钒和铌剪切性质的密度泛函理论轨道局部化误差
Orbital localization error of density functional theory in shear properties of vanadium and niobium
摘要：
一般认为，密度泛函理论（DFT）能很好地描述大多数具有s、p和d轨道的元素，除了某些具有强定域和关联价电子的材料。在这项工作中，我们发现，广泛使用的交换相关（xc）泛函，包括LDA，GGA和meta-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。这一观察结果证实了一个类似的失败的DFT+U和范德瓦尔斯泛函时，适用于V和Nb。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，它被观察到，包括密度导数略有改善的性能的半局部泛函，与元GGA优于GGA，后者是优于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，在Laplacian能级之外引入高阶密度导数是可能和必要的。同样的策略也适用于其他d电子和f电子系统。
英文摘要：
It is believed that the density functional theory (DFT) describes most elements with s, p and d orbitals very well, except some materials that having strongly localized and correlated valence electrons. In this work, we find that the widely employed exchange-correlation (xc) functionals, including LDA, 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 system, 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, an semi-empirical 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 semi-local 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 to remove the orbital localization error (mainly from d orbitals) and delocalization error (mainly from s and p orbitals) completely in V and Nb, so that to achieve a better description of their electronic structures. The same strategy can be applied to other d electron system and f electron system.
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