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.
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