Cluster Expansion Research Articles

Deciphering the actin structure-dependent preferential cooperative binding of cofilin.

The mechanism underlying the preferential and cooperative binding of cofilin and the expansion of clusters toward the pointed-end side of actin filaments remains poorly understood. To address this, we conducted a principal component analysis based on available filamentous actin (F-actin) and C-actin (cofilins were excluded from cofilactin) structures and compared to monomeric G-actin. The results strongly suggest that C-actin, rather than F-ADP-actin, represented the favourable structure for binding preference of cofilin. High-speed atomic force microscopy explored that the shortened bare half helix adjacent to the cofilin clusters on the pointed end side included fewer actin protomers than normal helices. The mean axial distance (MAD) between two adjacent actin protomers along the same long-pitch strand within shortened bare half helices was longer (5.0-6.3 nm) than the MAD within typical helices (4.3-5.6 nm). The inhibition of torsional motion during helical twisting, achieved through stronger attachment to the lipid membrane, led to more pronounced inhibition of cofilin binding and cluster formation than the presence of inorganic phosphate (Pi) in solution. F-ADP-actin exhibited more naturally supertwisted half helices than F-ADP.Pi-actin, explaining how Pi inhibits cofilin binding to F-actin with variable helical twists. We propose that protomers within the shorter bare helical twists, either influenced by thermal fluctuation or induced allosterically by cofilin clusters, exhibit characteristics of C-actin-like structures with an elongated MAD, leading to preferential and cooperative binding of cofilin.

Hierarchical binary black hole mergers in globular clusters: Mass function and evolution with redshift

Hierarchical black hole (BH) mergers are one of the most straightforward mechanisms producing BHs inside and above the pair-instability mass gap. We investigated the impact of globular cluster (GC) evolution on hierarchical mergers, accounting for the uncertainties related to BH mass pairing functions on the predicted primary BH mass, mass ratio, and spin distribution. We find that the evolution of the host GC quenches the hierarchical BH assembly at the third generation, mainly due to cluster expansion powered by a central BH subsystem. Hierarchical mergers match the primary BH mass distribution from GW events for m1 > 50 M⊙ regardless of the assumed BH pairing function. At lower masses, however, different pairing functions lead to dramatically different predictions on the primary BH mass merger-rate density. We find that the primary BH mass distribution evolves with redshift, with a larger contribution from mergers with m1 ≥ 30 M⊙ for z ≥ 2. Finally, we calculate the mixing fraction of binary black holes (BBHs) from GCs and isolated binary systems. Our predictions are very sensitive to the spins, which favor a large fraction (> 0.6) of BBHs born in GCs in order to reproduce misaligned spin observations.

Application of molecular epidemiology in revealing HIV-1 transmission network and recombination patterns in Tianjin, China.

Using a comprehensive molecular epidemiological approach, we characterized the transmission dynamics of HIV-1 among the MSM population in Tianjin, China. Our findings revealed that 38.56% (386/1001) of individuals clustered across 109 molecular transmission clusters (TCs), with MSM aged 50 and below being the group most commonly transmitting HIV-1. Among the identified TCs, CRF01_AE predominated, followed by CRF07_BC. Notably, CRF07_BC demonstrated a higher propensity for forming large clusters compared to CRF01_AE. Birth-death skyline analyses of the two largest clusters indicated that the HIV/AIDS transmission may be at a critical point, nearly all had Re approximately 1 by now. A retrospective analysis revealed that the rapid expansion of these large clusters was primarily driven by the introduction of viruses in 2021, highlighting the crucial importance of continuous molecular surveillance in identifying newly emerging high-risk transmission chains and adapting measures to address evolving epidemic dynamics. Furthermore, we detected the transmission of drug-resistant mutations (DRMs) within the TCs, particularly in the CRF07_BC clusters (K103N, Y181C, and K101E) and CRF01_AE clusters (P225H and K219R), emphasizing the importance of monitoring to support the continued efficacy of first-line therapies and pre-exposure prophylaxis (PrEP). Recombination analyses indicated that complex recombinant patterns, associated with increased amino acid variability, could confer adaptive traits to the viruses, potentially providing a competitive advantage in certain host populations or regions. Our study highlights the potential of integrating molecular epidemiological and phylodynamic approaches to inform targeted interventions.

Correlated Anion Disorder in Heteroanionic Cubic TiOF2.

Resolving anion configurations in heteroanionic materials is crucial for understanding and controlling their properties. For anion-disordered oxyfluorides, conventional Bragg diffraction cannot fully resolve the anionic structure, necessitating alternative structure determination methods. We have investigated the anionic structure of anion-disordered cubic (ReO3-type) TiOF2 using X-ray pair distribution function (PDF), 19F MAS NMR analysis, density functional theory (DFT), cluster expansion modeling, and genetic-algorithm structure prediction. Our computational data predict short-range anion ordering in TiOF2, characterized by predominant cis-[O2F4] titanium coordination, resulting in correlated anion disorder at longer ranges. To validate our predictions, we generated partially disordered supercells using genetic-algorithm structure prediction and computed simulated X-ray PDF data and 19F MAS NMR spectra, which we compared directly to experimental data. To construct our simulated 19F NMR spectra, we derived new transformation functions for mapping calculated magnetic shieldings to predicted magnetic chemical shifts in titanium (oxy)fluorides, obtained by fitting DFT-calculated magnetic shieldings to previously published experimental chemical shift data for TiF4. We find good agreement between our simulated and experimental data, which supports our computationally predicted structural model and demonstrates the effectiveness of complementary experimental and computational techniques in resolving anionic structure in anion-disordered oxyfluorides. From additional DFT calculations, we predict that increasing anion disorder makes lithium intercalation more favorable by, on average, up to 2 eV, highlighting the significant effect of variations in short-range order on the intercalation properties of anion-disordered materials.

Density-based clustering with differential privacy

In recent years, differentially private clustering has received increasing attention. However, most existing differentially private clustering algorithms cannot achieve better results when handling non-convex datasets. To enhance knowledge extraction from data while protecting users' sensitive information, we propose a density-based clustering algorithm with differential privacy. Specifically, we incorporate differential privacy mechanisms into the density-based clustering paradigm to enhance the effectiveness of differentially private clustering on non-convex datasets. Firstly, to avoid privacy leakage, we employ the Laplace mechanism for inject noise into the density during the density estimation stage. Then, we design a privacy budget allocation scheme in the cluster expansion stage to make it harder for attackers to access private information. Theoretical analysis demonstrates that our algorithm satisfies ϵ-differential privacy. Experimental outcomes in synthetic and real-world datasets show that our introduced algorithm can obtain high-quality clustering results when dealing with non-convex datasets. In the approximation experiments, it is evident that our algorithm outperforms others in terms of approximation.

Machine Learning Force Field-Aided Cluster Expansion Approach to Phase Diagram of Alloyed Materials.

First-principles approaches based on density functional theory (DFT) have played important roles in the theoretical study of multicomponent alloyed materials. Considering the highly demanding computational cost of direct DFT-based sampling of the configurational space, it is crucial to build efficient and low-cost surrogate Hamiltonian models with DFT accuracy for efficient simulation of alloyed systems with configurational disorder. Recently, the machine learning force field (MLFF) method has been proposed to tackle complicated multicomponent disordered systems. However, the importance of integrating significant physical considerations, including, in particular, convex hull preservation, which is the prerequisite for the accurate prediction of phase diagrams, into the training process of the MLFF remains rarely addressed. In this work, a workflow is proposed to train a convex-hull-preserved (CHP) MLFF for binary alloy systems, based on which the order-disorder phase boundary is predicted by using the Wang-Landau Monte Carlo (WLMC) technique. The predicted values for order-disorder phase transition temperatures agree well with the experiment. The CHP-MLFF is further used to build CE models with the same accuracy as the MLFF and higher efficiency in sampling configurational space. Using the results obtained from the MLFF-based WLMC simulation as a reference, the performances of different schemes for constructing CE models were evaluated in a transparent manner, which revealed the close correlation between the prediction accuracy of ground-state configurations and that of the order-disorder phase transition temperature. This work clearly indicates the great importance of reproducing the convex hull and energetics of ground-state configurations when constructing surrogate Hamiltonians for the statistical modeling of alloyed systems.

Tuning chemical short-range order for stainless behavior at reduced chromium concentrations in multi-principal element alloys

Single-phase multi-principal element alloys hold promise for improved mechanical properties as a result of multiple operative deformation modes. However, the use of many of these alloys in structural applications is limited as a consequence of their poor aqueous corrosion resistance. Here we introduce a new approach for significantly improving the passivation behavior of alloys by tuning the chemical short-range order parameter. We show that the addition of only 0.03 to 0.06 mole fraction of Al to a (FeCoNi)0.9Cr0.1 alloy changed both the magnitude and sign of the Cr-Cr order parameter resulting in passivation behavior similar to 304L stainless steel containing twice the amount of Cr. Our analysis is based on comparing electrochemical measures of the kinetics of passive film formation with chemical short-range order characterizations using time-of-flight neutron scattering, cluster expansion methods, density functional theory and Monte Carlo techniques. Our findings are interpreted within the framework of a recently proposed percolation theory of passivation that examines how selective dissolution of the non-passivating alloy components and short-range order results in excellent passive films at reduced levels of the passivating component.

Cartesian atomic cluster expansion for machine learning interatomic potentials

Machine learning interatomic potentials are revolutionizing large-scale, accurate atomistic modeling in material science and chemistry. Many potentials use atomic cluster expansion or equivariant message-passing frameworks. Such frameworks typically use spherical harmonics as angular basis functions, followed by Clebsch-Gordan contraction to maintain rotational symmetry. We propose a mathematically equivalent and simple alternative that performs all operations in the Cartesian coordinates. This approach provides a complete set of polynormially independent features of atomic environments while maintaining interaction body orders. Additionally, we integrate low-dimensional embeddings of various chemical elements, trainable radial channel coupling, and inter-atomic message passing. The resulting potential, named Cartesian Atomic Cluster Expansion (CACE), exhibits good accuracy, stability, and generalizability. We validate its performance in diverse systems, including bulk water, small molecules, and 25-element high-entropy alloys.

Benchmarking of machine learning interatomic potentials for reactive hydrogen dynamics at metal surfaces

Simulations of chemical reaction probabilities in gas surface dynamics require the calculation of ensemble averages over many tens of thousands of reaction events to predict dynamical observables that can be compared to experiments. At the same time, the energy landscapes need to be accurately mapped, as small errors in barriers can lead to large deviations in reaction probabilities. This brings a particularly interesting challenge for machine learning interatomic potentials, which are becoming well-established tools to accelerate molecular dynamics simulations. We compare state-of-the-art machine learning interatomic potentials with a particular focus on their inference performance on CPUs and suitability for high throughput simulation of reactive chemistry at surfaces. The considered models include polarizable atom interaction neural networks (PaiNN), recursively embedded atom neural networks (REANN), the MACE equivariant graph neural network, and atomic cluster expansion potentials (ACE). The models are applied to a dataset on reactive molecular hydrogen scattering on low-index surface facets of copper. All models are assessed for their accuracy, time-to-solution, and ability to simulate reactive sticking probabilities as a function of the rovibrational initial state and kinetic incidence energy of the molecule. REANN and MACE models provide the best balance between accuracy and time-to-solution and can be considered the current state-of-the-art in gas-surface dynamics. PaiNN models require many features for the best accuracy, which causes significant losses in computational efficiency. ACE models provide the fastest time-to-solution, however, models trained on the existing dataset were not able to achieve sufficiently accurate predictions in all cases.

Atomic cluster expansion without self-interaction

The Atomic Cluster Expansion (ACE) (Drautz (2019) [14]) has been widely applied in high energy physics, quantum mechanics and atomistic modeling to construct many-body interaction models respecting physical symmetries. Computational efficiency is achieved by allowing non-physical self-interaction terms in the model. We propose and analyze an efficient method to evaluate and parameterize an orthogonal, or, non-self-interacting cluster expansion model. We present numerical experiments demonstrating improved conditioning and more robust approximation properties than the original expansion in regression tasks both in simplified toy problems and in applications in the machine learning of interatomic potentials.

Gold-Thiolate Nanocluster Dynamics and Intercluster Reactions Enabled by a Machine Learned Interatomic Potential.

Monolayer protected metal clusters comprise a rich class of molecular systems and are promising candidate materials for a variety of applications. While a growing number of protected nanoclusters have been synthesized and characterized in crystalline forms, their dynamical behavior in solution, including prenucleation cluster formation, is not well understood due to limitations both in characterization and first-principles modeling techniques. Recent advancements in machine-learned interatomic potentials are rapidly enabling the study of complex interactions such as dynamical behavior and reactivity on the nanoscale. Here, we develop an Au-S-C-H atomic cluster expansion (ACE) interatomic potential for efficient and accurate molecular dynamics simulations of thiolate-protected gold nanoclusters (Aun(SCH3)m). Trained on more than 30,000 density functional theory calculations of gold nanoclusters, the interatomic potential exhibits ab initio level accuracy in energies and forces and replicates nanocluster dynamics including thermal vibration and chiral inversion. Long dynamics simulations (up to 0.1 μs time scale) reveal a mechanism explaining the thermal instability of neutral Au25(SR)18 clusters. Specifically, we observe multiple stages of isomerization of the Au25(SR)18 cluster, including a chiral isomer. Additionally, we simulate coalescence of two Au25(SR)18 clusters and observe series of clusters where the formation mechanisms are critically mediated by ligand exchange in the form of [Au-S]n rings.

Almost Optimal Upper Bound for the Ground State Energy of a Dilute Fermi Gas via Cluster Expansion

AbstractWe prove an upper bound on the energy density of the dilute spin-$$\frac{1}{2}$$ 1 2 Fermi gas capturing the leading correction to the kinetic energy $$8\pi a \rho _\uparrow \rho _\downarrow $$ 8 π a ρ ↑ ρ ↓ with an error of size smaller than $$a\rho ^{2}(a^3\rho )^{1/3-\varepsilon }$$ a ρ 2 ( a 3 ρ ) 1 / 3 - ε for any $$\varepsilon > 0$$ ε > 0 , where a denotes the scattering length of the interaction. The result is valid for a large class of interactions including interactions with a hard core. A central ingredient in the proof is a rigorous version of a fermionic cluster expansion adapted from the formal expansion of Gaudin et al. (Nucl Phys A 176(2):237–260, 1971. https://doi.org/10.1016/0375-9474(71)90267-3).

Deciphering chemical ordering in High Entropy Materials: A machine learning-accelerated high-throughput cluster expansion approach

The Cluster Expansion (CE) Method encounters significant computational challenges in multicomponent systems due to the computational expense of generating training data through density functional theory (DFT) calculations. This work aims to refine the cluster and structure selection processes to mitigate these challenges. We introduce a novel method that significantly reduces the computational load associated with the calculation of fitting parameters. This method employs a Graph Neural Network (GNN) model, leveraging the M3GNet network, which is trained using a select subset of DFT calculations at each ionic step. The trained surrogate model excels in predicting the volume and energy of the final structure for a relaxation run. By employing this model, we sample thousands of structures and fit a CE model to the energies of these GNN-relaxed structures. This approach, utilizing a large training dataset, effectively reduces the risk of overfitting, yielding a CE model with a root-mean-square error (RMSE) below 10 meV/atom. We validate our method’s effectiveness in two test cases: the (Ti, Cr, Zr, Mo, Hf, Ta)B2 diboride system and the Refractory High-Entropy Alloy (HEA) AlTiZrNbHfTa system. Our findings demonstrate the significant advantages of integrating a GNN model, specifically the M3GNet network, with CE methods for the efficient predictive analysis of chemical ordering in High Entropy Materials. The accelerating capabilities of the hybrid ML-CE approach to investigate the evolution of Short Range Ordering (SRO) in a large number of stoichiometric systems. Finally, we show how it is possible to correlate the strength of chemical ordering to easily accessible alloy parameters.

Multiple semi-coherent particles strengthened ultra-fine-grained Al composites for neutron shielding materials

Neutron shielding materials face imbalanced behaviors among shielding, strength, and ductility properties. Based on the requirement of the high property shielding particles, a superior semi-coherent τ(Al4MgGd) phase was designed and predicted by cluster expansion (CE) method using density functional theory calculations. To realize its shielding property, the Powder Metallurgy-based routines (i.e., powder fabrication, spark plasma sintering, and hot extrusion techniques) are used to fabricate 6TiB2/Al-6Mg-5Gd (wt.%) composite with dispersed refined τ phases and homogenized TiB2 distribution. The atomic structure of ternary phase τ is examined by aberration-corrected high-angle annual dark-field (HAADF) scanning transmission electron microscope (STEM) and energy dispersive X-ray spectroscopy (EDXS) STEM experiments, which is well complied with the calculated compound (Al4MgGd). In detail, the τ(Al4MgGd) phase has a semi-coherent interface both with α-Al and TiB2, which is consistent with the prediction of interface relationships. With the optimized interfaces, the TiB2 and τ phases can effectively promote recrystallization and suppress grain growth, leading to the formation of ultra-fine grain structure. Then, the composite exhibits advanced shielding properties (Macroscopic transmission cross section ∼24.1 /cm, higher than 30 %B4C/Al) and optimized synergic mechanical properties (Ultimate tensile strength ∼506 MPa, elongation ∼12.9 %), which are far higher than available Al-based neutron shielding materials. Finally, the underlying strength-ductility mechanisms are discussed. Critically, the design and optimization of shielding particle interfaces are reliable strategies for developing novel structural-functional integrated materials.

First-principles prediction of the Co–Al phase diagram including configurational, vibrational and magnetic contributions

Co-based superalloys have attracted attention to replace Ni-based superalloys in high temperature structural applications because of their higher melting temperature and corrosion resistance. Strengthening is provided by Co3(Al, X) (X = W, Cr, Mo, Ni) phases and optimization of their properties requires detailed information about the free energies of the different phases and of the phase diagram of the Co–Al system. This is achieved in this paper through first principles calculations in combination with statistical mechanics. Configurational entropic contributions to the free energy were included through Monte Carlo simulations using the cluster expansion formalism. The vibrational entropy of each phase was determined through the length-stiffness relationship while the magnetic entropy was also included through the Heisenberg Hamiltonian. The computed phase diagram is compared with the currently accepted experimental phase diagram and the different contributions to the stability of each phase are analyzed independently. The potential of this strategy to predict phase diagrams of magnetic systems is clearly established.

Structure–property relations of silicon oxycarbides studied using a machine learning interatomic potential

AbstractSilicon oxycarbides show outstanding versatility due to their highly tunable composition and microstructure. Consequently, a key challenge is a thorough knowledge of structure–property relations in the system. In this work, we fit an atomic cluster expansion potential to a set of actively learned density‐functional theory training data spanning a wide configurational space. We demonstrate the ability of the potential to produce realistic amorphous structures and rationalize the formation of different morphologies of the turbostratic free carbon phase. Finally, we relate the materials stiffness to its composition and microstructure, finding a delicate dependence on Si‐C bonds that contradicts commonly assumed relations to the free carbon phase.

The Limited Incorporation and Role of Fluorine in Mn-rich Disordered Rocksalt Cathodes.

Disordered rocksalt oxide (DRX) cathodes are promising candidates for next-generation Co- and Ni-free Li-ion batteries. While fluorine substitution for oxygen has been explored as an avenue to enhance their performance, the amount of fluorine incorporated into the DRX structure is particularly challenging to quantify and impedes our ability to relate fluorination to electrochemical performance. Herein, an experimental-computational method combining 7Li and 19F solid-state nuclear magnetic resonance, and ab initio cluster expansion Monte Carlo simulations, is developed to determine the composition of DRX oxyfluorides. Using this method, the synthesis of Mn- and Ti-containing DRX via standard high temperature sintering and microwave heating is optimized. Further, the upper fluorination limit attainable using each of these two synthesis routes is established for various Mn-rich DRX compounds. A comparison of their electrochemical performance reveals that the capacity and capacity retention mostly depend on the Mn content, while fluorination plays a secondary role.

Distribution Tendencies of Noble Metals on Fe(100) Using Lattice Gas Cluster Expansions.

Fe-based catalysts are highly selective for the hydrodeoxygenation of biomass-derived oxygenates but are prone to oxidative deactivation. Promotion with a noble metal has been shown to improve oxidative resistance. The chemical properties of such bimetallic systems depend critically on the surface geometry and spatial configuration of surface atoms in addition to their coverage (i.e., noble metal loading), so these aspects must be taken into account in order to develop reliable models for such complex systems. This requires sampling a vast configurational space, which is rather impractical using density functional theory (DFT) calculations alone. Moreover, "DFT-based" models are limited to length scales that are often too small for experimental relevance. Here, we circumvent this challenge by constructing DFT-parametrized lattice gas cluster expansions (LG CEs), which can describe these types of systems at significantly larger length scales. Here, we apply this strategy to Fe(100) promoted with four technologically relevant precious metals: Pd, Pt, Rh, and Ru. The resultant LG CEs have remarkable predictive accuracy, with predictive errors below 10 meV/site over a coverage range of 0 to 2 monolayers. The ground state configurations for each noble metal were identified, and the analysis of the cluster energies reveals a significant disparity in their dispersion tendency.

First-principles and cluster expansion study of the effect of magnetism on short-range order in Fe–Ni–Cr austenitic stainless steels

Short-range order (SRO), the regular and predictable arrangement of atoms over short distances, alters the mechanical properties of technologically relevant structural materials such as medium/high entropy alloys and austenitic stainless steels. In this study, we present a generalized spin cluster expansion (CE) model and show that magnetism is a primary factor influencing the level of SRO present in austenitic Fe–Ni–Cr alloys. The spin CE consists of a chemical cluster expansion combined with an Ising model for Fe–Ni–Cr austenitic alloys. It explicitly accounts for local magnetic exchange interactions, thereby capturing the effects of finite temperature magnetism on SRO. Model parameters are obtained by fitting to a first-principles data set comprising both chemically and magnetically diverse face-centered cubic configurations. The magnitude of the magnetic exchange interactions are found to be comparable to the chemical interactions. Compared to a conventional implicit magnetism CE built from only magnetic ground state configurations, the spin CE shows improved performance on several experimental benchmarks over a broad spectrum of compositions, particularly at higher temperatures due to the explicit treatment of magnetic disorder. We find that SRO is strongly influenced by alloy Cr content, since Cr atoms prefer to align antiferromagnetically with nearest neighbors but become magnetically frustrated with increasing Cr concentration. Using the spin CE, we predict that increasing the Cr concentration in typical austenitic stainless steels promotes the formation of SRO and increases order–disorder transition temperatures. This study underscores the significance of considering magnetic interactions explicitly when exploring the thermodynamic properties of complex transition metal alloys. It also highlights guidelines for customizing SRO through adjustments of alloy composition.

Graph Atomic Cluster Expansion for Semilocal Interactions beyond Equivariant Message Passing

The atomic cluster expansion provides local, complete basis functions that enable efficient parametrization of many-atom interactions. We extend the atomic cluster expansion to incorporate graph basis functions. This naturally leads to representations that enable the efficient description of semilocal interactions in physically and chemically transparent form. Simplification of the graph expansion by tensor decomposition results in an iterative procedure that comprises current message-passing machine learning interatomic potentials. We demonstrate the accuracy and efficiency of the graph atomic cluster expansion for a number of small molecules, clusters, and a general-purpose model for carbon. We further show that the graph atomic cluster expansion scales linearly with the number of neighbors and layer depth of the graph basis functions. Published by the American Physical Society 2024