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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Energy Flows in Static and Programmable Catalysts

Programmable catalysts that change on the time scale of a catalytic cycle provide a new opportunity to control the flow of energy to reactants and products to promote faster and more selective chemistry. While traditional chemical manufacturing processes consume energy to achieve favorable reaction conditions, programmable catalysts aim to dynamically add or remove energy to catalytic cycles through perturbations of the catalytic surface via strain, charge, or light. These surface energy flows are quantified by the changes in adsorbate binding energy with time, and the overall efficiency relating energy inputs to catalytic performance is defined by the characteristics of the undulating catalytic surface. Here, understanding and quantifying energy flows in programmable catalysts provides baseline definitions and metrics for comparing dynamic conditions and identifying optimal catalytic performance for more efficient chemical manufacturing.

Binding energy↗
DOE OSTI2020

Intramolecular Electrostatic Effects on O 2 , CO 2 , and Acetate Binding to a Cationic Iron Porphyrin

Noncovalent electrostatic interactions are important in many biological and chemical reactions, especially those that involve charged intermediates. There has been a growing interest in using electrostatic ligand designs—placing charges in the second coordination sphere—to improve molecular reactivity, catalysis, and electrocatalysis. For instance, an iron porphyrin bearing four cationic ortho -trimethylanilinium groups, Fe( o -TMA), has been reported to be an exceptional electrocatalyst for both the carbon dioxide reduction reaction (CO 2 RR) and the oxygen reduction reaction (ORR). These reactions involve many different steps, and it is not evident which steps are affected by the four positive charges, or why. By comparing Fe( o -TMA) with the related iron-tetraphenylporphyrin, this work examines how covalently positioned charged groups affect substrate binding and other key pre-equilibria of both the ORR and CO 2 RR, specifically acetate, dioxygen, and carbon dioxide binding. This study is among the first to directly measure the effects of electrostatics on ligand-binding. The results show that adding electrostatic groups to a catalyst design often results in a complex interplay of multiple effects, including changes in pre-equilibria prior to substrate binding, combinations of through-space and inductive contributions, and effects of ionic strength and solution dielectric. The inverse half-order dependence of binding constant on ionic strength is proposed as a clear marker for an electrostatic effect. Overall, the conclusions provide guidance for the increasingly popular electrostatic ligand designs in catalysis and other reactivity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Symmetry breaking of fluorophore binding to a G-quadruplex generates an RNA aptamer with picomolar K D

Fluorogenic RNA aptamer tags with high affinity enable RNA purification and imaging. The G-quadruplex (G4) based Mango (M) series of aptamers were selected to bind a thiazole orange based (TO1-Biotin) ligand. Using a chemical biology and reselection approach, we have produced a MII.2 aptamer–ligand complex with a remarkable set of properties: Its unprecedented K D of 45 pM, formaldehyde resistance (8% v/v), temperature stability and ligand photo-recycling properties are all unusual to find simultaneously within a small RNA tag. Crystal structures demonstrate how MII.2, which differs from MII by a single A23U mutation, and modification of the TO1-Biotin ligand to TO1-6A-Biotin achieves these results. MII binds TO1-Biotin heterogeneously via a G4 surface that is surrounded by a stadium of five adenosines. Breaking this pseudo-rotational symmetry results in a highly cooperative and homogeneous ligand binding pocket: A22 of the G4 stadium stacks on the G4 binding surface while the TO1-6A-Biotin ligand completely fills the remaining three quadrants of the G4 ligand binding face. Similar optimization attempts with MIII.1, which already binds TO1-Biotin in a homogeneous manner, did not produce such marked improvements. We use the novel features of the MII.2 complex to demonstrate a powerful optically-based RNA purification system.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Nd, SbNd and Sb 3 Nd 4 and their interactions with the cladding alloy HT9

Lanthanide fission products, such as neodymium, formed during the irradiation of metallic fuels are known to cause deleterious effects from chemical interactions occurring at the fuel-cladding interface; a phenomenon known as fuel-cladding chemical interaction (FCCI). The use of fuel-based additives that bind with the lanthanide elements within the fuel meat, alleviating their interactions at the fuel-cladding interface, is one potential method proposed to mitigate the FCCI phenomenon and extend the burnup potential of such metallic fuel systems. In this study, antimony (Sb) is evaluated as one such additive, and neodymium (Nd) is used to represent the lanthanides. A Sb-Nd alloy is fabricated, which consists of two intermetallic phases, SbNd and Sb 3 Nd 4 . Isothermal diffusion couple experiments are carried out at 675 °C for 24 h between Nd and the Fe-12Cr based HT9 cladding alloy. The results are compared against similar diffusion couple experiments carried out between the Sb-Nd alloy and also HT9. Inter-diffusion between Nd/HT9 diffusion couple is characterized and the phases Fe 17 Nd 5 and Fe 17 Nd 2 were found to form whereas no interactions were observed in the Sb-Nd/HT9 diffusion couple. The lack of compound forming tendencies between Fe, the primary alloying constituent of HT9, and SbNd is elucidated through density functional theory (DFT) calculations on enthalpy of mixing, aligning well with the experimental observations. Lastly, the strong binding of Nd with Sb appears to be favorable, alleviating Nd interactions with HT9 constituent elements.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Accelerated Steam Methane Reforming by Dynamically Applied Charges

Catalyst design has traditionally focused on tuning active site properties to optimally bind reaction intermediates and balance the kinetic requirements of multiple competing chemical processes, as necessitated by the Sabatier principle. It has recently been proposed that for reactions following certain potential energy landscapes, the activity limit imposed by the Sabatier principle may be overcome by using programmed oscillations of surface electron density at the timescales of surface reactions (i.e., “catalytic resonance”). Here, we use a combination of density functional theory (DFT) simulations and transient kinetic models (TKMs) to simulate the kinetics of steam methane reforming (SMR) on Ru(211) surfaces under statically and dynamically applied charges. DFT-calculated binding energies of SMR intermediates and transition states exhibit strong sensitivity to positively applied charges and follow unique scaling relationships that deviate from linear periodic trends across transition metals. Our simulations demonstrate that applying a small positive charge to Ru dramatically enhances the steady-state turnover frequency (TOF) of SMR by up to 5 orders of magnitude above the TOF observed over neutral Ru. Thus, statically charging Ru catalysts may be an effective strategy to lower the temperature requirements for SMR. Dynamic square-wave oscillations in charge resulted in SMR catalytic resonance with an onset frequency f ∼ 106 Hz and the corresponding average TOFs exceeding the statically charged Ru surface by an additional 15%. Here, based on sensitivity analyses performed for the two end points of oscillation, we propose that dynamic TOF improvement beyond the Sabatier maximum can be expected when the system oscillates between two kinetic regimes that are uniquely controlled by distinct elementary steps.

Catalysts↗
DOE OSTI2024

Effects of SARS-CoV-2 Main Protease Mutations at Positions L50, E166, and L167 Rendering Resistance to Covalent and Noncovalent Inhibitors

SARS-CoV-2 propagation under nirmatrelvir and ensitrelvir pressure selects for main protease (MPro) drug-resistant mutations E166V (DRM2), L50F/E166V (DRM3), E166A/L167F (DRM4), and L50F/E166A/L167F (DRM5). DRM2-DRM5 undergoes N-terminal autoprocessing to produce mature MPro with dimer dissociation constants (K dimer ) 2–3 times larger than that of the wildtype. Co-selection of L50F restores catalytic activity of DRM2 and DRM4 from ~10 to 30%, relative to that of the wild-type enzyme, without altering K dimer . Binding affinities and thermodynamic profiles that parallel the drug selection pressure, exhibiting significant decreases in affinity through entropy/enthalpy compensation, were compared with GC373. Reorganization of the active sites due to mutations observed in the inhibitor-free DRM3 and DRM4 structures as compared to MPro WT may account for the reduced binding affinities, although DRM2 and DRM3 complexes with ensitrelvir are almost identical to MPro WT -ensitrelvir. In conclusion, chemical reactivity changes of the mutant active sites due to differences in electrostatic and protein dynamics effects likely contribute to losses in binding affinities.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2025

Organophosphorus Binding Thermodynamics in Metal–Organic Frameworks: Interplay between Oxidation State, Lewis Acidity, and Node Structure

Organophosphorus compounds, including nerve agents and pesticides, represent a class of toxic chemicals causing harm to troops, civilians, and the environment. Metal–organic frameworks (MOFs) have emerged as a class of highly porous, crystalline, tunable materials adept at both capturing and catalytically neutralizing these harmful toxins. In particular, MOFs whose nodes display strong Lewis acidic character can hydrolyze such chemicals nearly instantaneously. However, without the help of a basic buffer to regenerate the active site, the benign organophosphorus product strongly binds to the node and prevents catalyst turnover. Here, we investigate a series of MOFs whose nodes contain metals of varying Lewis acidities and employ isothermal titration calorimetry (ITC) to directly measure the heat from the binding of an organophosphorus probe molecule, allowing the construction of a full thermodynamic binding profile (ΔH, ΔS, ΔG, K a ). We couple this with potentiometric titrations and solid state 31 P magic angle spinning (MAS) NMR to gain a clearer picture of how node identity, structure, and Lewis acidity interplay to impact binding strength and favorability. Furthermore, this study is the first to integrate these three complementary techniques to investigate binding interactions in MOFs, further showcasing the viability of ITC for probing MOF systems, which is still relatively underexplored.

Lewis acidity↗
DOE OSTI2025

Equivariant Graph Attention Network - 3D Conformers & Feature Fusion

EGAN-3F (Equivariant Graph Attention Network - 3D Conformers & Feature Fusion) presents an innovative approach for predicting binding affinity between small molecules and protein targets, a fundamental task in drug discovery. Traditional structure-based methods often depend on protein-ligand complex structures obtained from crystallography or molecular docking. In contrast, ligand-only machine learning models using 1D or 2D representations such as SMILES have been developed to predict binding affinity without structural information about the target; however, their accuracy is often limited due to the lack of 3D ligand information. EGAN-3F addresses this limitation by integrating spatially aware graph learning with traditional descriptor-based features. We systematically investigate how combining 2D and 3D molecular representations enhances binding affinity prediction from SMILES strings. This approach underscores the importance of modeling conformational diversity and incorporating chemically meaningful descriptors to improve predictive accuracy. The key innovation of EGAN-3F lies in its ability to achieve robust ligand-based binding affinity predictions without requiring protein-ligand complex structures, effectively bridging the gap between purely structural and ligand-only modeling paradigms.

Shim, Heesung [Lawrence Livermore National Laborat↗
DOE OSTI2022

Discovery of Complex Binding and Reaction Mechanisms from Ternary Gases in Rare Earth Metal–Organic Frameworks

Understanding the selectivity of metal–organic frameworks (MOFs) to complex acid gas streams will enable their use in industrial applications. In this study, ab initio molecular dynamic simulations (AIMD) were used to simulate ternary gas mixtures (H 2 O-NO 2 -SO 2 ) in rare earth 2,5-dihydroxyterephthalic acid (RE-DOBDC) MOFs. Stronger H 2 O gas-metal binding arose from thermal vibrations in the MOF sterically hindering access of SO 2 and NO 2 molecules to the metal sites. Gas-gas and gas-linker interactions within the MOF framework resulted in the formation of multiple secondary gas species including HONO, HNO 2 , NOSO, and HNO 3 ⁻. Four gas adsorption sites were identified along with a new de-protonation reaction mechanism not observable through experiment. This study not only provides valuable information on competitive gas binding energies in the MOF, but it also provides important chemical insights into transient chemical reactions and mechanisms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Spontaneous rearrangement of acetylated xylan on hydrophilic cellulose surfaces

The interaction of xylan, an abundant plant polysaccharide, with cellulose microfibrils is essential for secondary cell wall strength. A deeper understanding of these interactions is crucial both to improve our understanding of plant cell wall architecture and to design alternate strategies to overcome cellulose recalcitrance for the production of biofuels and sustainable biomaterials. Naturally occurring acetate or glucuronic acid substitutions on xylan have been shown to influence xylan-cellulose interactions. In this work, we use unrestrained molecular dynamics simulations to determine the interactions with the (110) hydrophilic face of cellulose fibers of four different xylans. In the absence of cellulose, all xylans, independent of the substitution pattern, adopt a highly flexible threefold helical screw conformation. However, when xylan is spatially close to a cellulose surface 1,2 linked acetyl xylans (2AcX) adopt rigid twofold helical screw conformations. The 2AcX conformations are primarily stabilized by interactions between the acetylated oxygen and the glycosidic linkage with C-O6 of cellulose. In contrast, the glycosidic oxygens and acetyl decorations for 1,3 linked acetyl groups (3AcX) are oriented away from the cellulose surface and the 3AcX xylans maintain threefold helical screw conformations on the cellulose surface. Our results show that evenly spaced chemical functionalization (with acetyl groups) and the position of substitution (1,2) on xylan backbone play key roles in tuning the xylan-cellulose interactions to stabilize the twofold helical screw conformations of xylan on the cellulose surface. A comparison with previous experimental findings further suggests that 1,2 substitutions induce twofold helical screw conformations of xylan on the cellulose surface irrespective of the chemical nature of the substituent, while 1,3 substitutions primarily bind lignin in threefold helical screw conformations rather than cellulose in plant cell walls.

1,2 Ac↗
DOE OSTI2025

Reactions of Np(VI) and Pu(VI) with Phenanthroline Result in Bending the [NpVIO2]2+ Unit and a Reduced Pu(V) Species

Despite decades of actinyl chemistry, genuinely bent actinyl structures remain rare beyond uranium. We report the first crystallographic characterization of a bent neptunyl(VI) complex, NpO 2 Cl 2 (phen) 2, along with a linear plutonyl species that, unexpectedly, adopts the +V oxidation state. Coordination of two 1,10-phenanthroline ligands to NpO 2 2+ enforces pronounced bending of the O yl –Np–O yl unit to 162° through steric clashes with the axial phenathroline ligand, representing the sharpest angle reported for any neptunyl(VI) complex. In contrast, synthesis with PuO 2 2+ produces a reduced linear Pu(V) species, PuO 2 Cl(phen) 2, underscoring the redox lability and the reluctance of plutonium to distort. Raman and IR spectra yield the first experimental stretching and interaction force constants for plutonyl(V). Comparison with values for plutonyl(VI) and bent and linear uranyl(VI) and neptunyl(VI) compounds shows that reduction perturbs the actinyl bond more than bending within one oxidation state. Electrochemical and spectroscopic studies clarify phenanthroline binding to Pu(VI) and the system’s reactivity. Quantum chemical calculations indicate that bending is energetically favored in the U–Np–Pu series, but the stabilization energy decreases as the actinide atomic number increases. NBO and QTAIM analyses reveal systematic trends: increasing 5f occupancy and decreasing An–O yl bond covalency from U to Pu. These results demonstrate that ligand-induced bending in neptunyl(VI) species is not only electronically feasible but also synthetically achievable, though plutonyl(VI) is constrained by redox reactivity. This work expands the frontier of nonlinear actinyl chemistry and illuminates how structure, oxidation state, and electronic configuration interrelate across the actinyl series.

actinides↗
DOE OSTI2025

ZnO quantum dot–molecule conjugates: Chemical interactions, charge dynamics, and spin polarization

Conjugates between molecules and quantum dots (QDs) have been explored for a range of potential applications from photocatalysis and photovoltaics to quantum information science technologies. A particularly ubiquitous material in many of these applications are ZnO QDs since they can accept and transport electrons and can also act as hosts for unique spin states. Conjugates between molecular light absorbers and ZnO QDs have been explored for decades as components in dye-sensitized solar cells. Recently, these materials have also attracted interest for their ability to produce spin-polarized states upon photoexcitation. The current paper employs a series of light absorbing perylene molecules with different ZnO QD sizes to explore key features of these QD–molecule conjugates: (1) chemical interactions, (2) charge dynamics, and (3) spin polarization. The chemical interactions between the molecules and QDs are determined with binding equilibria and reveal dramatic impact of ligand size. The charge transfer dynamics from photoexcited perylenes to ZnO QDs were found to depend exponentially on the linker length. Finally, time-resolved electron paramagnetic resonance experiments reveal that these conjugates generate spin-polarized states in the form of radical pairs and triplets. These spin states hold promise as potential qubits and also offer an avenue to efficiently sensitize molecular triplets.

Hernandez, Frida S. [Amherst College, MA (United S↗
DOE OSTI2024

Metal Independent Correlations for Site-specific Binding Energies of Relevant Catalytic Intermediates

Establishing energy correlations among different metals can accelerate the discovery of efficient and cost-effective catalysts for complex reactions. Using a recently introduced coordination-based model, we can predict site specific metal binding energies (∆EM) that can be used as a descriptor for chemical reactions. In this study, we have examined a range of metals including Ag, Au, Co, Cu, Ir, Ni, Os, Pd, Pt, Rh, and Ru and found linear correlations between predicted ∆EM and adsorption energies of CH and O (∆ECH and ∆EO) at various coordination environment for all the considered metals. Interestingly, all the metals correlate with one another under specific surface site coordination, indicating that different metals are interrelated in a particular coordination environment. Furthermore, we have tested and verified for PtPd and PtIr-based alloys that they follow a similar behavior. Moreover, we have expanded the metal space by taking some early transition metals along with few s-block metals and shown a cyclic behavior of the adsorbate binding energy (∆EA) versus ∆EM. Therefore, ∆ECH and ∆EO can be efficiently interpolated between metals, alloys and intermetallics based on information related to one metal only. This simplifies the process of screening new metal catalyst formulations and their reaction energies.

Density function theory↗
DOE OSTI2023

Surface Analysis Insight Note: Observations relating to photoemission peak shapes, oxidation state, and chemistry of titanium oxide films

It is common practice to describe the coordination of metal atoms in a binding configuration with their nearest neighbors in terms of oxidation state, a measure by which the number of electrons redistributed between atoms forming chemical bonds. In XPS terms, change to an oxidation state is commonly inferred by correlating photoemission signal with binding energy. The assumption, when classifying photoemission signals into distinct spectral shapes, is that a distribution of intensities shifted to lower binding energy is evidence of a reduction in oxidation state. In this Insight note, we raise the prospect that changes in photoemission peak shape may occur without obvious changes, determined by XPS in stoichiometry for a material. It is well known that TiO 2 measured by XPS yields reproducible Ti 2p photoemission peaks. However, on exposing TiO 2 to ion beams, Ti 2p photoemission evolves to complex distributions in intensity, which are particularly difficult to analyze by traditional fitting of bell-shaped curves to these data. For these reasons, in this Insight note, a thin film of TiO 2 deposited on a silicon substrate is chosen for analysis by XPS and linear algebraic techniques. Alterations in spectral shapes created from modified TiO 2 , which might be interpreted as the change in oxidation state, are assessed in terms of relative proportions of titanium to oxygen. It is found through detailed analysis of spectra that quantification by XPS, using procedures routinely used in practice, is not in accord with the typical interpretations of photoemission shapes. The data processing methods used and results presented in this work are of particular relevance to elucidating fundamental phenomena governing the surface evolution of materials-enabled energy processes where cyclic/non-steady usage changes the nature of bonding, especially in the presence of contaminants.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

A New Drug Discovery Platform: Application to DNA Polymerase Eta and Apurinic/Apyrimidinic Endonuclease 1

The ability to quickly discover reliable hits from screening and rapidly convert them into lead compounds, which can be verified in functional assays, is central to drug discovery. The expedited validation of novel targets and the identification of modulators to advance to preclinical studies can significantly increase drug development success. Our SaXPyTM (“SAR by X-ray Poses Quickly”) platform, which is applicable to any X-ray crystallography-enabled drug target, couples the established methods of protein X-ray crystallography and fragment-based drug discovery (FBDD) with advanced computational and medicinal chemistry to deliver small molecule modulators or targeted protein degradation ligands in a short timeframe. Our approach, especially for elusive or “undruggable” targets, allows for (i) hit generation; (ii) the mapping of protein–ligand interactions; (iii) the assessment of target ligandability; (iv) the discovery of novel and potential allosteric binding sites; and (v) hit-to-lead execution. These advances inform chemical tractability and downstream biology and generate novel intellectual property. We describe here the application of SaXPy in the discovery and development of DNA damage response inhibitors against DNA polymerase eta (Pol η or POLH) and apurinic/apyrimidinic endonuclease 1 (APE1 or APEX1). Notably, our SaXPy platform allowed us to solve the first crystal structures of these proteins bound to small molecules and to discover novel binding sites for each target.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Toward the origins of binding energy shifts and “satellites” formation during plasma-XPS measurements

In-plasma x-ray photoelectron spectroscopy (plasma-XPS) emerges as a powerful platform for real-time, in situ chemical analysis under conditions relevant to semiconductor processing and other plasma-enabled technologies. This study investigates the origins of binding energy (BE) shifts and the formation of “satellite” peaks observed during plasma-XPS measurements across conductive, dielectric, and gas-phase systems. Using a standard laboratory-based ambient pressure XPS apparatus coupled with an alternating current (AC)-driven capacitively coupled plasma source, we demonstrate that metastable surface species, such as transient Au oxides, can be detected during plasma exposure, revealing chemical states that are hardly accessible using conventional ultrahigh vacuum (UHV) XPS. In dielectric samples (e.g., undoped diamond, sapphire), we observe pressure- and plasma-type-dependent BE shifts of more than 50 eV, attributed to x-ray-induced and plasma-mediated surface charging. These shifts are mitigated at higher pressures/plasmas or in electronegative plasmas (e.g., O 2 ), the latter due to enhanced charge compensation mechanisms involving slow negative ions. For gas-phase species, AC-plasma excitation leads to spectral broadening and the emergence of “satellite” peaks with energy separations of a few electron volts, linked to oscillating local plasma potentials in the probing volume. Furthermore, these findings highlight the complex and important interplay between plasma parameters, surface charging, and local electric fields in shaping XPS spectra. Overall, plasma-XPS emerges as a critical metrological tool for probing transient surface chemistry, with implications for semiconductor processing, material synthesis, and plasma diagnostics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

How Does HF-DFT Achieve Chemical Accuracy for Water Clusters?

Bolstered by recent calculations of exact functional-driven errors (FEs) and density-driven errors (DEs) of semilocal density functionals in the water dimer binding energy , we investigate approximate FEs and DEs in neutral water clusters containing up to 20 monomers, charged water clusters, and alkali- and halide-water clusters. Our proxy for the exact density is r 2 SCAN 50, a 50% global hybrid of exact exchange with r 2 SCAN, which may be less correct than r 2 SCAN for the compact water monomer but importantly more correct for long-range electron transfers in the noncompact water clusters. We show that SCAN makes substantially larger FEs for neutral water clusters than r 2 SCAN, while both make essentially the same DEs. Unlike the case for barrier heights, these FEs are small in a relative sense and become large in an absolute sense only due to an increase in cluster size. SCAN@HF, short for SCAN evaluated on the Hartree–Fock (HF) density, produces a cancellation of errors that makes it chemically accurate for predicting the absolute binding energies of water clusters. Likewise, adding a long-range dispersion correction to r 2 SCAN@HF, as in the composite method HF-r 2 SCAN-DC4, makes its FE more negative than in r 2 SCAN@HF, permitting a near-perfect cancellation of FE and DE. r 2 SCAN by itself (and even more so, r 2 SCAN evaluated on the r 2 SCAN 50 density), is almost perfect for the energy differences between water hexamers, and thus probably also for liquid water away from the boiling point. Thus, the accuracy of composite methods like SCAN@HF and HF-r 2 SCAN-DC4 is not due to the HF density being closer to the exact density, but to a compensation of errors from its greater degree of localization. We also give an argument for the approximate reliability of this unconventional error cancellation for diverse molecular properties. Lastly, we confirm this unconventional error cancellation for the SCAN description of the water trimer via Kohn–Sham inversion of the CCSD(T) density.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗