Self-interaction error (SIE) in density functional theory (DFT) calculations can lead to inaccurate descriptions of catalytic processes. In this work, we investigate the effects of SIE on a catalytic NO activation cycle on a cluster model of the Cu-SSZ-13 zeolite, systematically identifying transition states and reaction pathways for both single- and multistep reactions. We assess SIE using the Perdew-Zunger self-interaction correction (PZSIC) method, implemented with the Fermi-Löwdin orbital SIC (FLOSIC) approach. We benchmark the performance of standard DFT functionals (LDA, PBE, and r2SCAN) and SI-corrected functionals (PZSIC-LDA and the locally scaled LSIC(zσ)-LDA) against CCSD(T) reference energies for both adsorption energies and reaction barriers. The standard functionals increase in accuracy in the order LDA < PBE < r2SCAN, but all three tend to overestimate adsorption energies and underestimate reaction barriers. While PZSIC-LDA improves the description of reaction energetics over LDA for several reaction steps, it introduces large errors for processes that involve a change in the Cu-oxidation state. These errors are linked to the spurious destabilization of a filled 3d10 electronic shell relative to 3d9 in PZSIC calculations as described recently by Maniar et al. (Proc. Nat. Acad. Sci. 122, e2418305122 (2025)). This causes 3d9-like electronic configurations for the Cu active site to be favored over reference 3d10 configurations at several points in the NO reaction cycle, giving rise to self-consistent PZSIC densities that are qualitatively incorrect. By locally scaling the SIC, LSIC mitigates some of the PZSIC errors and gives more consistent results than PZSIC-LDA. We conclude that to obtain accurate descriptions of catalytic reactions with SIC-based methods, the spurious energetics of transition metal complexes in competing oxidation states must be eliminated.

Molecular dipole moments are required for empirical correlations used to estimate thermophysical properties of zinc dialkyldithiophosphates (ZDDPs), an important class of anti-wear additives. We calculated dipole moments for three ZDDPs and their precursor dialkyldithiophosphates using density functional theory and explicitly accounted for their dependence on molecular conformation. We unexpectedly found that dipole ∗Corresponding author. Email: karlj@pitt.edu moments are highly sensitive to conformational degrees of freedom. The dipole moments for each of these six molecules range from almost zero to almost 5 D across different conformers. Surprisingly, this variation appears to be dominated by the conformations of the alkyl chains rather than the polar inorganic core. Despite this wide range, the arithmetic mean and Boltzmann weighted average dipole moments fall within a narrow range of 2.2–2.4 D for all six molecules examined. This consistency arises because the dipole moment shows no correlation with the conformational energy. The robust average value significantly simplifies property estimation by eliminating the need for conformation-specific dipole calculations. We recommend that thermophysical property correlations use a constant dipole moment of 2.3 D for ZDDPs and their precursors. We predict that experimental measurements will yield values close to this average, since they inherently sample an ensemble of conformations.

To accurately describe the energetics of transition metal systems, density functional approximations (DFAs) must provide a balanced description of s- and d- electrons. One measure of this is the sd transfer error, which has previously been defined as [Formula: see text]. Theoretical concerns have been raised about this definition due to its evaluation of excited-state energies using ground-state DFAs. A more serious concern appears to be strong correlation in the 4s2 configuration. Here, we define a ground-state measure of the sd energy imbalance, based on the errors of s- and d-electron second ionization energies of the 3d atoms, that effectively circumvents the aforementioned problems. We find an improved performance as we move from the local spin density approximation (LSDA) to the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) to the regularized and restored Strongly Constrained and Appropriately Normed (r2SCAN) meta-GGA for first-row transition metal atoms. However, we find large (∼2 eV) ground-state sd energy imbalances when applying a Perdew-Zunger 1981 self-interaction correction. This is attributed to an "energy penalty" associated with the noded 3d orbitals. A local scaling of the self-interaction correction to LSDA results in a balance of s- and d-errors.

Discovering chemical reaction pathways using quantum mechanics is impractical for many systems of practical interest because of unfavorable scaling and computational cost. While machine learning interatomic potentials (MLIPs) trained on quantum mechanical data offer a promising alternative, they face challenges for reactive systems due to the need for extensive sampling of the potential energy surface in regions that are far from equilibrium geometries. Unfortunately, traditional MLIP training protocols are not designed for comprehensive reaction exploration. We present a reactive active learning (RAL) framework that is designed to efficiently train MLIPs to achieve near-quantum mechanical accuracy for reactive systems for situations where one may not have prior knowledge of the possible transition states, reaction pathways, or even the potential products. Our method combines automated reaction exploration, uncertainty-driven active learning, and transition state sampling to build accurate potentials. We demonstrate RAL's effectiveness across three different systems: uncatalyzed ammonia synthesis (gas-phase), methanimine hydrolysis (solution phase), and methane activation on titanium carbide surfaces (heterogeneous). The resulting MLIPs accurately predict reaction barriers and transition states. For catalysis, we show that RAL-trained MLIPs identify Ti2C as the most active methane activation surface (90% decomposition at 1000 K) through C-vacancy mediated mechanisms. The framework's ability to simulate large systems (∼900 atoms) over nanosecond time scales provides previously inaccessible insights into surface poisoning and reaction networks. We show that reactive exploration is essential for adequately capturing the potential energy surface, with chemical and configurational sampling working synergistically to improve model accuracy. Our results establish general guidelines for training robust reactive potentials and open new possibilities for computational discovery of catalysts and reaction mechanisms.

The performance of proton-exchange membrane fuel cells is critically dependent on the conduction of protons. Conventional proton exchange membranes employ materials such as Nafion that conduct protons only when properly hydrated. If the relative humidity is too low or too high, the fuel cell will cease to operate. This limitation highlights the need to develop new materials that can rapidly conduct protons without the need to regulate hydration. We present detailed atomistic simulations predicting that graphamine, which is an aminated graphane, conducts protons anhydrously with a very low diffusion barrier compared to existing materials. We have constructed a deep-learning framework tailored to modeling graphamine, enabling us to fully characterize and evaluate proton conduction within this material. The trained deep-learning potential is computationally economical and has near-density functional theory accuracy. We used our deep-learning potential to calculate the proton diffusion coefficients at different temperatures and to estimate the activation energy barrier for proton diffusion and found a very low barrier of 63 meV. We estimate the proton conductivity of graphamine to be 1322 mS/cm at 300 K. We show that protons hop along Grotthuss chains containing several amine groups and that the multidirectional hydrogen bonding network intrinsic in graphamine is responsible for the fast conduction of protons.

Metal-organic framework (MOF) UiO-66 and its variants have been used for applications ranging from gas adsorption to catalyzing chemical warfare agent degradation. Intrinsic point defects, most commonly missing linkers, are usually present in UiO-66. At high concentrations, defects may significantly impact the material's properties, such as adsorption, transport, and catalytic activity. A quantitative description of how intrinsic defects affect adsorption and transport of guest molecules is required to design tailored materials. In this work, we identify how different arrangements of missing linker defects impact adsorption and diffusion of isopropyl alcohol (IPA). IPA is an ideal test molecule to quantify the impact of missing linker defects on adsorption and diffusion of polar molecules because it forms hydrogen bonds with other IPA molecules and the framework atoms, similar to some classes of chemical warfare agents and their simulants. We have generated 25% missing linker defect structures having ordered and nonordered arrangements of defects. We found that adsorption isotherms are fairly insensitive to the specific arrangement of defects. In contrast, diffusivities can depend strongly on ordering of the defects. Specifically, we found that structures that contain percolating defects, which allow diffusion through the material traversing only defective windows, exhibit faster diffusivities and lower diffusion barriers compared with structures having nonpercolating defects. All defective structures exhibited faster diffusivities at low to moderate IPA loadings than pristine UiO-66. At high IPA loading, diffusivity values in nonpercolating defective structures are less than in pristine UiO-66. This decrease at high loadings is due to IPA forming hydrogen-bonding ring-like structures facilitated by the larger defective pores. We show that an experimentally synthesized defective UiO-66 having a bcu net topology has percolating diffusion pathways, which serves as a proof-of-concept that it is possible to synthesize of MOFs having percolating diffusion pathways.

Metal-organic frameworks (MOFs) are promising candidate materials for photo-driven processes. Their crystalline and tunable structure makes them well-suited for placing photoactive molecules at controlled distances and orientations that support processes such as light harvesting and photocatalysis. In order to optimize their performance, it is important to understand how these molecules evolve shortly after photoexcitation. Here, we use resonance Raman intensity analysis (RRIA) to quantify the excited state nuclear distortions of four modified UiO-68 MOFs. We find that stretching vibrations localized on the central ring within the terphenyl linker are most distorted upon interaction with light. We use a combined computational and experimental approach to create a picture of the early excited state structure of the MOFs upon photoactivation. Overall, we show that RRIA is an effective method to probe the excited state structure of photoactive MOFs and can guide the synthesis and optimization of photoactive designs.

Incorporating diverse components into metal‐organic frameworks (MOFs) can expand their scope of properties and applications. Stratified MOFs (sMOFs) consist of compositionally unique concentric domains (strata), offering unprecedented complexity through partitioning of structural and functional components. However, the labile nature ofmetal‐ligand coordination handicaps achieving compositionally‐distinct domains due to ligand exchange reactions occurring concurrently with secondary strata growth. To achieve complex sMOF compositions, characterizing and controlling the competing processes of new strata growth and ligand exchange are vital. This work systematicallyexamines controlling ligand exchange in UiO‐67 sMOFs by tuning ligand sterics. We present quantitative methods for assessing and visualizing the outcomes of strata growth and ligand exchange that rely on high‐angle annular dark‐field images and elemental mapping via scanning transmission electron microscopy‐energy dispersive X‐ray spectroscopy. In addition, we leverage ligand sterics to create ‘blocking layers’ that minimize ligand exchange between strata which are particularly susceptible to ligand exchange and inter‐strata ligand mixing. Finally, we evaluate strata compositional integrity in various solvents and find that sMOFs can maintain their compositions for >12 months in some cases.Collectively, these studies and methods enhance understanding and control over ligand placement in multi‐domain MOFs, factors that underscore careful tunning of properties and function.

Density functional theory (DFT) suffers from self-interaction errors (SIEs) that generally result in the underestimation of chemical reaction barrier heights. This is commonly attributed to the tendency of density functional approximations to overstabilize delocalized densities that typically occur in the stretched bonds of transition state structures. The Perdew-Zunger self-interaction correction (PZSIC) and locally scaled self-interaction correction (LSIC) improve the prediction of barrier heights of chemical reactions, with LSIC giving better accuracy than PZSIC on average. These methods employ an orbital-by-orbital correction scheme to remove the one-electron SIE. In the context of barrier heights, this allows an analysis of how the self-interaction correction (SIC) for each orbital contributes to the calculated barriers using Fermi-Löwdin orbitals (FLOs). We hypothesize that the SIC contribution to the reaction barrier comes mainly from a limited number of orbitals that are directly involved in bond-breaking and bond-making in the reaction transition state. We call these participant orbitals (POs), in contrast to spectator orbitals (SOs) which are not directly involved in changes to the bonding. Our hypothesis is that ΔETotalSIC ≈ ΔEPOSIC, where ΔETotalSIC is the difference in the SIC corrections for the reactants or products and the transition state. We test this hypothesis for the reaction barriers of the BH76 benchmark set of reactions. We find that the stretched-bond orbitals indeed make the largest individual SIC contributions to the barriers. These contributions increase the barrier heights relative to LSDA, which underpredicts the barrier. However, the full stretched-bond hypothesis does not hold in all cases for either PZSIC or LSIC. There are many cases where the total SIC contribution from the SOs is significant and cannot be ignored. The size of the SIC contribution to the barrier height is a key indicator. A large SIC correction is correlated to a large LSDA error in the barrier, showing that PZSIC properly gives larger corrections when corrections are needed most. A comparison of the performance of PZSIC and LSIC shows that the two methods have similar accuracy for reactions with large LSDA errors, but LSIC is clearly better for reactions with small errors. We trace this to an improved description of reaction energies in LSIC.

Super-resolution structured illumination microscopy (SR-SIM) is an optical fluorescence microscopy method which is suitable for imaging a wide variety of cells and tissues in biological and biomedical research. Typically, SIM methods use high spatial frequency illumination patterns generated by laser interference. This approach provides high resolution but is limited to thin samples such as cultured cells. Using a different strategy for processing raw data and coarser illumination patterns, we imaged through a 150-micrometer-thick coronal section of a mouse brain expressing GFP in a subset of neurons. The resolution reached 144 nm, an improvement of 1.7-fold beyond conventional widefield imaging.

The UiO-6x family of metal-organic frameworks has been extensively studied for applications in chemical warfare agent (CWA) capture and destruction. An understanding of intrinsic transport phenomena, such as diffusion, is key to understanding experimental results and designing effective materials for CWA capture. However, the relatively large size of CWAs and their simulants makes diffusion in the small-pored pristine UiO-66 very slow and hence impractical to study directly with direct molecular simulations because of the time scales required. We used isopropanol (IPA) as a surrogate for CWAs to investigate the fundamental diffusion mechanisms of a polar molecule within pristine UiO-66. IPA can form hydrogen bonds with the μ3-OH groups bound to the metal oxide clusters in UiO-66, similar to some CWAs, and can be studied by direct molecular dynamics simulations. We report self, corrected, and transport diffusivities of IPA in pristine UiO-66 as a function of loading. Our calculations highlight the importance of the accurate modeling of the hydrogen bonding interactions on diffusivities, with about an order of magnitude decrease in diffusion coefficients when the hydrogen bonding between IPA and the μ3-OH groups is included. We found that a fraction of the IPA molecules have very low mobility during the course of a simulation, while a small fraction are highly mobile, exhibiting mean square displacements far greater than the ensemble average.

Development of new materials capable of conducting protons in the absence of water is crucial for improving the performance, reducing the cost, and extending the operating conditions for proton exchange membrane fuel cells. We present detailed atomistic simulations showing that graphanol (hydroxylated graphane) will conduct protons anhydrously with very low diffusion barriers. We developed a deep learning potential (DP) for graphanol that has near-density functional theory accuracy, but requires a very small fraction of the computational cost. We used our DP to calculate proton self-diffusion coefficients as a function of temperature, to estimate the overall barrier to proton diffusion, and to characterize the impact of thermal fluctuations as a function of system size. We propose and test a detailed mechanism for proton conduction on the surface of graphanol. We show that protons can rapidly hop along Grotthuss chains containing several hydroxyl groups aligned such that hydrogen bonds allow for conduction of protons forward and backward along the chain without hydroxyl group rotation. Long-range proton transport only takes place as new Grotthuss chains are formed by rotation of one or more hydroxyl groups in the chain. Thus, the overall diffusion barrier consists of a convolution of the intrinsic proton hopping barrier and the intrinsic hydroxyl rotation barrier. Our results provide a set of design rules for developing new anhydrous proton conducting membranes with even lower diffusion barriers.

There is a need to develop new materials for proton exchange mem- branes that can operate at higher temperatures and low humidities. Designing and evaluating novel membrane materials using density func- tional theory (DFT) is infeasible because of length and time scale limitations of the method. We have developed a deep-learning potential (DP) to evaluate double-sided graphanol (DSG), which is a poten- tial anhydrous proton conducting material. Our DP was trained on DFT data by employing an active learning approach. Our DP is com- putationally efficient and has near-DFT accuracy. We have analyzed DSG by computing phonon properties, estimating thermal fluctuations, and calculate self-diffusivity using our DP. Our results for DSG are compared with single-sided graphanol (SSG). We observed lower ther- mal fluctuation and similar proton self-diffusivity at 800 K in DSG compared to SSG. Our DP simulations show that the structural dif- ferences in DSG compared to SSG do not impact proton transport. DSG is a promising membrane material deserving of synthetic efforts.

Having access to accurate electron densities in chemical systems, especially for dynamical systems involving chemical reactions, ion transport, and other charge transfer processes, is crucial for numerous applications in materials chemistry. Traditional methods for computationally predicting electron density data for such systems include quantum mechanical (QM) techniques, such as density functional theory. However, poor scaling of these QM methods restricts their use to relatively small system sizes and short dynamic time scales. To overcome this limitation, we have developed a deep neural network machine learning formalism, which we call deep charge density prediction (DeepCDP), for predicting charge densities by only using atomic positions for molecules and condensed phase (periodic) systems. Our method uses the weighted smooth overlap of atomic positions to fingerprint environments on a grid-point basis and map it to electron density data generated from QM simulations. We trained models for bulk systems of copper, LiF, and silicon; for a molecular system, water; and for two-dimensional charged and uncharged systems, hydroxyl-functionalized graphane, with and without an added proton. We showed that DeepCDP achieves prediction R2 values greater than 0.99 and mean squared error values on the order of 10−5e2 Å−6 for most systems. DeepCDP scales linearly with system size, is highly parallelizable, and is capable of accurately predicting the excess charge in protonated hydroxyl-functionalized graphane. We demonstrate how DeepCDP can be used to accurately track the location of charges (protons) by computing electron densities at a few selected grid points in the materials, thus significantly reducing the computational cost. We also show that our models can be transferable, allowing prediction of electron densities for systems on which it has not been trained but that contain a subset of atomic species on which it has been trained. Our approach can be used to develop models that span different chemical systems and train them for the study of large-scale charge transport and chemical reactions.

An Achille's heel of lower-rung density-functional approximations is that the highest-occupied-molecular-orbital energy levels of anions, known to be stable or metastable in nature, are often found to be positive in the worst case or above the lowest-unoccupied-molecular-orbital levels on neighboring complexes that are not expected to accept charge. A trianionic example, [Cr(C2O4)3]3-, is of interest for constraining models linking Cr isotope ratios in rock samples to oxygen levels in Earth's atmosphere over geological timescales. Here we describe how crowd sourcing can be used to carry out self-consistent Fermi-Löwdin-Orbital-Self-Interaction corrected calculations (FLOSIC) on this trianion in solution. The calculations give a physically correct description of the electronic structure of the trianion and water. In contrast, uncorrected local density approximation (LDA) calculations result in approximately half of the anion charge being transferred to the water bath due to the effects of self-interaction error. Use of group-theory and the intrinsic sparsity of the theory enables calculations roughly 125 times faster than our initial implementation in the large N limit reached here. By integrating charge density densities and Coulomb potentials over regions of space and analyzing core-level shifts of the Cr and O atoms as a function of position and functional, we unambiguously show that FLOSIC, relative to LDA, reverses incorrect solute-solvent charge transfer in the trianion-water complex. In comparison to other functionals investigated herein, including Hartree-Fock and the local density approximation, the FLOSIC Cr 1s eigenvalues provide the best agreement with experimental core ionization energies.

Development of new materials capable of conducting protons in the absence of water is crucial for improving the performance, reducing the cost, and extending the operating conditions for proton exchange membrane fuel cells. We present detailed atomistic simulations showing that hydroxylated graphane, which we call graphanol, will conduct protons anhydrously with very low diffusion barriers. We developed a deep learning potential (DP) for graphanol that has near-density functional theory accuracy at a small fraction of the computational cost. We used our DP to calculate diffusion coefficients, estimate the diffusion barrier, and compute thermal fluctuations as a function of system size. We identified the mechanism for proton conduction on the surface of graphanol. We show that protons hop along Grotthuss chains containing several hydroxyl groups aligned such that hydrogen bonds allow for conduction of protons forward and backward along the chain without hydroxyl group rotation. Long-range proton transport takes place as new Grotthuss chains form by rotation of hydroxyl groups. Thus, the overall diffusion barrier consists of a convolution of the intrinsic proton hopping barrier and the intrinsic hydroxyl rotation barrier. Our results provide a set of design rules for developing new anhydrous proton conducting membranes with low diffusion barriers.

Color-tunable metal-organic frameworks (MOFs) are emerging materials for light harvesting, molecular sensing, biological imaging, and lighting applications, and their continued development necessitates straightforward and predictive approaches for adjusting the MOF optical absorption across the visible spectrum. We report a strategy for facile diversification of MOF color that combines (i) postsynthetic modification (PSM) of the chromophoric linkers of an amino-functionalized UiO-68 MOF and (ii) computationally guided selection of specific linker modifiers to rationally tune chromophore band gap. This approach is used to identify and generate a family of seven new modified MOFs having incrementally red-shifted absorption spectra spanning similar to 400-650 nm. This combination of experiment and computation provides a relatively simple pathway for the rational and facile tuning of MOF color and the creation of new families of light-responsive materials.

UiO-67 metal-organic frameworks (MOFs) show promise for use in a variety of areas, especially in industrial chemistry, as stable and customizable catalyst materials often driven by catalytically active defects (coordinatively unsaturated metal sites) present within the MOF crystallite. Thermal activation, or postsynthetic thermal treatment, of MOFs is a seldom used method to induce catalytically active defects. To investigate the effect of thermal activation on defect concentration in UiO-67, we performed Fourier transform infrared (FT-IR) spectroscopy studies of adsorbed CD3CN, a versatile infrared active probe molecule. Our results suggest that, under cryogenic, ultrahigh-vacuum conditions, CD3CN must be thermally diffused into UiO-67 to successfully detect binding sites and defects. Below dehydroxylation temperatures, blueshifted nu(CN) modes of diffused CD3CN indicate multiple avenues of hydrogen bonding within UiO-67, as well as binding to Lewis acid sites, assigned to be coordinately undersaturated Zr4+, consistent with in situ FT-IR of adsorbed CO. FT-IR of CD3CN diffused into UiO-67 activated to 623 K shows that while thermal activation eliminates hydrogen-bonding moieties, it also induces stronger Lewis acid sites, identified by a blueshifted nu(CN) doublet. Through density functional theory (DFT) calculations, we demonstrate that the nu(CN) doublet is a result of CD3CN interacting with two distinct nodal defect sites present in dehydroxylated UiO-67. Additionally, the infrared cross sections of CD3CN's nu(CN), nu(CD)(s) and nu(CD)(as) modes change, primarily due to hydrogen bonding, when diffused into UiO-67, as confirmed through DFT calculations. The nonlinear IR cross section behavior suggests that the Beer-Lambert law cannot trivially extrapolate the concentration of an analyte diffused into a MOF. These studies reveal the impact of postsynthetic thermal treatment on the concentration and type of Lewis acid defects in UiO-67 and caution the simple use of integrated infrared absorbance as a metric of analyte concentration within a MOF.

The vast majority of molecular simulations of adsorption in porous materials make use of the assumption that the framework of the porous material may be held rigid without significantly impacting the accuracy of the computed adsorption isotherm. One reason for this approximation is that explicit inclusion of framework flexibility in adsorption simulations dramatically increases the computational cost of the simulation. Approximate methods for including framework flexibility have been developed that are computationally efficient and have been applied to adsorption of gases in metal-organic frameworks (MOFs) by generating an ensemble of snapshots from a molecular dynamics calculation of an empty MOF and employing these snapshots to generate an isotherm averaged over all the snapshots, holding each snapshot rigid during the adsorption calculation. This method assumes that the adsorbate has negligible impact on the dynamic configurations of the MOF. We demonstrate an efficient method for including adsorbate-induced changes to the MOF framework and show that this assumption is not always valid. Specifically, for acetone and isopropyl alcohol adsorbed in UiO-66, the saturation loading and degree of hydrogen bonding with the framework significantly increased through the inclusion of adsorbate-induced framework flexibility. We show that adsorption simulations that include adsorbate-induced flexibility match the experimental data for these systems much better than simulations using either the rigid approximation or including the framework flexibility of the empty MOF. We expect that adsorbate-induced flexibility may be important for adsorption in many similar systems.

We study the effect of self-interaction errors on the barrier heights of chemical reactions. For this purpose, we use the well-known Perdew-Zunger self-interaction-correction (PZSIC) [J. P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981)] as well as two variations of the recently developed, locally scaled self-interaction correction (LSIC) [Zope et al., J. Chem. Phys. 151, 214108 (2019)] to study the barrier heights of the BH76 benchmark dataset. Our results show that both PZSIC and especially the LSIC methods improve the barrier heights relative to the local density approximation (LDA). The version of LSIC that uses the iso-orbital indicator z as a scaling factor gives a more consistent improvement than an alternative version that uses an orbital-dependent factor w based on the ratio of orbital densities to the total electron density. We show that LDA energies evaluated using the self-consistent and self-interaction-free PZSIC densities can be used to assess density-driven errors. The LDA reaction barrier errors for the BH76 set are found to contain significant density-driven errors for all types of reactions contained in the set, but the corrections due to adding SIC to the functional are much larger than those stemming from the density for the hydrogen transfer reactions and of roughly equal size for the non-hydrogen transfer reactions.