# 计算跃迁电偶极矩

1. 实例分析(双钙钛矿)

pymatgen画能带图方法-高通量计算初探

## 实例分析(双钙钛矿)

​ 通过替换掺杂，可以破坏该材料在直接带隙位置的对称性禁阻(parity-forbidden transition)，从而大大提高其光吸收效率。例如，下述两篇文章都用到该思路，并且计算了其参杂以后的跃迁电偶极矩变化。

### VASPKIT v1.00 计算跃迁偶极矩

The transition dipole moment (TDM) or transition moment, usually denoted for a transition between an initial state a and a final state b, is the electric dipole moment associated with the transition between the two states. In general the TDM is a complex vector quantity that includes the phase factors associated with the two states. Its direction gives the polarization of the transition, which determines how the system will interact with an electromagnetic wave of a given polarization, while the square of the magnitude gives the strength of the interaction due to the distribution of charge within the system. The SI unit of the transition dipole moment is the Coulomb-meter (Cm); a more conveniently sized unit is the Debye (D).

For a single, nonrelativistic particle of mass m, in zero magnetic field, the TDM can alternatively be written in terms of the momentum operator, using the relationship,

where $\psi_{a}$ and $\psi_{b}$ are energy eigenstates with energy $E_{a}$ and $E_{b}$. $\text{C}_{a}$, $\text{C}_{b}$ and $\text{G}$ are plane-wave coefficients and reciprocal space vector with the same k vector, respectively, summed over the the number of plane-waves. The transition probabilities between the valence and the conduction band are revealed by the calculated sum of the squares of TDM (in unit of Debey$). We task cubic CsPbI$_3$perovskite phase as an example and present the PBE calculated band structures and corresponding TDM in figure below. This system has 44 valence electrons in all. Next we calcualte the squares of transition dipole moment from the highest valence band (band index 22) to the lowest conduction band (band index 23). It is found the results are well agreement with the previous finding (see Ref. J. Phys. Chem. Lett. 2017, 8, 2999−3007). The calculating process is very similar with the band structure calcuation except for setting LWAVE= .TRUE. in the INCAR file. More details on these calculations are given in VASPKIT/examples/tdm. If one want to calculate the square of TDM between two state at single k-point. Just run VASPKIT with task 712, for example, Cleary, the calculate total-square of TDM at$\text{X}$point for cubic CsPbI$_3\$ is 201.62 Debey$$^2$$.