Environmental Effects via Frozen Density Embedding in Real-Time Time-Dependent Dirac–Kohn–Sham Theory: Solvation of Lead Halides

Accurately describing the electronic properties of heavy-element molecular systems in complex environments is essential for advancing technologies such as optoelectronics and solar cells. However, achieving accurate predictions remains challenging because both relativistic and electron correlation effects must be considered equally, along with interactions involving other species in the complex environment (e.g., solvent). This paper extends our real-time time-dependent Dirac-Kohn-Sham (rt-TDDKS) implementation in PyBERTHA-RT to include environmental effects using the "uncoupled" Frozen-Density-Embedding (FDE) scheme, where only the active subsystem evolves dynamically in time. This adaptation utilizes existing FDE functionality within the PyEmbed module of the PyADF scripting framework. The native Python APIs of PyBERTHA-RT and PyADF provide an ideal environment for development, enhancing readability and reusability. We demonstrate that the FDE potential maintains the numerical stability of the active subsystem's density matrix propagation. Illustrative results for lead halides (PbCl₂ and PbI₂) in γ-butyrolactone (GBL) solution show the effects of increasing solvent molecules on absorption spectra. This case study demonstrates the new implementation's applicability to realistic systems, offering a basis for studying electron dynamics in heavy-element molecules in complex environments under linear and nonlinear regimes, relevant to perovskite precursor chemistry.