赝原子轨道基础：ABO $_3$钙钛矿中的电子精度和软模畸变
The pseudoatomic orbital basis: electronic accuracy and soft-mode distortions in ABO$_3$ perovskites
摘要：
已知钙钛矿氧化物在与其母体立方结构相比时在长波长上易受结构畸变的影响。从从头算模拟的角度来看，这需要包括数千个原子的精确计算;这远远超出了传统的基于平面波的密度泛函理论（DFT）的任务。我们建议，这一空白可以使用在大规模DFT代码，CONQUEST，使用本地伪原子轨道（PAO）的基础上实现的方法来填充。虽然这个基础已经测试了一些结构和能量属性之前，没有处理的最基本量的理论，电荷密度$n(\mathbf{r})$本身。准确描述$n(\mathbf{r})$对钙钛矿氧化物至关重要，因为短程回复力（以键共价为特征）和长程库仑力起着至关重要的作用，如Cochran和Anderson的软模理论所建议的。我们发现，中等大小的基组的PAO可以重现平面波电荷密度的总集成误差优于0.5%，并提供巴德分区离子电荷，体积和平均电荷密度的准确度相似。此外，多模式的反铁电变形的PbZrO $_3$和它的相关的能量被再现时，优于99%的平面波相比。这项工作表明，电子结构计算使用有效的和紧凑的基组的赝原子轨道可以达到相同的精度高截止能量平面波计算。当与CONQUEST代码配合使用时，现在可以对数千个原子进行高电子和结构精度的计算，即使是像钙钛矿氧化物这样微妙的系统。
英文摘要：
The perovskite oxides are known to be susceptible to structural distortions over a long wavelength when compared to their parent cubic structures. From an ab initio simulation perspective, this requires accurate calculations including many thousands of atoms; a task well beyond the remit of traditional plane wave-based density functional theory (DFT). We suggest that this void can be filled using the methodology implemented in the large-scale DFT code, CONQUEST, using a local pseudoatomic orbital (PAO) basis. Whilst this basis has been tested before for some structural and energetic properties, none have treated the most fundamental quantity to the theory, the charge density $n(\mathbf{r})$ itself. An accurate description of $n(\mathbf{r})$ is vital to the perovskite oxides due to the crucial role played by short-range restoring forces (characterised by bond covalency) and long range coulomb forces as suggested by the soft-mode theory of Cochran and Anderson. We find that modestly sized basis sets of PAOs can reproduce the plane-wave charge density to a total integrated error of better than 0.5% and provide Bader partitioned ionic charges, volumes and average charge densities to similar degree of accuracy. Further, the multi-mode antiferroelectric distortion of PbZrO$_3$ and its associated energetics are reproduced by better than 99% when compared to plane-waves. This work suggests that electronic structure calculations using efficient and compact basis sets of pseudoatomic orbitals can achieve the same accuracy as high cutoff energy plane-wave calculations. When paired with the CONQUEST code, calculations with high electronic and structural accuracy can now be performed on many thousands of atoms, even on systems as delicate as the perovskite oxides.
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