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At least 541 records · Page 30

Observation of backscattering induced by magnetism in a topological edge state

Significance One of the predicted characteristics of helical topological boundary modes is the absence of backscattering when time-reversal symmetry (TRS) is preserved. While previous experiments have provided evidence for this topological protection, inducing backscattering by breaking TRS has yet to be demonstrated. We test this fundamental property by investigating quasiparticle scattering in the one-dimensional topological edge state of bismuth bilayers, coupled to ferromagnetic iron clusters, using a scanning tunneling microscope. Our experimental observations demonstrate that backscattering is induced by magnetism of iron clusters in these topological edge modes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Tunable-fidelity wave functions for the ab initio description of scattering and reactions

Here, the no-core shell model (NCSM) is an ab initio method that solves the nuclear many-body problem by expanding the many-particle wave function into a (typically) harmonic oscillator basis and minimizing the energy to obtain the expansion coefficients. Extensions of the NCSM, such as its coupling with microscopic-cluster basis states, further allow for an ab initio treatment of light-ion nuclear reactions of interest for both astrophysics and nuclear technology applications. A downside of the method is the exponential scaling of the basis size with increasing number of nucleons and excitation quanta, which limits its applicability to mass A ≲ 16 nuclei, except for variants where the basis is further down-selected via some truncation scheme. We consider a basis selection method for the NCSM that was first introduced in the context of the large-scale shell model and captures the essential degrees of freedom of the nuclear wave function leading to a favorable complexity scaling for calculations and enabling ab initio reaction calculations in sd-shell nuclei. The particle configurations within the NCSM basis are ordered based on their contribution to the first moment of the Hamiltonian matrix that results from the projection onto the many-body basis. The truncation scheme then consists in retaining only the lowest-first-moment configurations, which typically contain only few many-body basis states (Slater determinants). As the energy threshold above which configurations are disregarded is increased, the size of the basis becomes an almost-continuous variable, allowing for tunable fidelity in the obtained wave functions. The resulting wave functions can then be used directly in ab initio reaction calculations. We present calculations for 7 Li and n + 12 C scattering using nucleon-nucleon interactions derived from chiral effective field theory and softened using the similarity renormalization group method. The obtained energy levels invariably demonstrate exponential convergence with the size of the basis, and we find improved convergence in scattering calculations. To demonstrate the possibilities enabled by the approach, we also present a first calculation for the scattering of neutrons from 24 Mg. The method presented in this work appears promising for future studies of nuclei with mass A > 16, opening multiple future research directions impacting both nuclear astrophysics and nuclear technology applications.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Structure and magnetism in epitaxial Fe 1 + x VSb nanocomposite films

The combination of ferromagnetism and semiconducting behavior offers an avenue for realizing novel spintronics and spin-enhanced thermoelectrics. Here we demonstrate the synthesis of doped and nanocomposite half-Heusler Fe 1+x VSb films by molecular beam epitaxy. For dilute excess Fe (x < 0.1), we observe a decrease in the Hall electron concentration and no secondary phases in x-ray diffraction. Magnetotransport measurements suggest weak ferromagnetism that onsets at a temperature of T c ≈ 5 K. For higher Fe content (x > 0.1), ferromagnetic Fe nanostructures precipitate from the semiconducting FeVSb matrix. The Fe/FeVSb interfaces are epitaxial, as observed by transmission electron microscopy and x-ray diffraction. Further, magnetotransport measurements suggest proximity-induced magnetism in the FeVSb from the Fe/FeVSb interfaces, or superparamagnetically coupled Fe-rich clusters, at an onset temperature of T c ≈ 20 K.

36 MATERIALS SCIENCE↗

Multi-scale modeling of fuel fragmentation and microstructural evolution

An overview of NEAMS program activities to model fuel fragmentation and microstructual evolution to a group of industry attendees at a meeting hosted by EPRI. Topics include atomistic methods to determine grain boundary strength, phase-field fracture modeling to determine critical pressure at grain boundaries, and coupled phase-field-cluster dynamics to model microstructural evolution.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Assessing CESM2 Clouds and Their Response to Climate Change Using Cloud Regimes

Abstract The Community Earth System Model, version 2 (CESM2), has a very high climate sensitivity driven by strong positive cloud feedbacks. To evaluate the simulated clouds in the present climate and characterize their response with climate warming, a clustering approach is applied to three independent satellite cloud products and a set of coupled climate simulations. Using k -means clustering with a Wasserstein distance cost function, a set of typical cloud configurations is derived for the satellite cloud products. Using satellite simulator output, the model clouds are classified into the observed cloud regimes in both current and future climates. The model qualitatively reproduces the observed cloud configurations in the historical simulation using the same time period as the satellite observations, but it struggles to capture the observed heterogeneity of clouds which leads to an overestimation of the frequency of a few preferred cloud regimes. This problem is especially apparent for boundary layer clouds. Those low-level cloud regimes also account for much of the climate response in the late twenty-first century in four shared socioeconomic pathway simulations. The model reduces the frequency of occurrence of these low-cloud regimes, especially in tropical regions under large-scale subsidence, in favor of regimes that have weaker cloud radiative effects.

58 GEOSCIENCES↗

Novel CHI3L1 ‐Associated Angiogenic Phenotypes Define Glioma Microenvironments: Insights From Multi‐Omics Integration

ABSTRACT The CHI3L1 signaling pathway significantly influences glioma angiogenesis, but its role in the tumor microenvironment (TME) remains elusive. We propose a novelCHI3L1‐associated vascular phenotype classification for glioma through integrative analyses of multiple datasets with bulk and single‐cell transcriptome, genomics, digital pathology, and clinical data. We investigated the biological characteristics, genomic alterations, therapeutic vulnerabilities, and immune profiles within these phenotypes through a comprehensive multi‐omics approach. We constructed the vascular‐related risk (VR) score based onCHI3L1‐associated vascular signatures (CAVS) identified by machine learning algorithms. Utilizing unsupervised consensus clustering, gliomas were stratified into three distinct vascular phenotypes: Cluster A, marked by high vascularization and stromal activation with a relatively low levels of tumor‐infiltrating lymphocytes (TILs); Cluster B, characterized by moderate vascularization and stromal activity, coupled with a high density of TILs; and Cluster C, defined by low vascularization and sparse immune cell infiltration. We observed that the CAVS effectively indicated glioma‐associated angiogenesis and immune suppression by single‐cell RNA‐seq analysis. Moreover, the high‐VR‐score group exhibited enhanced angiogenic activity, reduced immune response, resistance to immunotherapy, and poorer clinical outcomes. The VR score independently predicted glioma prognosis and, combined with a nomogram, provided a robust clinical decision‐making tool. Potential drug prediction based on transcription factors for high‐risk patients was also performed. Our study reveals thatCHI3L1‐associated vascular phenotypes shape distinct immune landscapes in gliomas, offering insights for optimizing therapeutic strategies to improve patient outcomes.

Oncology↗

How Well Can Quantum Embedding Method Predict the Reaction Profiles for Hydrogenation of Small Li Clusters?

Quantum computing leverages the principles of quantum mechanics in novel ways to tackle complex chemistry problems that cannot be accurately addressed using traditional quantum chemistry methods. However, the high computational cost and available number of physical qubits with high fidelity limit its application to small chemical systems. This work employed a quantum-classical framework which features a quantum active space-embedding approach to perform simulations of chemical reactions that require up to 14 qubits. This framework was applied to prototypical example metal hydrogenation reactions: the coupling between hydrogen and Li 2 , Li 3 , and Li 4 clusters. Particular attention was paid to the computation of barriers and reaction energies. The predicted reaction profiles compare well with advanced classical quantum chemistry methods, demonstrating the potential of the quantum embedding algorithm to map out reaction profiles of realistic gas-phase chemical reactions to ascertain qualitative energetic trends. Additionally, the predicted potential energy curves provide a benchmark to compare against both current and future quantum embedding approaches.

36 MATERIALS SCIENCE↗

Enabling Efficient and Accurate Computational Studies of MOF Reactivity via QM/MM and QM/QM Methods

Electronic structure calculations can provide unique insight into metal–organic framework (MOF) reactivity and defect formation. Such calculations can be broadly categorized as utilizing either periodic or cluster models, each with their respective advantages and disadvantages. In the present study, we demonstrate how multiscale methods can leverage the advantages of both approaches to enable high levels of accuracy and computational efficiency in studies of MOF reactivity. Using defect formation in a zeolitic imidazolate framework (ZIF) as a prototypical example, we benchmark a quantum mechanics/molecular mechanics (QM/MM) scheme that enables highly efficient cluster-based calculations on MOFs. We demonstrate the importance of correctly accounting for the influence of both dative bond cleavage in the QM cluster and long-range mechanical coupling to the bulk to achieving accurate QM/MM studies of MOFs. We subsequently leverage these cluster models in a QM/QM scheme that goes beyond standard DFT to yield “gold-standard” correlated wave function results on MOFs at modest computational cost. Crucially, we find several cases in which the incorporation of these correlated corrections yields qualitatively important corrections over conventional DFT values.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Cluster Frustration in the Breathing Pyrochlore Magnet LiGaCr 4 S 8

We present a comprehensive neutron scattering study of the breathing pyrochlore magnet LiGaCr 4 S 8 . We observe an unconventional magnetic excitation spectrum with a separation of high and low-energy spin dynamics in the correlated paramagnetic regime above a spin-freezing transition at 12(2) K. By fitting to magnetic diffuse-scattering data, we parameterize the spin Hamiltonian. We find that interactions are ferromagnetic within the large and small tetrahedra of the breathing pyrochlore lattice, but antiferromagnetic further-neighbor interactions are also essential to explain our data, in qualitative agreement with density-functional theory predictions [Ghosh et al., npj Quantum Mater. 4, 63 (2019)]. We explain the origin of geometrical frustration in LiGaCr 4 S 8 in terms of net antiferromagnetic coupling between emergent tetrahedral spin clusters that occupy a face-centered lattice. Furthermore, our results provide insight into the emergence of frustration in the presence of strong further-neighbor couplings, and a blueprint for the determination of magnetic interactions in classical spin liquids.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Electronic tuning of confined sub-nanometer cobalt oxide clusters boosting oxygen catalysis and rechargeable Zn–air batteries.

Reasonable design of robust bifunctional oxygen catalysts from an electronic structure perspective is intriguing and challenging for the development of high active rechargeable zinc-air batteries (ZABs). In this study, the favorable regulation of the electronic structure of the cobalt oxide nanoclusters was firstly predicted by density functional theory (DFT) simulation, and then experimentally verified by confining sub-nanometer CoOx clusters (0.86 nm) into the small pore of ZIF-8 derived N-doped nanomaterials (PNC) using a microporous MOFs confinement strategy. The confined effect of the MOF micropores not only enhanced the stability of the subnanometer cobalt oxide clusters, but also make it coupled with Co-Nx to further regulate the electronic structure of the former, synergistic resulting in enhanced ORR/OER actives. As a result, the optimized 0.05CoOx@PNC catalyst demonstrates outstanding bifunctional oxygen performance with a smaller potential gap of 0.67 V. Moreover, the rechargeable Zn-air batteries integrated 0.05CoOx@PNC air cathode displays encouraging performance with a peak power density of 157.1 mW cm(-2), a specific capacity of 887 mAh g(Zn)(-1)at 10 mA cm(-2) and long-term cyclability for over 200 h, significantly outperforming the benchmark electrode couple consisted of Pt/C/RuO2. DFT calculation further revealed that reducing particle size and coupling with Co-N could effectively regulate the charge distribution of CoOx nanoclusters and downshift the D-band center of Co adsorption sites in CoOx nanoclusters, which reduced the reaction barrier of intermediate O-2* and OH* and ORR/ OER over potential, thus accelerating the overall ORR/OER kinetic process. This work offers a novel reference for the construction of a robust sub-nanometer cluster catalysts in the field of ZABs.

Bifunctional oxygen electrocatalysts↗

Low-Temperature Activation and Coupling of Methane on MgO Nanostructures Embedded in Cu 2 O/Cu(111)

Here, the efficient conversion of methane into valuable hydrocarbons such as ethane and ethylene at relatively low temperatures without deactivation issues is crucial for advancing sustainable energy solutions. Herein, AP-XPS and STM studies show that MgO nanostructures (0.2-0.5 nm wide, 0.4-0.6 Å high) embedded in a Cu 2 O/Cu(111) substrate activate methane at room temperature, mainly dissociating it into CH x (x = 2 or 3) and H adatoms, with minimal conversion to C adatoms. These MgO nanostructures in contact with Cu 2 O/Cu(111) exhibit unique reactivity, enabling C-C coupling into ethane and ethylene at 500 K, a significantly lower temperature than that required for bulk MgO catalysts (>700 K), with negligible carbon deposition and no deactivation. DFT calculations corroborate these experimental findings. The CH 4,gas → *CH 3 +*H reaction is a downhill process on MgO/Cu 2 O/Cu(111) surfaces. The activation of methane is facilitated by an electron transfer from copper to MgO and the existence of Mg and O atoms with a low coordination number in the oxide nanostructures. The formation of O-CH 3 and O-H bonds overcomes the energy necessary for the cleavage of a C-H bond in methane. DFT studies reveal that smaller Mg 2 O 2 model clusters provide stronger binding and lower activation barriers for C-H dissociation in CH 4 , while larger Mg 3 O 3 clusters promote C-C coupling due to weaker *CH 3 binding. All these results emphasize the importance of size when optimizing the catalytic performance of MgO nanostructures in the selective conversion of methane.

36 MATERIALS SCIENCE↗

Charge Transport in Zirconium-Based Metal–Organic Frameworks

Metal–organic frameworks (MOFs) are a class of crystalline porous materials characterized by inorganic nodes and multitopic organic linkers. Because of their molecular-scale porosity and periodic intraframework chemical functionality, MOFs are attractive scaffolds for supporting and/or organizing catalysts, photocatalysts, chemical-sensing elements, small enzymes, and numerous other functional-property-imparting, nanometer-scale objects. Notably, these objects can be installed after the synthesis of the MOF, eliminating the need for chemical and thermal compatibility of the objects with the synthesis milieu. Thus, postsynthetically functionalized MOFs can present three-dimensional arrays of high-density, yet well-separated, active sites. Depending on the application and corresponding morphological requirements, MOF materials can be prepared in thin-film form, pelletized form, isolated single-crystal form, polycrystalline powder form, mixed-matrix membrane form, or other forms. For certain applications, most obviously catalytic hydrolysis and electro- or photocatalytic water splitting, but also many others, an additional requirement is water stability. MOFs featuring hexa-zirconium(IV)-oxy nodes satisfy this requirement. For applications involving electrocatalysis, charge storage, photoelectrochemical energy conversion, and chemiresistive sensing, a further requirement is electrical conductivity, as embodied in electron or hole transport. As most MOFs, under most conditions, are electrically insulating, imparting controllable charge-transport behavior is both a chemically intriguing and chemically compelling challenge. Herein, we describe three strategies to render zirconium-based metal–organic frameworks (MOFs) tunably electrically conductive and, therefore, capable of transporting charge on the few nanometers (i.e., several molecular units) to few micrometers (i.e., typical dimensions for MOF microcrystallites) scale. The first strategy centers on redox-hopping between periodically arranged, chemically equivalent sites, essentially repetitive electron (or hole) self-exchange. Zirconium nodes are electrically insulating, but they can function as grafting sites for (a) redox-active inorganic clusters or (b) molecular redox couples. Alternatively, charge hopping based on linker redox properties can be exploited. Marcus’s theory of electron transfer has proven useful for understanding/predicting trends in redox-hopping based conductivity, most notably, in accounting for variations as great as 3000-fold depending on the direction of charge propagation through structurally anisotropic MOFs. In MOF environments, propagation of electronic charge via redox hopping is necessarily accompanied by movement of charge-compensating ions. Consequently, rates of redox hopping can depend on both the identity and concentration of ions permeating the MOF. In the context of electrocatalysis, an important goal is to transport electronic charge fast enough to match or exceed the inherent activity of MOF-based or MOF-immobilized catalysts. Bandlike electronic conductivity is the focus of an alternative strategy: one based on the introduction of molecular guests capable of forming donor–acceptor charge transfer complexes with the host framework. Theory again can be applied predictively to alter conductivity. A third strategy similarly emphasizes electronic conductivity, but it makes use of added bridges in the form of molecular oligomers or inorganic clusters that can then be linked to span the length of a MOF crystallite. For all strategies, retention of molecular-scale porosity is emphasized, as this property is key to many applications. Lastly, while our focus is on Zr-MOFs, the described approaches clearly are extendable to other MOF compositions, as has already been demonstrated, in part, in studies by others.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Spin–orbit coupling of electrons on separate lanthanide atoms of Pr 2 O 2 and its singly charged cation

Although it plays a critical role in the photophysics and catalysis of lanthanides, spin–orbit coupling of electrons on individual lanthanide atoms in small clusters is not well understood. The major objective of this work is to probe such coupling of the praseodymium (Pr) 4f and 6s electrons in Pr 2 O 2 and Pr 2 O 2 +. The approach combines mass-analyzed threshold ionization spectroscopy and spin–orbit multiconfiguration second-order quasi-degenerate perturbation theory. The energies of six ionization transitions are precisely measured; the adiabatic ionization energy of the neutral cluster is 38 045 (5) cm –1 . Most of the electronic states involved in these transitions are identified as spin–orbit coupled states consisting of two or more electron spins. The electron configurations of these states are 4f 4 6s 2 for the neutral cluster and 4 f 46 s for the singly charged cation, both in planar rhombus-type structures. Finally, the spin–orbit splitting due to the coupling of the electrons on the separate Pr atoms is on the order of hundreds of wavenumbers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Machine-learning predictions of the shale wells’ performance

The ultra-low permeability nature of shale reservoirs leads to an extended linear flow and necessitates horizontal wells with multi-stage engineered fractures to efficiently extract hydrocarbons resources. These artificially-generated and naturally-occurring fractures form complex networks that create complex flow regimes which control oil production. These fractures are neither identical nor equally-spaced, which leads to a production profile with a masked onset of the boundary-dominated flow. The combination of the extended linear flow with the indeterminate onset of the boundary-dominated flow challenges the current deterministic analytic approaches to forecast the estimated ultimate recovery (EUR). In this work, we propose a novel machine-learning approach which overcomes these challenges and provides reliable EUR estimates based on field-wide analyses. We implement a novel unsupervised machine learning (ML) methodology, which allows for automatic identification of the optimal number of features (signals) present in the data based on non-negative matrix/tensor factorization coupled with k-means clustering incorporating regularization and physics constraints. In the presented analyses, the input data to the ML algorithm is the available (public) production history from the field collected at existing unconventional reservoirs. We validate our approach through hindcasting of the production data, where we achieved an excellent agreement. In addition, our approach is able to identify the poorly-performing wells, which could benefit from early refracing. Our approach provides fast and accurate estimations of the well performance without presumptions about the state of the well or the flow regime.

03 NATURAL GAS↗

First-Principles Statistical Mechanics Study of Magnetic Fluctuations and Order–Disorder in the Spinel LiNi 0.5 Mn 1.5 O 4 Cathode

While significant magnetic interactions exist in lithium transition metal oxides, commonly used as Li-ion cathodes, the interplay between magnetic couplings, disorder, and redox processes remains poorly understood. In this work, we focus on the high-voltage spinel LiNi 0.5 Mn 1.5 O 4 (LNMO) cathode as a model system on which to apply a computational framework that uses first principles-based statistical mechanics methods to predict the finite temperature magnetic properties of materials and provide insights into the complex interplay between magnetic and chemical degrees of freedom. Density functional theory calculations on multiple distinct Ni–Mn orderings within the LNMO system, including the ordered ground-state structure (space group P4332), reveal a preference for a ferrimagnetic arrangement of the Ni and Mn sublattices due to strong antiferromagnetic superexchange interactions between neighboring Mn 4+ and Ni 2+ ions and ferromagnetic Mn–Mn and Ni–Ni couplings, as revealed by magnetic cluster expansions. These results are consistent with qualitative predictions using the Goodenough-Kanamori-Anderson rules. Simulations of the finite temperature magnetic properties of LNMO are conducted using Metropolis Monte Carlo. We find that a “semiclassical” Monte Carlo sampling method based on the Heisenberg Hamiltonian accurately predicts experimental magnetic transition temperatures observed in magnetometry measurements. This study highlights the importance of a robust computational toolkit that accurately captures the complex chemomagnetic interactions and predicts finite temperature magnetic behavior to help analyze experimental magnetic and magnetic resonance spectroscopy data acquired ex situ and operando.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

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

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

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Three rate-determining protein roles in photosynthetic O 2 -evolution addressed by time-resolved experiments on genetically modified photosystems

Light-driven water splitting by plants, algae and cyanobacteria is pivotal for global bioenergetics and biomass formation. A manganese cluster bound to the photosystem II proteins catalyzes the complex reaction at high rate, but the rate-determining factors are insufficiently understood. Here we trace the oxygen-evolution transition by time-resolved polarography and infrared spectroscopy for cyanobacterial photosystems genetically modified at two strategic sites, complemented by computational chemistry. Our results highlight three rate-determining roles of the protein environment of the metal cluster: acceleration of proton-coupled electron transfer, acceleration of substrate-water insertion after O 2 -formation, and balancing of rate-determining enthalpic and entropic contributions. Whereas in general the substrate-water insertion step may be unresolvable in time-resolved experiments, here it likely becomes traceable because of deceleration by genetic modification. Our results may stimulate new time-resolved experiments on substrate-water insertion in photosynthesis, clarification of enthalpy-entropy compensation in enzyme catalysis, and knowledge-guided development of inorganic catalyst materials.

Bioenergetics↗

Permutation-adapted complete and independent basis for atomic cluster expansion descriptors

In many recent applications, particularly in the field of atom-centered descriptors for interatomic potentials, tensor products of spherical harmonics have been used to characterize complex atomic environments. When coupled with a radial basis, the atomic cluster expansion (ACE) basis is obtained. However, symmetrization with respect to both rotation and permutation results in an overcomplete set of ACE descriptors with linear dependencies occurring within blocks of functions corresponding to particular generalized Wigner symbols. All practical applications of ACE employ semi-numerical constructions to generate a complete, fully independent basis. While computationally tractable, the resultant basis cannot be expressed analytically, is susceptible to numerical instability, and thus has limited reproducibility. Here we present a procedure for generating explicit analytic expressions for a complete and independent set of ACE descriptors. The procedure uses a coupling scheme that is maximally symmetric w.r.t. permutation of the atoms, exposing the permutational symmetries of the generalized Wigner symbols, and yields a permutation-adapted rotationally and permutationally invariant basis (PA-RPI ACE). Theoretical support for the approach is presented, as well as numerical evidence of completeness and independence. A summary of explicit enumeration of PA-RPI functions up to rank 6 and polynomial degree 32 is provided. The PA-RPI blocks corresponding to particular generalized Wigner symbols may be either larger or smaller than the corresponding blocks in the simpler rotationally invariant basis. Finally, we demonstrate that basis functions of high polynomial degree persist under strong regularization, indicating the importance of not restricting the maximum degree of basis functions in ACE models a priori.

74 ATOMIC AND MOLECULAR PHYSICS↗