BiVO₄ (BVO) is an important photocatalytic and ferroelastic material. It has been extensively studied using density functional theory (DFT). However, on optimization, at a commonly employed level of theory using the Perdew–Burke–Ernzerhof (PBE) exchange–correlation functional, the monoclinic scheelite (ms-BVO) structure transforms into a higher-symmetry tetragonal scheelite (ts-BVO) phase spontaneously, which has also been confirmed by other groups. Such a transformation is highly unusual, as one would expect the transition to a lower symmetry structure to be modeled well at this level of theory, as is the case with, for example, the perovskite BaTiO₃, and hints at a subtle interplay between structural and electronic properties. In this work, we demonstrate that this phase transition nevertheless can be described accurately with DFT but only using a hybrid density functional with ∼60% Hartree–Fock (HF) exchange. We find a soft phonon mode in ts-BVO, which corresponds to the phase transition from ts-BVO to ms-BVO associated with a double-well potential characterizing this phase transition, implying that the transition is of the second order. We find two key factors that can explain this surprising behavior. First, the polarizability of the Bi³⁺ ion, with an on-site contribution from the hybridization of its 6s and 6p states, is notably underestimated by DFT. Moreover, the effective radius of the Bi³⁺ ion proves to be too large. With the 60% HF exchange hybrid functional, the description of the polarizability of Bi³⁺ does not improve but the radii of the Bi³⁺ ions approach more realistic values. The polarizability of the O and V ions are reasonably described already by PBE. To gain further insight into the problem, we investigated the structural stability of other ABO₄ oxides, including ScVO₄, LaNbO₄, YTaO₄, and CaWO₄, and related materials. Some of them have similar behavior to BVO, whose ground-state monoclinic structure proves to be unstable using commonly employed DFT approaches. In particular, for ScVO₄, we found that the scheelite tetragonal and fergusonite monoclinic structures cannot be distinguished using the PBEsol functional. But the fergusonite monoclinic structure becomes stable using the hybrid functionals with high fractions of HF exchange, which points to the crucial role of the accurate ionic size reproduction by the method of choice as the on-site Sc³⁺ polarizability is too low to have a significant effect. Our findings would be of high interest for the study of other problematic materials with subtle size and polarization properties, especially ABO₄ oxides that undergo similar phase transitions.

中文翻译：

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用密度泛函理论洞察 ABO4 型氧化物的辉铜矿-白钨矿相变：以 BiVO4 基态的微妙之处为例

BiVO ₄ (BVO)是一种重要的光催化和铁弹性材料。使用密度泛函理论 (DFT) 对其进行了广泛的研究。然而，在优化时，在使用 Perdew-Burke-Ernzerhof (PBE) 交换相关泛函的常用理论水平上，单斜白钨 ( ms -BVO) 结构转变为更高对称性的四方白钨 ( ts -BVO) 相自发的，这也得到了其他团体的证实。这种转变是非常不寻常的，因为人们预计在这一理论水平上可以很好地模拟向较低对称结构的转变，例如钙钛矿 BaTiO _3的情况，并暗示结构和电子特性之间存在微妙的相互作用。在这项工作中，我们证明了这种相变仍然可以用 DFT 准确描述，但只能使用具有 ∼60% Hartree-Fock (HF) 交换的混合密度泛函。我们在ts -BVO中发现了一个软声子模式，它对应于从ts -BVO 到ms -BVO 的相变，与表征该相变的双阱电位相关，这意味着该转变是二阶的。我们发现两个关键因素可以解释这种令人惊讶的行为。一、Bi ^{3+的极化率}离子，由于其 6s 和 6p 状态的杂交产生了现场贡献，DFT 明显低估了它。^{此外，证明Bi 3+}离子的有效半径太大。在 60% HF 交换杂化泛函下，对 Bi ³⁺极化率的描述没有改善，但 Bi ³⁺离子的半径接近更现实的值。PBE 已经合理地描述了 O 和 V 离子的极化率。为了进一步了解这个问题，我们研究了其他 ABO ₄氧化物的结构稳定性，包括 ScVO ₄、LaNbO ₄、YTaO ₄和 CaWO ₄, 及相关材料。其中一些具有与 BVO 相似的行为，其基态单斜结构使用常用的 DFT 方法证明是不稳定的。特别是，对于 ScVO ₄，我们发现使用 PBEsol 泛函无法区分白钨矿四方和铁锰矿单斜晶结构。但是使用具有高比例 HF 交换的杂化泛函使铁镁合金单斜晶结构变得稳定，这表明通过选择的方法精确再现离子尺寸的关键作用，因为现场 Sc ³⁺极化率太低而无法获得显着的效果。我们的发现对于研究其他具有细微尺寸和极化特性的问题材料，尤其是 ABO ₄经历类似相变的氧化物。