We describe a systematic approach to building ab initio tight-binding models and apply this to hexagonal metals Mg and Zr. Our models contain three approximations to plane-wave density functional theory (DFT): (i) we use a small basis set, (ii) we approximate self-consistency, and (iii) we approximate many-center exchange and correlation effects. We test a range of approximations for many-center exchange-correlation and self-consistency to gauge the accuracy of each in isolation. This systematic approach also allows us to combine multiple approximations in the optimal manner for our final tight-binding models. Furthermore, the breakdown of errors into those from individual approximations is expected to be a useful guide for which approximations to include in other tight-binding models. We attempt to correct any remaining errors in our models by fitting a pair potential. Our final tight-binding model for Mg shows excellent agreement with plane-wave results for a wide range of properties (e.g., errors below 10% for self-interstitial formation energies and below 3% for equilibrium volumes) and is expected to be highly transferable due to the minimal amount of fitting. Calculations with our Zr model also show good agreement with plane-wave results (e.g., errors below 2% for equilibrium volumes) except for properties where self-consistency is important, such as self-interstitial formation energies. However, for these properties we are able to generate a tight-binding model which shows excellent agreement with non-self-consistent DFT with a small basis set (i.e., many-center effects are captured accurately by our approximations). As we understand the source of remaining errors in our Zr model we are able to outline the methods required to build upon it to describe the remaining properties with greater accuracy.

中文翻译：

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超越两中心紧密结合：Mg和Zr的模型

我们描述了一种从头开始的系统方法紧密结合模型，并将其应用于六角形金属Mg和Zr。我们的模型包含对平面波密度泛函理论（DFT）的三个近似：（i）我们使用小的基集，（ii）近似自洽，（iii）近似多中心交换和相关效应。我们测试了多中心交换相关性和自洽性的一系列近似值，以评估每个隔离器的准确性。这种系统的方法还使我们能够以最佳方式将多个近似值组合到最终的紧密绑定模型中。此外，将误差分解成各个单独的近似值将被认为是将近似值包括在其他紧密绑定模型中的有用指南。我们尝试通过拟合对势来纠正模型中所有剩余的错误。我们最终的Mg紧密结合模型显示出与多种性质的平面波结果极好的一致性（例如，自填隙地层能量的误差低于10％，平衡体积的误差低于3％），并且有望高度转移由于安装量极小。用我们的Zr模型进行的计算也显示出与平面波结果（例如，平衡体积的误差低于2％）具有良好的一致性，除了自洽性很重要的属性（例如自填隙地层能量）。但是，对于这些属性，我们能够生成一个紧密绑定的模型，该模型显示了与具有较小基集的非自洽DFT的极好的一致性（即，我们的近似值准确地捕获了许多中心效应）。