Generalized Kohn-Sham density functional theory is a popular computational tool for the ground state of extended systems, particularly within range-separated hybrid (RSH) functionals that capture the long-range electronic interaction. Unfortunately, the heavy computational cost of the nonlocal exchange operator in RSH-DFT usually confines the approach to systems with at most a few hundred electrons. A significant reduction in the computational cost is achieved by representing the density matrix with stochastic orbitals and a stochastic decomposition of the Coulomb convolution (J. Phys. Chem. A 2016, 120, 3071). Here, we extend the stochastic RSH approach to excited states within the framework of linear-response generalized Kohn-Sham time-dependent density functional theory (GKS-TDDFT) based on the plane-wave basis. As a validation of the stochastic GKS-TDDFT method, the excitation energies of small molecules N2 and CO are calculated and compared to the deterministic results. The computational efficiency of the stochastic method is demonstrated with a two-dimensional MoS2 sheet (∼1500 electrons), whose excitation energy, exciton charge density, and (excited state) geometric relaxation are determined in the absence and presence of a point defect.

中文翻译：

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具有随机范围分离混合动力的线性响应时间相关密度泛函理论。

广义Kohn-Sham密度泛函理论是用于扩展系统基态的流行计算工具，尤其是在捕获远程电子交互作用的范围分隔混合（RSH）功能中。不幸的是，RSH-DFT中非本地交换算符的沉重计算成本通常将方法限制在最多具有数百个电子的系统中。通过用随机轨道和库仑卷积的随机分解表示密度矩阵，可以显着降低计算成本（J. Phys。Chem。A 2016，120，3071）。在这里，我们在平面波基础上，在线性响应广义Kohn-Sham时变密度泛函理论（GKS-TDDFT）的框架内，将随机RSH方法扩展到激发态。作为对随机GKS-TDDFT方法的验证，计算了小分子N2和CO的激发能，并将其与确定性结果进行了比较。用二维MoS2片（约1500个电子）证明了随机方法的计算效率，该片的激发能，激子电荷密度和（激发态）几何弛豫是在不存在和存在点缺陷的情况下确定的。