Crystal-Structure Analysis with Moments of the Density-of-States: Application to Intermetallic Topologically Close-Packed Phases

Hammerschmidt, Thomas; Ladines, Alvin Noe Collado; Koßmann, Jörg; Drautz, Ralf

doi:10.3390/cryst6020018

Cited by 14 publications

(11 citation statements)

References 58 publications

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“…90 Within the analytic BOP formalism, these properties can be computed efficiently in an approximate way 71,73 and used as per-atom features that discriminate and classify the local atomic environment. 74,91 For each atom j, the nth moment µ n (j) is computed by multiplying pairwise model Hamiltonians along selfreturning paths (i.e., start and end at the same atom) up to length n. The representation of local atomic environments uses scaled recursion coefficients a i (j) and b i (j) obtained from µ n (j) with scaled volumes v j as described in refs. 74,91 In this work, a total of 12 moments corresponding to the atomic environment up to the sixth nearest-neighbor shell were used.…”

Section: Atomic and Bond-order-potential Derived Featuresmentioning

confidence: 99%

“…74,91 For each atom j, the nth moment µ n (j) is computed by multiplying pairwise model Hamiltonians along selfreturning paths (i.e., start and end at the same atom) up to length n. The representation of local atomic environments uses scaled recursion coefficients a i (j) and b i (j) obtained from µ n (j) with scaled volumes v j as described in refs. 74,91 In this work, a total of 12 moments corresponding to the atomic environment up to the sixth nearest-neighbor shell were used. This procedure is to some degree comparable to the n-gram approach of the first-place solution with regard to sampling the environment.…”

Section: Atomic and Bond-order-potential Derived Featuresmentioning

confidence: 99%

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Crowd-sourcing materials-science challenges with the NOMAD 2018 Kaggle competition

Sutton

Ghiringhelli

Yamamoto³

et al. 2019

npj Comput Mater

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A public data-analytics competition was organized by the Novel Materials Discovery (NOMAD) Centre of Excellence and hosted by the online platform Kaggle by using a dataset of 3,000 (Al x Ga y In 1-x-y) 2 O 3 compounds. Its aim was to identify the best machinelearning (ML) model for the prediction of two key physical properties that are relevant for optoelectronic applications: the electronic bandgap energy and the crystalline formation energy. Here, we present a summary of the top-three ranked ML approaches. The first-place solution was based on a crystal-graph representation that is novel for the ML of properties of materials. The second-place model combined many candidate descriptors from a set of compositional, atomic-environment-based, and average structural properties with the light gradient-boosting machine regression model. The third-place model employed the smooth overlap of atomic position representation with a neural network. The Pearson correlation among the prediction errors of nine ML models (obtained by combining the top-three ranked representations with all three employed regression models) was examined by using the Pearson correlation to gain insight into whether the representation or the regression model determines the overall model performance. Ensembling relatively decorrelated models (based on the Pearson correlation) leads to an even higher prediction accuracy.

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Section: Atomic and Bond-order-potential Derived Featuresmentioning

confidence: 99%

Section: Atomic and Bond-order-potential Derived Featuresmentioning

confidence: 99%

Crowd-sourcing materials-science challenges with the NOMAD 2018 Kaggle competition

Sutton

Ghiringhelli

Yamamoto³

et al. 2019

npj Comput Mater

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show abstract

“…We show the different atomic environments of topologically close-packed (TCP) phases that are briefly introduced in App. C. The moments of the DOS have been applied to quantify the difference between TCP phases and to identify trends of the local moments with coordination number 27,36,37 . The 12-fold coordinated atoms in the TCP phases are close to the fcc and hcp structures in the map.…”

Section: B Crystal Structures With Multiple Inequivalent Lattice Sitesmentioning

confidence: 99%

“…The formal relation between the moments of the DOS and the local crystal structure was introduced explicitly with the moments theorem 16 . The moments theorem enables the computation of the moments of the local DOS without the computationally expensive calculation of the eigenspectrum and is used for linear scaling expansions of the band energy [17][18][19][20][21][22][23][24][25][26] and more recently also to define difference vectors between pairs of crystal structures 27 .…”

Section: Introductionmentioning

confidence: 99%

Electronic structure based descriptor for characterizing local atomic environments

et al. 2018

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A quantitative descriptor of local atomic environments is often required for the analysis of atomistic data. Descriptors of the local atomic environment ideally provide physically and chemically intuitive insight. This requires descriptors that are low-dimensional representations of the interplay between atomic geometry and electronic bond formation. The moments of the local density of states (DOS) relate the atomic structure to the electronic structure and bond chemistry. This makes it possible to construct electronic structure based descriptors of the local atomic environment that have an immediate relation to the binding energy. We show that a low-dimensional moments-descriptor is sufficient as the lowest moments, calculated from the closest atomic neighborhood, carry the largest contributions to the local bond energy. Here, we construct moments-descriptors that project the space of local atomic environments on a 2-D map. We discuss in detail the separation of various atomic environments and their connections in the map. The distances in the map may be related to energy differences between local atomic environments as we show by analytic considerations based on analytic bond-order potentials (BOP) and by numerical assessment using TB and density-functional theory calculations. Possible applications of the proposed moments-descriptors include the classification of local atomic environments in molecular-dynamic simulations, the selection of structure sets for developing and testing interatomic potentials, as well as the construction of descriptors for machine-learning applications.

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“…Here we describe our implementation of analytic BOPs in the software package BOPfox 10 . BOPfox has already been used in several publications 8,[11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] and is being continuously extended and optimised. We point out similarities of TB/BOP calculations and computations carried out using other electronic structure methods, and discuss the peculiarities of analytic BOPs in detail.…”

Section: Introductionmentioning

confidence: 99%

BOPfox program for tight-binding and analytic bond-order potential calculations

Hammerschmidt

Seiser

Ford

et al. 2019

Computer Physics Communications

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Bond-order potentials (BOPs) provide a local and physically transparent description of the interatomic interaction. Here we describe the efficient implementation of analytic BOPs in the BOPfox program and library. We discuss the integration of the underlying non-magnetic, collinear-magnetic and noncollinear-magnetic tight-binding models that are evaluated by the analytic BOPs. We summarize the flow of an analytic BOP calculation including the determination of self-returning paths for computing the moments, the self-consistency cycle, the estimation of the band-width from the recursion coefficients, and the termination of the BOP expansion. We discuss the implementation of the calculations of forces, stresses and magnetic torques with analytic BOPs. We show the scaling of analytic BOP calculations with the number of atoms and moments, present options for speeding up the calculations and outline different concepts of parallelisation. In the appendix we compile the implemented equations of the analytic BOP methodology and comments on the implementation. This description should be relevant for other implementations and further developments of analytic bond-order potentials.arXiv:1803.07491v2 [physics.comp-ph]

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Crystal-Structure Analysis with Moments of the Density-of-States: Application to Intermetallic Topologically Close-Packed Phases

Cited by 14 publications

References 58 publications

Crowd-sourcing materials-science challenges with the NOMAD 2018 Kaggle competition

Crowd-sourcing materials-science challenges with the NOMAD 2018 Kaggle competition

Electronic structure based descriptor for characterizing local atomic environments

BOPfox program for tight-binding and analytic bond-order potential calculations

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