Departamento de Química Inorgánica, MALTA Consolider Team, Facultad de CC Químicas, Universidad Complutense de Madrid, Madrid, Spain.
J Chem Phys. 2011 Aug 7;135(5):054503. doi: 10.1063/1.3617244.
This work investigates crystal lattice, electronic structure, relative stability, and high pressure behavior of TiO(2) polymorphs (anatase, rutile, and columbite) using the density functional theory (DFT) improved by an on-site Coulomb self-interaction potential (DFT+U). For the latter the effect of the U parameter value (0 < U < 10 eV) is analyzed within the local density approximation (LDA+U) and the generalized gradient approximation (GGA+U). Results are compared to those of conventional DFT and Heyd-Scuseria-Ernzehorf screened hybrid functional (HSE06). For the investigation of the individual polymorphs (crystal and electronic structures), the GGA+U/LDA+U method and the HSE06 functional are in better agreement with experiments compared to the conventional GGA or LDA. Within the DFT+U the reproduction of the experimental band-gap of rutile/anatase is achieved with a U value of 10/8 eV, whereas a better description of the crystal and electronic structures is obtained for U < 5 eV. Conventional GGA∕LDA and HSE06 fail to reproduce phase stability at ambient pressure, rendering the anatase form lower in energy than the rutile phase. The LDA+U excessively stabilizes the columbite form. The GGA+U method corrects these deficiencies; U values between 5 and 8 eV are required to get an energetic sequence consistent with experiments (E(rutile) < E(anatase) < E(columbite)). The computed phase stability under pressure within the GGA+U is also consistent with experimental results. The best agreement between experimental and computed transition pressures is reached for U ≈ 5 eV.
这项工作使用密度泛函理论（DFT）改进的局域密度近似（LDA）和广义梯度近似（GGA）研究了 TiO(2)多晶型体（锐钛矿、金红石和铌铁矿）的晶体晶格、电子结构、相对稳定性和高压行为。对于后者，分析了 U 参数值（0 < U < 10 eV）在局域密度近似加自相互作用库仑修正（LDA+U）和广义梯度近似加自相互作用库仑修正（GGA+U）中的影响。结果与传统 DFT 和 Heyed-Scuseria-Ernzerhof 屏蔽混合泛函（HSE06）的结果进行了比较。对于单个多晶型体（晶体和电子结构）的研究，GGA+U/LDA+U 方法和 HSE06 泛函与实验结果的一致性优于传统的 GGA 或 LDA。在 DFT+U 中，通过 U 值为 10/8 eV 可以再现金红石/锐钛矿的实验能带隙，而通过 U < 5 eV 可以获得更好的晶体和电子结构描述。传统的 GGA∕LDA 和 HSE06 无法在常压下重现相稳定性，使得锐钛矿形式的能量低于金红石相。LDA+U 过度稳定了铌铁矿形式。GGA+U 方法纠正了这些缺陷；需要 5 到 8 eV 之间的 U 值才能得到与实验一致的能量序列（E(rutile) < E(anatase) < E(columbite)）。GGA+U 下的计算压力相稳定性也与实验结果一致。对于 U ≈ 5 eV，实验和计算的转变压力之间的最佳一致性。
