One of the main drawbacks in the density functional theory (DFT) formalism is the underestimation of the energy gaps in semiconducting materials. The combination of DFT with an explicit treatment of the electronic correlation with a Hubbard-like model, known as the DFT+U method, has been extensively applied to open up the energy gap in materials. Here, we introduce a systematic study where the selection of the U parameter is analyzed considering two different basis sets: plane-waves and numerical atomic orbitals (NAOs), together with different implementations for including U, to investigate the structural and electronic properties of a well-defined bipyramidal (TiO₂)₃₅ nanoparticle. This study reveals, as expected, that a certain U value can reproduce the experimental value for the energy gap. However, there is a high dependence on the choice of basis set and on the U parameter employed. The present study shows that the linear combination of the NAO basis functions, as implemented in Fritz Haber Institute ab initio molecular simulation (FHI-aims), requires, requires a lower U value than the simplified rotationally invariant approach, as implemented in the Vienna ab initio simulation package (VASP). Therefore, the transfer of U values between codes is unfeasible and not recommended, demanding initial benchmark studies for the property of interest as a reference to determine the appropriate value of U.

中文翻译：

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关于使用DFT + U描述TiO2纳米粒子的电子结构：（TiO2）35作为案例研究。

密度泛函理论（DFT）形式主义的主要缺点之一是低估了半导体材料中的能隙。DFT与类似Hubbard模型的电子相关性的显式处理相结合，被称为DFT + U方法，已被广泛应用于打开材料的能隙。在这里，我们介绍了一项系统研究，其中考虑了两个不同的基础集来分析U参数的选择：平面波和数值原子轨道（NAO），以及包括U的不同实现，以研究a的结构和电子性质。明确的双锥体（TiO ₂）₃₅纳米粒子。这项研究表明，正如预期的那样，一定的U值可以重现能隙的实验值。但是，高度依赖于基础集的选择和所采用的U参数。本研究表明，如Fritz Haber Institute从头算分子模拟（FHI-aims）所实现的那样，NAO基函数的线性组合所需的U值比在维也纳ab中实现的简化旋转不变方法要低。初始仿真程序包（VASP）。因此，转移U代码之间的值不可行，也不建议使用，要求对感兴趣的属性进行初始基准研究，以作为确定U适当值的参考。