We have studied the barium titanate (BaTiO₃) by using the CASTEP which based on density functional theory (DFT) under the correlation function of GGA and PBE. Material under study has been doped by Lanthanum (La) at the sites of Barium (Ba). Before and after doping we have calculated the different optical, structural and electronic properties and have been discussed in detail. After doping, reduction of band gap is noticed and as well as nature of band gap is also changed from indirect band gap (IBG) to direct band gap (DBG). This variation in band gap has been explained clearly on the behalf of partially and total density of states. Refractive index ($n$) is 2.598 for pure and 2.482 for doped system. Absorption peak also effected by inclusion of La.

我们利用基于密度泛函理论（DFT）的CASTEP在GGA和PBE的相关函数下研究了钛酸钡（BaTiO ₃）。所研究的材料已在钡（Ba）处被镧（La）掺杂。在掺杂之前和之后，我们已经计算了不同的光学，结构和电子性质，并进行了详细讨论。掺杂后，带隙减小，并且带隙的性质也从间接带隙（IBG）更改为直接带隙（DBG）。带隙的这种变化已经以部分和全部状态密度的形式清楚地解释了。折光率（$ñ$）对于纯系统是2.598，对于掺杂系统是2.482。吸收峰也受夹杂La的影响。