Cluster expansions of multicomponent ionic materials: Formalism and methodology

Barroso-Luque, Luis; Zhong, Peichen; Yang, Julia H.; Xie, Fengyu; Chen, Tina; Ouyang, Bin; Ceder, Gerbrand

doi:10.1103/physrevb.106.144202

Cited by 26 publications

(40 citation statements)

References 92 publications

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“…Furthermore, the accurate representation and encoding of the full charge density is another demanding task requiring substantial computational resources [28,29]. An established approach is to rely on the magnetic moment for a given atom site as an indicator of its atomic charge, which can be derived from the difference in localized upspin and down-spin electron densities in spin-polarized DFT calculations [8,30]. Compared with the direct use of charge density, magmoms are found to contain more comprehensive information regarding the electron orbital occupancy and therefore the chemical behavior of ions, as demonstrated in previous studies.…”

Section: Charge-constraints and Charge-inference From Magnetic Momentsmentioning

confidence: 99%

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CHGNet: Pretrained universal neural network potential for charge-informed atomistic modeling

Deng¹,

Zhong²,

Jun³

et al. 2023

Preprint

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The simulation of large-scale systems with complex electron interactions remains one of the greatest challenges for the atomistic modeling of materials. Although classical force-fields often fail to describe the coupling between electronic states and ionic rearrangements, the more accurate ab-initio molecular dynamics suffers from computational complexity that prevents long-time and large-scale simulations, which are essential to study many technologically relevant phenomena, such as reactions, ion migrations, phase transformations, and degradation.In this work, we present the Crystal Hamiltonian Graph neural Network (CHGNet) as a novel machine-learning interatomic potential (MLIP), using a graph-neural-network-based force-field to model a universal potential energy surface. CHGNet is pretrained on the energies, forces, stresses, and magnetic moments from the Materials Project Trajectory Dataset, which consists of over 10 years of density functional theory static and relaxation trajectories of ∼ 1.5 million inorganic structures. The explicit inclusion of magnetic moments enables CHGNet to learn and accurately represent the orbital occupancy of electrons, enhancing its capability to describe both atomic and electronic degrees of freedom. We demonstrate several applications of CHGNet in solid-state materials, including charge-informed molecular dynamics in LixMnO2, the finite temperature phase diagram for LixFePO4 and Li diffusion in garnet conductors. We critically analyze the significance of including charge information for capturing appropriate chemistry, and we provide new insights into ionic systems with additional electronic degrees of freedom that can not be observed by previous MLIPs.

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Section: Charge-constraints and Charge-inference From Magnetic Momentsmentioning

confidence: 99%

“…In addition, the non-charge-decorated CE is defined only on Li + /vacancy sites. In the charge-decorated CE, Fe 2+ /Fe 3+ is classified with magmom in [3µ B , 4µ B ] and [4µ B , 5µ B ], respectively [30].…”

Section: F Phase Diagram Calculationsmentioning

confidence: 99%

CHGNet: Pretrained universal neural network potential for charge-informed atomistic modeling

Deng¹,

Zhong²,

Jun³

et al. 2023

Preprint

View full text Add to dashboard Cite

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“…The cluster expansion fits were done using a mixedinteger quadratic problem (MIQP) formulation of a grouped 0 pseudo-norm and 2 norm regularization to obtain hierarchically constrained structured sparsity between cluster interactions [11,48]. This regularization ensures that strong hierarchy constraints are respected in the resulting expansions [49,51,52].…”

Section: Uniqueness Of the Cluster Decompositionmentioning

confidence: 99%

“…Parameterized lattice models are actively used in materials science to study metallic alloys [1-3], semi-conductors [4,5], super-ionic conductors [6,7], battery electrodes [8], and surface catalysis [9]. The cluster expansion (CE) method constitutes a mathematical formalism for the representation and parameterization of generalized lattice models [10][11][12]. The CE method coupled with Monte Carlo (MC) sampling has become an established technique to compute thermodynamic properties of multi-component crystals [13,14].…”

mentioning

confidence: 99%

“…The use of Tikhonov regularization can be used as a way to more finely set variance cutoffs for specific cluster interaction terms. Recently proposed groupwise regularization [11], can be directly motivated as a judicious form to regularize cluster interactions H B by weighing coefficients with their permutation multiplicities m β . Finally, estimation algorithms with hierarchical inclusion/exclusion of clusters [11,13,[46][47][48], can be motivated by appealing to statistical concepts of hierarchically well-formulated models [49] that satisfy marginality constraints [50], or that abide by heredity principles which satisfy either strong or weak hierarchy constraints [51,52].…”

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confidence: 99%

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The cluster decomposition of the configurational energy of multicomponent alloys

Barroso-Luque¹,

Ceder²

2023

Preprint

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Lattice models parameterized using first-principles calculations constitute an effective framework to simulate the thermodynamic behavior of physical systems. The cluster expansion method is a flexible lattice-based method used extensively in the study of multicomponent alloys. Yet despite its prevalent use, a well-defined understanding of expansion terms has remained elusive. In this letter, we introduce the cluster decomposition as a unique and basis-agnostic decomposition of any general function of the atomic configuration in a crystal. We demonstrate that cluster expansions constructed from arbitrary orthonormal basis sets are all representations of the same cluster decomposition. We show how the norms of expansion coefficients associated with the same crystallographic orbit are invariant to changes between orthonormal bases. Based on its uniqueness and orthogonality properties, we identify the cluster decomposition as an invariant ANOVA decomposition. We leverage these results to illustrate how functional analysis of variance and sensitivity analysis can be used to directly interpret interactions among species and gain insight into computed thermodynamic properties. The work we present in this letter opens new directions for parameter estimation, interpretation, and use of applied lattice models on well-established mathematical and statistical grounds.

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Thermodynamic Stability Prediction of Triple Transition‐Metal (Ti−Mo−V)3C2${\rm (Ti-Mo-V)}_3{\rm C}_2$ MXenes via Cluster Correlation‐Based Machine Learning

Atthapak,

Ektarawong,

Pakornchote

et al. 2024

Advcd Theory and Sims

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The representation of atomic configurations through cluster correlations, along with the cluster expansion approach, has long been used to predict formation energies and determine the thermodynamic stability of alloys. In this work, a comparison is conducted between the traditional cluster expansion method based on density functional theory and other potential machine learning models, including decision tree‐based ensembles and multi‐layer perceptron regression, to explore the alloying behavior of different elements in multi‐component alloys. Specifically, these models are applied to investigate the thermodynamic stability of triple transition‐metal MXenes, a multi‐component alloy in the largest family of 2D materials that are gaining attention for several outstanding properties. The findings reveal the triple transition‐metal ground‐state configurations in this system and demonstrate how the configuration of transition metal atoms (Ti, Mo, and V atoms) influences the formation energy of this alloy. Moreover, the performance of machine learning algorithms in predicting formation energies and identifying ground‐state structures is thoroughly discussed from various aspects.

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Cluster expansions of multicomponent ionic materials: Formalism and methodology

Cited by 26 publications

References 92 publications

CHGNet: Pretrained universal neural network potential for charge-informed atomistic modeling

CHGNet: Pretrained universal neural network potential for charge-informed atomistic modeling

The cluster decomposition of the configurational energy of multicomponent alloys

Thermodynamic Stability Prediction of Triple Transition‐Metal (Ti−Mo−V)3C2${\rm (Ti-Mo-V)}_3{\rm C}_2$ MXenes via Cluster Correlation‐Based Machine Learning

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