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At least 37 records · Page 2

Precision measurement of Compton scattering in silicon with a skipper CCD for dark matter detection

Experiments aiming to directly detect dark matter through particle recoils can achieve energy thresholds of $\mathcal{O}(1\,\mathrm{eV})$. In this regime, ionization signals from small-angle Compton scatters of environmental $\gamma$-rays constitute a significant background. Monte Carlo simulations used to build background models have not been experimentally validated at these low energies. We report a precision measurement of Compton scattering on silicon atomic shell electrons down to 23$\,$eV. A skipper charge-coupled device (CCD) with single-electron resolution, developed for the DAMIC-M experiment, was exposed to a $^{241}$Am $\gamma$-ray source over several months. Features associated with the silicon K, L$_{1}$, and L$_{2,3}$-shells are clearly identified, and scattering on valence electrons is detected for the first time below 100$\,$eV. We find that the relativistic impulse approximation for Compton scattering, which is implemented in Monte Carlo simulations commonly used by direct detection experiments, does not reproduce the measured spectrum below 0.5$\,$keV. The data are in better agreement with $ab$$initio$ calculations originally developed for X-ray absorption spectroscopy.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

The Zintl phases A In 2 As 2 (A = Ca, Sr, Ba): new topological insulators and thermoelectric material candidates

Recently, there has been a lot of interest in topological insulators (TIs), being electronic materials, which are insulating in their bulk but with the gapless exotic metallic state on their surface. The surface states observed in such materials behave as a perfect conductor thereby making them more suited for several cutting-edge technological applications such as spintronic devices. Here, we report the synthesis and structural characterization of the Zintl phases AIn 2 As 2 (A = Ca, Sr, Ba), which could become a new class of TIs. Crystal structure elucidation by single-crystal X-ray diffraction reveals that CaIn 2 As 2 and SrIn 2 As 2 are isostructural and crystallize in the EuIn 2 P 2 structure type (space group P6 3 /mmc, no. 194, Z = 2) with unit cell parameters a = 4.1482(6) Å, c = 17.726(4) Å; and a = 4.2222(6) Å, c = 18.110(3) Å, respectively. Their hexagonal structure is made up of alternating [In 2 As 2 ] 2– layers separated by slabs of A 2+ cations. BaIn 2 As 2 on the other hand crystallizes in the monoclinic EuGa 2 P 2 structure type (space group P2/m, no. 10, Z = 4) with unit cell parameters a = 10.2746(11) Å, b = 4.3005(5) Å, c = 13.3317(14) Å and β = 95.569(2)°. This structure is also layered, and it is made up of different type of polyanionic [In 2 As 2 ] 2– units and Ba 2+ cations. The valence electron count for all three compounds adheres to the Zintl-Klemm formalism, and all elements achieve closed-shell electronic configurations. Bulk electronic structure calculations indicate the opening of a bandgap E g ~ 0.03 eV (CaIn 2 As 2 and Sr 2 In 2 As 2 ), and E g ~0.21 eV (BaIn 2 As 2 ) in the absence of strain and spin–orbit coupling (SOC). Furthermore, these results argue in favor of the realization of a nontrivial topological insulator state under the influence of tensile strain and SOC. Preliminary transport properties on BaIn 2 As 2 are suggestive of a degenerate p-type semiconductor—a behavior which is sought after in thermoelectric (TE) materials. Since both TIs and excellent TE materials are known to favor the same material properties such as narrow bandgap, heavy elements, and strong SOC, these three Zintl phases are also projected as candidates TE materials.

36 MATERIALS SCIENCE↗

Electronic Structure and Anion Photoelectron Spectroscopy of Uranium–Gold Clusters UAu n – , n = 3–7

A collaborative effort between experiment and theory towards elucidating the electronic and molecular structures of uranium-gold clusters is presented. Anion photoelectron spectra of UAu n – (n=3-7) were taken at third (355 nm) and fourth (266 nm) harmonics of a Nd:YAG laser, as well as excimer (ArF 193nm) photon energies, where the experimental adiabatic electron affinities (AEA) and vertical detachment energies (VDE) values were measured. Complementary first principles calculations were subsequently carried out to corroborate experimentally determined electron detachment energies and to determine the geometry and electronic structure for each cluster. Except for the ring-like neutral isomer of UAu 6 where one unpaired electron is spread over the Au atoms, all other neutral and anionic UAu n clusters (n = 3 - 7) were calculated to possess open-shell electrons with the unpaired electrons localized on the central U atom. The smaller clusters closely resemble the analogous UF n species, but significant deviations are seen starting with UAu 5 where a competition between U-Au and Au-Au bonding begins to become apparent. The UAu 6 system appears to mark a transition where Au-Au interactions begin to dominate, where both a ring-like and two heavily distorted octahedral structures around the central U atom are to be nearly isoenergetic. With UAu 7 , only ring-like structures are calculated. Altogether, the calculated electron detachment energies are in good agreement with the experimental values

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Nonideal mixing effects in warm dense matter studied with first-principles computer simulations

Here, we study nonideal mixing effects in the regime of warm dense matter (WDM) by computing the shock Hugoniot curves of BN, MgO, and MgSiO 3 . First, we derive these curves from the equations of state (EOS) of the fully interacting systems, which were obtained using a combination of path integral Monte Carlo calculations at high temperature and density functional molecular dynamics simulations at lower temperatures. We then use the ideal mixing approximation at constant pressure and temperature to rederive these Hugoniot curves from the EOS tables of the individual elements. We find that the linear mixing approximation works remarkably well at temperatures above ~2 × 10 5 K, where the shock compression ratio exceeds ~3.2. The shape of the Hugoniot curve of each compound is well reproduced. Regions of increased shock compression, which emerge because of the ionization of L and K shell electrons, are well represented, and the maximum compression ratio of the Hugoniot curves is reproduced with high precision. Some deviations are seen near the onset of the L shell ionization regime, where ionization equilibrium in the fully interacting system cannot be well reproduced by the ideal mixing approximation. This approximation also breaks down at lower temperatures, where chemical bonds play an increasingly important role. However, the results imply that the equilibrium properties of binary and ternary mixtures in the regime of WDM can be derived from the EOS tables of the individual elements. This significantly simplifies the characterization of binary and ternary mixtures in the WDM and plasma phases, which otherwise requires large numbers of more computationally expensive first-principles computer simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Measurement of coherent vibrational dynamics with X-ray Transient Absorption Spectroscopy simultaneously at the Carbon K- and Chlorine L 2,3 - edges

X-ray Transient Absorption Spectroscopy (XTAS) is a powerful probe for ultrafast molecular dynamics. The evolution of XTAS signal is controlled by the shapes of potential energy surfaces of the associated core-excited states, which are difficult to directly measure. Here, we study the vibrational dynamics of Raman activated CCl 4 with XTAS targeting the C 1s and Cl 2p electrons. The totally symmetric stretching mode leads to concerted elongation or contraction in bond lengths, which in turn induce an experimentally measurable red or blue shift in the X-ray absorption energies associated with inner-shell electron excitations to the valence antibonding levels. The ratios between slopes of different core-excited potential energy surfaces (CEPESs) thereby extracted agree very well with Restricted Open-Shell Kohn-Sham calculations. The other, asymmetric, modes do not measurably contribute to the XTAS signal. The results highlight the ability of XTAS to reveal coherent nuclear dynamics involving < 0.01 Å atomic displacements and also provide direct measurement of forces on CEPESs.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Path integral Monte Carlo and density functional molecular dynamics simulations of warm dense MgSiO 3

In order to provide a comprehensive theoretical description of MgSiO 3 at extreme conditions, we combine results from path integral Monte Carlo and density functional molecular dynamics simulations and generate a consistent equation of state for this material. We consider a wide range of temperature and density conditions from 10 4 to 10 8 K and from 0.321 to 64.2 g/cm -3 (0.1- to 20-fold the ambient density). We study how the L and K shell electrons are ionized with increasing temperature and pressure. We derive the shock Hugoniot curve and compare with experimental results. Our Hugoniot curve is in good agreement with the experiments, and we predict a broad compression maximum that is dominated by the K shell ionization of all three nuclei while the peak compression ratio of 4.70 is obtained when the Si and Mg nuclei are ionized. To conclude, we analyze the heat capacity and structural properties of the liquid.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Path Integral Monte Carlo Simulations of Iron Plasmas (Final Technical Report)

This documents is the final technical report for our grant entitled "Path Integral Monte Carlo Simulations of Iron Plasmas" that focused on developing path integral Monte Carlo (PIMC) computer simulations. This techniques will be developed to study plasmas composed of heavier elements including iron and other third row elements. Equations of state (EOS) and transport properties will be derived in the regime of warm dense matter (WDM) and dense plasmas where existing first-principles methods cannot be applied. While standard density functional theory (DFT) has been used to accurately predict the structure of many solids and liquids up to temperatures on the order of 100,000 K, this method is not applicable at much higher temperature because the number of partially occupied electronic orbitals reaches intractably large numbers or the use of finite-temperature free energy functionals in orbital-free DFT introduces an uncontrolled approximation. Here we focus on PIMC methods that become more and more efficient with increasing temperatures and still include all electronic correlation effects. In this approach, electronic excitations increase the efficiency rather than reduce it. While it had commonly been assumed this method could only be applied to elements without core electrons, we showed that PIMC with free-particle nodes works well for first-row elements (PRL 108 (2012) 115502). Most recently, we extended the applicability range of all-electron PIMC to second-row elements by adopting localized nodal surfaces (PRL 115 (2015) 176403). To simulate third-row elements efficiently under WDM conditions, we propose a new method to remove core electrons by introducing pseudo-nodes. We explain our approach step by step and present preliminary results. We focus our method development on getting PIMC simulations of iron to work because of its fundamental importance for WDM and astrophysics. Then we move on to krypton and copper-doped beryllium, a ICF ablator material. We plan to continue working on key second-row material such as Na, Mg, MgO, Al, silica, and silicon-doped plastic ablators. Our collaborators at LLNL, will use our PIMC EOS data both as comparisons to existing semi-empirical, EOS-generating schemes, and as input for continuum radiation hydrodynamics simulations. We will establish an efficient pipeline from PIMC to macroscopic continuum studies of materials response. An emphasis will be placed on benchmarking such methods for plasmas of heavy elements at the very high temperatures (~100 eV) and low densities that are generated when Hohlraum radiation heats the ablator material in indirect drive laser experiments. Results from changes to the EOS will be of immeasurable importance to the designers at the National Ignition Facility (NIF) and at other facilities. Starting with our EOS of Cu-doped Be, our second collaborator at LLE, will perform real-time simulations of laser fusion experiments at the Omega laser and at the NIF to determine how sensitive the compression path depends on the ablator EOS. Since our collaborator also has experience in performing orbital-free DFT calculations, we propose to compare predictions from this method with PIMC results. In joint publications, we plan to analyze the accuracy of different free-energy functionals in order to understand why existing orbital-free DFT calculations do not predict compression peaks along the shock Hugoniot curve that we see with PIMC. The peaks are caused by the ionization of various electron shells. Their accurate characterization is important to compare with experimental results. We will break new ground by developing PIMC techniques that can simulate iron and all other third row elements in the plasma and WDM regimes. We introduce the concept of pseudo-nodes for the efficient treatment of the core-electrons. The EOS and transport properties will be derived and published online in the form of a new WDM database. Our PIMC EOS calculations will benchmark and possibly replace semi-analytical EOS tables like QEOS or SESAME, which will impact the hydrocode simulation community and will affect the design of NIF targets. Our PIMC results will help to improve the accuracy of orbital-free DFT simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Indications of flat bands driving the δ to α volume collapse of plutonium

On cooling from the melt, plutonium (Pu) undergoes a series of structural transformations accompanied by a ≈ 28% reduction in volume from its δ phase to its α phase at low temperatures. While Pu’s partially filled 5 f -electron shells are known to be involved, their precise role in the transformations has remained unclear. By using calorimetry measurements on α -Pu and gallium-stabilized δ -Pu combined with resonant ultrasound and X-ray scattering data to account for the anomalously large softening of the lattice with temperature, we show here that the difference in electronic entropy between the α and δ phases dominates over the difference in phonon entropy. Rather than finding an electronic specific heat characteristic of broad f -electron bands in α -Pu, as might be expected to occur within a Kondo collapsed phase in analogy with cerium, we find it to be indicative of flatter subbands. An important role played by Pu’s 5 f electrons in the formation of its larger unit cell α phase comprising inequivalent lattice sites and varying bond lengths is therefore suggested.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Indications of flat bands driving the δ to α volume collapse of plutonium

On cooling from the melt, plutonium (Pu) undergoes a series of structural transformations accompanied by a ≈ 28% reduction in volume from its δ phase to its α phase at low temperatures. While Pu’s partially filled 5f -electron shells are known to be involved, their precise role in the transformations has remained unclear. By using calorimetry measurements on α-Pu and gallium-stabilized δ-Pu combined with resonant ultrasound and X-ray scattering data to account for the anomalously large softening of the lattice with temperature, we show here that the difference in electronic entropy between the α and δ phases dominates over the difference in phonon entropy. Rather than finding an electronic specific heat characteristic of broad $f$-electron bands in α-Pu, as might be expected to occur within a Kondo collapsed phase in analogy with cerium, we find it to be indicative of flatter subbands. An important role played by Pu’s 5$f$ electrons in the formation of its larger unit cell α phase comprising inequivalent lattice sites and varying bond lengths is therefore suggested.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Electron-ion coincidence measurements of molecular dynamics with intense X-ray pulses

Molecules can sequentially absorb multiple photons when irradiated by an intense X-ray pulse from a free-electron laser. If the time delay between two photoabsorption events can be determined, this enables pump-probe experiments with a single X-ray pulse, where the absorption of the first photon induces electronic and nuclear dynamics that are probed by the absorption of the second photon. Here we show a realization of such a single-pulse X-ray pump-probe scheme on N 2 molecules, using the X-ray induced dissociation process as an internal clock that is read out via coincident detection of photoelectrons and fragment ions. By coincidence analysis of the kinetic energies of the ionic fragments and photoelectrons, the transition from a bound molecular dication to two isolated atomic ions is observed through the energy shift of the inner-shell electrons. Via ab-initio simulations, we are able to map characteristic features in the kinetic energy release and photoelectron spectrum to specific delay times between photoabsorptions. In contrast to previous studies where nuclear motions were typically revealed by measuring ion kinetics, our work shows that inner-shell photoelectron energies can also be sensitive probes of nuclear dynamics, which adds one more dimension to the study of light-matter interactions with X-ray pulses.

74 ATOMIC AND MOLECULAR PHYSICS↗

Spectroscopic and theoretical studies of UN and UN +

The low-energy electronic states of UN and UN+ have been examined using high-level electronic structure calculations and two-color photoionization techniques. The experimental measurements provided an accurate ionization energy for UN (IE = 50 802 +/- 5 cm -1 ). Spectra for UN+ yielded ro-vibrational constants and established that the ground state has the electronic angular momentum projection omega = 4. Ab initio calculations were carried out using the spin-orbit state interacting approach with the complete active space second-order perturbation theory method. A series of correlation consistent basis sets were used in conjunction with small-core relativistic pseudopotentials on U to extrapolate to the complete basis set limits. The results for UN correctly obtained an omega = 3.5 ground state and demonstrated a high density of configurationally related excited states with closely similar ro-vibrational constants. Similar results were obtained for UN + , with reduced complexity owing to the smaller number of outer-shell electrons. The calculated IE for UN was in excellent agreement with the measured value. Improved values for the dissociation energies of UN and UN + , as well as their heats of formation, were obtained using the Feller-Peterson-Dixon composite thermochemistry method, including corrections up through coupled cluster singles, doubles, triples and quadruples. An analysis of the ab initio results from the perspective of the ligand field theory shows that the patterns of electronic states for both UN and UN + can be understood in terms of the underlying energy level structure of the atomic metal ion.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Magnetization reversal driven by electron localization-delocalization crossover in the inverse spinel Co 2 VO 4

Neutron diffraction, magnetization, and muon spin relaxation measurements, supplemented by density functional theory (DFT) calculations are employed to unravel temperature-driven magnetization reversal in inverse spinel Co 2 VO 4 . All measurements show a second-order magnetic phase transition at T C = 168 K to a collinear ferrimagnetic phase. Neutron diffraction measurements reveal two antiparallel ferromagnetic (FM) sublattices, belonging to magnetic ions on two distinct crystal lattice sites, where the relative balance between the two sublattices determine the net FM moment in the unit cell. As the evolution of the ordered moment with temperature differs between the two sublattices, the net magnetic moment reaches a maximum at T NC = 138 K and reverses its sign at T MR = 65 K. The DFT results suggest that the underlying microscopic mechanism for the reversal is a delocalization of the unfilled 3d -shell electrons on one sublattice just below T C , followed by a gradual localization as the temperature is lowered. Furthermore, this delocalized-localized crossover is supported by muon spectroscopy results, as strong T 1 relaxation observed below T C indicates fluctuating internal fields.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Site-specific interrogation of an ionic chiral fragment during photolysis using an X-ray free-electron laser

Abstract Short-wavelength free-electron lasers with their ultrashort pulses at high intensities have originated new approaches for tracking molecular dynamics from the vista of specific sites. X-ray pump X-ray probe schemes even allow to address individual atomic constituents with a ‘trigger’-event that preludes the subsequent molecular dynamics while being able to selectively probe the evolving structure with a time-delayed second X-ray pulse. Here, we use a linearly polarized X-ray photon to trigger the photolysis of a prototypical chiral molecule, namely trifluoromethyloxirane (C 3 H 3 F 3 O), at the fluorine K-edge at around 700 eV. The created fluorine-containing fragments are then probed by a second, circularly polarized X-ray pulse of higher photon energy in order to investigate the chemically shifted inner-shell electrons of the ionic mother-fragment for their stereochemical sensitivity. We experimentally demonstrate and theoretically support how two-color X-ray pump X-ray probe experiments with polarization control enable XFELs as tools for chiral recognition.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Synthesis and Transport Properties of the Family of Zintl Phases Ca 3 RESb 3 (RE = La–Nd, Sm, Gd–Tm, Lu): Exploring the Roles of Crystallographic Disorder and Core 4f Electrons for Enhancing Thermoelectric Performance

Zintl phases with complex crystal structures have been studied as promising candidate-materials for thermoelectric (TE) applications. Here, we report the syntheses of the family of rare-earth metal Zintl phases with the general formula Ca 4–x RE x Sb 3 (x ≈ 1; RE = La–Nd, Sm, Gd–Tm, Lu). The structural elucidation is based on refinements of single-crystal X-ray diffraction data for 12 unique chemical compositions. The cubic structure is confirmed as belonging to the anti-Th 3 P 4 structure type (space group I4¯3d, no. 220, Z = 4), where the Ca and RE atoms share the same atomic site with ca. 75% and 25% occupancies, respectively. Such crystallographic disordering of divalent Ca and trivalent RE atoms in the structure provides a pathway to intricate bonding. The latter, together with the presence of heavy elements such as Sb and the lanthanides, are expected to enhance the scattering probability of phonons, thereby leading to as low thermal conductivity κ as that of the ordered RE 4 Sb 3 . The drive of the hypothetical parent compound Ca 4 Sb 3 to be stabilized by alloying with rare-earth metals can be understood following the Zintl-Klemm concept, as the resultant formula may be rationalized as (Ca 2+ ) 3 RE 3+ (Sb 3– ) 3 , indicating the realization of closed-shell electronic configurations for all elements. This notion is confirmed by electronic structure calculations, which reveal narrow bandgaps E g = 0.77 and 0.53 eV for Ca 3 LaSb 3 and Ca 3 LuSb 3 , respectively. Additionally, the incorporation of RE atoms into the structure drives the phase into a state of a degenerate semiconductor with dominant hole charge carriers.

36 MATERIALS SCIENCE↗

Synthesis, Structure, and Electric Conductivity of Higher Hydrides of Ytterbium at High Pressure

While most of the rare-earth metals readily form trihydrides, due to increased stability of the filled 4f electronic shell for Yb(II), only YbH 2.67 , formally corresponding to Yb II (Yb III H 4 ) 2 (or Yb 3 H 8 ), remains the highest hydride of ytterbium. Utilizing the diamond anvil cell methodology and synchrotron powder X-ray diffraction, we have attempted to push this limit further via hydrogenation of metallic Yb and Yb 3 H 8 . Compression of the latter has also been investigated in a neutral pressure-transmitting medium (PTM). While the in situ heating of Yb facilitates the formation of YbH 2+x hydrides, we have not observed clear qualitative differences between the systems compressed in H 2 and He or Ne PTM. In all of these cases, a sequence of phase transitions occurred within ca. 13–18 GPa (P$\bar{31}$m–I4/m phase) and around 27 GPa (to the I4/mmm phase). The molecular volume of the systems compressed in H 2 PTM is ca. 1.5% larger than of those compressed in inert gases, suggesting a small hydrogen uptake. Nevertheless, hydrogenation toward YbH 3 is incomplete, and polyhydrides do not form up to the highest pressure studied here (ca. 75 GPa). As pointed out by electronic transport measurements, the mixed-valence Yb 3 H 8 retains its semiconducting character up to >50 GPa, although the very low remnant activation energy of conduction (<5 meV) suggests that metallization under further compression should be achievable. Finally, we provide a theoretical description of a hypothetical stoichiometric YbH 3 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

High‐Spin and Reactive Fe 13 Cluster with Exposed Metal Sites

Abstract Atomically defined large metal clusters have applications in new reaction development and preparation of materials with tailored properties. Expanding the synthetic toolbox for reactive high nuclearity metal complexes, we report a new class of Fe clusters, Tp* 4 W 4 Fe 13 S 12 , displaying a Fe 13 core with M−M bonds that has precedent only in main group and late metal chemistry. M 13 clusters with closed shell electron configurations can show significant stability and have been classified as superatoms. In contrast, Tp* 4 W 4 Fe 13 S 12 displays a large spin ground state of S =13. This compound performs small molecule activations involving the transfer of up to 12 electrons resulting in significant cluster rearrangements.

Scott, Anna G.↗

High-Spin and Reactive Fe 13 Cluster with Exposed Metal Sites

We report atomically defined large metal clusters have applications in new reaction development and preparation of materials with tailored properties. Expanding the synthetic toolbox for reactive high nuclearity metal complexes, we report a new class of Fe clusters, Tp* 4 W 4 Fe 13 S 12 , displaying a Fe 13 core with M-M bonds that has precedent only in main group and late metal chemistry. M 13 clusters with closed shell electron configurations can show significant stability and have been classified as superatoms. In contrast, Tp* 4 W 4 Fe 13 S 12 displays a large spin ground state of S=13. This compound performs small molecule activations involving the transfer of up to 12 electrons resulting in significant cluster rearrangements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Understanding Superatomic Ag Nanohydrides

Abstract Bulk Ag hydrides are extremely challenging to make even at very high pressures, but they may become stable as the particle size shrinks to the nanometer regime. Here, the formation and electronic structure of Ag nanohydrides are investigated from a superatomic perspective by density functional theory. It is found that as the coverage increases, adsorption energy of hydrogen atoms on Ag 38 cluster to form Ag 38 H 2 n nanohydride ( n is from 1 to 15) can be energetically favorable with respect to bare Ag 38 and H 2 . Furthermore, the adsorbed hydrogen atoms contribute their 1s electrons to the superatom electron count and behave as a metal instead of a ligand. The electronic structure of the silver nanohydrides follows the superatomic complex model, leading to magic or relatively more stable compositions such as Ag 38 H 2 , Ag 38 H 20 , and Ag 38 H 30 , which correspond to 40‐electron, 58‐electron, and 68‐electron shell closings, respectively. Angular momentum analyses of the superatomic orbitals suggest a convoluted interaction of geometry, symmetry, and orbital splitting.

He, Xiang↗