Optical Gaps of Ionic Materials from GW/BSE-in-DFT and CC2-in-DFT

This work presents a density functional theory (DFT)-based embedding technique for the calculation of optical gaps in ionic solids. The approach partitions the supercell of the ionic solid and embeds a small molecule-like cluster in a periodic environment using a cluster-in-periodic embedding method. The environment is treated with DFT, and its influence on the cluster is captured by a DFT-based embedding potential. The optical gap is estimated as the lowest singlet excitation energy of the embedded cluster, obtained using a wave function theory method: second-order approximate coupled-cluster singles and doubles (CC2), and a many-body perturbation theory method: GW approximation combined with the Bethe–Salpeter equation (GW/BSE). The calculated excitation energies are benchmarked against the periodic GW/BSE values, equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) results, and experiments. Both CC2-in-DFT and GW/BSE-in-DFT deliver excitation energies that are in good agreement with experimental values for several ionic solids (MgO, CaO, LiF, NaF, KF, and LiCl) while incurring negligible computational costs. Notably, GW/BSE-in-DFT exhibits remarkable accuracy with a mean absolute error (MAE) of just 0.38 eV with respect to experiments, demonstrating the effectiveness of the embedding strategy. In addition, the versatility of the method is highlighted by investigating the optical gap of a 2D MgCl2 system and the excitation energy of an oxygen vacancy in MgO, with results in good agreement with reported values.本工作提出了一种基于密度泛函理论（DFT）的嵌入技术，用于计算离子晶体的光学带隙。该方法对离子晶体的超胞进行分区，采用团簇嵌入周期性环境方法，将类小分子团簇嵌入至周期性环境中。环境部分采用DFT进行处理，其对团簇的影响通过基于DFT的嵌入势加以捕捉。光学带隙通过嵌入团簇的最低单重激发能进行估算，该激发能分别采用两种方法计算：一类是波函数理论方法——二阶近似耦合簇单双激发（CC2），另一类是多体微扰理论方法——结合贝特-萨尔皮特方程（BSE）的GW近似（GW/BSE）。我们将计算得到的激发能与周期性GW/BSE值、运动方程耦合簇单双激发（EOM-CCSD）结果以及实验数据进行了基准对比。结果表明，DFT嵌入下的CC2方法与DFT嵌入下的GW/BSE方法，均可为多种离子晶体（MgO、CaO、LiF、NaF、KF及LiCl）提供与实验值吻合良好的激发能，且计算成本可忽略不计。值得注意的是，DFT嵌入下的GW/BSE方法展现出了极高的精度，相对于实验值的平均绝对误差（MAE）仅为0.38 eV，证实了该嵌入策略的有效性。此外，本研究还通过计算二维氯化镁体系的光学带隙以及氧化镁中氧空位的激发能，进一步验证了该方法的普适性，所得结果与已报道的数值吻合良好。