At ambient pressure tin transforms from its ground state, the semimetal $\alpha$-Sn (diamond structure), to metallic $\beta$-Sn at $13{}^{\circ }\mathrm{C}$ (286 K). There may be a further transition to a simple hexagonal phase, $\gamma$-Sn, above 450 K. These relatively low transition temperatures are due to the small energy differences between the structures, $\approx 20$ meV/atom between $\alpha$- and $\beta$-Sn, which makes tin an exceptionally sensitive test of the accuracy of density functionals and computational methods used in calculating electronic and vibrational energy, including zero-point energy. 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 and examine the vibrational contributions to the free energy with the AFLOW Automatic Phonon Library (APL). We look at the successes and deficiencies of each functional. We also discuss the necessity of testing high-throughput calculations for convergence of systems with small energy differences.

中文翻译：

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锡虫问题作为使用高通量计算的密度泛函测试

在环境压力下，锡从其基态转变，半金属 $\alpha$-Sn（金刚石结构），到金属 $\beta$-Sn在 $13{}^{\circ }\mathrm{C}$(286 K)。可能会进一步过渡到简单的六边形相，$\gamma$-Sn，高于 450 K。这些相对较低的转变温度是由于结构之间的能量差异很小， $\approx 20$ meV/原子之间 $\alpha$- 和 $\beta$-Sn，这使得锡成为用于计算电子和振动能量（包括零点能量）的密度泛函和计算方法准确性的异常敏感测试。在这里，我们使用高通量自动流动 (AFLOW) 方法使用各种密度泛函研究多种结构中锡的能量学，并使用 AFLOW 自动声子库 (APL) 检查对自由能的振动贡献。我们着眼于每个功能的成功和不足。我们还讨论了为具有小能量差异的系统收敛而测试高通量计算的必要性。