wide range of molecules, including radicals. In this work, we investigate the ability of quantum alchemy to capture the bonding behavior of hypothetical chemical compounds, specifically diatomic molecules involving hydrogen with various electronic structures. We evaluate equilibrium bond lengths, ionization energies, and electron affinities of these fundamental systems. We compare and contrast how well manual quantum alchemy calculations, i.e., quantum mechanics calculations in which the nuclear charge is altered, and quantum alchemy approximations using a Taylor series expansion can predict these molecular properties. Our results suggest that while manual quantum alchemy calculations outperform Taylor series approximations, truncations of Taylor series approximations after the second order provide the most accurate Taylor series predictions. Furthermore, these results suggest that trends in quantum alchemy predictions are generally dependent on the predicted property (i.e., equilibrium bond length, ionization energy, or electron affinity). Taken together, this work provides insight into how quantum alchemy predictions using a Taylor series expansion may be applied to future studies of non-singlet systems as well as the challenges that remain open for predicting the bonding behavior of such systems.

Evaluating quantum alchemy of atoms with thermodynamic cycles: Beyond ground electronic states.

Due to the sheer size of chemical and materials space, high-throughput computational screening thereof will require the development of new computational methods that are accurate, efficient, and transferable. These methods need to be applicable to electron configurations beyond ground states. To this end, we have systematically studied the applicability of quantum alchemy predictions using a Taylor series expansion on quantum mechanics (QM) calculations for single atoms with different electronic structures arising from different net charges and electron spin multiplicities. We first compare QM method accuracy to experimental quantities, including first and second ionization energies, electron affinities, and spin multiplet energy gaps, for a baseline understanding of QM reference data. Next, we investigate the intrinsic accuracy of "manual" quantum alchemy. This method uses QM calculations involving nuclear charge perturbations of one atom's basis set to model another. We then discuss the reliability of quantum alchemy based on Taylor series approximations at different orders of truncation. Overall, we find that the errors from finite basis set treatments in quantum alchemy are significantly reduced when thermodynamic cycles are employed, which highlights a route to improve quantum alchemy in explorations of chemical space. This work establishes important technical aspects that impact the accuracy of quantum alchemy predictions using a Taylor series and provides a foundation for further quantum alchemy studies.

Computational predictions of metal-macrocycle stability constants require accurate treatments of local solvent and pH effects.

Rational design of molecular chelating agents requires a detailed understanding of physicochemical ligand-metal interactions in solvent phase. Computational quantum chemistry methods should be able to provide this, but computational reports have shown poor accuracy when determining absolute binding constants for many chelating molecules. To understand why, we compare and benchmark static- and dynamics-based computational procedures for a range of monovalent and divalent cations binding to a conventional cryptand molecule: 2.2.2-cryptand ([2.2.2]). The benchmarking comparison shows that dynamics simulations using standard OPLS-AA classical potentials can reasonably predict binding constants for monovalent cations, but these procedures fail for divalent cations. We also consider computationally efficient static procedure using Kohn-Sham density functional theory (DFT) and cluster-continuum modeling that accounts for local microsolvation and pH effects. This approach accurately predicts binding energies for monovalent and divalent cations with an average error of 3.2 kcal mol-1 compared to experiment. This static procedure thus should be useful for future molecular screening efforts, and high absolute errors in the literature may be due to inadequate modeling of local solvent and pH effects.

Quantifying Uncertainties in Solvation Procedures for Modeling Aqueous Phase Reaction Mechanisms.

Computational quantum chemistry provides fundamental chemical and physical insights into solvated reaction mechanisms across many areas of chemistry, especially in homogeneous and heterogeneous renewable energy catalysis. Such reactions may depend on explicit interactions with ions and solvent molecules that are nontrivial to characterize. Rigorously modeling explicit solvent effects with molecular dynamics usually brings steep computational costs while the performance of continuum solvent models such as polarizable continuum model (PCM), charge-asymmetric nonlocally determined local-electric (CANDLE), conductor-like screening model for real solvents (COSMO-RS), and effective screening medium method with the reference interaction site model (ESM-RISM) are less well understood for reaction mechanisms. Here, we revisit a fundamental aqueous hydride transfer reaction-carbon dioxide (CO2) reduction by sodium borohydride (NaBH4)-as a test case to evaluate how different solvent models perform in aqueous phase charge migrations that would be relevant to renewable energy catalysis mechanisms. For this system, quantum mechanics/molecular mechanics (QM/MM) molecular dynamics simulations almost exactly reproduced energy profiles from QM simulations, and the Na+ counterion in the QM/MM simulations plays an insignificant role over ensemble averaged trajectories that describe the reaction pathway. However, solvent models used on static calculations gave much more variability in data depending on whether the system was modeled using explicit solvent shells and/or the counterion. We pinpoint this variability due to unphysical descriptions of charge-separated states in the gas phase (i.e., self-interaction errors), and we show that using more accurate hybrid functionals and/or explicit solvent shells lessens these errors. This work closes with recommended procedures for treating solvation in future computational efforts in studying renewable energy catalysis mechanisms.

First-principles modeling of chemistry in mixed solvents: Where to go from here?

Mixed solvents (i.e., binary or higher order mixtures of ionic or nonionic liquids) play crucial roles in chemical syntheses, separations, and electrochemical devices because they can be tuned for specific reactions and applications. Apart from fully explicit solvation treatments that can be difficult to parameterize or computationally expensive, there is currently no well-established first-principles regimen for reliably modeling atomic-scale chemistry in mixed solvent environments. We offer our perspective on how this process could be achieved in the near future as mixed solvent systems become more explored using theoretical and computational chemistry. We first outline what makes mixed solvent systems far more complex compared to single-component solvents. An overview of current and promising techniques for modeling mixed solvent environments is provided. We focus on so-called hybrid solvation treatments such as the conductor-like screening model for real solvents and the reference interaction site model, which are far less computationally demanding than explicit simulations. We also propose that cluster-continuum approaches rooted in physically rigorous quasi-chemical theory provide a robust, yet practical, route for studying chemical processes in mixed solvents.

Thermodynamic Hydricities of Biomimetic Organic Hydride Donors.

Thermodynamic hydricities (Δ GH-) in acetonitrile and dimethyl sulfoxide have been calculated and experimentally measured for several metal-free hydride donors: NADH analogs (BNAH, CN-BNAH, Me-MNAH, HEH), methylene tetrahydromethanopterin analogs (BIMH, CAFH), acridine derivatives (Ph-AcrH, Me2N-AcrH, T-AcrH, 4OH, 2OH, 3NH), and a triarylmethane derivative (6OH). The calculated hydricity values, obtained using density functional theory, showed a reasonably good match (within 3 kcal/mol) with the experimental values, obtained using "potential p Ka" and "hydride-transfer" methods. The hydride donor abilities of model compounds were in the 48.7-85.8 kcal/mol (acetonitrile) and 46.9-84.1 kcal/mol (DMSO) range, making them comparable to previously studied first-row transition metal hydride complexes. To evaluate the relevance of entropic contribution to the overall hydricity, Gibbs free energy differences (Δ GH-) obtained in this work were compared with the enthalpy (Δ HH-) values obtained by others. The results indicate that, even though Δ HH- values exhibit the same trends as Δ GH-, the differences between room-temperature Δ GH- and Δ HH- values range from 3 to 9 kcal/mol. This study also reports a new metal-free hydride donor, namely, an acridine-based compound 3NH, whose hydricity exceeds that of NaBH4. Collectively, this work gives a perspective of use metal-free hydride catalysts in fuel-forming and other reduction processes.

Quantum Chemical Analyses of BH4- and BH3 OH- Hydride Transfers to CO2 in Aqueous Solution with Potentials of Mean Force.

Biomimetic hydride transfer catalysts are a promising route to efficiently convert CO2 into more useful products, but a lack of understanding about their atomic-scale reaction mechanisms slows their development. To this end, we report a computational quantum chemistry study of how aqueous solvation influences CO2 reduction reactions facilitated by sodium borohydride (NaBH4 ) and a partially oxidized derivative (NaBH3 OH). This work compares 0 K reaction barriers from nudged elastic band calculations to free-energy barriers obtained at 300 K using potentials of mean force from umbrella sampling simulations. We show that explicitly treating free energies from reaction pathway sampling has anywhere from a small to a large effect on the reaction-energy profiles for aqueous-phase hydride transfers to CO2 . Sampling along predefined reaction coordinates is thus recommended when it is computationally feasible.

Structural and Substituent Group Effects on Multielectron Standard Reduction Potentials of Aromatic N-Heterocycles.

Aromatic N-heterocycles have been used in electrochemical CO2 reduction, but their precise role is not yet fully understood. We used first-principles quantum chemistry to determine how the molecular sizes and substituent groups of these molecules affect their standard redox potentials involving various proton and electron transfers. We then use that data to generate molecular Pourbaix diagrams to find the electrochemical conditions at which the aromatic N-heterocycle molecules could participate in multiproton and electron shuttling in accordance with the Sabatier principle. While one-electron standard redox potentials for aromatic N-heterocycles can vary significantly with molecule size and the presence of substituent groups, the two-electron and two-proton standard redox potentials depend much less on structural modifications and substituent groups. This indicates that a wide variety of aromatic N-heterocycles can participate in proton, electron, and/or hydride shuttling under suitable electrochemical conditions.

Oxygen transport in perovskite-type solid oxide fuel cell materials: insights from quantum mechanics.

CONSPECTUS: Global advances in industrialization are precipitating increasingly rapid consumption of fossil fuel resources and heightened levels of atmospheric CO2. World sustainability requires viable sources of renewable energy and its efficient use. First-principles quantum mechanics (QM) studies can help guide developments in energy technologies by characterizing complex material properties and predicting reaction mechanisms at the atomic scale. QM can provide unbiased, qualitative guidelines for experimentally tailoring materials for energy applications. This Account primarily reviews our recent QM studies of electrode materials for solid oxide fuel cells (SOFCs), a promising technology for clean, efficient power generation. SOFCs presently must operate at very high temperatures to allow transport of oxygen ions and electrons through solid-state electrolytes and electrodes. High temperatures, however, engender slow startup times and accelerate material degradation. SOFC technologies need cathode and anode materials that function well at lower temperatures, which have been realized with mixed ion-electron conductor (MIEC) materials. Unfortunately, the complexity of MIECs has inhibited the rational tailoring of improved SOFC materials. Here, we gather theoretically obtained insights into oxygen ion conductivity in two classes of perovskite-type materials for SOFC applications: the conventional La1-xSrxMO3 family (M = Cr, Mn, Fe, Co) and the new, promising class of Sr2Fe2-xMoxO6 materials. Using density functional theory + U (DFT+U) with U-J values obtained from ab initio theory, we have characterized the accompanying electronic structures for the two processes that govern ionic diffusion in these materials: (i) oxygen vacancy formation and (ii) vacancy-mediated oxygen migration. We show how the corresponding macroscopic oxygen diffusion coefficient can be accurately obtained in terms of microscopic quantities calculated with first-principles QM. We find that the oxygen vacancy formation energy is a robust descriptor for evaluating oxide ion transport properties. We also find it has a direct relationship with (i) the transition metal-oxygen bond strength and (ii) the extent to which electrons left behind by the departing oxygen delocalize onto the oxygen sublattice. Design principles from our QM results may guide further development of perovskite-based MIEC materials for SOFC applications.

Trends in bond dissociation energies of alcohols and aldehydes computed with multireference averaged coupled-pair functional theory.

As part of our ongoing investigation of the combustion chemistry of oxygenated molecules using multireference correlated wave function methods, we report bond dissociation energies (BDEs) in C1-C4 alcohols (from methanol to the four isomers of butanol) and C1-C4 aldehydes (from methanal to butanal). The BDEs are calculated with a multireference averaged coupled-pair functional-based scheme. We compare these multireference BDEs with those derived from experiment and single-reference methods. Trends in BDEs for the alcohols and aldehydes are rationalized by considering geometry relaxations of dissociated radical fragments, resonance stabilization, and hyperconjugation. Lastly, we discuss the conjectured association between bond strengths and rates of hydrogen abstraction by hydroxyl radicals. In general, abstraction reaction rates are higher at sites where the C-H bond energies are lower (and vice versa). However, comparison with available rate data shows this inverse relationship between bond strengths and abstraction rates does not hold at all temperatures.

Accurate bond energies of biodiesel methyl esters from multireference averaged coupled-pair functional calculations.

Accurate bond dissociation energies (BDEs) are important for characterizing combustion chemistry, particularly the initial stages of pyrolysis. Here we contribute to evaluating the thermochemistry of biodiesel methyl ester molecules using ab initio BDEs derived from a multireference averaged coupled-pair functional (MRACPF2)-based scheme. Having previously validated this approach for hydrocarbons and a variety of oxygenates, herein we provide further validation for bonds within carboxylic acids and methyl esters, finding our scheme predicts BDEs within chemical accuracy (i.e., within 1 kcal/mol) for these molecules. Insights into BDE trends with ester size are then analyzed for methyl formate through methyl crotonate. We find that the carbonyl group in the ester moiety has only a local effect on BDEs. C═C double bonds in ester alkyl chains are found to increase the strengths of bonds adjacent to the double bond. An important exception are bonds beta to C═C or C═O bonds, which produce allylic-like radicals upon dissociation. The observed trends arise from different degrees of geometric relaxation and resonance stabilization in the radicals produced. We also compute BDEs in various small alkanes and alkenes as models for the long hydrocarbon chain of actual biodiesel methyl esters. We again show that allylic bonds in the alkenes are much weaker than those in the small methyl esters, indicating that hydrogen abstractions are more likely at the allylic site and even more likely at bis-allylic sites of alkyl chains due to more electrons involved in π-resonance in the latter. Lastly, we use the BDEs in small surrogates to estimate heretofore unknown BDEs in large methyl esters of biodiesel fuels.

Size-extensivity-corrected multireference configuration interaction schemes to accurately predict bond dissociation energies of oxygenated hydrocarbons.

Oxygenated hydrocarbons play important roles in combustion science as renewable fuels and additives, but many details about their combustion chemistry remain poorly understood. Although many methods exist for computing accurate electronic energies of molecules at equilibrium geometries, a consistent description of entire combustion reaction potential energy surfaces (PESs) requires multireference correlated wavefunction theories. Here we use bond dissociation energies (BDEs) as a foundational metric to benchmark methods based on multireference configuration interaction (MRCI) for several classes of oxygenated compounds (alcohols, aldehydes, carboxylic acids, and methyl esters). We compare results from multireference singles and doubles configuration interaction to those utilizing a posteriori and a priori size-extensivity corrections, benchmarked against experiment and coupled cluster theory. We demonstrate that size-extensivity corrections are necessary for chemically accurate BDE predictions even in relatively small molecules and furnish examples of unphysical BDE predictions resulting from using too-small orbital active spaces. We also outline the specific challenges in using MRCI methods for carbonyl-containing compounds. The resulting complete basis set extrapolated, size-extensivity-corrected MRCI scheme produces BDEs generally accurate to within 1 kcal/mol, laying the foundation for this scheme's use on larger molecules and for more complex regions of combustion PESs.

A Co-Doping Materials Design Strategy for Selective Ozone Electrocatalysts.

Catalysts for electrochemical ozone production (EOP) face inherent selectivity challenges stemming from thermodynamic constraints. This work establishes a design strategy for minimizing these limitations and inducing EOP activity in tin oxide, which is an intrinsically EOP-inactive material. We propose that selective ozone production using tin oxide catalysts can be broadly achieved by co-doping with two elements: first, n-type dopants to enhance electrical conductivity, and second, transition metal dopants that leach and homogeneously generate essential hydroperoxyl radical intermediates. Synthesizing tantalum, antimony, and tungsten n-type dopants with nickel, cobalt, and iron as transition metal dopants confirms that properly co-doping tin oxide yields EOP-active catalysts. This study offers a robust framework for advancing EOP catalyst design and serves as a case study for the application of fundamental co-catalysis and solid-state physics principles to induce catalytic activity in inert materials.

Interplay between Catalyst Corrosion and Homogeneous Reactive Oxygen Species in Electrochemical Ozone Production.

Electrochemical ozone production (EOP), a six-electron water oxidation reaction, offers promising avenues for creating value-added oxidants and disinfectants. However, progress in this field is slowed by a dearth of understanding of fundamental reaction mechanisms. In this work, we combine experimental electrochemistry, spectroscopic detection of reactive oxygen species (ROS), oxygen-anion chemical ionization mass spectrometry, and computational quantum chemistry calculations to determine a plausible reaction mechanism on nickel- and antimony-doped tin oxide (Ni/Sb-SnO2, NATO), one of the most selective EOP catalysts. Antimony doping is shown to increase the conductivity of the catalyst, leading to improved electrochemical performance. Spectroscopic analysis and electrochemical experiments combined with quantum chemistry predictions reveal that hydrogen peroxide (H2O2) is a critical reaction intermediate. We propose that leached Ni4+ cations catalyze hydrogen peroxide into solution phase hydroperoxyl radicals (•OOH); these radicals are subsequently oxidized to ozone. Isotopic product analysis shows that ozone is generated catalytically from water and corrosively from the catalyst oxide lattice without regeneration of lattice oxygens. Further quantum chemistry calculations and thermodynamic analysis suggest that the electrochemical corrosion of tin oxide itself might generate hydrogen peroxide, which is then catalyzed to ozone. The proposed pathways explain both the roles of dopants in NATO and its lack of stability. Our study interrogates the possibility that instability and electrochemical activity are intrinsically linked through the formation of ROS. In doing so, we provide the first mechanism for EOP that is consistent with computational and experimental results and highlight the central challenge of instability as a target for future research efforts.

Elucidation of the selectivity of proton-dependent electrocatalytic CO2 reduction by fac-Re(bpy)(CO)3Cl.

A complete mechanism for the proton-dependent electrocatalytic reduction of CO2 to CO by fac-Re(bpy)(CO)3Cl that is consistent with experimental observations has been developed using first principles quantum chemistry. Calculated one-electron reduction potentials, nonaqueous pKa's, reaction free energies, and reaction barrier heights provide deep insight into the complex mechanism for CO2 reduction as well as the origin of selectivity for this catalyst. Protonation and then reduction of a metastable Re-CO2 intermediate anion precedes Brønsted-acid-catalyzed C-O cleavage and then rapid release of CO at negative applied potentials. Conceptually understanding the mechanism of this rapid catalytic process provides a useful blueprint for future work in artificial photosynthesis.

Theoretical insights into pyridinium-based photoelectrocatalytic reduction of CO2.

The role of pyridinium cations in electrochemistry has been believed known for decades, and their radical forms have been proposed as key intermediates in modern photoelectrocatalytic CO(2) reduction processes. Using first-principles density functional theory and continuum solvation models, we have calculated acidity constants for pyridinium cations and their corresponding pyridinyl radicals, as well as their electrochemical redox potentials. Contrary to previous assumptions, our results show that these species can be ruled out as active participants in homogeneous electrochemistry. A comparison of calculated acidities and redox potentials indicates that pyridinium cations behave differently than previously thought, and that the electrode surface plays a critical (but still unknown) role in pyridinium reduction. This work substantially alters the mechanistic view of pyridinium-catalyzed photoelectrochemical CO(2) reduction.

Water oxidation on pure and doped hematite (0001) surfaces: prediction of Co and Ni as effective dopants for electrocatalysis.

In photoelectrochemical cells, sunlight may be converted into chemical energy by splitting water into hydrogen and oxygen molecules. Hematite (α-Fe(2)O(3)) is a promising photoanode material for the water oxidation component of this process. Numerous research groups have attempted to improve hematite's photocatalytic efficiency despite a lack of foundational knowledge regarding its surface reaction kinetics. To elucidate detailed reaction mechanisms and energetics, we performed periodic density functional theory + U calculations for the water oxidation reaction on the fully hydroxylated hematite (0001) surface. We investigate two different concentrations of surface reactive sites. Our best model involves calculating water oxidation mechanisms on a pure (1×1) hydroxylated hematite slab (corresponding to 1/3 ML of reactive sites) with an additional overlayer of water molecules to model solvation effects. This yields an overpotential of 0.77 V, a value only slightly above the 0.5-0.6 V experimental range. To explore whether doped hematite can exhibit an even lower overpotential, we consider cation doping by substitution of Fe by Ti, Mn, Co, Ni, or Si and F anion doping by replacing O on the fully hydroxylated surface. The reaction energetics on pure or doped hematite surfaces are described using a volcano plot. The relative stabilities of holes on the active O anions are identified as the underlying cause for trends in energetics predicted for different dopants. We show that moderately charged O anions give rise to smaller overpotentials. Co- or Ni-doped hematite surfaces give the most thermodynamically favored reaction pathway (lowest minimum overpotential) among all dopants considered. Very recent measurements (Electrochim. Acta 2012, 59, 121-127) reported improved reactivity with Ni doping, further validating our predictions.

The reaction mechanism of the enantioselective Tsuji allylation: inner-sphere and outer-sphere pathways, internal rearrangements, and asymmetric C-C bond formation.

We use first principles quantum mechanics (density functional theory) to report a detailed reaction mechanism of the asymmetric Tsuji allylation involving prochiral nucleophiles and nonprochiral allyl fragments, which is consistent with experimental findings. The observed enantioselectivity is best explained with an inner-sphere mechanism involving the formation of a 5-coordinate Pd species that undergoes a ligand rearrangement, which is selective with regard to the prochiral faces of the intermediate enolate. Subsequent reductive elimination generates the product and a Pd(0) complex. The reductive elimination occurs via an unconventional seven-centered transition state that contrasts dramatically with the standard three-centered C-C reductive elimination mechanism. Although limitations in the present theory prevent the conclusive identification of the enantioselective step, we note that three different computational schemes using different levels of theory all find that inner-sphere pathways are lower in energy than outer-sphere pathways. This result qualitatively contrasts with established allylation reaction mechanisms involving prochiral nucleophiles and prochiral allyl fragments. Energetic profiles of all reaction pathways are presented in detail.

A Bond-Energy/Bond-Order and Populations Relationship.

We report an analytical bond energy from bond orders and populations (BEBOP) model that provides intramolecular bond energy decompositions for chemical insight into the thermochemistry of molecules. The implementation reported here employs a minimum basis set Mulliken population analysis on well-conditioned Hartree-Fock orbitals to decompose total electronic energies into physically interpretable contributions. The model's parametrization scheme is based on atom-specific parameters for hybridization and atom pair-specific parameters for short-range repulsion and extended Hückel-type bond energy term fitted to reproduce CBS-QB3 thermochemistry data. The current implementation is suitable for molecules involving H, Li, Be, B, C, N, O, and F atoms, and it can be used to analyze intramolecular bond energies of molecular structures at optimized stationary points found from other computational methods. This first-generation model brings the computational cost of a Hartree-Fock calculation using a large triple-ζ basis set, and its atomization energies are comparable to those from widely used hybrid Kohn-Sham density functional theory (DFT, as benchmarked to 109 species from the G2/97 test set and an additional 83 reference species). This model should be useful for the community by interpreting overall ab initio molecular energies in terms of physically insightful bond energy contributions, e.g., bond dissociation energies, resonance energies, molecular strain energies, and qualitative energetic contributions to the activation barrier in chemical reaction mechanisms. This work reports a critical benchmarking of this method as well as discussions of its strengths and weaknesses compared to hybrid DFT (i.e., B3LYP, M062X, PBE0, and APF methods), and other cost-effective approximate Hamiltonian semiempirical quantum methods (i.e., AM1, PM6, PM7, and DFTB3).