# Real-Time Propagation TDDFT and Density Analysis for Exciton Couplings Calculations in Large Systems

## TL;DR

This paper introduces a real-time propagation TDDFT method combined with a local density decomposition technique to analyze exciton couplings and transition properties in large, multi-chromophore systems, enabling detailed exciton dynamics studies.

## Contribution

The authors extend their local density decomposition method to compute exciton dynamic properties using Real-Time Propagation TDDFT, providing a new analytical expression for transition density applicable to complex systems.

## Key findings

- Validated method for transition dipole moments and densities
- Analyzed exciton coupling in benzaldehyde dimers and clusters
- Mapped exciton interactions in a 14-molecule benzaldehyde system

## Abstract

Photo-active systems are characterized by their capacity of absorbing light energy and transforming it. Usually, more than one chromophore is involved in the light absorption and excitation transport processes in complex systems. Linear-Response Time-Dependent Density Functional (LR-TDDFT) is commonly used to identify excitation energies and transition properties by solving well-known Casida's equation for single molecules. However, this methodology is not useful in practice when dealing with multichromophore systems. In this work, we extend our local density decomposition method that enables to disentangle individual contributions into the absorption spectrum to computation of exciton dynamic properties, such as exciton coupling parameters. We derive an analytical expression for the transition density from Real-Time Propagation TDDFT (P-TDDFT) based on Linear Response theorems. We demonstrate the validity of our method to determine transition dipole moments, transition densities and exciton coupling for systems of increasing complexity. We start from the isolated benzaldehyde molecule, perform a distance analysis for $\pi$-stacked dimers and finally map the exciton coupling for a 14 benzaldehyde cluster.