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Electronic excited states from a variance-based contracted quantum eigensolver

Electronic excited states of molecules are central to many physical and chemical processes, and yet they are typically more difficult to compute than ground states. Here, in this paper we leverage the advantages of quantum computers to develop an algorithm for the highly accurate calculation of excited states. We solve a contracted Schrödinger equation (CSE)—a contraction (projection) of the Schrödinger equation onto the space of two electrons—whose solutions correspond identically to the ground and excited states of the Schrödinger equation. While recent quantum algorithms for solving the CSE, known as contracted quantum eigensolvers (CQE), have focused on ground states, we develop a CQE based on the variance that is designed to optimize rapidly to a ground or excited state. We apply the algorithm to compute the ground and excited states of H 2 , H 4 , and BH.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Accurate machine-learning predictions of coercivity in high-performance permanent magnets

Increased demand for high-performance permanent magnets in the electric vehicle and wind-turbine industries has prompted the search for cost-effective alternatives. Discovering magnetic materials with the desired intrinsic and extrinsic permanent magnet properties presents a significant challenge to researchers because of issues with the global supply of rare-earth elements, material stability, and a low maximum magnetic energy product BH max . While first-principles density functional theory (DFT) predicts materials’ magnetic moments, magnetocrystalline anisotropy constants, and exchange interactions, it cannot compute extrinsic properties such as coercivity (H c ). Although it is possible to calculate H c theoretically with micromagnetic simulations, the predicted value is larger than the experiment by almost an order of magnitude due to the Brown paradox. To circumvent these issues, we employ machine-learning (ML) methods on an extensive database obtained from experiments, DFT calculations, and micromagnetic modeling. The use of a large experimental dataset enables realistic H c predictions for materials such as Ce-doped Nd 2 ⁢Fe 14 ⁢B, comparing favorably against micromagnetically simulated coercivities. Remarkably, our ML model accurately identifies uniaxial magneto-crystalline anisotropy as the primary contributor to H c . With DFT calculations, we predict the Nd-site-dependent magnetic anisotropy behavior in Nd 2 ⁢Fe 14 ⁢B, confirming that Nd 4⁢g sites mainly contribute to uniaxial magnetocrystalline anisotropy, and also calculate the Curie temperature (T c ). Finally, both calculated results are in good agreement with the experiments. The coupled experimental dataset and ML modeling with DFT input predict H c with far greater accuracy and speed than was previously possible using micromagnetic modeling. Further, we reverse engineer the grain-boundary and intergrain exchange coupling with micromagnetic simulations by employing the ML predictions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Signatures of deconfined quark phases in binary neutron star mergers

We investigate the quark deconfinement phase transition in the context of binary neutron star (BNS) mergers. We employ a new finite-temperature composition-dependent equation of state (EOS) with a first order phase transition between hadrons and deconfined quarks to perform numerical relativity simulations of BNS mergers. Here, the softening of the EOS due to the phase transition causes the merger remnants to be more compact and to collapse to a black hole (BH) at earlier times. The phase transition is imprinted on the postmerger gravitational wave (GW) signal duration, amplitude, and peak frequency. However, this imprint is only detectable for binaries with sufficiently long-lived remnants. Moreover, the phase transition does not result in significant deviations from quasi-universal relations for the postmerger GW peak frequency. We also study the impact of the phase transition on dynamical ejecta, remnant accretion disk masses, r-process nucleosynthetic yields and associated electromagnetic (EM) counterparts. While there are differences in the EM counterparts and nucleosynthesis yields between the purely hadronic models and the models with phase transitions, these can be primarily ascribed to the difference in remnant collapse time between the two. An exception is the non-thermal afterglow caused by the interaction of the fastest component of the dynamical ejecta and the interstellar medium, which is systematically boosted in the binaries with phase transition as a consequence of the more violent merger they experience.

79 ASTRONOMY AND ASTROPHYSICS↗

Deep Learning Based Workflow for Accelerated Industrial X-Ray Computed Tomography

X-ray computed tomography (XCT) is an important tool for high-resolution non-destructive characterization of additively-manufactured metal components. XCT reconstructions of metal components may have beam hardening artifacts such as cupping and streaking which makes reliable detection of flaws and defects challenging. Furthermore, traditional workflows based on using analytic reconstruction algorithms require a large number of projections for accurate characterization - leading to longer measurement times and hindering the adoption of XCT for in-line inspections. In this paper, we introduce a new workflow based on the use of two neural networks to obtain high-quality accelerated reconstructions from sparse-view XCT scans of single material metal parts. The first network, implemented using fully-connected layers, helps reduce the impact of BH in the projection data without the need of any calibration or knowledge of the component material. The second network, a convolutional neural network, maps a low-quality analytic 3D reconstruction to a high-quality reconstruction. Using experimental data, we demonstrate that our method robustly generalizes across several alloys, and for a range of sparsity levels without any need for retraining the networks thereby enabling accurate and fast industrial XCT inspections.

Rahman, Obaid↗

Development of Dy-free Nd-Fe-B-based sintered magnet through grain boundary engineering using Pr-Cu alloys

For this study, Dy-free sintered magnets were fabricated by mixing Nd-Fe-B powder with various amounts of Pr-Cu powder followed by the common procedures for making Nd-Fe-B based sintered magnets. With the Pr-Cu addition increasing from 0 to 10 wt.%, the obtained magnets’ H cj increases from the original 14.5 kOe to 18.6 kOe. The highest (BH) max achieved was 35.0 MGOe with 7.5 wt.% PrCu. The distribution of the Pr and Cu elements was primarily at grain boundary and triple junctions, leading to a reduced coupling among grains, thus an enhanced H cj .

36 MATERIALS SCIENCE↗

Effect of different grain boundary diffusion alloys on magnetic properties of Dy-free sintered NdFeB magnet

Dy-free sintered magnets were fabricated by blending Neo powder with different grain boundary diffusion alloy powders. Cu, CeAl and CeAlCu have a negative effect on H cj of magnets, while PrAlCu and AlCuGa have a positive effect. The PrAlCu-added magnet achieves the best magnetic properties among all magnets with the additions of different diffusion alloys. With increasing PrAlCu from 0-10 wt.%, H cj of the magnets gradually increases from the original 14.5 kOe to 19.2 kOe. The magnet with 7.5 wt.% PrAlCu obtains a H cj of 18 kOe and (BH) max of 39.1 MGOe. It is found that Pr and Cu in PrAlCu alloy is mainly distributed at grain boundary and triple junctions, leading to a reduced coupling among grains, thus an enhanced H cj . Here, the grain boundary engineering by adding an appropriate alloy is an effective method to improve H cj of Dy-free NdFeB magnets.

36 MATERIALS SCIENCE↗

Atomic layer deposition of HfO 2 films using carbon-free tetrakis(tetrahydroborato)hafnium and water

Thin hafnium oxide films were prepared by atomic layer deposition using a carbon-free precursor, tetrakis(tetrahydroborato)hafnium [Hf(BH 4 )( 4 )], and H 2 O. Film growth was studied using an in situ quartz crystal microbalance and Fourier transform infrared spectroscopy measurements. Self-limiting growth was observed between 100 and 175 degrees C, but the thermal decomposition of the Hf precursor occurred at higher temperatures. The film properties were investigated using x-ray photoelectron spectroscopy, x-ray reflectivity, x-ray diffraction, ellipsometry, time-of-flight secondary ion mass spectrometry, and x-ray absorption spectroscopy. The as-deposited films were found to consist of an amorphous mixture of HfO 2 and B 2 O 3 , and had a lower density and lower refractive index compared to pure HfO 2 thin films. Finally, annealing the films to >750 degrees C yielded crystalline monoclinic HfO 2 with a density of 9g/cm 3 and a refractive index of 2.10.

36 MATERIALS SCIENCE↗

Electrochemical Reactivity of Hydrogen Storage Materials: Exploring Borohydride and Hydrazinium Salt Mixtures

Electrochemical characterization of hydrogen storage materials was conducted in a non-aqueous environment to investigate the direct electrochemical release and consumption of hydrogen and the potential for regeneration. We first address the challenge of minimal solubility of the synthetic precursors, sodium borohydride (NaBH 4 ) and hydrazinium bromide (N 2 H 5 Br), in both organic and inorganic solvents. We next determine and calibrate a reference electrode formulation compatible with our non-aqueous media and analytes that demonstrates a stable reference potential. We employ cyclic voltammetry (CV) to characterize the precursors and mixtures thereof. Each CV peak is assigned to a corresponding electrochemical reaction. Using the rate-dependent CV method and Randles–Ševčík equation, we calculate the diffusion coefficient of each chemical (NaBH 4 and N 2 H 5 Br). Analysis of the CVs, coupled with 11B NMR analysis, reveals a room temperature chemical transformation of NaBH 4 and N 2 H 5 Br mixtures into hydrazine borane (N 2 H 4 BH 3 ). These results are particularly significant, considering the limited information available on the electrochemical characterization of metal borohydride and hydrazinium salt in non-aqueous media. This work establishes a foundation for adapting a non-aqueous electrochemical system to further study the borohydride family of chemistries and to design and develop electrochemical devices for direct electrical and chemical energy interconversion with hydrogen storage materials.

08 HYDROGEN↗

Comprehensive Physical Activity Assessment During U.S. Army Basic Combat Training

Abstract Alemany, JA, Pierce, JR, Bornstein, DB, Grier, TL, Jones, BH, and Glover, SH. Comprehensive physical activity assessment during U.S. Army Basic Combat Training. J Strength Cond Res 36(12): 3505–3512, 2022—Physical activity (PA) volume, intensity, and qualitative contextual information regarding activity type and loads carried are limited during U.S. Army Basic Combat Training (BCT). The purpose of this study was to characterize daily (05:00–20:00 hours) PA during BCT using a comprehensive approach. During 2 10-week BCT cycles ( n = 40 trainees per cycle), pedometers, accelerometers, and direct observation were used to estimate daily step count, PA volume, and intensity. Physical activity intensity was categorized by metabolic equivalents (METs) such as “sedentary” (1–2 METs), “light” (2–3 METs), “moderate” (3–6 METs), or “vigorous” (≥6 METs). Daily PA data were analyzed longitudinally using linear mixed models, with significance set at p ≤ 0.05. The mean daily step count was 13,459 ± 4,376 steps, and the mean daily accelerometer-assessed PA volume and intensity were as follows: sedentary: 505 ± 98 minutes, light: 190 ± 78 minutes, moderate: 168 ± 51 minutes, and vigorous: 14 ± 14 minutes, with no differences between cycles for all measures ( p > 0.50). Cumulative time on feet (∼50%) and sitting (20–25%) accounted for most daily activity types during both cycles. Trainees, on average, carried between 3 and 9 kg, and ≥9 kg, for 60% and 10% of the monitored day, respectively. Basic Combat Training's physical demands are high, where trainees achieved 1.7 to 2.7 times greater daily ambulation and 6 times the recommended weekly moderate-to-vigorous PA compared with civilian counterparts and performed weight-bearing load carriage for nearly half of the day. Basic Combat Training-associated PA may increase injury risk among trainees unaccustomed to arduous PA and exercise. Implementing national PA policies to improve physical fitness and facilitate acclimatization to BCT's high physical demands could reduce public health burdens and military nonreadiness.

Sport Sciences↗

Materials Data on B13H19 by Materials Project

B5H8(BH)4B4H7 crystallizes in the monoclinic P2_1/c space group. The structure is zero-dimensional and consists of sixteen boranediylradical molecules, four B4H7 clusters, and four B5H8 clusters. In each B4H7 cluster, there are four inequivalent B+1.15- sites. In the first B+1.15- site, B+1.15- is bonded in a distorted water-like geometry to two H+0.79+ atoms. There is one shorter (1.20 Å) and one longer (1.32 Å) B–H bond length. In the second B+1.15- site, B+1.15- is bonded in a distorted water-like geometry to two H+0.79+ atoms. There is one shorter (1.19 Å) and one longer (1.32 Å) B–H bond length. In the third B+1.15- site, B+1.15- is bonded in a distorted trigonal non-coplanar geometry to three H+0.79+ atoms. There are a spread of B–H bond distances ranging from 1.19–1.36 Å. In the fourth B+1.15- site, B+1.15- is bonded in a distorted trigonal non-coplanar geometry to three H+0.79+ atoms. There is one shorter (1.19 Å) and two longer (1.35 Å) B–H bond length. There are seven inequivalent H+0.79+ sites. In the first H+0.79+ site, H+0.79+ is bonded in a single-bond geometry to one B+1.15- atom. In the second H+0.79+ site, H+0.79+ is bonded in a single-bond geometry to one B+1.15- atom. In the third H+0.79+ site, H+0.79+ is bonded in an L-shaped geometry to two B+1.15- atoms. In the fourth H+0.79+ site, H+0.79+ is bonded in a single-bond geometry to one B+1.15- atom. In the fifth H+0.79+ site, H+0.79+ is bonded in an L-shaped geometry to two B+1.15- atoms. In the sixth H+0.79+ site, H+0.79+ is bonded in a single-bond geometry to one B+1.15- atom. In the seventh H+0.79+ site, H+0.79+ is bonded in an L-shaped geometry to two B+1.15- atoms. In each B5H8 cluster, there are five inequivalent B+1.15- sites. In the first B+1.15- site, B+1.15- is bonded in a distorted trigonal non-coplanar geometry to three H+0.79+ atoms. There are a spread of B–H bond distances ranging from 1.19–1.36 Å. In the second B+1.15- site, B+1.15- is bonded in a distorted trigonal non-coplanar geometry to three H+0.79+ atoms. There are a spread of B–H bond distances ranging from 1.19–1.36 Å. In the third B+1.15- site, B+1.15- is bonded in a distorted water-like geometry to two H+0.79+ atoms. There is one shorter (1.20 Å) and one longer (1.32 Å) B–H bond length. In the fourth B+1.15- site, B+1.15- is bonded in a distorted trigonal non-coplanar geometry to three H+0.79+ atoms. There are a spread of B–H bond distances ranging from 1.19–1.33 Å. In the fifth B+1.15- site, B+1.15- is bonded in a distorted single-bond geometry to one H+0.79+ atom. The B–H bond length is 1.40 Å. There are eight inequivalent H+0.79+ sites. In the first H+0.79+ site, H+0.79+ is bonded in an L-shaped geometry to two B+1.15- atoms. In the second H+0.79+ site, H+0.79+ is bonded in an L-shaped geometry to two B+1.15- atoms. In the third H+0.79+ site, H+0.79+ is bonded in an L-shaped geometry to two B+1.15- atoms. In the fourth H+0.79+ site, H+0.79+ is bonded in a single-bond geometry to one B+1.15- atom. In the fifth H+0.79+ site, H+0.79+ is bonded in a single-bond geometry to one B+1.15- atom. In the sixth H+0.79+ site, H+0.79+ is bonded in an L-shaped geometry to two B+1.15- atoms. In the seventh H+0.79+ site, H+0.79+ is bonded in a single-bond geometry to one B+1.15- atom. In the eighth H+0.79+ site, H+0.79+ is bonded in a single-bond geometry to one B+1.15- atom.

36 MATERIALS SCIENCE↗

Materials Data on CsB9H14 by Materials Project

CsB7H12(BH)2 crystallizes in the triclinic P-1 space group. The structure is one-dimensional and consists of four boranediylradical molecules and two CsB7H12 ribbons oriented in the (1, 0, 0) direction. In each CsB7H12 ribbon, Cs1+ is bonded in a 1-coordinate geometry to six H1+ atoms. There are a spread of Cs–H bond distances ranging from 2.90–3.24 Å. There are seven inequivalent B+1.67- sites. In the first B+1.67- site, B+1.67- is bonded in a distorted water-like geometry to two H1+ atoms. There is one shorter (1.20 Å) and one longer (1.34 Å) B–H bond length. In the second B+1.67- site, B+1.67- is bonded in a distorted bent 120 degrees geometry to two H1+ atoms. Both B–H bond lengths are 1.21 Å. In the third B+1.67- site, B+1.67- is bonded in a distorted water-like geometry to two H1+ atoms. There is one shorter (1.20 Å) and one longer (1.30 Å) B–H bond length. In the fourth B+1.67- site, B+1.67- is bonded in a distorted trigonal non-coplanar geometry to three H1+ atoms. There are a spread of B–H bond distances ranging from 1.21–1.37 Å. In the fifth B+1.67- site, B+1.67- is bonded in a distorted water-like geometry to two H1+ atoms. There is one shorter (1.20 Å) and one longer (1.38 Å) B–H bond length. In the sixth B+1.67- site, B+1.67- is bonded in a distorted trigonal non-coplanar geometry to three H1+ atoms. There are a spread of B–H bond distances ranging from 1.19–1.33 Å. In the seventh B+1.67- site, B+1.67- is bonded in a single-bond geometry to one H1+ atom. The B–H bond length is 1.20 Å. There are twelve inequivalent H1+ sites. In the first H1+ site, H1+ is bonded in a single-bond geometry to one Cs1+ and one B+1.67- atom. In the second H1+ site, H1+ is bonded in a single-bond geometry to one B+1.67- atom. In the third H1+ site, H1+ is bonded in a single-bond geometry to one Cs1+ and one B+1.67- atom. In the fourth H1+ site, H1+ is bonded in a single-bond geometry to one B+1.67- atom. In the fifth H1+ site, H1+ is bonded in a single-bond geometry to one Cs1+ and one B+1.67- atom. In the sixth H1+ site, H1+ is bonded in a single-bond geometry to one B+1.67- atom. In the seventh H1+ site, H1+ is bonded in an L-shaped geometry to two B+1.67- atoms. In the eighth H1+ site, H1+ is bonded in an L-shaped geometry to two B+1.67- atoms. In the ninth H1+ site, H1+ is bonded in a single-bond geometry to one Cs1+ and one B+1.67- atom. In the tenth H1+ site, H1+ is bonded in a single-bond geometry to one Cs1+ and one B+1.67- atom. In the eleventh H1+ site, H1+ is bonded in a distorted single-bond geometry to one Cs1+ and one B+1.67- atom. In the twelfth H1+ site, H1+ is bonded in an L-shaped geometry to two B+1.67- atoms.

36 MATERIALS SCIENCE↗

Materials Data on B7H10 by Materials Project

B4H7(BH)3 crystallizes in the orthorhombic P2_12_12_1 space group. The structure is zero-dimensional and consists of twenty-four boranediylradical molecules and eight B4H7 clusters. In each B4H7 cluster, there are four inequivalent B sites. In the first B site, B is bonded in a distorted trigonal non-coplanar geometry to three H atoms. There are a spread of B–H bond distances ranging from 1.19–1.35 Å. In the second B site, B is bonded in a distorted water-like geometry to two H atoms. There is one shorter (1.19 Å) and one longer (1.32 Å) B–H bond length. In the third B site, B is bonded in a distorted water-like geometry to two H atoms. There is one shorter (1.19 Å) and one longer (1.33 Å) B–H bond length. In the fourth B site, B is bonded in a distorted trigonal non-coplanar geometry to three H atoms. There are a spread of B–H bond distances ranging from 1.19–1.35 Å. There are seven inequivalent H sites. In the first H site, H is bonded in an L-shaped geometry to two B atoms. In the second H site, H is bonded in a single-bond geometry to one B atom. In the third H site, H is bonded in a single-bond geometry to one B atom. In the fourth H site, H is bonded in a single-bond geometry to one B atom. In the fifth H site, H is bonded in an L-shaped geometry to two B atoms. In the sixth H site, H is bonded in a single-bond geometry to one B atom. In the seventh H site, H is bonded in an L-shaped geometry to two B atoms.

36 MATERIALS SCIENCE↗

Materials Data on B2H3 by Materials Project

B4H7B2H3(BH)2 crystallizes in the orthorhombic Pbca space group. The structure is zero-dimensional and consists of sixteen boranediylradical molecules, eight diborane molecules, and eight B4H7 clusters. In each B4H7 cluster, there are four inequivalent B sites. In the first B site, B is bonded in a distorted trigonal non-coplanar geometry to three H atoms. There are a spread of B–H bond distances ranging from 1.19–1.41 Å. In the second B site, B is bonded in a distorted trigonal non-coplanar geometry to three H atoms. There are a spread of B–H bond distances ranging from 1.19–1.40 Å. In the third B site, B is bonded in a distorted water-like geometry to two H atoms. There is one shorter (1.19 Å) and one longer (1.31 Å) B–H bond length. In the fourth B site, B is bonded in a distorted water-like geometry to two H atoms. There is one shorter (1.19 Å) and one longer (1.31 Å) B–H bond length. There are seven inequivalent H sites. In the first H site, H is bonded in an L-shaped geometry to two B atoms. In the second H site, H is bonded in a single-bond geometry to one B atom. In the third H site, H is bonded in a single-bond geometry to one B atom. In the fourth H site, H is bonded in an L-shaped geometry to two B atoms. In the fifth H site, H is bonded in a single-bond geometry to one B atom. In the sixth H site, H is bonded in a single-bond geometry to one B atom. In the seventh H site, H is bonded in an L-shaped geometry to two B atoms.

36 MATERIALS SCIENCE↗

Materials Data on B5H11N2 by Materials Project

B2H3(BH)2BNH4NH2 crystallizes in the monoclinic C2/c space group. The structure is zero-dimensional and consists of eight ammonia molecules, eight azaniumylboron molecules, sixteen boranediylradical molecules, and eight diborane molecules.

36 MATERIALS SCIENCE↗

Materials Data on B5H9N by Materials Project

(BH)2B2H3BNH4 crystallizes in the orthorhombic Pnma space group. The structure is zero-dimensional and consists of eight azaniumylboron molecules, sixteen boranediylradical molecules, and eight diborane molecules.

36 MATERIALS SCIENCE↗

Materials Data on B9H11C2 by Materials Project

B13C4H17(BH)5 crystallizes in the monoclinic C2/c space group. The structure is zero-dimensional and consists of forty boranediylradical molecules and eight B13C4H17 clusters. In each B13C4H17 cluster, there are thirteen inequivalent B+0.33- sites. In the first B+0.33- site, B+0.33- is bonded in a distorted single-bond geometry to one B+0.33- and one H1+ atom. The B–B bond length is 1.70 Å. The B–H bond length is 1.34 Å. In the second B+0.33- site, B+0.33- is bonded in a distorted bent 120 degrees geometry to one C4- and one H1+ atom. The B–C bond length is 1.52 Å. The B–H bond length is 1.19 Å. In the third B+0.33- site, B+0.33- is bonded in a 3-coordinate geometry to two C4- and one H1+ atom. There is one shorter (1.69 Å) and one longer (1.71 Å) B–C bond length. The B–H bond length is 1.19 Å. In the fourth B+0.33- site, B+0.33- is bonded in a distorted bent 120 degrees geometry to one C4- and one H1+ atom. The B–C bond length is 1.66 Å. The B–H bond length is 1.19 Å. In the fifth B+0.33- site, B+0.33- is bonded in a distorted bent 120 degrees geometry to one C4- and one H1+ atom. The B–C bond length is 1.70 Å. The B–H bond length is 1.19 Å. In the sixth B+0.33- site, B+0.33- is bonded in a single-bond geometry to one B+0.33- and one H1+ atom. The B–B bond length is 1.78 Å. The B–H bond length is 1.19 Å. In the seventh B+0.33- site, B+0.33- is bonded in a distorted bent 120 degrees geometry to one B+0.33-, one C4-, and one H1+ atom. The B–B bond length is 1.79 Å. The B–C bond length is 1.69 Å. The B–H bond length is 1.19 Å. In the eighth B+0.33- site, B+0.33- is bonded in a 3-coordinate geometry to two C4- and one H1+ atom. Both B–C bond lengths are 1.72 Å. The B–H bond length is 1.19 Å. In the ninth B+0.33- site, B+0.33- is bonded in a distorted bent 120 degrees geometry to one C4- and one H1+ atom. The B–C bond length is 1.70 Å. The B–H bond length is 1.19 Å. In the tenth B+0.33- site, B+0.33- is bonded in a distorted bent 120 degrees geometry to one B+0.33-, one C4-, and one H1+ atom. The B–B bond length is 1.79 Å. The B–C bond length is 1.69 Å. The B–H bond length is 1.19 Å. In the eleventh B+0.33- site, B+0.33- is bonded in a 6-coordinate geometry to four B+0.33- and two C4- atoms. Both B–C bond lengths are 1.73 Å. In the twelfth B+0.33- site, B+0.33- is bonded in a distorted trigonal non-coplanar geometry to three H1+ atoms. There is one shorter (1.19 Å) and two longer (1.33 Å) B–H bond length. In the thirteenth B+0.33- site, B+0.33- is bonded in a 3-coordinate geometry to one C4- and two H1+ atoms. The B–C bond length is 1.75 Å. There is one shorter (1.19 Å) and one longer (1.33 Å) B–H bond length. There are four inequivalent C4- sites. In the first C4- site, C4- is bonded in a 2-coordinate geometry to two B+0.33-, one C4-, and one H1+ atom. The C–C bond length is 1.46 Å. The C–H bond length is 1.09 Å. In the second C4- site, C4- is bonded in a 1-coordinate geometry to three B+0.33-, one C4-, and one H1+ atom. The C–H bond length is 1.09 Å. In the third C4- site, C4- is bonded in a 1-coordinate geometry to four B+0.33- and one H1+ atom. The C–H bond length is 1.09 Å. In the fourth C4- site, C4- is bonded in a 1-coordinate geometry to four B+0.33- and one H1+ atom. The C–H bond length is 1.09 Å. There are sixteen inequivalent H1+ sites. In the first H1+ site, H1+ is bonded in a single-bond geometry to one B+0.33- atom. In the second H1+ site, H1+ is bonded in a single-bond geometry to one B+0.33- atom. In the third H1+ site, H1+ is bonded in a single-bond geometry to one B+0.33- atom. In the fourth H1+ site, H1+ is bonded in a single-bond geometry to one C4- atom. In the fifth H1+ site, H1+ is bonded in a single-bond geometry to one C4- atom. In the sixth H1+ site, H1+ is bonded in a single-bond geometry to one B+0.33- atom. In the seventh H1+ site, H1+ is bonded in a single-bond geometry to one B+0.33- atom. In the eighth H1+ site, H1+ is bonded in a single-bond geometry to one B+0.33- atom. In the ninth H1+ site, H1+ is bonded in a single-bond geometry to one B+0.33- atom. In the tenth H1+ site, H1+ is bonded in a single-bond geometry to one B+0.33- atom. In the eleventh H1+ site, H1+ is bonded in a single-bond geometry to one B+0.33- atom. In the twelfth H1+ site, H1+ is bonded in an L-shaped geometry to two B+0.33- atoms. In the thirteenth H1+ site, H1+ is bonded in an L-shaped geometry to two B+0.33- atoms. In the fourteenth H1+ site, H1+ is bonded in a single-bond geometry to one B+0.33- atom. In the fifteenth H1+ site, H1+ is bonded in a single-bond geometry to one C4- atom. In the sixteenth H1+ site, H1+ is bonded in a single-bond geometry to one C4- atom.

36 MATERIALS SCIENCE↗

Materials Data on B20H26O by Materials Project

(B3H4)2(BH)8B6H8OH2 crystallizes in the monoclinic C2/c space group. The structure is zero-dimensional and consists of thirty-two boranediylradical molecules, eight hydrogen molecules, eight B3H4 clusters, and four B6H8O clusters. In each B3H4 cluster, there are three inequivalent B+1.20- sites. In the first B+1.20- site, B+1.20- is bonded in a distorted water-like geometry to two H1+ atoms. There is one shorter (1.19 Å) and one longer (1.40 Å) B–H bond length. In the second B+1.20- site, B+1.20- is bonded in a distorted water-like geometry to two H1+ atoms. Both B–H bond lengths are 1.28 Å. In the third B+1.20- site, B+1.20- is bonded in a distorted water-like geometry to two H1+ atoms. There is one shorter (1.19 Å) and one longer (1.40 Å) B–H bond length. There are four inequivalent H1+ sites. In the first H1+ site, H1+ is bonded in a single-bond geometry to one B+1.20- atom. In the second H1+ site, H1+ is bonded in a single-bond geometry to one B+1.20- atom. In the third H1+ site, H1+ is bonded in an L-shaped geometry to two B+1.20- atoms. In the fourth H1+ site, H1+ is bonded in an L-shaped geometry to two B+1.20- atoms. In each B6H8O cluster, there are three inequivalent B+1.20- sites. In the first B+1.20- site, B+1.20- is bonded in a distorted water-like geometry to two H1+ atoms. There is one shorter (1.19 Å) and one longer (1.30 Å) B–H bond length. In the second B+1.20- site, B+1.20- is bonded in a 3-coordinate geometry to two H1+ and one O2- atom. Both B–H bond lengths are 1.41 Å. The B–O bond length is 1.37 Å. In the third B+1.20- site, B+1.20- is bonded in a water-like geometry to two H1+ atoms. There is one shorter (1.19 Å) and one longer (1.30 Å) B–H bond length. There are four inequivalent H1+ sites. In the first H1+ site, H1+ is bonded in a single-bond geometry to one B+1.20- atom. In the second H1+ site, H1+ is bonded in a single-bond geometry to one B+1.20- atom. In the third H1+ site, H1+ is bonded in an L-shaped geometry to two B+1.20- atoms. In the fourth H1+ site, H1+ is bonded in an L-shaped geometry to two B+1.20- atoms. O2- is bonded in a bent 150 degrees geometry to two equivalent B+1.20- atoms.

36 MATERIALS SCIENCE↗

Materials Data on B9H11N4 by Materials Project

B3H5(BH)3B3N4H3 crystallizes in the monoclinic P2_1/c space group. The structure is zero-dimensional and consists of twelve boranediylradical molecules, four B3H5 clusters, and four B3N4H3 clusters. In each B3H5 cluster, there are three inequivalent B+0.33+ sites. In the first B+0.33+ site, B+0.33+ is bonded in a water-like geometry to two H+0.82+ atoms. There is one shorter (1.19 Å) and one longer (1.31 Å) B–H bond length. In the second B+0.33+ site, B+0.33+ is bonded in a trigonal non-coplanar geometry to three H+0.82+ atoms. There are a spread of B–H bond distances ranging from 1.19–1.39 Å. In the third B+0.33+ site, B+0.33+ is bonded in a water-like geometry to two H+0.82+ atoms. There is one shorter (1.19 Å) and one longer (1.30 Å) B–H bond length. There are five inequivalent H+0.82+ sites. In the first H+0.82+ site, H+0.82+ is bonded in a single-bond geometry to one B+0.33+ atom. In the second H+0.82+ site, H+0.82+ is bonded in a single-bond geometry to one B+0.33+ atom. In the third H+0.82+ site, H+0.82+ is bonded in an L-shaped geometry to two B+0.33+ atoms. In the fourth H+0.82+ site, H+0.82+ is bonded in an L-shaped geometry to two B+0.33+ atoms. In the fifth H+0.82+ site, H+0.82+ is bonded in a single-bond geometry to one B+0.33+ atom. In each B3N4H3 cluster, there are three inequivalent B+0.33+ sites. In the first B+0.33+ site, B+0.33+ is bonded in a bent 120 degrees geometry to one N3- and one H+0.82+ atom. The B–N bond length is 1.51 Å. The B–H bond length is 1.19 Å. In the second B+0.33+ site, B+0.33+ is bonded in a bent 120 degrees geometry to two N3- atoms. There is one shorter (1.46 Å) and one longer (1.49 Å) B–N bond length. In the third B+0.33+ site, B+0.33+ is bonded in a bent 120 degrees geometry to one N3- and one H+0.82+ atom. The B–N bond length is 1.65 Å. The B–H bond length is 1.19 Å. There are four inequivalent N3- sites. In the first N3- site, N3- is bonded in a 4-coordinate geometry to three B+0.33+ and one H+0.82+ atom. The N–H bond length is 1.02 Å. In the second N3- site, N3- is bonded in a single-bond geometry to one N3- atom. The N–N bond length is 1.15 Å. In the third N3- site, N3- is bonded in a linear geometry to two N3- atoms. The N–N bond length is 1.22 Å. In the fourth N3- site, N3- is bonded in a distorted bent 120 degrees geometry to one B+0.33+ and one N3- atom. There are three inequivalent H+0.82+ sites. In the first H+0.82+ site, H+0.82+ is bonded in a single-bond geometry to one B+0.33+ atom. In the second H+0.82+ site, H+0.82+ is bonded in a single-bond geometry to one B+0.33+ atom. In the third H+0.82+ site, H+0.82+ is bonded in a single-bond geometry to one N3- atom.

36 MATERIALS SCIENCE↗