使用局域基函数的实时含时密度泛函理论中基于冻结密度嵌入的环境效应
Environmental effects with Frozen Density Embedding in Real-Time Time-Dependent Density Functional Theory using localized basis functions
AI总结：
本文将基于局域基函数和Psi4NumPy框架的实时含时Kohn-Sham方法扩展至冻结密度嵌入（FDE）方案，实现了活性子系统的非耦合时间演化，并证明该方法在弱场和强场下均能稳定传播密度矩阵且结果可靠。
摘要：
Frozen Density Embedding (FDE) 是一种通用的嵌入方案，用于描述分子系统中环境对电子动力学的影响。FDE 通用理论向实时含时 Kohn-Sham 方法的扩展此前已被提出，并在平面波和周期性边界条件下实现 (Pavanello et al. J. Chem. Phys. 142, 154116, 2015)。在本文中，我们将近期基于局域基函数集合并于 Psi4NumPy 框架内开发的实时含时 Kohn-Sham 方法表述 (De Santis et al. J. Chem. Theory Comput. 2020, 16, 2410) 扩展至 FDE 方案。后者以其“非耦合”形式实现（即时间演化仅在活性子系统上进行，而环境子系统保持在其基态），使用并改编了 PyADF 脚本框架的 PyEmbed 模块中已有的 FDE 实现。由于 Psi4NumPy 和 PyADF 均为原生 Python API，这为利用 Python 在代码可读性和可重用性方面的优势进行开发提供了理想框架，从而促进了该实现。我们证明，引入 FDE 势不会在活性子系统密度矩阵的时间传播中引入任何数值不稳定性，并且在外部弱场极限下，低激发态能量的数值结果与使用基于线性响应 TDDFT 的参考 FDE 计算所得结果一致。研究发现，在存在引发非线性效应的强外部场时，该方法也能给出稳定的数值结果。
英文摘要：
Frozen Density Embedding (FDE) represents a versatile embedding scheme to describe the environmental effect on the electron dynamics in molecular systems. The extension of the general theory of FDE to the real-time time-dependent Kohn-Sham method has previously been presented and implemented in plane-waves and periodic boundary conditions (Pavanello et al. J. Chem. Phys. 142, 154116, 2015). In the current paper, we extend our recent formulation of real-time time-dependent Kohn-Sham method based on localized basis set functions and developed within the Psi4NumPy framework (De Santis et al. J. Chem. Theory Comput. 2020, 16, 2410) to the FDE scheme. The latter has been implemented in its "uncoupled" flavor (in which the time evolution is only carried out for the active subsystem, while the environment subsystems remain at their ground state), using and adapting the FDE implementation already available in the PyEmbed module of the scripting framework PyADF. The implementation was facilitated by the fact that both Psi4NumPy and PyADF, being native Python API, provided an ideal framework of development using the Python advantages in terms of code readability and reusability. We demonstrate that the inclusion of the FDE potential does not introduce any numerical instability in time propagation of the density matrix of the active subsystem and in the limit of weak external field, the numerical results for low-lying transition energies are consistent with those obtained using the reference FDE calculations based on the linear response TDDFT. The method is found to give stable numerical results also in the presence of strong external field inducing non-linear effects.
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