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

## TL;DR

This paper introduces a new method to study the electronic behavior of heavy-element molecules in complex environments, like solvents, using advanced computational techniques.

## Contribution

The novel contribution is extending real-time time-dependent Dirac-Kohn–Sham theory with frozen density embedding to model environmental effects on heavy-element systems.

## Key findings

- The FDE scheme maintains numerical stability in density matrix propagation for active subsystems.
- The method was successfully applied to lead halides in γ-butyrolactone solution, showing solvent effects on absorption spectra.
- The approach is suitable for studying electron dynamics in realistic systems under various regimes.

## Abstract

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.