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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 397 records · Page 22
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DOE OSTI2022

Trends in Siting of Metals in Heterometallic Nd–Yb Metal–Organic Frameworks and Molecular Crystals

Several studies suggest that metal ordering within metal–organic frameworks (MOFs) is important for understanding how MOFs behave in relevant applications; however, these siting trends can be difficult to determine experimentally. To garner insight into the energetic driving forces that may lead to nonrandom ordering within heterometallic MOFs, we employ density functional theory (DFT) calculations on several bimetallic metal–organic crystals composed of Nd and Yb metal atoms. We also investigate the metal siting trends for a newly synthesized MOF. Our DFT-based energy of mixing results suggest that Nd will likely occupy sites with greater access to electronegative atoms and that local homometallic domains within a mixed-metal Nd–Yb system are favored. We also explore the use of less computationally extensive methods such as classical force fields and cluster expansion models to understand their feasibility for large system sizes. Here, this study highlights the impact of metal ordering on the energetic stability of heterometallic MOFs and crystal structures.

energy of mixing↗
DOE OSTI2022

Sulfated Zirconium Metal–Organic Frameworks as Well-Defined Supports for Enhancing Organometallic Catalysis

Understanding heterogeneous catalysts is a challenging pursuit due to surface site nonuniformity and aperiodicity in traditionally-used materials. One example is sulfated metal oxides, which function as highly-active catalysts and as supports for organometallic complexes. These applications are due to traits such as acidity, ability to act as a weakly coordinating ligand, and aptitude for promoting transformations via radical cation intermediates. Research is ongoing about the structural features of sulfated metal oxides that imbue the aforementioned properties, such as sulfate geometry and coordination. To better understand these materials, metal–organic frameworks (MOFs) have been targeted as structurally-defined analogs. Composed of inorganic nodes and organic linkers, MOFs possess features such as high porosity and crystallinity, which make them attractive for mechanistic studies of heterogeneous catalysts. In this work, a Zr 6 -based MOF NU-1000 is sulfated and characterized using atomically-precise techniques such as single crystal X-ray diffraction (SCXRD) in addition to diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS). Here, the dynamic nature of the sulfate binding motif is found to transition from monodentate, to bidentate, to tridentate depending on the degree of hydration, as supported by density functional theory (DFT) calculations. Heightened Brønsted acidity compared to the parent MOF was observed upon sulfation, and probed through trimethylphosphine oxide (TMPO) physisorption, ammonia sorption, in-situ ammonia DRIFTS, and DFT studies. With the support structure benchmarked, an organoiridium complex was chemisorbed onto the sulfated MOF node and the efficacy of this supported catalyst was demonstrated for stoichiometric and catalytic activation of benzene-d6 and toluene with structure-activity relationships derived.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Comparing Classical and Machine Learning Force Fields for Modeling Deformation of Metal–Organic Frameworks Relevant for Direct Air Capture

Deformation of metal–organic frameworks (MOFs) induced by adsorbate molecules can affect adsorption properties such as capacity and selectivity, but most computational studies of MOFs assume framework rigidity to simplify calculations. Although flexible force fields (FFs) for MOFs have been parametrized for specific materials, the generality of FFs for reliably modeling adsorbate-induced deformation to accuracy nearing that of density functional theory (DFT) has not been established. This work confirms using DFT calculations that adsorbate-induced deformation can affect CO 2 and H 2 O adsorption energies in a considerable fraction of MOFs promising for direct air capture (DAC). We then benchmark the efficacy of several general-purpose FFs in describing adsorbate-induced deformation for DAC against DFT. Our results show that current classical FFs are insufficient for describing MOF deformation, especially in cases of interest for DAC where strong interactions exist between adsorbed molecules and MOF frameworks. Some emerging machine learning force fields (MLFFs) we tested, particularly CHGNet, MACE-MP-0, and Equiformer V2, appear to be more promising than the classical FF for emulating the deformation behavior described by DFT. The best performing FF (CHGNet), however, fails to achieve the accuracy required for practical predictions with a mean absolute adsorption energy error of 0.124 eV.

adsorption↗
DOE OSTI2022

Electron Counting and High-Pressure Phase Transformations in Metal Hexaborides

Pressure-induced structural transitions of the alkaline earth hexaborides, CaB 6 , SrB 6 , and BaB 6 , are studied theoretically using electron counting rules and density functional theory calculations. Here, we demonstrate the applicability of gas-phase borane electron counting methods to solid-state metal borides under pressure and validate the assumptions of the rules by density functional theory (DFT) calculations. All three compounds share ambient-pressure and high-pressure structures, but BaB 6 differs from CaB 6 and SrB 6 at intermediate pressures. The unique BaB 6 phase is shown to break electron counting rules, while all other phases obey them. This anomaly is resolved by DFT, which reveals B–Ba covalency and unusual B–B π bonding under pressure. The relationships between structure and bonding can help us to understand the exotic behavior of lanthanide hexaborides and design new borides with desirable properties. Developing electron counting procedures for solids will enhance materials discovery efforts with chemical intuition.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Bulk Fermi surfaces of the Dirac type-II semimetallic candidate NiTe 2

Here, we present a study on the Fermi surface of the Dirac type-II semimetallic candidate NiTe 2 via the temperature and angular dependence of the de Haas–van Alphen (dHvA) effect measured in single crystals grown through Te flux. In contrast to its isostructural compounds like PtSe 2 , band-structure calculations predict NiTe 2 to display a tilted Dirac node very close to its Fermi level that is located along the Γ to A high-symmetry direction within its first Brillouin zone. The angular dependence of the dHvA frequencies is found to be in agreement with the first-principles calculations when the electronic bands are slightly shifted with respect to the Fermi level (ε F ), and therefore provide support for the existence of a Dirac type-II node in NiTe 2 . Nevertheless, we observed mild disagreements between experimental observations and density functional theory (DFT) calculations as, for example, nearly isotropic and light experimental effective masses. This indicates that the dispersion of the bands is not well captured by DFT. Despite the coexistence of Dirac-like fermions with topologically trivial carriers, samples of the highest quality display an anomalous and large either linear or sublinear magnetoresistivity. Finally, this suggests that Lorentz invariance breaking Dirac-like quasiparticles dominate the carrier transport in this compound.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Hydride Accessibility and Reactivity in the Configurational and Stoichiometric Space of β-Ga 2 O 3 for CO 2 Hydrogenation

Understanding how surface species evolve under reaction conditions is essential for improving catalyst design for efficient CO 2 hydrogenation. This work combines systematic DFT calculations with grand canonical sampling to investigate the stability and reactivity of Ga–H species on β-Ga 2 O 3 across a range of reaction conditions. Initial DFT studies reveal that when Ga–H species are present, they facilitate formate formation via a low-barrier pathway, largely independent of the surface termination or hydrogen site. However, grand canonical sampling shows that under a broad range of reaction conditions─especially at high oxygen chemical potentials associated with high water content─Ga–H species are thermodynamically inaccessible. Furthermore, adsorbed water molecules can block reactive sites, inhibiting CO 2 activation even when hydrides are present. These findings suggest that the lack of accessible hydride species, rather than their intrinsic reactivity, could contribute to reduced catalytic performance of β-Ga 2 O 3 under more oxidizing, high-conversion conditions.

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

Kohn–Sham accuracy from orbital-free density functional theory via Δ-machine learning

Here, we present a Δ-machine learning model for obtaining Kohn–Sham accuracy from orbital-free density functional theory (DFT) calculations. In particular, we employ a machine-learned force field (MLFF) scheme based on the kernel method to capture the difference between Kohn–Sham and orbital-free DFT energies/forces. We implement this model in the context of on-the-fly molecular dynamics simulations and study its accuracy, performance, and sensitivity to parameters for representative systems. We find that the formalism not only improves the accuracy of Thomas–Fermi–von Weizsäcker orbital-free energies and forces by more than two orders of magnitude but is also more accurate than MLFFs based solely on Kohn–Sham DFT while being more efficient and less sensitive to model parameters. We apply the framework to study the structure of molten Al 0.88 Si 0.12 , the results suggesting no aggregation of Si atoms, in agreement with a previous Kohn–Sham study performed at an order of magnitude smaller length and time scales.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Ground State Properties of the Wide Band Gap Semiconductor Beryllium Sulfide (BeS)

We report the results from self-consistent calculations of electronic, transport, and bulk properties of beryllium sulfide (BeS) in the zinc-blende phase, and employed an ab-initio local density approximation (LDA) potential and the linear combination of atomic orbitals (LCAO). We obtained the ground state properties of zb-BeS with the Bagayoko, Zhao, and Williams (BZW) computational method, as enhanced by Ekuma and Franklin (BZW-EF). Our findings include the electronic energy bands, the total (DOS) and partial (pDOS) densities of states, electron and hole effective masses, the equilibrium lattice constant, and the bulk modulus. The calculated band structure clearly shows that zb-BeS has an indirect energy band gap of 5.436 eV, from Γ to a point between Γ and X, for an experimental lattice constant of 4.863 Å. This is in excellent agreement with the experiment, unlike the findings of more than 15 previous density functional theory (DFT) calculations that did not perform the generalized minimization of the energy functional, required by the second DFT theorem, which is inherent to the implementation of our BZW-EF method.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Highly tunable band inversion in AB 2 X 4 (A=Ge, Sn, Pb; B=As, Sb, Bi; X=Se, Te) compounds

Topological materials have been discovered so far largely by searching for existing compounds in crystallographic databases, but there are potentially new topological materials with desirable features that have not been synthesized. One of the desirable features is high tunability resulting from the band inversion with a very small direct band gap, which can be tuned by changes in pressure or strain to induce a topological phase transition. Here, using density-functional theory (DFT) calculations, we have studied the septuple layered AB 2 X 4 series compounds, where A=(Ge, Sn and Pb), B=(As, Sb and Bi), and X=(Se and Te). With the DFT thermodynamic stability validated by the already-reported compounds in these series, we predict stable Se compounds, which are not found in crystallographic database. Among them, we find that GeBi 2 Se 4 and GeSb 2 Se 4 having a small direct band gap at the Z point are very close to a strong topological insulator, which can be tuned by a moderate pressure to induce the band inversion. Importantly, the topological features with the small direct band gap are well isolated in both momentum and energy windows, which offers high tunability for studying the topological phase transition.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Effect of applied potential on metal surfaces: Surface energy, Wulff shape and charge distribution

Here we use grand canonical density functional theory to predict the surface energies, Wulff shapes, charge distributions and catalytically active sites of different metal surfaces under electrochemical conditions. We propose a method for computing surface energies from grand canonical density functional theory (GC-DFT) calculations of periodic slab models and use it to compute the surface energies of the facets of Pt, Cu, and Ag crystals to predict their Wulff shapes under electrochemical conditions. GC-DFT predicts that, for the pure metals studied, solvation only slightly affects the Wulff shape while applied potentials considerably affect the surface energies and corresponding Wulff shapes. We used Bader charge analysis of GC-DFT computed electron densities to investigate the effect of applied potential on the distribution of electron density over the atoms of the surfaces of Pt, Cu, Ag, and the 75–25 Ag-Pt and Au-Ni alloys. This analysis shows that, under an applied potential, the electron density is unevenly distributed over the surface atoms and that the charges of atoms more exposed to solvent are more sensitive to bias. Our results show that the most sensitive atom to bias can be used to identify the most favorable adsorption site and thus, the active sites of electrochemical reactions, which is computationally less demanding than calculating the adsorption energies on all possible adsorption sites.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Understanding of Active Sites and Interconversion of Pd and PdO during CH 4 Oxidation

Pd-based catalysts are widely used in the oxidation of CH 4 and have a significant impact on global warming. However, understanding their active sites remains controversial, because interconversion between Pd and PdO occurs consecutively during the reaction. Understanding the intrinsic active sites under reaction conditions is critical for developing highly active and selective catalysts. In this study, we demonstrated that partially oxidized palladium (PdO x ) on the surface plays an important role for CH 4 oxidation. Regardless of whether the initial state of Pd corresponds to oxides or metallic clusters, the topmost surface is PdO x , which is formed during CH4 oxidation. A quantitative analysis using CO titration, diffuse reflectance infrared Fourier-transform spectroscopy, X-ray diffraction, and scanning transmission electron microscopy demonstrated that a surface PdO layer was formed on top of the metallic Pd clusters during the CH 4 oxidation reaction. Furthermore, the time-on-stream test of CH 4 oxidation revealed that the presence of the PdO layer on top of the metallic Pd clusters improves the catalytic activity. Our periodic density functional theory (DFT) calculations with a PdO x slab and nanoparticle models aided the elucidation of the structure of the experimental PdO particles, as well as the experimental C-O bands. The DFT results also revealed the formation of a PdO layer on the metallic Pd clusters. This study helps achieve a fundamental understanding of the active sites of Pd and PdO for CH 4 oxidation and provides insights into the development of active and durable Pd-based catalysts through molecular-level design.

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

Density Matrix Implementation of the Fermi–Löwdin Orbital Self-Interaction Correction Method

The Fermi–Löwdin orbital self-interaction correction (FLOSIC) method effectively provides a transformation from canonical orbitals to localized Fermi–Löwdin orbitals which are used to remove the self-interaction error in the Perdew–Zunger (PZ) framework. This transformation is solely determined by a set of points in space, called Fermi–Löwdin descriptors (FODs), and the occupied canonical orbitals or the density matrix. In this work, we provide a detailed workflow for the implementation of the FLOSIC method for removal of self-interaction error in DFT calculations in an orbital-by-orbital basis that takes advantage of the unitary invariant nature of the FLOSIC method. In this way, it is possible to cast the self-consistent energy minimization at fixed FODs in the same manner than standard Kohn–Sham with one additional term in the Kohn–Sham Hamiltonian that introduces the PZ self-interaction correction. Each energy minimization iteration is divided in two substeps, one for the density matrix and one for the FODs. Expressions for the effective Kohn–Sham matrix and FOD gradients are provided such that its implementation is suitable for most electronic structure codes. Here, we analyze the convergence characteristics of the algorithm and present applications for the evaluation of NMR shielding constants and real-time time-dependent DFT simulations based on the Liouville–von Neumann equation to calculate excitation energies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Temperature-dependent lattice dynamics in polycrystalline ZrN

Zirconium nitride holds promise for improving nuclear reactor components, where thermal conductivity is important, highlighting the need for a detailed understanding of its phonons. However, the phonon dispersion derived from previous inelastic neutron scattering data is in disagreement with modern theoretical calculations, pointing to the necessity for further experimental validation. Here, in this study, we use inelastic neutron scattering experiments on polycrystalline ZrN at 6, 100, 300, 400, and 600 K, and density functional theory (DFT) calculations to study the momentum-resolved scattering and the phonon density of states. Both experimental and theoretical results reveal a phonon cutoff energy near 65 meV, in stark disagreement with previous single-crystal neutron scattering measurements indicating a cutoff near 75 meV. The 65 meV cutoff energy is, however, in reasonable agreement with previous measurements on ZrN 0.9 . Consistency between our theoretical and experimental results confirms that ZrN is a wide phonon band gap system and that DFT provides a reliable description of its phonons.

DFT↗
DOE OSTI2021

Inelastic Neutron Spectra of Uranium Tetrafluoride Hydrate, UF 4 (H 2 O) 2.5

Uranium tetrafluoride hydrate (UFH) is formed by immersing anhydrous UF4 under water for 12 h. UFH is therefore clearly a chemical species of environmental concern, as anhydrous UF4 is an intermediate uranium form in the nuclear fuel cycle. We use inelastic neutron scattering (INS) to probe the full vibrational spectra of UFH and its deuterated analogue in an effort to improve the fundamental understanding of its vibrational spectra. Coupled with density functional theory (DFT) calculations, the first for this compound, and full spectral modeling, we generate the complete vibrational spectra of UFH and compare them to prior optical spectroscopic results. In particular, the combination of DFT with INS allows us to identify multiple distinct chemical environments in the water bending and OH stretching regions. Whereas the water molecules directly bound to the U atoms execute OH stretching around 3600 cm –1 , a second class of H-bonded waters vibrate below 3000 cm –1 , an indicator of strong H bonding. In addition, a class of librational water modes are observed between 400 and 900 cm–1, which themselves can be separated in energy according to their chemical environments. Furthermore, measurements presented herein directly assist in the assignment of certain spectral features in the infrared spectrum and will inform future investigations of UFH for environmental or forensics purposes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Machine-Learned Force Field for Molecular Dynamics Simulations of Nonequilibrium Ammonia Synthesis on Iron Catalysts

Ammonia (NH 3 ) is one of the most important industrial chemicals. The conventional NH 3 synthesis method-the Haber–Bosch process-converts atmospheric nitrogen (N 2 ) into NH 3 using H 2 with an iron (Fe) catalyst. However, this process requires high pressures (100–200 atm) and temperatures (700–800 K) near thermal equilibrium. Recently, Fe-based nanocatalysts have been reported to produce promising NH 3 yields under atmospheric pressures and temperature-modulated nonequilibrium conditions. Understanding the mechanism of nonequilibrium catalysis with programmed temperature variation could help to optimize this fully electrified and less energy-intensive process. Although reactive molecular dynamics (RMD) simulations can be a useful tool to model nonequilibrium catalytic processes, they require the development of accurate force fields (i.e., interatomic potentials). Here, we present a machine-learned (ML) force field within the Deep Potential MD (DPMD) framework, trained using periodic density functional theory (DFT) calculations, to model NH 3 synthesis on Fe catalysts with various surface adsorbates such as *N, *H, *N 2 , *H 2 , *NH, *NH 2 , and *NH 3 . Here, we generated the DFT data from static models of elementary reactions on the most stable (110) surface of body-centered cubic Fe, which then were augmented by data from constant number of particles–volume–temperature (NVT) DFT-MD trajectories at various temperatures. Finally, we utilized the fully optimized ML force field to investigate reaction dynamics at an Fe(110) surface at linearly increasing temperatures using NVT-DPMD simulations. Our simulations indicate that pulsed temperature ramping could prove favorable for NH3 synthesis. For example, we conducted ramping under multiple sets of conditions: (i) from 900 to 1200 K over periods of 0.1–0.3 ns for Fe surfaces precovered with N or NH along with H; and (ii) from 300 to 600 K over 0.1–0.3 ns for Fe surfaces precovered with NH 3 . While our simulations so far are limited to short time scales (very rapid heating), these observations shed light on the mechanism of the high NH 3 synthesis rate achieved in a novel temperature-modulated nonequilibrium catalytic reactor using pulsed heating and cooling.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Machine learning-based interatomic potential development and phase transition analysis of ferroelectric hafnium dioxide

The ferroelectric phase (𝑃⁢𝑐⁢𝑎⁢2 1 , which is in orthorhombic symmetry) of hafnium dioxide (HfO 2 ) has gained much attention due to its potential applications in nanoelectronics and advanced memory devices. However, its complex phase behavior under external stimuli, such as pressure and temperature, remains a subject of intense investigation. This study focuses on developing a machine learning-based interatomic potential (MLIP) that is trained with data from density-functional theory (DFT) calculations to simulate phase transitions and mechanical properties of HfO 2 . The developed MLIP predicts lattice parameters, equations of state, bulk and shear moduli, and elastic constants that closely align with DFT predictions for several phases and at various pressures. Once validated, the MLIP is used to investigate the phase transitions of ferroelectric HfO 2 (𝑃⁢𝑐⁢𝑎⁢2 1 ) under both isobaric and constant stress conditions at elevated temperatures ranging from 200 to 2500 K. We used several complementary methods, including local symmetry identification, radial distribution function, and x-ray diffraction characterization, to identify interesting phase transitions among several competitive hafnia phases predicted from our simulations. The suggested methods uniformly reveal that under pure deviatoric condition, the system favors a transition from the orthorhombic 𝑃⁢𝑐⁢𝑎⁢2 1 phase to a tetragonal (𝑃⁢4 2 /𝑛⁢𝑚⁢𝑐) phase, whereas a zero stress condition drives the system from the 𝑃⁢𝑐⁢𝑎⁢2 1 phase to another orthorhombic (𝑃⁢𝑏⁢𝑐⁢𝑛) phase. These findings provide crucial insights into stress and temperature-induced phase behavior of hafnia, guiding future experimental and theoretical studies for optimizing hafnia-based ferroelectric devices.

Ferroelectric HfO2↗
DOE OSTI2022

Data-Driven and Multiscale Modeling of DNA-Templated Dye Aggregates

Dye aggregates are of interest for excitonic applications, including biomedical imaging, organic photovoltaics, and quantum information systems. Dyes with large transition dipole moments (μ) are necessary to optimize coupling within dye aggregates. Extinction coefficients (ε) can be used to determine the μ of dyes, and so dyes with a large ε (>150,000 M –1 cm –1 ) should be engineered or identified. However, dye properties leading to a large ε are not fully understood, and low-throughput methods of dye screening, such as experimental measurements or density functional theory (DFT) calculations, can be time-consuming. In order to screen large datasets of molecules for desirable properties (i.e., large ε and μ), a computational workflow was established using machine learning (ML), DFT, time-dependent (TD-) DFT, and molecular dynamics (MD). ML models were developed through training and validation on a dataset of 8802 dyes using structural features. A Classifier was developed with an accuracy of 97% and a Regressor was constructed with an R2 of above 0.9, comparing between experiment and ML prediction. Using the Regressor, the ε values of over 18,000 dyes were predicted. The top 100 dyes were further screened using DFT and TD-DFT to identify 15 dyes with a μ relative to a reference dye, pentamethine indocyanine dye Cy5. Two benchmark MD simulations were performed on Cy5 and Cy5.5 dimers, and it was found that MD could accurately capture experimental results. The results of this study exhibit that our computational workflow for identifying dyes with a large μ for excitonic applications is effective and can be used as a tool to develop new dyes for excitonic applications.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2023

Density Functional Theory Guided Investigation of Ligand‐Induced Neptunyl‐Neptunyl Interactions

Abstract Actinyl‐actinyl interactions are particularly prevalent for the pentavalent neptunyl cation (Np(V)O 2 ) + where these interactions appear either as a T ‐ or D ‐shape (diamond‐shape). T ‐shaped interactions have been previously identified in high concentration Np(V) solutions containing simple anions (NO 3 − , ClO 4 − , Cl − ) whereas D ‐shaped have only been isolated in the solid‐state in the presence of carboxylate ligands. In this study, Density Functional Theory (DFT) calculations were paired with Raman spectroscopy to evaluate the formation of D ‐shaped interactions in the presence of aliphatic (R=H (formate), CH 3 (acetate), CH 2 CH 3 (propionate)) and aromatic (R=C 6 H 5 (benzoate), C 6 H 4 OH (4‐hydroxybenzoate), C 5 H 4 N (isonicotinate)) carboxylate ligands. DFT studies indicate that the Δ G to form hydrated T ‐ and D ‐shaped forms are not spontaneous but become so with the addition of the carboxylate ligands. Raman spectra of the Np(V) carboxylate solutions contained vibrational modes associated with the D ‐shaped interactions, but spectral changes observed over time indicate a dynamic system. Crystallization experiments from the Np(V) carboxylate systems confirmed the presence of D‐ shaped dimers for the aromatic carboxylates, suggesting that the choice of the anion in solution favors actinyl‐actinyl interactions even at low concentrations (≤20 mM) of Np(V).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗