A general representation scheme for crystalline solids based on Voronoi-tessellation real feature values and atomic property data

Randy Jalem,Masanobu Nakayama,Yusuke Noda,Tam Le,Ichiro Takeuchi,Yoshitaka Tateyama,Hisatsugu Yamazaki

doi:10.1080/14686996.2018.1439253

Abstract

Increasing attention has been paid to materials informatics approaches that promise efficient and fast discovery and optimization of functional inorganic materials. Technical breakthrough is urgently requested to advance this field and efforts have been made in the development of materials descriptors to encode or represent characteristics of crystalline solids, such as chemical composition, crystal structure, electronic structure, etc. We propose a general representation scheme for crystalline solids that lifts restrictions on atom ordering, cell periodicity, and system cell size based on structural descriptors of directly binned Voronoi-tessellation real feature values and atomic/chemical descriptors based on the electronegativity of elements in the crystal. Comparison was made vs. radial distribution function (RDF) feature vector, in terms of predictive accuracy on density functional theory (DFT) material properties: cohesive energy (CE), density (d), electronic band gap (BG), and decomposition energy (Ed). It was confirmed that the proposed feature vector from Voronoi real value binning generally outperforms the RDF-based one for the prediction of aforementioned properties. Together with electronegativity-based features, Voronoi-tessellation features from a given crystal structure that are derived from second-nearest neighbor information contribute significantly towards prediction.

Highlights

IntroductionJ, J1, J2 ≤ Jmax denote the spatial resolution limit defining the atomic neighborhood
Materials informatics in tandem with high-throughput density functional theory (DFT) calculations has become increasingly deployed for exploration, optimization, and property forecasting of inorganic materials
Clebsch–Gordan coefficients, and J, J1, J2 ≤ Jmax denote the spatial resolution limit defining the atomic neighborhood. Another class of material representation was defined by decomposing infinite and periodic crystal structures into finite number of representative fragments based on rules of chemical bonding coordination sphere determined from Voronoi-tessellation cells of atom centers

Summary

Introduction

J, J1, J2 ≤ Jmax denote the spatial resolution limit defining the atomic neighborhood Another class of material representation was defined by decomposing infinite and periodic crystal structures into finite number of representative fragments based on rules of chemical bonding coordination sphere determined from Voronoi-tessellation cells of atom centers. Where A is for adjacency matrix element encompassing all atom pairing I and J in one subgraph type [33] In these schemes, it is obvious that: (i) both chemical/ atomic and geometrical properties are always considered in an attempt to make the representation universal, (ii) atomic or chemical descriptors from the literature may be made suitable for defining the ‘chemical identity’ of materials, and (iii) Voronoi cell features may provide the criteria to describe the ‘structure identity’ of materials. Our proposed scheme offers a simple, robust and cost-effective alternative for generating feature vector representations for a wide variety of crystalline materials

Computational details

Formulation of generalized vector-form material descriptors

Supervised learning details

Predictive power of formulated vector-form descriptors

Feature importance analysis from GBR modeling

Conclusions