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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

ZMPY3D: accelerating protein structure volume analysis through vectorized 3D Zernike moments and Python-based GPU integration

Abstract Motivation Volumetric 3D object analyses are being applied in research fields such as structural bioinformatics, biophysics, and structural biology, with potential integration of artificial intelligence/machine learning (AI/ML) techniques. One such method, 3D Zernike moments, has proven valuable in analyzing protein structures (e.g., protein fold classification, protein–protein interaction analysis, and molecular dynamics simulations). Their compactness and efficiency make them amenable to large-scale analyses. Established methods for deriving 3D Zernike moments, however, can be inefficient, particularly when higher order terms are required, hindering broader applications. As the volume of experimental and computationally-predicted protein structure information continues to increase, structural biology has become a “big data” science requiring more efficient analysis tools. Results This application note presents a Python-based software package, ZMPY3D, to accelerate computation of 3D Zernike moments by vectorizing the mathematical formulae and using graphical processing units (GPUs). The package offers popular GPU-supported libraries such as CuPy and TensorFlow together with NumPy implementations, aiming to improve computational efficiency, adaptability, and flexibility in future algorithm development. The ZMPY3D package can be installed via PyPI, and the source code is available from GitHub. Volumetric-based protein 3D structural similarity scores and transform matrix of superposition functionalities have both been implemented, creating a powerful computational tool that will allow the research community to amalgamate 3D Zernike moments with existing AI/ML tools, to advance research and education in protein structure bioinformatics. Availability and implementation ZMPY3D, implemented in Python, is available on GitHub (https://github.com/tawssie/ZMPY3D) and PyPI, released under the GPL License.

Lai, Jhih-Siang (ORCID:0000000156775890)↗
DOE OSTI2024

Random Forest Prediction of Crystal Structure from Electron Diffraction Patterns

Transmission electron microscopy (TEM) diffraction patterns are regularly used to determine the structure of crystalline materials. Electron diffraction is the most common method to solve for unknown or partially known crystal structures, as it provides direct and interpretable feedback on the orientation of crystal grains under the beam [1]. However, it remains a challenge to determine the crystal structure of a new material or even a new phase of an existing material. Analysis of such materials commonly requires manual exploration and comparison with simulated diffraction patterns. This is often a time consuming process with no obvious start point when many similar structures are possible, and this method cannot be used to determine crystal structure or orientation from structures not included in the diffraction libraries. Therefore, we have developed a machine learning model to determine the crystal structure of a material from its electron diffraction pattern.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Contrasting structural reversibility and magnetic correlations in isostructural honeycomb magnets CrCl3 and 𝛼−RuCl3

We report a comparative neutron single crystal diffraction study of the structural and magnetic properties of layered halides CrCl3 and 𝛼−RuCl3. They host a honeycomb arrangement of transition metal ions with distinct electronic configurations and undergo a first-order structural transition between high-temperature 𝐶⁢2/𝑚 and low-temperature 𝑅⁢‾‾‾3. Both compounds show a step-like change in the 𝑐-lattice parameter across the structure transition. In contrast, the in-plane lattice response is quite different: 𝛼−RuCl3 exhibits an abrupt hysteretic change across the transition accompanied by progressive crystalline degradation upon thermal cycling, whereas CrCl3 shows a smooth in-plane lattice evolution and remains structurally robust. Magnetically, CrCl3 orders into an A-type antiferromagnetic structure at 𝑇𝑁=14 K and exhibits pronounced diffuse magnetic scattering extending up to about 40 K. 𝛼−RuCl3 shows no observable magnetic diffuse scattering above its zigzag antiferromagnetic ordering temperature 𝑇𝑁=7.6 K. These results suggest that the contrasting structural responses arise from an interplay between interlayer sliding energetics, stacking-strain coupling, and elastic accommodation of the stacking transition. The distinct chemical bonding and electronic configurations of the two compounds provide a microscopic basis for their different lattice responses to the structure transition and magnetic correlations.

Morgan, Zachary [ORNL] (ORCID:0000000243625911)↗
DOE OSTI2025

Structure refinement and anisotropic atomic displacement parameters of 1M Illite: Rietveld and pair distribution function analysis using synchrotron X-ray radiation

Illite, a widespread clay mineral, plays a pivotal role in geological processes, notably as an indicator in diagenetic and hydrothermal alteration environments, and possesses significant industrial relevance in applications including ceramics, construction and catalysis. However, challenges including its nanoscale crystallinity, structural disorder and frequent interstratification with other clay minerals have hindered detailed structural characterization using conventional X-ray diffraction (XRD) techniques. This study employs integrated synchrotron XRD and pair distribution function (PDF) analysis to elucidate the crystal structure of the 1M illite polytype, yielding the first determination of its anisotropic atomic displacement parameters (U aniso ). TheseU aniso parameters provide critical insights into atomic dynamics and static disorder within the structure, enabling a more refined understanding of structure–property relationships. This integrated approach, combining synchrotron XRD, Rietveld refinement and PDF analysis, yields a comprehensive structural characterization, capturing both average crystallographic and local atomic arrangements. Considering illite's widespread geological occurrence and industrial importance, this high-precision structural dataset, especially the determinedU aniso values, provides a crucial benchmark for future modeling and simulation efforts targeting accurate prediction of its physicochemical behavior.

Chemistry↗
DOE OSTI2024

X-ray crystal structure of a designed rigidified imaging scaffold in the ligand-free conformation

Imaging scaffolds composed of designed protein cages fused to designed ankyrin repeat proteins (DARPins) have enabled the structure determination of small proteins by cryogenic electron microscopy (cryo-EM). One particularly well characterized scaffold type is a symmetric tetrahedral assembly composed of 24 subunits, 12 A and 12 B, which has three cargo-binding DARPins positioned on each vertex. Here, the X-ray crystal structure of a representative tetrahedral scaffold in the apo state is reported at 3.8 Å resolution. The X-ray crystal structure complements recent cryo-EM findings on a closely related scaffold, while also suggesting potential utility for crystallographic investigations. As observed in this crystal structure, one of the three DARPins, which serve as modular adaptors for binding diverse `cargo' proteins, present on each of the vertices is oriented towards a large solvent channel. The crystal lattice is unusually porous, suggesting that it may be possible to soak crystals of the scaffold with small (≤30 kDa) protein cargo ligands and subsequently determine cage–cargo structures via X-ray crystallography. The results suggest the possibility that cryo-EM scaffolds may be repurposed for structure determination by X-ray crystallography, thus extending the utility of electron-microscopy scaffold designs for alternative structural biology applications.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Optimizing Management of Persistent Data Structures in High-Performance Analytics

Large-scale data analytics workflows ingest massive input data into various data structures, including graphs and key-value datastores. These data structures undergo multiple transformations and computations and are typically reused in incremental and iterative analytics workflows. Persisting in-memory views of these data structures enables reusing them beyond the scope of a single program run while avoiding repetitive raw data ingestion overheads. Memory-mapped I/O enables persisting in-memory data structures without data serialization and deserialization overheads. However, memory-mapped I/O lacks the key feature of persisting consistent snapshots of these data structures for incremental ingestion and processing. The obstacles to efficient virtual memory snapshots using memory-mapped I/O include background writebacks outside the application’s control, and the significantly high storage footprint of such snapshots. To address these limitations, we present Privateer, a memory and storage management tool that enables storage-efficient virtual memory snapshotting while also optimizing snapshot I/O performance. Here, we integrated Privateer into Metall, a state-of-the-art persistent memory allocator for C++, and the Lightning Memory-Mapped Database (LMDB), a widely-used key-value datastore in data analytics and machine learning. Privateer optimized application performance by 1.22× when storing data structure snapshots to node-local storage, and up to 16.7× when storing snapshots to a parallel file system. Privateer also optimizes storage efficiency of incremental data structure snapshots by up to 11× using data deduplication and compression.

Computer science↗
DOE OSTI2024

Structure and identification of the native PLP synthase complex from Methanosarcina acetivorans lysate

Many protein-protein interactions behave differently in biochemically purified forms as compared to their in vivo states. As such, determining native protein structures may elucidate structural states previously unknown for even well-characterized proteins. Here, we apply the bottom-up structural proteomics method, cryoID , toward a model methanogenic archaeon. While they are keystone organisms in the global carbon cycle and active members of the human microbiome, there is a general lack of characterization of methanogen enzyme structure and function. Through the cryoID approach, we successfully reconstructed and identified the native Methanosarcina acetivorans pyridoxal 5′-phosphate (PLP) synthase (PdxS) complex directly from cryogenic electron microscopy (cryo-EM) images of fractionated cellular lysate. We found that the native PdxS complex exists as a homo-dodecamer of PdxS subunits, and the previously proposed supracomplex containing both the synthase (PdxS) and glutaminase (PdxT) was not observed in cellular lysate. Our structure shows that the native PdxS monomer fashions a single 8α/8β TIM-barrel domain, surrounded by seven additional helices to mediate solvent and interface contacts. A density is present at the active site in the cryo-EM map and is interpreted as ribose 5-phosphate. In addition to being the first reconstruction of the PdxS enzyme from a heterogeneous cellular sample, our results reveal a departure from previously published archaeal PdxS crystal structures, lacking the 37-amino-acid insertion present in these prior cases. This study demonstrates the potential of applying the cryoID workflow to capture native structural states at atomic resolution for archaeal systems, for which traditional biochemical sample preparation is nontrivial.

Methanosarcina acetivorans↗
DOE OSTI2025

Chromatin structures from integrated AI and polymer physics model

The physical organization of the genome in three-dimensional space regulates many biological processes, including gene expression and cell differentiation. Three-dimensional characterization of genome structure is critical to understanding these biological processes. Direct experimental measurements of genome structure are challenging; computational models of chromatin structure are therefore necessary. We develop an approach that combines a particle-based chromatin polymer model, molecular simulation, and machine learning to efficiently and accurately estimate chromatin structure fromindirectmeasures of genome structure. More specifically, we introduce a new approach where the interaction parameters of the polymer model are extracted from experimental Hi-C data using a graph neural network (GNN). We train the GNN on simulated data from the underlying polymer model, avoiding the need for large quantities of experimental data. The resulting approach accurately estimates chromatin structures across all chromosomes and across several experimental cell lines despite being trained almost exclusively on simulated data. The proposed approach can be viewed as a general framework for combining physical modeling with machine learning, and it could be extended to integrate additional biological data modalities. Ultimately, we achieve accurate and high-throughput estimations of chromatin structure from Hi-C data, which will be necessary as experimental methodologies, such as single-cell Hi-C, improve.

Biochemistry & Molecular Biology↗
DOE OSTI2025

Structural Evolution of the Hogback Monocline and Its Tectonic Significance in the San Juan Basin

The San Juan Basin is recognized as a Laramide foreland basin. It is located within the Colorado Plateau, a broad tectonic province characterized by a thick sedimentary sequence that was segmented into smaller sub basins during the Late Cretaceous to Paleogene Laramide orogeny. The Hogback Monocline lies along the northwestern margin of the San Juan Basin and is considered a Laramide-age structure formed in response to compressional stress. In this study, we interpret surface and subsurface datasets to construct a structural geological model and evaluate its tectonic significance. Through seismic data, we identify key fault and fold geometries at depth. The seismic dataset used in this study was reprocessed in depth and constrained with well log velocity data to enhance seismic imaging quality. Additionally, we performed well log correlations to identify formation tops and assess variations in basin infill and thickness geometry. A series of structural cross-sections, constructed using seismic data and a high density of boreholes, are presented to evaluate geometric variations along the structure and its evolution during basin development. Furthermore, kinematic restoration and forward modeling analyses were conducted to validate our structural interpretation. This work suggests that the Hogback Monocline formed through fault-propagation folding and flexural slip affecting the pre-Laramide sedimentary sequence under compressional stresses associated with the Laramide orogeny. This structure is interpreted as a high-angle reverse fault that influenced the geometry of the late basin infill. Additionally, monocline bending along the structure may have been controlled by fault relay systems and, in some cases, influenced by strike-slip faulting.

Reyes, Martin [New Mexico Bureau o fGeology and Mi↗
DOE OSTI2025

Protein-ligand binding affinity prediction using multi-instance learning with docking structures

Recent advances in 3D structure-based deep learning approaches demonstrate improved accuracy in predicting protein-ligand binding affinity in drug discovery. These methods complement physics-based computational modeling such as molecular docking for virtual high-throughput screening. Despite recent advances and improved predictive performance, most methods in this category primarily rely on utilizing co-crystal complex structures and experimentally measured binding affinities as both input and output data for model training. Nevertheless, co-crystal complex structures are not readily available and the inaccurate predicted structures from molecular docking can degrade the accuracy of the machine learning methods. We introduce a novel structure-based inference method utilizing multiple molecular docking poses for each complex entity. Our proposed method employs multi-instance learning with an attention network to predict binding affinity from a collection of docking poses. We validate our method using multiple datasets, including PDBbind and compounds targeting the main protease of SARS-CoV-2. The results demonstrate that our method leveraging docking poses is competitive with other state-of-the-art inference models that depend on co-crystal structures. This method offers binding affinity prediction without requiring co-crystal structures, thereby increasing its applicability to protein targets lacking such data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Evolution of the Fermi Surface of 1T-VSe 2 across a Structural Phase Transition

Periodic lattice distortion, known as the charge density wave, is generally attributed to electron–phonon coupling. This correlation is expected to induce a pseudogap at the Fermi level in order to gain the required energy for stable lattice distortion. The transition metal dichalcogenide 1T-VSe 2 also undergoes such a transition at 110 K. Here, we present detailed angle-resolved photoemission spectroscopy experiments to investigate the electronic structure in 1T-VSe 2 across the structural transition. Previously reported warping of the electronic structure and the energy shift of a secondary peak near the Fermi level as the origin of the charge density wave phase are shown to be temperature independent and hence cannot be attributed to the structural transition. Our work reveals new states that were not resolved in previous studies. Earlier results can be explained by the different dispersion natures of these states and temperature-induced broadening. Only the overall size of the Fermi surface is found to change across the structural transition. These observations, quite different from the charge density wave scenario commonly considered for 1T-VSe 2 and other transition metal dichalcogenides, bring fresh perspectives toward correctly describing structural transitions. Therefore, these new results can be applied to material families in which the origin of the structural transition has not been resolved.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Temperature-Dependent Structural Transition in Cu-Intercalated Trigonal CuYbSe 2

Rare-earth delafossites, ARCh 2 ; A = alkali metal, R = rare-earth, Ch = chalcogen which consist of intercalated rare-earth metal dichalcogenides, host frustrated triangular lattices that are fertile ground for exotic phenomena. In most cases, the triangular rare-earth sublattice arises from R-3m (No. 166) structures with three layers of rare-earth metal dichalcogenide octahedra or P6 3 /mmc (No. 194) structures with two such layers, analogous to those found in transition metal dichalcogenides. Substituting the alkali metal with Cu + yields a distinct trigonal crystal symmetry P-3m1 (No. 164) in these structures. This symmetry change alters the coordination environment from ASe 6 octahedra in R-3m AYbSe 2 to CuSe 4 tetrahedra in CuYbSe 2 , resulting in shortened rare-earth to rare-earth separations and significantly reduced interlayer distances. Using X-ray single-crystal diffraction, powder neutron diffraction, resistance, and specific heat measurements, a structural transition slightly below room temperature (258 K) is observed. The low-temperature structure is a lower-symmetry I2/m structure, accompanied by partial Cu-site vacancy ordering. The combination of Cu disorder and the triangular lattice geometry in CuYbSe 2 provides a promising platform for investigating frustrated magnetism and unconventional transport phenomena.

Chemical structure↗
DOE OSTI2024

Adjusting the Energy Profile for CH–O Interactions Leads to Improved Stability of RNA Stem-Loop Structures in MD Simulations

The role of ribonucleic acid (RNA) in biology continues to grow, but insight into important aspects of RNA behavior is lacking, such as dynamic structural ensembles in different environments, how flexibility is coupled to function, and how function might be modulated by small molecule binding. In the case of proteins, much progress in these areas has been made by complementing experiments with atomistic simulations, but RNA simulation methods and force fields are less mature. It remains challenging to generate stable RNA simulations, even for small systems where well-defined, thermostable structures have been established by experiments. Further many different aspects of RNA energetics have been adjusted in force fields, seeking improvements that are transferable across a variety of RNA structural motifs. In this work, the role of weak CH···O interactions is explored, which are ubiquitous in RNA structure but have received less attention in RNA force field development. By comparing data extracted from high-resolution RNA crystal structures to energy profiles from quantum mechanics and force field calculations, it is shown that CH···O interactions are overly repulsive in the widely used Amber RNA force fields. A simple, targeted adjustment of CH···O repulsion that leaves the remainder of the force field unchanged was developed. Then, the standard and modified force fields were tested using molecular dynamics (MD) simulations with explicit water and salt, amassing over 300 μs of data for multiple RNA systems containing important features such as the presence of loops, base stacking interactions as well as canonical and noncanonical base pairing. In this work and others, standard force fields lead to reproducible unfolding of the NMR-based structures. Including a targeted CH···O adjustment in an otherwise identical protocol dramatically improves the outcome, leading to stable simulations for all RNA systems tested.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Structure Sensitive Reaction Kinetics of Chiral Molecules on Intrinsically Chiral Surfaces

Enantiospecific heterogeneous catalysis utilizes chiral surfaces to resolve enantiomers via structure sensitive surface chemistry. The catalyst design challenge is the identification of chiral surface structures that maximize enantiospecificity. Herein, we develop data driven models for the enantiospecificity of tartaric acid reactions on chiral Cu(hkl) R&S surfaces. Measurements of enantiospecific rate constants were obtained by using curved Cu(hkl) R&S surfaces that enable kinetic measurements on hundreds of chiral surface orientations. One model uses feature vectors derived from generalized coordination numbers to capture the local structure around Cu atoms exposed by the Cu(hkl) R&S surfaces. The second model introduces the use of chiral cubic harmonic functions to capture the symmetry constraints of the face-centered cubic Cu structure. The model using 58 generalized coordination numbers has a fitting error similar to that of the model using only 5 cubic harmonic functions. The two models predict maxima in the enantiospecificity on surfaces with very similar surface orientations. The models developed in this work are applicable for any enantiospecific reaction happening on any chiral material with a cubic lattice structure, opening the way to understanding the surface structure sensitivity of the enantiospecific reaction kinetics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Ring Size Effects on the Structures of Sandwich Compounds with a Stoichiometry of C 12 H 12 M (M = Ti–Ni)

Ring size effects on geometries and electronic structures were investigated for the (C n H n )M(C m H m ) (n = 4, 5, or 6; m = 8, 7, or 6; m + n = 12; M = Ti–Ni) systems using density functional theory. The lowest-energy C 12 H 12 M structures for the early transition metals titanium, vanadium, and chromium are the experimentally known singlet (η 5 -C 5 H 5 )Ti(η 7 -C 7 H 7 ), doublet (η 5 -C 5 H 5 )V(η 7 -C 7 H 7 ), and singlet (η 6 -C 6 H 6 ) 2 Cr, respectively. The likewise experimentally known singlet (η 6 -C 6 H 6 ) 2 Ti, doublet (η 6 -C 6 H 6 ) 2 V, and singlet (η 5 -C 5 H 5 )Cr(η 7 -C 7 H 7 ) are the secondlowest- energy structures with only a small energy difference between the two vanadium structures. For the later transition metals, dibenzenemetal complexes are the lowest-energy C 12 H 12 M species with two fully bonded hexahapto benzene rings in the lowest-energy manganese and iron derivatives and one hexahapto and one dihapto benzene ring in the lowest-energy cobalt and nickel derivatives. The lowest-energy (C 5 H 5 )M(C 7 H 7 ) structures for the later transition metals iron, cobalt, and nickel have partially bonded nonplanar C 7 H 7 rings with one or two uncomplexed C=C bonds. The (C 4 H 4 )M(C 8 H 8 ) (M = Ti–Ni) structures with the metal sandwiched between four- and eight-membered rings were found to be much higher in energy than their (C 5 H 5 )M(C 7 H 7 ) and (C 6 H 6 ) 2 M isomers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Active Palladium Structures on Ceria Obtained by Tuning Pd–Pd Distance for Efficient Methane Combustion

Efficiently removing/converting methane via methane combustion imposes challenges on catalyst design: how to design local structures of a catalytic site so that it has both high intrinsic activity and atomic efficiency? By manipulating the atomic distance of isolated Pd atoms, herein we show that the intrinsic activity of Pd catalysts can be significantly improved for methane combustion via a stable Pd 2 structure on a ceria nanorod support. Guided by theory and confirmed by experiment, we find that the turnover frequency (TOF) of the Pd 2 structure with the Pd–Pd distance of 2.99 Å is higher than that of the Pd 2 structure with the Pd–Pd distance of 2.75 Å; at least 26 times that of ceria supported Pd single atoms and 4 times that of ceria supported PdO nanoparticles. The high intrinsic activity of the 2.99 Å Pd–Pd structure is attributed to the conductive local redox environment from the two O atoms bridging the two Pd 2+ ions, which facilitates both methane adsorption and activation as well as the production of water and carbon dioxide during the methane oxidation process. In conclusion, this work highlights the sensitivity of catalytic behavior on the local structure of active sites and the fine-tuning of the metal–metal distance enabled by a support local environment for guiding the design of efficient catalysts for reactions that highly rely on Pt-group metals.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Nanometer Resolution Structure‐Emission Correlation of Individual Quantum Emitters via Enhanced Cathodoluminescence in Twisted Hexagonal Boron Nitride

Understanding the atomic structure of quantum emitters, often originating from point defects or impuritie, is essential for designing and optimizing materials for quantum technologies such as quantum computing, communication, and sensing. Despite the availability of atomic-resolution scanning transmission electron microscopy and nanoscale cathodoluminescence microscopy, experimentally determining the atomic structure of individual emitters is challenging due to the conflicting needs for thick samples to generate strong cathodoluminescence signals and thin samples for structural analysis. To overcome this challenge, significantly enhanced cathodoluminescence at twisted interfaces is leveraged to achieve sub-nanometer localization precision for the first time in mapping individual quantum emitters in carbon-implanted hexagonal boron nitride. This unprecedent spatial sensitivity, together with correlative electron energy loss spectroscopy quantitative scanning transmission electron microscopy imaging, and first principles density functional theory calculations, enables the identification of the atomic structure of the 440 nm blue emitter in hexagonal boron nitride as a substituted vertical carbon dimer. Building on the atomic structure insights, nanoscale spatially precise creation of blue emitters is demonstrated by electron beam irradiation of carbon-coated hexagonal boron nitride. This advancement in correlating atomic structures with optical properties lays the foundation for a deeper understanding and precise engineering of quantum emitters, significantly advancing the development of cutting-edge quantum information technologies.

2D material↗
DOE OSTI2024

Local lattice distortions and the structural instabilities in bcc Nb–Ta–Ti–Hf high-entropy alloys: An ab initio computational study

Local lattice distortions (LLD) and structural stability of body-centered cubic (bcc) Nb–Ta–Ti–Hf high-entropy alloys (HEAs) are studied as functions of composition employing ab initio density-functional theory calculations, with specific focus on the role of the relative concentrations of group IV (Ti and Hf) versus group V (Nb and Ta) elements. Calculated results are presented as a function of composition x in Nb x Ta 0.25 Ti (0.75-x)/2 Hf (0.75-x)/2 alloys, for elastic moduli, phonon spectral functions, LLD and structural energy differences for the bcc and competing hexagonal close-packed (hcp) and ω phases. The results highlight the important role of group V elements and LLD in stabilizing the bcc structure. They further reveal how composition x can be tuned to alter both the magnitude of the LLD and structural energy differences. Specifically, the magnitude of the structural energy differences, and elastic and dynamic stability of the bcc phase, are enhanced with increasing x, while the LLD increase in magnitude as this concentration is decreased. The results also show evidence of correlated LLD at lower values of x, reflecting local structural distortions towards the ω phase, but not hcp. The degree of ω-collapse is nevertheless partial i.e., transformation towards this phase is not observed to be complete due to the presence of Ta and Nb. At lower values of x we further find an energy landscape characterized by multiple, nearly degenerate local energy minima for different values of the LLD.

36 MATERIALS SCIENCE↗