A non-orthogonal representation of the chemical space

TL;DR

This paper introduces a novel non-orthogonal chemical space representation called Pettifor embedding, which improves machine learning predictions and visualizes material relationships effectively.

Contribution

The paper proposes a new non-orthogonal chemical embedding that enhances the interpretability and predictive power of models for crystalline materials.

Findings

Pettifor embeddings outperform traditional elemental embeddings in machine learning tasks.

The method enables a two-dimensional map of stable crystalline compounds.

The map effectively separates material classes based on physical properties.

Abstract

We present a novel approach to generate a fingerprint for crystalline materials that balances efficiency for machine processing and human interpretability, allowing its application in both machine learning inference and understanding of structure-property relationships. Our proposed material encoding has two components: one representing the crystal structure and the other characterizing the chemical composition, that we call Pettifor embedding. For the latter we construct a non-orthogonal space where each axis represents a chemical element and where the angle between the axes quantifies a measure of the similarity between them. The chemical composition is then defined by the point on the unit sphere in this non-orthogonal space. We show that the Pettifor embeddings systematically outperform other commonly used elemental embeddings in compositional machine learning models. Using the Pettifor embeddings to define a distance metric and applying dimension reduction techniques, we construct a two-dimensional global map of the space of thermodynamically stable crystalline compounds. Despite their simplicity, such maps succeed in providing a physical separation of material classes according to basic physical properties.