The Tin Pest Problem as a Test of Density Functionals Using High-Throughput Calculations

TL;DR

This study uses high-throughput calculations to evaluate the accuracy of various density functionals in predicting tin's phase transitions, highlighting the importance of convergence testing and the potential of Hubbard U corrections.

Contribution

It systematically assesses multiple density functionals for tin's phase energetics and demonstrates how Hubbard U corrections can improve phase transition predictions.

Findings

No functional perfectly predicts all phase energetics.

Hubbard U corrections can improve phase transition temperature predictions.

Convergence testing is crucial for systems with small energy differences.

Abstract

At ambient pressure tin transforms from its ground-state semi-metal $\alpha$-Sn (diamond structure) phase to the compact metallic $\beta$-Sn phase at 13$^\circ$C (286K). There may be a further transition to the simple hexagonal $\gamma$-Sn above 450K. These relatively low transition temperatures are due to the small energy differences between the structures, $\approx 20$\,meV/atom between $\alpha$- and $\beta$-Sn. This makes tin an exceptionally sensitive test of the accuracy of density functionals and computational methods. Here we use the high-throughput Automatic-FLOW (AFLOW) method to study the energetics of tin in multiple structures using a variety of density functionals. We look at the successes and deficiencies of each functional. As no functional is completely satisfactory, we look Hubbard U corrections and show that the Coulomb interaction can be chosen to predict the correct phase transition temperature. We also discuss the necessity of testing high-throughput calculations for convergence for systems with small energy differences.