This work investigates the consequences of various exchange correlations on brookite titanium dioxide’s (TiO₂) structural, electronic, and optical properties. For the first time, statistical analysis of the obtained result compared to experimental data is done to find the best methods for numerous properties. It provides an in-depth study on brookite TiO₂ by implementing OLCAODFTLBFGS algorithms along with GGA-PBE, GGA-PBES, GGA-PW91, GGA-BPW91, GGA-BP86, MGGA-TB09, and Hubbard U parameters to find out multiple properties. Investigated lattice parameters using GGA-PBES shows 0.43%, 0.56%, and 0.09% variation with experimental data, which further improved as 0.08%, 0%, and 0.21%, including Hubbard U parameter in the calculations. E _g using OLCAO-MGGA-TB09 shows no variations with the experimental value. Obtained range of absorption offers good agreement with experimental spectra. The statistical analysis using different methods for various properties described here can help find the best suitable ways for other materials. From the analyzed results, it revealed that GGA-PBES+U gives improved structural properties, whereas OLCAO-MGGA-TB09 gives an improvement in electronic properties. DFT provides good results for optical properties than DFT+U.

这项工作研究了各种交换相关性对板钛矿二氧化钛 (TiO ₂ ) 结构、电子和光学特性的影响。首次对获得的结果与实验数据进行统计分析，以找到针对众多特性的最佳方法。它通过实施 OLCAODFTLBFGS 算法以及 GGA-PBE、GGA-PBES、GGA-PW91、GGA-BPW91、GGA-BP86、MGGA-TB09 和 Hubbard U 参数来深入研究板钛矿 TiO ₂以找出多种特性. 使用 GGA-PBES 研究的晶格参数与实验数据显示 0.43%、0.56% 和 0.09% 的变化，进一步改进为 0.08%、0% 和 0.21%，包括计算中的哈伯德 U 参数。Ë _{g ^} 使用 OLCAO-MGGA-TB09 显示与实验值没有变化。获得的吸收范围与实验光谱非常吻合。此处描述的对各种属性使用不同方法的统计分析可以帮助找到最适合其他材料的方法。从分析结果可以看出，GGA-PBES+U 提高了结构性能，而 OLCAO-MGGA-TB09 提高了电子性能。DFT 提供了比 DFT+U 更好的光学特性结果。