Orbital localization error of density functional theory in shear properties of vanadium and niobium.
Orbital localization error of density functional theory in shear properties of vanadium and niobium.
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DOI：
10.1063/1.5136052
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发表时间：
2020-01
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影响因子：
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通讯作者：
Yi X Wang;H. Geng;Q. Wu;Xiang-Rong Chen
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作者：
Yi X Wang;H. Geng;Q. Wu;Xiang-Rong Chen
密度泛函理论（DFT）可以很好地描述大多数具有s，p和d轨道的元素，除了一些具有强定域和相关价电子的材料。在这项工作中，我们发现，广泛使用的交换相关（XC）泛函，包括局域密度近似（LDA），广义梯度近似（GGA），和元GGA，低估了剪切模量和相稳定性的V和Nb大大。另一方面，通常对相关系统更好的高级混合泛函在这两种简单金属中完全失效。这一惊人的失败是由于GGA的轨道定位误差，这是进一步恶化的混合泛函。DFT+U和货车德瓦耳斯泛函应用于V和Nb时的类似失效证实了这一观察。为了解决这个问题，提出了一种半经验的DFT+J方法，它可以通过促进原位交换来使电子离域。此外，还观察到，包含密度导数稍微改善了半局部泛函的性能，其中元GGA优于GGA，后者优于LDA。这一发现表明，为了完全消除V和Nb中的轨道定域误差（主要来自d轨道）和离域误差（主要来自s和p轨道），从而更好地描述它们的电子结构，包括拉普拉斯水平以外的高阶密度导数的可能性和必要性。同样的策略也适用于其他d电子系统和f电子系统。
It is believed that the density functional theory (DFT) describes most elements with s, p, and d orbitals very well, except some materials that have strongly localized and correlated valence electrons. In this work, we find that the widely employed exchange-correlation (XC) functionals, including local-density approximation (LDA), generalized gradient approximation (GGA), and meta-GGA, underestimate the shear modulus and phase stability of V and Nb greatly. The advanced hybrid functional that is usually better for correlated systems, on the other hand, completely fails in these two simple metals. This striking failure is revealed due to the orbital localization error in GGA, which is further deteriorated by hybrid functionals. This observation is corroborated by a similar failure of DFT+U and van der Waals functionals when applied to V and Nb. To remedy this problem, a semiempirical approach of DFT+J is proposed, which can delocalize electrons by facilitating the on-site exchange. Furthermore, it is observed that including density derivatives slightly improves the performance of the semilocal functionals, with meta-GGA outperforms GGA, and the latter is better than LDA. This discovery indicates the possibility and necessity to include higher-order density derivatives beyond the Laplacian level for the purpose of removing the orbital localization error (mainly from d orbitals) and delocalization error (mainly from s and p orbitals) completely in V and Nb so that a better description of their electronic structures is achieved. The same strategy can be applied to the other d electron system and f electron system.