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At least 217 records · Page 12

Filling-enforced obstructed atomic insulators

Topological band theory has achieved great success in the high-throughput search for topological band structures both in paramagnetic and magnetic crystal materials. However, a significant proportion of materials are topologically trivial insulators at the Fermi level. In this paper, we show that, remarkably, for a subset of the topologically trivial insulators, knowing only their electron number and the Wyckoff positions of the atoms we can separate them into two groups: the obstructed atomic insulator (OAI) and the atomic insulator (AI). The interesting group, the OAI, have a center of charge not localized on the atoms. Using the theory of topological quantum chemistry, in this work we first derive the necessary and sufficient conditions for a topologically trivial insulator to be a filling enforced obstructed atomic insulator (feOAI) in the 1651 Shubnikov space groups. Remarkably, the filling enforced criteria enable the identification of obstructed atomic bands without knowing the representations of the band structures. Hence, no calculations are needed for the filling enforced criteria, although they are needed to obtain the band gaps. With the help of the Topological Quantum Chemistry website, we have performed a high-throughput search for feOAIs and have found that 957 ICSD entries (638 unique materials) are paramagnetic feOAIs, among which 738 (475) materials have an indirect gap. The metallic obstructed surface states of feOAIs are also showcased by several material examples. Published by the American Physical Society 2024

Materials Science↗

Insulating moiré homobilayers lack a threefold symmetric second-harmonic generation

Atoms within moiré bilayers relax in plane to minimize elastic energy; such relaxation brings their space group symmetries down to P1. Here, the ab initio second harmonic generation (SHG) of twisted and atomistically optimized hBN bilayers was determined at four twist angles (θ = 38.21°, 60.00°, 73.17°, and 98.21°) and for three displacements τ measured away from the ground state AA' configuration. All moiré bilayers have a P1 space symmetry after structural optimization. This situation is quite different to monolayers with hexagonal lattices, which retain a threefold symmetry. We point out that the actual symmetries of the SHG reported for hBN bilayers on two experimental works do not coincide with the sixfold symmetric theoretical profiles they provide [either sin 2 ⁡(3⁢Φ) or cos 2 ⁡(3⁢Φ)], and show that the intrinsic low structural symmetry of (atomically optimized) hBN bilayer moirés can in fact be read out from experimental SHG intensity profiles—which are tunable by θ and by the frequency of light ω: The SHG is most definitely not sixfold symmetric because moirés do not retain a threefold symmetry. Furthermore, an extrinsic twofold symmetry of the SHG emission is realized by tilting the pump by an angle α away from the 2D material's normal, regardless of θ and ω. Furthermore, the design of in-plane and ultrathin sources of SHG with low symmetry could be useful for the eventual creation of entanglement sources from 2D materials.

2-dimensional systems↗

Results from teleoperated free-flying spacecraft simulations in the Martin Marietta space operations simulator lab

To augment the capabilities of the Space Transportation System, NASA has funded studies and developed programs aimed at developing reusable, remotely piloted spacecraft and satellite servicing systems capable of delivering, retrieving, and servicing payloads at altitudes and inclinations beyond the reach of the present Shuttle Orbiters. Since the mid 1970's, researchers at the Martin Marietta Astronautics Group Space Operations Simulation (SOS) Laboratory have been engaged in investigations of remotely piloted and supervised autonomous spacecraft operations. These investigations were based on high fidelity, real-time simulations and have covered a wide range of human factors issues related to controllability. Among these are: (1) mission conditions, including thruster plume impingements and signal time delays; (2) vehicle performance variables, including control authority, control harmony, minimum impulse, and cross coupling of accelerations; (3) maneuvering task requirements such as target distance and dynamics; (4) control parameters including various control modes and rate/displacement deadbands; and (5) display parameters involving camera placement and function, visual aids, and presentation of operational feedback from the spacecraft. This presentation includes a brief description of the capabilities of the SOS Lab to simulate real-time free-flyer operations using live video, advanced technology ground and on-orbit workstations, and sophisticated computer models of on-orbit spacecraft behavior. Sample results from human factors studies in the five categories cited above are provided.

Hartley, Craig S.↗

Unified Picture of Superconductivity and Magnetism in CeRh 2 ⁢As 2

Here, we propose a theory for the microscopic origin of the multiple superconducting and magnetic phases observed in CeRh 2 ⁢As 2 based on the existence of Van Hove singularities near the Fermi energy. The nonsymmorphic symmetry of this material implies that these singularities are located away from high-symmetry momenta; i.e., they have so-called type-II character. This allows us to include the significant Rashba spin-orbit coupling in CeRh 2 ⁢As 2 in a parquet renormalization group approach. When Fermi-surface nesting is strong, our analysis reveals two closely competing superconducting states with opposite parities, as well as an instability toward spin-density wave states that support both of them, consistent with the phase diagram of CeRh 2 ⁢As 2 . Type-II Van Hove singularities are generic to nonsymmorphic space groups, and so our theory implies that many other compounds may support closely competing even- and odd-parity superconductivity.

Rashba coupling↗

On the Crystal Structure of Colloidally Prepared Metastable Ag2Se Nanocrystals

Structural polymorphism is known for many bulk materials; however, on the nanoscale metastable polymorphs tend to form more readily than in the bulk, and with more structural variety. One such metastable polymorph observed for colloidal Ag2Se nanocrystals has traditionally been referred to as the “tetragonal” phase of Ag2Se. While there are reports on the chemistry and properties of this metastable polymorph, its crystal structure, and therefore electronic structure, has yet to be determined. We report that an anti-PbCl2-like structure type (space group P21/n) accurately describes the powder X-ray diffraction and X-ray total scattering patterns of colloidal Ag2Se nanocrystals prepared by several different methods. Density functional theory (DFT) calculations indicate that the anti-PbCl2-like Ag2Se polymorph is a dynamically stable, narrow-band gap semiconductor. DFT results reveal a dense theoretical Ag2Se phase space with many low-energy polymorphs, which helps explain the large number of polymorphs reported in the literature. Analysis and calculation data are stored in the zip archive. The `ag2se-calcs.aiida.` contains the provenance of the calculations and can be imported into an AiiDA database instance. The antiPbCl2like_Ag2Se_laboratory.cif file is the Reitveld refined Ag2Se structure starting from the PbCl2 structure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Structure determination of ζ-N 2 from single-crystal X-ray diffraction and theoretical suggestion for the formation of amorphous nitrogen

The allotropy of solid molecular nitrogen is the consequence of a complex interplay between fundamental intermolecular as well as intramolecular interactions. Understanding the underlying physical mechanisms hinges on knowledge of the crystal structures of these molecular phases. That is especially true for ζ-N 2 , key to shed light on nitrogen’s polymerization. Here, we perform single-crystal X-ray diffraction on laser-heated N 2 samples at 54, 63, 70 and 86 GPa and solve and refine the hitherto unknown structure of ζ-N 2 . In its monoclinic unit cell (space group C 2/ c ), 16 N 2 molecules are arranged in a configuration similar to that of ε-N 2 . The structure model provides an explanation for the previously identified Raman and infrared lattice and vibrational modes of ζ-N 2 . Density functional theory calculations give an insight into the gradual delocalization of electronic density from intramolecular bonds to intermolecular space and suggest a possible pathway towards nitrogen’s polymerization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Exploring the Role of Organic Functional Groups in the Ionothermal Synthesis of Uranyl Phosphate Materials

Four new hybrid organic-inorganic uranyl phosphate compounds were structurally characterized after single crystals were grown via ionothermal synthesis using the ionic liquids 1-ethyl-3-methylimidazolium dimethyl phosphate and 1-ethyl-3-methylimidazolium dibutyl phosphate. Three of the new crystal structures presented here incorporate dimethyl or monomethyl phosphate ligands into the structural unit to form one chain-based compound and two sheet-based compounds. One of the structures utilizes dibutyl phosphate to form a previously reported uranyl compound, a structural polymorph that crystallized in space group P2 1 /c in contrast to the previously reported P-1 structure. The structural and topological relationships are compared to those of uranyl phosphate minerals as well as previously reported organophosphate compounds. Finally, the roles of the organics on the phosphate anions in impacting uranyl coordination and stabilizing the crystal structures are discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Vibrational Spectroscopy of Hexahalo Complexes

Halogenated inorganic complexes A x [MHal y ] (A = alkali metal or alkaline earth, M = transition or main group metal, x = 1–3, and y = 2–9) are an archetypal class of compounds that provide entry points to large areas of inorganic and physical chemistry. All of the hexahalo complexes adopt an octahedral, O h , symmetry (or nearly so). Consequently, one of the bending modes is forbidden in both the infrared and Raman spectra. In the solid state, many of the complexes crystallize in the cubic space group Fm3̅m, which preserves the octahedral symmetry. Even for those that are not cubic, the octahedral symmetry of the [MHal 6 ] n- ion is largely retained and, to a good approximation, so are the selection rules. In the present work, we show that by using the additional information provided by neutron vibrational spectroscopy, in combination with conventional optical spectroscopies, we can generate complete and unambiguous assignments for all the modes. Comparison of the experimental and calculated transition energies for the systems where periodic-density functional theory was possible (i.e., those for which the crystal structure is known) shows that the agreement is almost quantitative. We also provide a linear relationship that enables the prediction of the forbidden mode.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

BaCu 4/3 Si 2/3 P 2 and BaCu 2–( x + y ) Zn x Si y P 2 : Expanding the Semiconducting Landscape in the ThCr 2 Si 2 -Type Family

ThCr 2 Si 2 -type layered materials are a large family of compounds with applications ranging from thermoelectricity to magnetism, with the vast majority of the members exhibiting metallic behavior. Here, in this study, we synthesized a new group of materials with Cu-Si and Cu-Zn-Si square nets with the general formula BaCu 1.33 Si 0.67 P 2 and BaCu 2–(x+y) Zn x Si y P 2 (0 ≤ x ≤ 0.9; 0.3 ≤ y ≤ 0.7). Several synthesized compounds are charge-balanced semiconductors, which are rare in the ThCr 2 Si 2 family. All the reported compounds crystallize in the ThCr 2 Si 2 -type tetragonal I4/mmm space group, with Cu/Zn/Si jointly occupying the same 4d crystallographic site. In the Zn-free composition, BaCu 1.33 Si 0.67 P 2 , Ba, and P each occupy a single crystallographic site. The introduction of Zn results in the expansion of the unit cell and splitting the Ba atomic sites along the [001] direction. Such structural displacement of the Ba atoms was confirmed by the heat capacity measurements. Band structure and density-of-states calculations on ordered hypothetical structural models reveal either a small bandgap (∼0.2 eV) or semimetallic band structures. The compounds reported here exhibit high Seebeck coefficients and ultralow thermal conductivity, making them promising candidates for the development of thermoelectric materials.

crystal structure↗

Synthesis and structural characterization of the new Zintl phases Eu 10 Mn 6 Bi 12 and Yb 10 Zn 6 Sb 12

Two new ternary compounds, Eu 10 Mn 6 Bi 12 and Yb 10 Zn 6 Sb 12 , were synthesized and structurally characterized. The synthesis was achieved either through reactions in sealed niobium tubes or in alumina crucibles by combining the elements in excess molten Sb. Their structures were elucidated using single-crystal X-ray diffraction, and they were determined to crystallize in the orthorhombic space group Cmmm (no. 65) with the Eu 10 Cd 6 Bi 12 structure type. Akin to the archetype phase, both Mn and Zn sites contain about 25% of vacancies. Furthermore, the anionic substructure of the title phases can be described as [M 6 Pn 12 ] (M = Zn, Mn; Pn = Sb, Bi) double layers composed of the corner and edge-sharing [MPn 4 ] tetrahedra, linked by [Pn 2 ] 4– dumbbells. Eu 2+ /Yb 2+ cations fill the space between the layers, with the valence electron counts adhering closely to the Zintl–Klemm rules, i.e., both Eu 10 Mn 6 Bi 12 and Yb 10 Zn 6 Sb 12 are expected to be valence-precise compounds. Analysis of the electronic structure and transport properties of Yb 10 Zn 6 Sb 12 indicate semimetallic behavior with relatively low Seebeck coefficient and resistivity that slightly decreases as a function of temperature.

36 MATERIALS SCIENCE↗

Space environmental effects on LDEF low Earth orbit exposed graphite reinforced polymer matrix composites

The Long Duration Exposure Facility (LDEF) was deployed on April 7, 1984 in low earth orbit (LEO) at an altitude of 482 kilometers. On board experiments experienced the harsh LEO environment including atomic oxygen (AO), ultraviolet radiation (UV), and thermal cycling. During the 5.8 year mission, the LDEF orbit decayed to 340 kilometers where significantly higher AO concentrations exist. LDEF was retrieved on January 12, 1990 from this orbit. One experiment on board LDEF was M0003, Space Effects on Spacecraft Materials. As a subset of M0003 nearly 500 samples of polymer, metal, and glass matrix composites were flown as the Advanced Composites Experiment M0003-10. The Advanced Composites Experiment is a joint effort between government and industry with the Aerospace Corporation serving as the experiment integrator. A portion of the graphite reinforced polymer matrix composites were furnished by the Boeing Defense and Space Group, Seattle, Washington. Test results and discussions for the Boeing portion of M0003-10 are presented. Experiment and specimen location on the LDEF are presented along with a quantitative summary of the pertinent exposure conditions. Matrix materials selected for the test were epoxy, polysulfone, and polyimide. These composite materials were selected due to their suitability for high performance structural capability in spacecraft applications. Graphite reinforced polymer matrix composites offer higher strength to weight ratios along with excellent dimensional stability. The Boeing space exposed and corresponding ground control composite specimens were subjected to post flight mechanical, chemical, and physical testing in order to determine any changes in critical properties and performance characteristics. Among the more significant findings are the erosive effect of atomic oxygen on leading edge exposed specimens and microcracking in non-unidirectionally reinforced flight specimens.

George, Pete↗

On the New Oxyarsenides Eu 5 Zn 2 As 5 O and Eu 5 Cd 2 As 5 O

The new quaternary phases Eu5Zn2As5O and Eu5Cd2As5O have been synthesized by metal flux reactions and their structures have been established through single-crystal X-ray diffraction. Both compounds crystallize in the centrosymmetric space group Cmcm (No. 63, Z = 4; Pearson symbol oC52), with unit cell parameters a = 4.3457(11) Å, b = 20.897(5) Å, c = 13.571(3) Å; and a = 4.4597(9) Å, b = 21.112(4) Å, c = 13.848(3) Å, for Eu5Zn2As5O and Eu5Cd2As5O, respectively. The crystal structures include one-dimensional double-strands of corner-shared MAs4 tetrahedra (M = Zn, Cd) and As–As bonds that connect the tetrahedra to form pentagonal channels. Four of the five Eu atoms fill the space between the pentagonal channels and one Eu atom is contained within the channels. An isolated oxide anion O2– is located in a tetrahedral hole formed by four Eu cations. Applying the valence rules and the Zintl concept to rationalize the chemical bonding in Eu5M2As5O (M = Zn, Cd) reveals that the valence electrons can be counted as follows: 5 × [Eu2+] + 2 × [M2+] + 3 × [As3–] + 2 × [As2–] + O2–, which suggests an electron-deficient configuration. The presumed h+ hole is confirmed by electronic band structure calculations, where a fully optimized bonding will be attained if an additional valence electron is added to move the Fermi level up to a narrow band gap (Eu5Zn2As5O) or pseudo-gap (Eu5Cd2As5O). In order to achieve such a formal charge balance, and hence, narrow-gap semiconducting behavior in Eu5M2As5O (M = Zn, Cd), europium is theorized to be in a mixed-valent Eu2+/ Eu3+ state.

36 MATERIALS SCIENCE↗

Thermally Stable Heterocyclic Imines as New Potential Nonlinear Optical Materials

In the course of a search for new thermostable acentric nonlinear optical crystalline materials, several heterocyclic imine derivatives were designed, with the general structure D-pi-A(D'). Introduction of a donor amino group (D') into the acceptor moiety was expected to bring H-bonds into their crystal structures, and so to elevate their melting points and assist in an acentric molecular packing. Six heterocycle-containing compounds of this type were prepared, single crystals were grown for five of them, and these crystals were characterized by X-ray analysis. A significant melting temperature elevation was found for all of the synthesized compounds. Three of the compounds were also found to crystallize in acentric space groups. One of the acentric compounds is built as a three-dimensional H-bonded molecular network. In the other two compounds, with very similar molecular structure, the molecules form one-dimensional H-bonded head-to-head associates (chains). These chains are parallel in two different crystallographic directions and form very unusual interpenetrating chain patterns in an acentric crystal. Two of the compounds crystallized with centrosymmetric molecular packing.

Nesterov, Volodymyr V.↗

International Space Exploration Coordination Group Assessment of Technology Gaps for Dust Mitigation for the Global Exploration Roadmap

The International Space Exploration Coordination Group (ISECG) formed two Gap Assessment teams to evaluate topic discipline areas that had not been worked at an international level to date. Accordingly, the ISECG Technology Working Group (TWG) recommended two discipline areas based on Global Exploration Roadmap (GER) Critical Technology Needs reflected within the GER Technology Development Map (GTDM): Dust Mitigation and LOX/Methane Propulsion, with this paper addressing the former. The ISECG approved the recommended Gap Assessment teams, and tasked the TWG to formulate the new teams with subject matter experts (SMEs) from the participating agencies. The participating agencies for the Dust Mitigation Gap Assessment Team were ASI, CSA, ESA, JAXA, and NASA. The team was asked to identify and make a presentation on technology gaps related to the GER2 mission scenario (including cislunar and lunar mission themes and long-lead items for human exploration of Mars) at the international level. In addition the team was tasked to produce a gap assessment in the form of a summary report and presentation identifying those GER Critical Technology Needs, including opportunities for international coordination and cooperation in closing the identified gaps. Dust is still a principal limiting factor in returning to the lunar surface for missions of any extended duration. However, viable technology solutions have been identified, but need maturation to be available to support both lunar and Mars missions.

dust↗

International Space Exploration Coordination Group Assessment of Technology Gaps for Dust Mitigation for the Global Exploration Roadmap

The International Space Exploration Coordination Group (ISECG) formed two Gap Assessment teams to evaluate topic discipline areas that had not been worked at an international level to date. Accordingly, the ISECG Technology Working Group (TWG) recommended two discipline areas based on Global Exploration Roadmap (GER) Critical Technology Needs reflected within the GER Technology Development Map (GTDM): Dust Mitigation and LOX/Methane Propulsion, with this paper addressing the former. The ISECG approved the recommended Gap Assessment teams, and tasked the TWG to formulate the new teams with subject matter experts (SMEs) from the participating agencies. The participating agencies for the Dust Mitigation Gap Assessment Team were ASI, CSA, ESA, JAXA, and NASA. The team was asked to identify and make a presentation on technology gaps related to the GER2 mission scenario (including cislunar and lunar mission themes and long-lead items for human exploration of Mars) at the international level. In addition the team was tasked to produce a gap assessment in the form of a summary report and presentation identifying those GER Critical Technology Needs, including opportunities for international coordination and cooperation in closing the identified gaps. Dust is still a principal limiting factor in returning to the lunar surface for missions of any extended duration. However, viable technology solutions have been identified, but need maturation to be available to support both lunar and Mars missions.

dust↗

Structural Investigation of Six Quinary Sulfides Synthesized via the Flux-Assisted Boron-Chalcogen Mixture (BCM) Method: Eu 2+ Containing Members of the RE 3 MTQ 7 (M and T = Transition or Main Group Metals, Q = Chalcogens) Family

For this work, a series of six quinary rare-earth sulfides Ce 4+ 1.85 Eu 2+ 1.15 Na 0.30 SiS 7 , Ce 4+ 1.91 Eu 2+ 1.09 K 0.18 SiS 7 , Ce 4+ 1.96 Eu 2+ 1.04 Rb 0.08 SiS 7 , Ce 4+ 1.98 Eu 2+ 1.02 Cs 0.05 SiS 7 , Ce 4+ 1.97 Eu 2+ 1.03 Ag 0.06 SiS 7 , and Ce 4+ 1.50 Eu 2+ 1.50 CuSiS 7 were obtained in an alkali iodide flux using the boron-chalcogen mixture (BCM) method. Single crystal X-ray diffraction was used to determine the structures of the high quality single crystals that were grown; their elemental compositions were confirmed by energy-dispersive spectroscopy (EDS). The compounds crystallize in the hexagonal crystal system in the noncentrosymmetric space group P63. The crystal structure consists of a three-dimensional network composed of mixed cerium and europium bicapped trigonal prisms, isolated SiS4 tetrahedra, and monovalent metals (Na, K, Rb, Cs, Ag, and Cu) located in cavities created by linked Ce/EuS 8 polyhedra. The structures are charge-balanced when Ce and Eu are in their +4 and +2 oxidation states, respectively. The effective magnetic moment of Ce 1.50 4+ Eu 1.50 2+ CuSiS 7 determined from the temperature dependence of the magnetic susceptibility data is consistent with the presence of Ce 4+ and Eu 2+ . Clear correlations between the alkali ion site occupancy, the ionic radius of the alkali cations, and the average bond length of Ce 4+ /Eu 2+ –S, were established. UV–vis diffuse reflectance data were collected for Ce 1.50 4+ Eu 1.50 2+ CuSiS 7 and a band gap of 1.9(1) eV was established.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The Subchalcogenides Ir 2 In 8 Q (Q = S, Se, Te): Dirac Semimetal Candidates with Re-entrant Structural Modulation

Subchalcogenides are uncommon compounds where the metal atoms are in unusually low formal oxidation states. They bridge the gap between intermetallics and semiconductors and can have unexpected structures and properties because of the exotic nature of their chemical bonding as they contain both metal–metal and metal–main group (e.g., halide, chalcogenide) interactions. Finding new members of this class of materials presents synthetic challenges as attempts to make them often result in phase separation into binary compounds. We overcome this difficulty by utilizing indium as a metal flux to synthesize large (millimeter scale) single crystals of novel subchalcogenide materials. Herein, we report two new compounds Ir 2 In 8 Q (Q = Se, Te) and compare their structural and electrical properties to the previously reported Ir 2 In 8 S analogue. Ir 2 In 8 Se and Ir 2 In 8 Te crystallize in the $P_{4_2}$/mnm space group and are isostructural to Ir2In8S, but also have commensurately modulated (with q vectors q = 1/6a* + 1/6b* and q = 1/10a* + 1/10b* for Ir 2 In 8 Se and Ir 2 In 8 Te, respectively) low-temperature phase transitions, where the chalcogenide anions in the channels experience a distortion in the form of In–Q bond alternation along the ab plane. Both compounds display re-entrant structural behavior, where the supercells appear on cooling but revert to the original subcell below 100 K, suggesting competing structural and electronic interactions dictate the overall structure. Notably, these materials are topological semimetal candidates with symmetry-protected Dirac crossings near the Fermi level and exhibit high electron mobilities (~1500 cm 2 V –1 s –1 at 1.8 K) and moderate carrier concentrations (~10 20 cm –3 ) from charge transport measurements. This work highlights metal flux as a synthetic route to high quality single crystals of novel intermetallic subchalcogenides with Dirac semimetal behavior.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Magnetic Properties of Tetravalent Pu in the Perovskites BaPuO 3 and SrPuO 3

BaPuO 3 and SrPuO 3 were synthesized, and their structures were refined in the orthorhombic space group Pbnm , a common distortion from the classic $Pm\bar{3}$m over barm cubic perovskite. Magnetic-susceptibility measurements, obtained as a function of temperature over the range of 1.8-320 K, exhibit temperature-dependent behavior, with evidence of long-range magnetic order at temperatures higher than their lanthanide and actinide analogues: BaPuO 3 below 164(1) K and SrPuO 3 below 76(1) K. Effective moments of 1.66(10)μ B for BaPuO 3 and 1.84(8)μ B for SrPuO 3 were obtained by fitting their paramagnetic susceptibilities using the Curie-Weiss law. Further, both are below the free-ion value of 2.68 μ B expected for a Pu 4+ 5 $\mid$ 4 ground level. Ab initio wave function calculations, performed at the relativistic complete active space level including spin-orbit coupling and with an embedded cluster approach that neglects interactions between Pu centers, were used to generate embedded-cluster Pu 4+ magnetic susceptibilities. The calculations agree well with experimental data at higher temperatures, providing evidence that a single-ion representation is sufficient to account for the observed paramagnetic behavior without the need to invoke charge transfer, disproportionation, strong covalent bonding, or other more complex electronic behavior.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗