The group V and VI transition metals share a common Fermi surface feature of hole ellipsoids at the $N$ point in the Brillouin zone. In clear contrast to the other Fermi surface sheets, which are purely of $d$ character, these arise from a band that has a significant proportion of $p$ character. By performing local density approximation (LDA), generalized gradient approximation (GGA), strongly constrained and appropriately normed (SCAN) meta-GGA, and $GW$ approximation calculations, we find that the $p$ character part of this band (and therefore the Fermi surface) is particularly sensitive to the exchange-correlation approximation. LDA and GGA calculations inadequately describe this feature, predicting $N$ hole ellipsoid sizes that are consistently too large in comparison to various experimental measurements, whereas quasiparticle self-consistent $GW$ calculations predict a size that is slightly too small (and non-self-consistent $GW$ calculations that use an LDA starting point predict a size that is much too small). Overall, for the metals tested here, SCAN provides the most accurate Fermi surface predictions, mostly correcting the discrepancies between measurements and calculations that were observed when LDA calculations were used. However, none of the tested exchange-correlation approximations succeeds in simultaneously bringing all of the measurable properties of these metals into good experimental agreement, particularly where magnetism is concerned. The SCAN calculations predict antiferromagnetic moments for Cr that are 3 times larger than the experimental value ($1.90{\mu }_B$ compared to $0.62{\mu }_B$).

中文翻译：

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费米面对交换和相关处理的敏感性

V 族和 VI 族过渡金属在 $N$点在布里渊区。与其他费米表面片形成鲜明对比，后者纯粹是$d$ 特征，这些来自一个具有很大比例的乐队 $磷$特点。通过执行局部密度近似 (LDA)、广义梯度近似 (GGA)、强约束和适当归一化 (SCAN) 元 GGA，以及$G宽$ 近似计算，我们发现 $磷$该带的特征部分（因此是费米面）对交换相关近似特别敏感。LDA 和 GGA 计算不足以描述这个特征，预测$N$ 与各种实验测量相比，孔椭球尺寸始终过大，而准粒子自洽 $G宽$ 计算预测的大小稍微太小（并且不自洽 $G宽$使用 LDA 起点的计算预测的大小太小）。总体而言，对于此处测试的金属，SCAN 提供了最准确的费米表面预测，主要纠正了使用 LDA 计算时观察到的测量和计算之间的差异。然而，经过测试的交换相关近似都没有成功地同时将这些金属的所有可测量特性纳入良好的实验一致性，特别是在涉及磁性的情况下。SCAN 计算预测 Cr 的反铁磁矩比实验值大 3 倍（$1.90{\mu }_{乙}$ 相比 $0.62{\mu }_{乙}$）。