Equivariant analytical mapping of first principles Hamiltonians to accurate and transferable materials models

Zhang, Liwei; Onat, Berk; Dusson, Genviève; Anand, G.; Maurer, Reinhard J.; Ortner, Christoph; Kermode, James R.

doi:10.48550/arxiv.2111.13736

Cited by 5 publications

(5 citation statements)

References 40 publications

(63 reference statements)

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“…For atomistic molecular dynamics simulations, ML has become a key tool to facilitate dynamics of large systems or dynamics over long time-scales. 89,90 More recently, ML models of excited-state properties and whole Hamiltonians have become available [91][92][93] There has been substantial recent progress in machine learning with Julia. [94][95][96] For example the ACE.jl package 97,98 provides for the parametrization of interatomic potentials based on the Atomic Cluster Expansion.…”

Section: B Performing Dynamicsmentioning

confidence: 99%

NQCDynamics.jl: A Julia package for nonadiabatic quantum classical molecular dynamics in the condensed phase

Gardner

Douglas-Gallardo

Stark

et al. 2022

The Journal of Chemical Physics

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Accurate and efficient methods to simulate nonadiabatic and quantum nuclear effects in high-dimensional and dissipative systems are crucial for the prediction of chemical dynamics in condensed phase. To facilitate effective development, code sharing and uptake of newly developed dynamics methods, it is important that software implementations can be easily accessed and built upon.Using the Julia programming language, we have developed the \pkgname ~ package which provides a framework for established and emerging methods for performing semiclassical and mixed quantum-classical dynamics in condensed phase. The code provides several interfaces to existing atomistic simulation frameworks, electronic structure codes, and machine learning representations. In addition to the existing methods, the package provides infrastructure for developing and deploying new dynamics methods which we hope will benefit reproducibility and code sharing in the field of condensed phase quantum dynamics. Herein, we present our code design choices and the specific Julia programming features from which they benefit.We further demonstrate the capabilities of the package on two examples of chemical dynamics in condensed phase: the population dynamics of the spin-boson model as described by a wide variety of semi-classical and mixed quantum-classical nonadiabatic methods and the reactive scattering of H2 on Ag(111) using the Molecular Dynamics with Electronic Friction method. Together, they exemplify the broad scope of the package to study effective model Hamiltonians and realistic atomistic systems.

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Section: B Performing Dynamicsmentioning

confidence: 99%

NQCDynamics.jl: A Julia package for nonadiabatic quantum classical molecular dynamics in the condensed phase

Gardner

Douglas-Gallardo

Stark

et al. 2022

The Journal of Chemical Physics

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“…Starting from ab initio density functional theory calculations for a material, one can manually construct an effective Hamiltonian with maximally localized Wannier functions [48] (though this is significantly more computationally intensive than the present approach). Other methods attempting to construct a tight binding model database [49] or generate tight binding models from ab initio calculations can also be considered [50][51][52][53]. Finally, we propose that this general framework of high-throughput tight-binding and graph isomorphism analysis can be applied to a broader range of materials searches, for example, in searching for systems with symmetry protected band nodes, nodal points, or massless dispersions.…”

Section: Discussionmentioning

confidence: 99%

Crystal Net Catalog of Model Flat Band Materials

Neves¹,

P.²,

Fang³

et al. 2023

Preprint

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Flat band systems are currently under intense investigation in quantum materials, optical lattices, and metamaterials. These efforts are motivated by potential realization of strongly correlated phenomena enabled by frustration-induced flat band dispersions; identification of candidate platforms plays an important role in these efforts. Here, we develop a highthroughput materials search for bulk crystalline flat bands by automated construction of uniform-hopping near-neighbor tight binding models. We show that this approach captures many of the essential features relevant to identifying flat band lattice motifs in candidate materials in a computationally inexpensive manner. We apply this algorithm to 139,367 materials in the Materials Project database and identify 63,076 materials that host at least one flat band elemental sublattice. We further categorize these candidate systems into at least 31,635 unique flat band crystal nets and identify candidates of interest from both lattice and band structure perspectives. This work expands the number of known flat band lattices that exist in physically realizable crystal structures and classifies the majority of these systems by the underlying lattice, providing new insights for familiar (e.g. kagome, pyrochlore, Lieb, and dice) as well as previously unknown motifs.

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“…The construction of Eq. ( 13) is readily generalized if equivariant features are required [35,37,44]. If the action of a rotation Q on a feature h is represented by a matrix D(Q), then we can write the equivariance constraint as…”

Section: Symmetrization Of Basis Functionsmentioning

confidence: 99%

The Design Space of E(3)-Equivariant Atom-Centered Interatomic Potentials

Batatia¹,

Batzner²,

Kovács³

et al. 2022

Preprint

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The rapid progress of machine learning interatomic potentials over the past couple of years produced a number of new architectures. Particularly notable among these are the Atomic Cluster Expansion (ACE), which unified many of the earlier ideas around atom density-based descriptors, and Neural Equivariant Interatomic Potentials (NequIP), a message passing neural network with equivariant features that showed state of the art accuracy. In this work, we construct a mathematical framework that unifies these models: ACE is generalised so that it can be recast as one layer of a multi-layer architecture. From another point of view, the linearised version of NequIP is understood as a particular sparsification of a much larger polynomial model. Our framework also provides a practical tool for systematically probing different choices in the unified design space. We demonstrate this by an ablation study of NequIP via a set of experiments looking at in-and out-of-domain accuracy and smooth extrapolation very far from the training data, and shed some light on which design choices are critical for achieving high accuracy. Finally, we present BOTNet (Body-Ordered-Tensor-Network), a much-simplified version of NequIP, which has an interpretable architecture and maintains accuracy on benchmark datasets.

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Equivariant analytical mapping of first principles Hamiltonians to accurate and transferable materials models

Cited by 5 publications

References 40 publications

NQCDynamics.jl: A Julia package for nonadiabatic quantum classical molecular dynamics in the condensed phase

NQCDynamics.jl: A Julia package for nonadiabatic quantum classical molecular dynamics in the condensed phase

Crystal Net Catalog of Model Flat Band Materials

The Design Space of E(3)-Equivariant Atom-Centered Interatomic Potentials

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