# Propagation of maximally localized Wannier functions in real-time TDDFT

## TL;DR

This paper introduces a method to propagate maximally localized Wannier functions within real-time TDDFT, enabling improved analysis of excited-state phenomena and electronic dynamics in extended systems.

## Contribution

The authors develop and demonstrate a novel approach for propagating Wannier functions in RT-TDDFT simulations, enhancing the interpretability of electronic excitations and charge transport.

## Key findings

- Effective propagation of Wannier functions demonstrated in optical excitation simulations.
- Application to electronic stopping and quantized charge transport shown.
- Implementation within QB@LL code with performance analysis provided.

## Abstract

Real-time, time-dependent density functional theory (RT-TDDFT) has gained popularity as a first-principles approach to study a variety of excited-state phenomena such as optical excitations and electronic stopping. Within RT-TDDFT simulations, the gauge freedom of the time-dependent electronic orbitals can be exploited for numerical and scientific convenience while the unitary transformation does not alter physical properties calculated from the quantum dynamics of electrons. Exploiting this gauge freedom, we demonstrate propagation of maximally localized Wannier functions within RT-TDDFT. We illustrate its great utility through a number of examples including its application to optical excitation in extended systems using the so-called length gauge, interpreting electronic stopping excitation, and simulating electric field-driven quantized charge transport. We implemented the approach within our plane-wave pseudopotential RT-TDDFT module of the QB@LL code, and performance of the implementation is also discussed.