非经验密度泛函研究的Jeltron：自旋极化表面，球状团簇和体线性响应
Nonempirical Density Functionals Investigated for Jellium: Spin-Polarized Surfaces, Spherical Clusters, and Bulk Linear Response
摘要：
早期的测试表明，Tao-Perdew-Staroverov-Scuseria（TPSS）的交换相关能的非经验元广义梯度近似（meta-GGA）比自旋非极化凝胶的局域自旋密度（LSD）近似产生更准确的表面能。在这项研究中，在"内部“和外部磁场的存在下的果冻金属的功函数和表面能计算与LSD，Perdew-Burke-Ernzerhof（PBE）GGA，和TPSS元GGA及其前身，几乎非经验Perdew-Kurth-Zupan-Blaha（PKZB）元GGA，使用自洽的LSD轨道和密度。结果表明：（i）对于正常的堆积密度，TPSS中的表面相关能与PBE中的表面相关能相同，因为TPSS努力代表对PBE的自相关校正;（ii）正常的表面密度分布可以均匀地缩放到低密度或强相互作用极限，并且TPSS提供了对该极限的估计，该估计与（但可能更准确）其他估计;（iii）对于正常和低密度，TPSS提供了相同的描述表面磁性PBE，这表明这些近似可能是一般等同的磁性。使用密度泛函计算了具有多达106个电子的jeldom球的能量，并与用扩散量子蒙特卡罗数据获得的能量进行了比较，包括我们对固定节点校正的估计。最后，我们使用这些密度泛函计算的线性响应的体胶态，并发现不仅LSD，而且PBE GGA和TPSS元GGA产生的线性响应与量子蒙特卡罗方法的很好的协议，为波矢量的扰动外势的费米波矢量的两倍。
英文摘要：
Earlier tests show that the Tao-Perdew-Staroverov-Scuseria (TPSS) nonempirical meta-generalized gradient approximation (meta-GGA) for the exchange-correlation energy yields more accurate surface energies than the local spin density (LSD) approximation for spin-unpolarized jellium. In this study, work functions and surface energies of a jellium metal in the presence of ``internal'' and external magnetic fields are calculated with LSD, Perdew-Burke-Ernzerhof (PBE) GGA, and TPSS meta-GGA and its predecessor, the nearly nonempirical Perdew-Kurth-Zupan-Blaha (PKZB) meta-GGA, using self-consistent LSD orbitals and densities. The results show that: (i) For normal bulk densities, the surface correlation energy is the same in TPSS as in PBE, as it should be since TPSS strives to represent a self-correlation correction to PBE; (ii) Normal surface density profiles can be scaled uniformly to the low-density or strong-interaction limit, and TPSS provides an estimate for that limit that is consistent with (but probably more accurate than) other estimates; (iii) For both normal and low densities, TPSS provides the same description of surface magnetism as PBE, suggesting that these approximations may be generally equivalent for magnetism. The energies of jellium spheres with up to 106 electrons are calculated using density functionals and compared to those obtained with Diffusion Quantum Monte Carlo data, including our estimate for the fixed-node correction. Finally we calculate the linear response of bulk jellium using these density functionals, and find that not only LSD but also PBE GGA and TPSS meta-GGA yield a linear-response in good agreement with that of the Quantum Monte Carlo method, for wavevectors of the perturbing external potential up to twice the Fermi wavevector.
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