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Energy-Screened Many-Body Expansion for Protein–Ligand Interactions: Examining Convergence for Metalloenzymes Through Seven–Body Interactions

Fragment-based quantum chemistry is a powerful strategy for calculating protein−ligand interaction energies using quantum chemistry methods. Rigorous convergence often requires hundreds of atoms in the protein binding-site model, especially if that model is constructed using distance-based criteria to select amino acid residues, while three- and four-body calculations exhibit instability related to combinatorial proliferation in the number of subsystem calculations. Here, we report an energy-based screening protocol for the many-body expansion applied to protein−ligand interactions, implemented in the open-source FRAGME∩T code. Using a combination of aggressive screening based on semiempirical quantum chemistry, with an improved graph-theoretical algorithm to eliminate unimportant subsystems, we are able to perform n-body calculations up to n = 7 using density functional theory in triple-ζ basis sets. Distance cutoffs further reduce the cost without compromising accuracy. Rapid and stable convergence of the many-body expansion is obtained by n = 4, for a pair of metalloenzymes in which a divalent ion coordinates directly to the ligand. As compared to previous results that relied solely on distance cutoffs, oscillations in the n-body corrections are reduced or eliminated, although residual errors remain in one case. This work demonstrates that benchmark-quality protein−ligand interaction energies can be systematically converged using a method with excellent parallel efficiency and scalability.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Materials Data on Fe11Co5 by Materials Project

Fe11Co5 is Tungsten-derived structured and crystallizes in the tetragonal P4/mmm space group. The structure is three-dimensional. there are four inequivalent Fe sites. In the first Fe site, Fe is bonded in a distorted body-centered cubic geometry to three Fe and five Co atoms. All Fe–Fe bond lengths are 2.47 Å. All Fe–Co bond lengths are 2.47 Å. In the second Fe site, Fe is bonded in a distorted body-centered cubic geometry to eight equivalent Fe atoms. In the third Fe site, Fe is bonded in a distorted body-centered cubic geometry to eight equivalent Fe atoms. In the fourth Fe site, Fe is bonded in a distorted body-centered cubic geometry to eight equivalent Fe and six Co atoms. There are two shorter (2.85 Å) and four longer (2.86 Å) Fe–Co bond lengths. There are three inequivalent Co sites. In the first Co site, Co is bonded in a distorted body-centered cubic geometry to eight equivalent Fe atoms. In the second Co site, Co is bonded in a distorted body-centered cubic geometry to ten Fe atoms. In the third Co site, Co is bonded in a distorted body-centered cubic geometry to ten Fe atoms.

36 MATERIALS SCIENCE↗

Materials Data on Mn2CrNiSb2 by Materials Project

CrMn2NiSb2 is half-Heusler-derived structured and crystallizes in the trigonal R3m space group. The structure is three-dimensional. Cr is bonded to six Mn and four Sb atoms to form distorted CrMn6Sb4 tetrahedra that share corners with four equivalent MnCr3Ni3Sb4 tetrahedra, edges with six MnCr3Ni3Sb4 tetrahedra, and faces with six equivalent CrMn6Sb4 tetrahedra. There are three shorter (3.00 Å) and three longer (3.02 Å) Cr–Mn bond lengths. All Cr–Sb bond lengths are 2.64 Å. There are two inequivalent Mn sites. In the first Mn site, Mn is bonded to three equivalent Cr, three equivalent Ni, and four Sb atoms to form distorted MnCr3Ni3Sb4 tetrahedra that share corners with six equivalent MnCr3Ni3Sb4 tetrahedra, edges with three equivalent CrMn6Sb4 tetrahedra, and faces with twelve MnCr3Ni3Sb4 tetrahedra. All Mn–Ni bond lengths are 3.02 Å. There are three shorter (2.63 Å) and one longer (2.66 Å) Mn–Sb bond lengths. In the second Mn site, Mn is bonded to three equivalent Cr, three equivalent Ni, and four Sb atoms to form distorted MnCr3Ni3Sb4 tetrahedra that share corners with four equivalent CrMn6Sb4 tetrahedra, corners with six equivalent MnCr3Ni3Sb4 tetrahedra, edges with three equivalent CrMn6Sb4 tetrahedra, and faces with twelve MnCr3Ni3Sb4 tetrahedra. All Mn–Ni bond lengths are 3.05 Å. There are three shorter (2.59 Å) and one longer (2.61 Å) Mn–Sb bond lengths. Ni is bonded in a 10-coordinate geometry to six Mn and four Sb atoms. There are three shorter (2.59 Å) and one longer (2.60 Å) Ni–Sb bond lengths. There are two inequivalent Sb sites. In the first Sb site, Sb is bonded in a body-centered cubic geometry to three equivalent Cr, four Mn, and one Ni atom. In the second Sb site, Sb is bonded in a body-centered cubic geometry to one Cr, four Mn, and three equivalent Ni atoms.

36 MATERIALS SCIENCE↗

Materials Data on Fe2Si by Materials Project

Fe2Si crystallizes in the trigonal P-3m1 space group. The structure is three-dimensional. there are three inequivalent Fe2+ sites. In the first Fe2+ site, Fe2+ is bonded in a body-centered cubic geometry to three equivalent Fe2+ and five equivalent Si4- atoms. All Fe–Fe bond lengths are 2.43 Å. There are a spread of Fe–Si bond distances ranging from 2.37–2.43 Å. In the second Fe2+ site, Fe2+ is bonded in a 8-coordinate geometry to eight Fe2+ and six equivalent Si4- atoms. Both Fe–Fe bond lengths are 2.42 Å. All Fe–Si bond lengths are 2.74 Å. In the third Fe2+ site, Fe2+ is bonded in a body-centered cubic geometry to two equivalent Fe2+ and six equivalent Si4- atoms. All Fe–Si bond lengths are 2.43 Å. Si4- is bonded in a distorted body-centered cubic geometry to eleven Fe2+ atoms.

36 MATERIALS SCIENCE↗

Search for new phenomena in multi-body invariant masses in events with at least one isolated lepton and two jets using $\sqrt{s}$ = 13 TeV proton–proton collision data collected by the ATLAS detector

A search for resonances in events with at least one isolated lepton (e or μ ) and two jets is performed using 139 fb -1 of $\sqrt{s}$ = 13 TeV proton–proton collision data recorded by the ATLAS detector at the LHC. Deviations from a smoothly falling background hypothesis are tested in three- and four-body invariant mass distributions constructed from leptons and jets, including jets identified as originating from bottom quarks. Model-independent limits on generic resonances characterised by cascade decays of particles leading to multiple jets and leptons in the final state are presented. The limits are calculated using Gaussian shapes with different widths for the invariant masses. The multi-body invariant masses are also used to set 95% confidence level upper limits on the cross-section times branching ratios for the production and subsequent decay of resonances predicted by several new physics scenarios.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Materials Data on Mg4Si7 by Materials Project

Mg4Si7 crystallizes in the triclinic P1 space group. The structure is three-dimensional. there are eight inequivalent Mg sites. In the first Mg site, Mg is bonded in a 11-coordinate geometry to eleven Si atoms. There are a spread of Mg–Si bond distances ranging from 2.84–3.20 Å. In the second Mg site, Mg is bonded in a rectangular see-saw-like geometry to four Si atoms. There are a spread of Mg–Si bond distances ranging from 2.69–2.80 Å. In the third Mg site, Mg is bonded in a 6-coordinate geometry to six Si atoms. There are a spread of Mg–Si bond distances ranging from 2.65–3.03 Å. In the fourth Mg site, Mg is bonded in a 7-coordinate geometry to seven Si atoms. There are a spread of Mg–Si bond distances ranging from 2.80–3.11 Å. In the fifth Mg site, Mg is bonded in a 8-coordinate geometry to nine Si atoms. There are a spread of Mg–Si bond distances ranging from 2.79–3.20 Å. In the sixth Mg site, Mg is bonded in a 10-coordinate geometry to ten Si atoms. There are a spread of Mg–Si bond distances ranging from 2.69–3.04 Å. In the seventh Mg site, Mg is bonded in a 8-coordinate geometry to eight Si atoms. There are a spread of Mg–Si bond distances ranging from 2.85–3.10 Å. In the eighth Mg site, Mg is bonded in a 7-coordinate geometry to nine Si atoms. There are a spread of Mg–Si bond distances ranging from 2.86–3.14 Å. There are fourteen inequivalent Si sites. In the first Si site, Si is bonded in a 7-coordinate geometry to five Mg and three Si atoms. There are a spread of Si–Si bond distances ranging from 2.43–2.52 Å. In the second Si site, Si is bonded in a 7-coordinate geometry to three Mg and four Si atoms. There are a spread of Si–Si bond distances ranging from 2.42–2.55 Å. In the third Si site, Si is bonded in a 6-coordinate geometry to three Mg and three Si atoms. In the fourth Si site, Si is bonded in a distorted body-centered cubic geometry to three Mg and five Si atoms. There are two shorter (2.51 Å) and one longer (2.58 Å) Si–Si bond lengths. In the fifth Si site, Si is bonded in a 9-coordinate geometry to seven Mg and two Si atoms. There are one shorter (2.39 Å) and one longer (2.41 Å) Si–Si bond lengths. In the sixth Si site, Si is bonded in a 9-coordinate geometry to seven Mg and two Si atoms. The Si–Si bond length is 2.46 Å. In the seventh Si site, Si is bonded in a 6-coordinate geometry to two Mg and four Si atoms. There are one shorter (2.44 Å) and one longer (2.69 Å) Si–Si bond lengths. In the eighth Si site, Si is bonded in a 8-coordinate geometry to four Mg and four Si atoms. There are a spread of Si–Si bond distances ranging from 2.46–2.49 Å. In the ninth Si site, Si is bonded in a 9-coordinate geometry to six Mg and three Si atoms. There are a spread of Si–Si bond distances ranging from 2.45–2.52 Å. In the tenth Si site, Si is bonded in a 8-coordinate geometry to four Mg and four Si atoms. There are a spread of Si–Si bond distances ranging from 2.44–2.49 Å. In the eleventh Si site, Si is bonded in a 9-coordinate geometry to seven Mg and two Si atoms. In the twelfth Si site, Si is bonded in a 10-coordinate geometry to six Mg and four Si atoms. In the thirteenth Si site, Si is bonded in a 9-coordinate geometry to five Mg and four Si atoms. In the fourteenth Si site, Si is bonded in a 2-coordinate geometry to two Mg and four Si atoms.

36 MATERIALS SCIENCE↗

Materials Data on GaFe2Co4Si by Materials Project

Fe2Co4GaSi is Tungsten-derived structured and crystallizes in the trigonal R-3m space group. The structure is three-dimensional. Fe is bonded in a distorted body-centered cubic geometry to eight Co atoms. There are a spread of Fe–Co bond distances ranging from 2.41–2.51 Å. There are four inequivalent Co sites. In the first Co site, Co is bonded in a distorted body-centered cubic geometry to four equivalent Fe, one Ga, and three equivalent Si atoms. There are one shorter (2.41 Å) and three longer (2.49 Å) Co–Fe bond lengths. The Co–Ga bond length is 2.53 Å. All Co–Si bond lengths are 2.44 Å. In the second Co site, Co is bonded in a body-centered cubic geometry to four equivalent Fe, three equivalent Ga, and one Si atom. All Co–Ga bond lengths are 2.48 Å. The Co–Si bond length is 2.38 Å. In the third Co site, Co is bonded in a distorted body-centered cubic geometry to four equivalent Fe, one Ga, and three equivalent Si atoms. The Co–Ga bond length is 2.53 Å. All Co–Si bond lengths are 2.44 Å. In the fourth Co site, Co is bonded in a distorted body-centered cubic geometry to four equivalent Fe, one Ga, and three equivalent Si atoms. The Co–Ga bond length is 2.53 Å. All Co–Si bond lengths are 2.44 Å. Ga is bonded in a distorted body-centered cubic geometry to eight Co atoms. Si is bonded in a distorted body-centered cubic geometry to eight Co atoms.

36 MATERIALS SCIENCE↗

Body Mass Variation in an Introduced Wild Pig Population with Changing Ancestry

Total body mass variation was studied in a single wild pig (Sus scrofa) population that originated from three introductions of varying ancestry. Body mass data from 12,257 wild pigs collected over more than five decades were analyzed for differences due to the effects of sex, age class, reproductive status, season, and historic subpopulation groupings. Total body mass data from this population averaged 38 kg and ranged from 0.511 to 189 kg. The overall observed range of body mass data was consistent with previous studies. Very heavy individuals (i.e., >150 kg) made up only a small percentage of the overall population. Males were significantly larger than females, being on average 1.09 times heavier. This significant sexual dimorphic difference was seen in all but the piglet age class. This percent dimorphic difference increased with age. Body mass variation and overlap between the age classes also increased with age. Males were more variable than females within the same age class. The study area’s wild pigs were on average born at slightly less than one percent of their adult body mass. Percent weight gain toward the adult body mass increased with age and was slightly greater in females than in males. In contrast, absolute weight gain between age classes was greater in males. Pregnant sows were significantly heavier than non-pregnant females in all age class comparisons; however, this difference decreased with age. There was a seasonal shift in body mass with age, with younger age classes being heaviest in the fall-winter period and the older age classes being heaviest in spring-summer. Having originated from different ancestral stocks, two major subpopulations of wild pigs on the study area differed significantly in body mass in all sex and age class comparisons. The SRS wild pig population showed a decrease in body mass during the 1990s that was significant. This change may have been the result of both ancestral and population density variation, as well as unspecified environmental factors

59 BASIC BIOLOGICAL SCIENCES↗

Materials Data on Al2CrFeCo4 by Materials Project

CrFeCo4Al2 is Tungsten-derived structured and crystallizes in the trigonal R-3m space group. The structure is three-dimensional. Cr is bonded in a body-centered cubic geometry to eight Co atoms. All Cr–Co bond lengths are 2.47 Å. Fe is bonded in a distorted body-centered cubic geometry to eight Co and six equivalent Al atoms. There are two shorter (2.46 Å) and six longer (2.47 Å) Fe–Co bond lengths. All Fe–Al bond lengths are 2.85 Å. There are three inequivalent Co sites. In the first Co site, Co is bonded in a body-centered cubic geometry to three equivalent Cr, one Fe, and four equivalent Al atoms. All Co–Al bond lengths are 2.46 Å. In the second Co site, Co is bonded in a body-centered cubic geometry to one Cr, three equivalent Fe, and four equivalent Al atoms. All Co–Al bond lengths are 2.47 Å. In the third Co site, Co is bonded in a body-centered cubic geometry to three equivalent Cr, one Fe, and four equivalent Al atoms. All Co–Cr bond lengths are 2.47 Å. The Co–Fe bond length is 2.46 Å. All Co–Al bond lengths are 2.46 Å. Al is bonded in a body-centered cubic geometry to three equivalent Fe and eight Co atoms.

36 MATERIALS SCIENCE↗

Materials Data on Mn4Cr(Co2Ge)5 by Materials Project

CrMn4(Co2Ge)5 is Tungsten-derived structured and crystallizes in the trigonal R-3m space group. The structure is three-dimensional. Cr is bonded in a distorted body-centered cubic geometry to eight Co and six equivalent Ge atoms. There are two shorter (2.47 Å) and six longer (2.48 Å) Cr–Co bond lengths. All Cr–Ge bond lengths are 2.86 Å. There are two inequivalent Mn sites. In the first Mn site, Mn is bonded in a distorted body-centered cubic geometry to eight Co and six Ge atoms. There are a spread of Mn–Co bond distances ranging from 2.46–2.49 Å. There are three shorter (2.86 Å) and three longer (2.88 Å) Mn–Ge bond lengths. In the second Mn site, Mn is bonded in a distorted body-centered cubic geometry to eight Co and six Ge atoms. There are two shorter (2.47 Å) and six longer (2.49 Å) Mn–Co bond lengths. All Mn–Ge bond lengths are 2.86 Å. There are nine inequivalent Co sites. In the first Co site, Co is bonded in a body-centered cubic geometry to three equivalent Cr, one Mn, and four equivalent Ge atoms. All Co–Cr bond lengths are 2.48 Å. The Co–Mn bond length is 2.49 Å. There are one shorter (2.44 Å) and three longer (2.49 Å) Co–Ge bond lengths. In the second Co site, Co is bonded in a body-centered cubic geometry to one Cr, three equivalent Mn, and four Ge atoms. There are one shorter (2.46 Å) and three longer (2.49 Å) Co–Ge bond lengths. In the third Co site, Co is bonded in a body-centered cubic geometry to four equivalent Mn and four Ge atoms. There are one shorter (2.46 Å) and three longer (2.49 Å) Co–Ge bond lengths. In the fourth Co site, Co is bonded in a body-centered cubic geometry to four Mn and four Ge atoms. There are one shorter (2.46 Å) and three longer (2.49 Å) Co–Ge bond lengths. In the fifth Co site, Co is bonded in a body-centered cubic geometry to three equivalent Cr, one Mn, and four equivalent Ge atoms. There are one shorter (2.44 Å) and three longer (2.49 Å) Co–Ge bond lengths. In the sixth Co site, Co is bonded in a body-centered cubic geometry to four Mn and four Ge atoms. There are one shorter (2.48 Å) and three longer (2.49 Å) Co–Ge bond lengths. In the seventh Co site, Co is bonded in a body-centered cubic geometry to three equivalent Cr, one Mn, and four equivalent Ge atoms. The Co–Mn bond length is 2.49 Å. There are one shorter (2.44 Å) and three longer (2.49 Å) Co–Ge bond lengths. In the eighth Co site, Co is bonded in a body-centered cubic geometry to four equivalent Mn and four Ge atoms. There are one shorter (2.46 Å) and three longer (2.49 Å) Co–Ge bond lengths. In the ninth Co site, Co is bonded in a body-centered cubic geometry to four equivalent Mn and four Ge atoms. There are one shorter (2.47 Å) and three longer (2.49 Å) Co–Mn bond lengths. There are one shorter (2.46 Å) and three longer (2.49 Å) Co–Ge bond lengths. There are three inequivalent Ge sites. In the first Ge site, Ge is bonded in a distorted body-centered cubic geometry to three equivalent Cr, three equivalent Mn, and eight Co atoms. In the second Ge site, Ge is bonded in a distorted body-centered cubic geometry to six equivalent Mn and eight Co atoms. In the third Ge site, Ge is bonded in a distorted body-centered cubic geometry to six Mn and eight Co atoms.

36 MATERIALS SCIENCE↗

Materials Data on Mn4Cr(Co2Sn)5 by Materials Project

CrMn4(Co2Sn)5 is Tungsten-derived structured and crystallizes in the trigonal R-3m space group. The structure is three-dimensional. Cr is bonded in a distorted body-centered cubic geometry to eight Co and six equivalent Sn atoms. There are six shorter (2.59 Å) and two longer (2.60 Å) Cr–Co bond lengths. All Cr–Sn bond lengths are 2.99 Å. There are two inequivalent Mn sites. In the first Mn site, Mn is bonded in a distorted body-centered cubic geometry to eight Co and six Sn atoms. There are seven shorter (2.59 Å) and one longer (2.60 Å) Mn–Co bond lengths. There are three shorter (2.99 Å) and three longer (3.00 Å) Mn–Sn bond lengths. In the second Mn site, Mn is bonded in a distorted body-centered cubic geometry to eight Co and six Sn atoms. There are seven shorter (2.59 Å) and one longer (2.60 Å) Mn–Co bond lengths. All Mn–Sn bond lengths are 2.99 Å. There are seven inequivalent Co sites. In the first Co site, Co is bonded in a body-centered cubic geometry to three equivalent Cr, one Mn, and four equivalent Sn atoms. The Co–Mn bond length is 2.60 Å. All Co–Sn bond lengths are 2.59 Å. In the second Co site, Co is bonded in a body-centered cubic geometry to one Cr, three equivalent Mn, and four Sn atoms. There are three shorter (2.59 Å) and one longer (2.60 Å) Co–Sn bond lengths. In the third Co site, Co is bonded in a body-centered cubic geometry to four equivalent Mn and four Sn atoms. All Co–Sn bond lengths are 2.59 Å. In the fourth Co site, Co is bonded in a body-centered cubic geometry to four Mn and four Sn atoms. All Co–Sn bond lengths are 2.59 Å. In the fifth Co site, Co is bonded in a body-centered cubic geometry to three equivalent Cr, one Mn, and four equivalent Sn atoms. All Co–Sn bond lengths are 2.59 Å. In the sixth Co site, Co is bonded in a body-centered cubic geometry to four Mn and four Sn atoms. There are three shorter (2.59 Å) and one longer (2.60 Å) Co–Sn bond lengths. In the seventh Co site, Co is bonded in a body-centered cubic geometry to three equivalent Cr, one Mn, and four equivalent Sn atoms. All Co–Cr bond lengths are 2.59 Å. The Co–Mn bond length is 2.60 Å. All Co–Sn bond lengths are 2.59 Å. There are three inequivalent Sn sites. In the first Sn site, Sn is bonded in a distorted body-centered cubic geometry to three equivalent Cr, three equivalent Mn, and eight Co atoms. In the second Sn site, Sn is bonded in a distorted body-centered cubic geometry to six equivalent Mn and eight Co atoms. In the third Sn site, Sn is bonded in a distorted body-centered cubic geometry to six Mn and eight Co atoms.

36 MATERIALS SCIENCE↗

Single-nucleon knockout cross sections for reactions producing resonance states at or beyond the drip line

Single-nucleon knockout cross sections from fast secondary beams of the proton-drip-line nuclei 9 C, 13 O, and 17 Ne on a 9 Be target have been studied with emphasis on the production of resonance states. These states were identified by their invariant mass, and resonances with two-, three-, and five-body exit channels were examined. The measured cross sections for these states were compared with eikonal-model predictions using shell-model or variational Monte Carlo spectroscopic factors. The experimental yields were found to be suppressed relative to the model predictions, especially when a well-bound neutron or proton is removed. This suppression exceeds that found systematically in measured inclusive cross sections to particle-bound final states. In neutron knockout from 9 C and 13 O projectiles, this suppression of the unbound ground-state residuals yield is a factor of two to three times larger than that found in the bound final-state studies. Modifications to the structure of these systems due to coupling of the shell-model configurations to the continuum is expected to contribute to this extra suppression, especially when the final state is a near-threshold resonance. Furthermore, other considerations including the role of nuclear dynamics may be required to explain all the observed trends.

6 ≤ A ≤ 19↗

Materials Data on NaLi5Sn4 by Materials Project

NaLi5Sn4 crystallizes in the trigonal R3m space group. The structure is three-dimensional. Na is bonded in a 10-coordinate geometry to seven Li and three equivalent Sn atoms. There are a spread of Na–Li bond distances ranging from 2.90–3.19 Å. All Na–Sn bond lengths are 3.22 Å. There are five inequivalent Li sites. In the first Li site, Li is bonded in a 4-coordinate geometry to three equivalent Na, one Li, and four Sn atoms. The Li–Li bond length is 2.72 Å. There are one shorter (2.85 Å) and three longer (3.02 Å) Li–Sn bond lengths. In the second Li site, Li is bonded in a 3-coordinate geometry to one Li and three equivalent Sn atoms. All Li–Sn bond lengths are 3.10 Å. In the third Li site, Li is bonded to one Na and four Sn atoms to form distorted corner-sharing LiNaSn4 tetrahedra. There are three shorter (2.98 Å) and one longer (3.09 Å) Li–Sn bond lengths. In the fourth Li site, Li is bonded in a distorted body-centered cubic geometry to three equivalent Na, one Li, and four Sn atoms. The Li–Li bond length is 2.63 Å. There are one shorter (2.79 Å) and three longer (3.04 Å) Li–Sn bond lengths. In the fifth Li site, Li is bonded in a 3-coordinate geometry to one Li and six Sn atoms. There are three shorter (3.12 Å) and three longer (3.29 Å) Li–Sn bond lengths. There are four inequivalent Sn sites. In the first Sn site, Sn is bonded in a 11-coordinate geometry to three equivalent Na, seven Li, and one Sn atom. The Sn–Sn bond length is 2.84 Å. In the second Sn site, Sn is bonded in a distorted body-centered cubic geometry to four Li and four Sn atoms. All Sn–Sn bond lengths are 3.03 Å. In the third Sn site, Sn is bonded in a distorted trigonal non-coplanar geometry to three equivalent Li and four Sn atoms. The Sn–Sn bond length is 2.93 Å. In the fourth Sn site, Sn is bonded in a 7-coordinate geometry to seven Li and one Sn atom.

36 MATERIALS SCIENCE↗

Materials Data on Li2CeGe by Materials Project

Li2CeGe crystallizes in the hexagonal P6_3/mmc space group. The structure is three-dimensional. Li is bonded in a distorted body-centered cubic geometry to one Li, three equivalent Ce, and four equivalent Ge atoms. The Li–Li bond length is 2.15 Å. All Li–Ce bond lengths are 2.87 Å. There are one shorter (2.64 Å) and three longer (2.97 Å) Li–Ge bond lengths. Ce is bonded to six equivalent Li and six equivalent Ge atoms to form a mixture of distorted face and corner-sharing CeLi6Ge6 cuboctahedra. All Ce–Ge bond lengths are 3.33 Å. Ge is bonded in a 2-coordinate geometry to eight equivalent Li and six equivalent Ce atoms.

36 MATERIALS SCIENCE↗

Materials Data on Fe11Si5 by Materials Project

Fe11Si5 is Tungsten-derived structured and crystallizes in the cubic Pm-3m space group. The structure is three-dimensional. there are two inequivalent Fe sites. In the first Fe site, Fe is bonded in a distorted body-centered cubic geometry to three equivalent Fe and five Si atoms. All Fe–Fe bond lengths are 2.42 Å. There are a spread of Fe–Si bond distances ranging from 2.39–2.44 Å. In the second Fe site, Fe is bonded in a 8-coordinate geometry to eight equivalent Fe and six Si atoms. All Fe–Si bond lengths are 2.79 Å. There are five inequivalent Si sites. In the first Si site, Si is bonded in a body-centered cubic geometry to eight equivalent Fe atoms. In the second Si site, Si is bonded in a distorted body-centered cubic geometry to twelve Fe atoms. All Si–Fe bond lengths are 2.79 Å. In the third Si site, Si is bonded in a distorted body-centered cubic geometry to twelve Fe atoms. In the fourth Si site, Si is bonded in a distorted body-centered cubic geometry to twelve Fe atoms. In the fifth Si site, Si is bonded in a distorted body-centered cubic geometry to fourteen Fe atoms.

36 MATERIALS SCIENCE↗

Realizable hyperuniform and nonhyperuniform particle configurations with targeted spectral functions via effective pair interactions

The capacity to identify realizable many-body configurations associated with targeted functional forms for the pair correlation function $g_2(r)$ or its corresponding structure factor $\textit{S(k)}$ is of great fundamental and practical importance. While there are obvious necessary conditions that a prescribed structure factor at number density ρ must satisfy to be configurationally realizable, sufficient conditions are generally not known due to the infinite degeneracy of configurations with different higher-order correlation functions. A major aim of this paper is to expand our theoretical knowledge of the class of pair correlation functions or structure factors that are realizable by classical disordered ensembles of particle configurations, including exotic “hyperuniform” varieties. We first introduce a theoretical formalism that provides a means to draw classical particle configurations from canonical ensembles with certain pairwise-additive potentials that could correspond to targeted analytical functional forms for the structure factor. This formulation enables us to devise an improved algorithm to construct systematically canonical-ensemble particle configurations with such targeted pair statistics, whenever realizable. As a proof of concept, we test the algorithm by targeting several different structure factors across dimensions that are known to be realizable and one hyperuniform target that is known to be nontrivially unrealizable. Our algorithm succeeds for all realizable targets and appropriately fails for the unrealizable target, demonstrating the accuracy and power of the method to numerically investigate the realizability problem. Subsequently, we also target several families of structure-factor functions that meet the known necessary realizability conditions but are not known to be realizable by disordered hyperuniform point configurations, including $\textit{d}$-dimensional Gaussian structure factors, $\textit{d}$-dimensional generalizations of the two-dimensional one-component plasma (OCP), and the $\textit{d}$-dimensional Fourier duals of the previous OCP cases. Moreover, we also explore unusual nonhyperuniform targets, including “hyposurficial” and “antihyperuniform” examples. In all of these instances, the targeted structure factors are achieved with high accuracy, suggesting that they are indeed realizable by equilibrium configurations with pairwise interactions at positive temperatures. Remarkably, we also show that the structure factor of nonequilibrium perfect glass, specified by two-, three-, and four-body interactions, can also be realized by equilibrium pair interactions at positive temperatures. In this work, our findings lead us to the conjecture that any realizable structure factor corresponding to either a translationally invariant equilibrium or nonequilibrium system can be attained by an equilibrium ensemble involving only effective pair interactions. Our investigation not only broadens our knowledge of analytical functional forms for $g_2(r)$ and $\textit{S(k)}$ associated with disordered point configurations across dimensions but also deepens our understanding of many-body physics. Moreover, our work can be applied to the design of materials with desirable physical properties that can be tuned by their pair statistics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Proteomic Profiling of the Substantia Nigra to Identify Determinants of Lewy Body Pathology and Dopaminergic Neuronal Loss

Proteinaceous aggregates containing ?-synuclein protein called Lewy bodies in the substantia nigra is a hallmark of Parkinson’s disease. The molecular mechanisms of Lewy body formation and associated neuronal loss remain largely unknown. To gain insights on proteins and pathways associated with Lewy body pathology, we performed quantitative profiling of the proteome. We analyzed substantia nigra tissue from 51 subjects arranged into three groups: cases with Lewy body pathology, Lewy body-negative controls with matching neuronal loss and controls with no neuronal loss. Using label-free LC-MS/MS approach we quantified the 2,963 most abundant proteins. Statistical testing for differential protein abundance, followed by pathway enrichment and Bayesian learning of the causal network structure were performed to identify likely drivers of Lewy body formation and dopaminergic neuronal loss. The identified pathways include (1) Arp2/3 complex-mediated actin nucleation; (2) synaptic function; (3) poly(A) RNA binding; (4) basement membrane and endothelium; and (5) hydrogen peroxide metabolic process. According to the data, the endothelial/basement membrane pathway is tightly connected with both pathologies and likely to be one of the drivers of the neuronal loss. The poly(A) RNA-binding proteins, including the ones relevant to other neurodegenerative disorders (e.g. TDP-43 and FUS) have strong inverse correlation with Lewy bodies and may reflect alternative mechanism of nigral neurodegeneration.

Petyuk, Vladislav A.↗

Materials Data on CrCu4NiSn2 by Materials Project

CrNiCu4Sn2 is Tungsten-derived structured and crystallizes in the trigonal R-3m space group. The structure is three-dimensional. Cr is bonded in a distorted body-centered cubic geometry to eight Cu atoms. All Cr–Cu bond lengths are 2.68 Å. Ni is bonded in a distorted body-centered cubic geometry to eight Cu atoms. There are two shorter (2.63 Å) and six longer (2.66 Å) Ni–Cu bond lengths. There are three inequivalent Cu sites. In the first Cu site, Cu is bonded in a distorted body-centered cubic geometry to three equivalent Cr, one Ni, and four equivalent Sn atoms. There are three shorter (2.66 Å) and one longer (2.69 Å) Cu–Sn bond lengths. In the second Cu site, Cu is bonded in a distorted body-centered cubic geometry to one Cr, three equivalent Ni, and four equivalent Sn atoms. There are one shorter (2.62 Å) and three longer (2.67 Å) Cu–Sn bond lengths. In the third Cu site, Cu is bonded in a distorted body-centered cubic geometry to one Cr, three equivalent Ni, and four equivalent Sn atoms. There are one shorter (2.62 Å) and three longer (2.67 Å) Cu–Sn bond lengths. Sn is bonded in a distorted body-centered cubic geometry to eight Cu atoms.

36 MATERIALS SCIENCE↗