Self-consistent DFT+U+V study of oxygen vacancies in SrTiO3

Contradictory theoretical results for oxygen vacancies (VO) in SrTiO3 (STO) were often related to the peculiar properties of STO, which is a d0 transition metal oxide with mixed ionic-covalent bonding. Here, we apply, for the first time, density functional theory (DFT) within the extended Hubbard DFT+U+V approach, including on-site as well as inter-site electronic interactions, to study oxygen-deficient STO with Hubbard U and V parameters computed self-consistently (SC) via density-functional perturbation theory. Our results demonstrate that the extended Hubbard functional is a promising approach to study defects in materials with electronic properties similar to STO. Indeed, DFT+U+V provides a better description of stoichiometric STO compared to standard DFT or DFT+U, the band gap and crystal field splitting being in good agreement with experiments.
In turn, also the description of the electronic properties of oxygen vacancies in STO is improved, with formation energies in excellent agreement with experiments as well as results obtained with the most frequently used hybrid functionals, however at a fraction of the computational cost. While our results do not fully resolve the contradictory findings reported in literature, our systematic approach leads to a deeper understanding of their origin, which stems from different cell sizes, STO phases, the exchange-correlation functional, and the treatment of structural relaxations and spin-polarization.

针对钛酸锶（SrTiO3，STO）中氧空位（VO）的矛盾理论结果，常与STO的特殊性质相关联——STO是一类兼具混合离子-共价键的d0过渡金属氧化物（d0 transition metal oxide）。本研究首次将扩展Hubbard DFT+U+V框架下的密度泛函理论（density functional theory, DFT）应用于缺氧型STO的研究，该方法纳入了在位电子相互作用与跨位电子相互作用，其中Hubbard U和V参数通过密度泛函微扰理论（density-functional perturbation theory）自洽（SC）计算得到。
本研究结果证实，扩展Hubbard泛函是研究电子性质与STO相近的材料中缺陷的极具前景的方法。诚然，相较于标准DFT或DFT+U方法，DFT+U+V能够更准确地描述化学计量比STO，其计算得到的带隙与晶体场分裂结果均与实验值吻合良好。
与此同时，该方法对STO中氧空位的电子性质描述也得到优化，其计算的形成能不仅与实验结果高度一致，也与当前最常用的杂化泛函所得结果相符，但计算成本仅为后者的极小一部分。尽管本研究结果并未完全解决文献中报道的矛盾结论，但本系统性研究使我们对矛盾的根源有了更深入的认识——其根源在于不同的晶胞尺寸、STO晶相、交换关联泛函（exchange-correlation functional）的选择，以及结构弛豫与自旋极化的处理方式差异。