# Voronoi-based similarity distances between arbitrary crystal lattices

arXiv: https://arxiv.org/abs/2002.11165 · HTML: https://mlsanity.com/paper/2002.11165/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Feb 2020.

## Built on by (most cited first, 2 of 2)

- [Recognizing Rigid Patterns of Unlabeled Point Clouds by Complete and Continuous Isometry Invariants with no False Negatives and no False Positives](https://mlsanity.com/paper/2303.15385/) (2023)
- [Fast predictions of lattice energies by continuous isometry invariants of crystal structures](https://mlsanity.com/paper/2108.07233/) (2021)

## Abstract (arXiv)

This paper develops a new continuous approach to a similarity between periodic lattices of ideal crystals. Quantifying a similarity between crystal structures is needed to substantially speed up the Crystal Structure Prediction, because the prediction of many target properties of crystal structures is computationally slow and is essentially repeated for many nearly identical simulated structures. The proposed distances between arbitrary periodic lattices of crystal structures are invariant under all rigid motions, satisfy the metric axioms and continuity under atomic perturbations. The above properties make these distances ideal tools for clustering and visualizing large datasets of crystal structures. All the conclusions are rigorously proved and justified by experiments on real and simulated crystal structures reported in the Nature 2017 paper "Functional materials discovery using energy-structure-function maps".