The first-principles (ab initio) computations of the structural, electronic, and phonon properties have been performed for cubic and low-temperature tetragonal phases of BaTiO₃ and SrTiO₃ perovskite crystals, both stoichiometric and non-stoichiometric (with neutral oxygen vacancies). Calculations were performed with the CRYSTAL17 computer code within the linear combination of atomic orbitals approximation, using the B1WC advanced hybrid exchange-correlation functional of the density-functional-theory (DFT) and the periodic supercell approach. Various possible spin states of the defective systems were considered by means of unrestricted (open shell) DFT calculations. It was demonstrated that oxygen reduction leads to the appearance of new local vibrational modes associated with oxygen vacancies and new first-order peaks in the Raman spectra, which could be used for defect identification. The calculated Raman spectra for different vacancy positions and spins of the system, as well as other properties of defective crystals, are compared with the relevant experimental data.

中文翻译：

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具有氧空位的BaTiO3和SrTiO3钙钛矿晶体的结构，电子和振动性质的从头算

对BaTiO ₃和SrTiO _3的立方和低温四方相进行了结构，电子和声子性质的第一性原理计算（从头算）化学计量和非化学计量的钙钛矿晶体（具有中性的氧空位）。使用CRYSTAL17计算机代码在原子轨道近似的线性组合内，使用密度泛函理论（DFT）的B1WC高级混合交换相关函数和周期超单元方法进行计算。通过无限制（开壳）DFT计算来考虑缺陷系统的各种可能的自旋状态。结果表明，氧还原导致出现与氧空位相关的新的局部振动模式和拉曼光谱中新的一阶峰，这些可用于缺陷识别。针对系统的不同空位和自旋以及缺陷晶体的其他特性计算得出的拉曼光谱，