Real-time time-dependent density functional theory simulations with range-separated hybrid functionals for periodic systems

TL;DR

This paper develops a real-time TDDFT method with range-separated hybrid functionals for periodic systems, improving the accuracy of ultrafast excitonic dynamics simulations by addressing Coulomb singularity and gauge choices.

Contribution

It introduces a new implementation of RT-TDDFT with RSH functionals for periodic systems, benchmarking Coulomb treatment schemes and gauge choices for enhanced accuracy.

Findings

Auxiliary-function correction outperforms truncated Coulomb potential in convergence.

Hybrid gauge with position-dependent phases yields more accurate excitonic absorption.

Implementation improves modeling of ultrafast excitonic dynamics in materials.

Abstract

Real-time time-dependent density functional theory (RT-TDDFT) is a powerful approach for investigating various ultrafast phenomena in materials. However, most existing RT-TDDFT studies rely on adiabatic local or semi-local approximations, which suffer from several shortcomings, including the inability to accurately capture excitonic effects in periodic systems. Combining RT-TDDFT with range-separated hybrid (RSH) functionals has emerged as an effective strategy to overcome these limitations. The RT-TDDFT-RSH implementation for periodic systems requires careful treatment of the Coulomb singularity and choosing proper gauges for the incorporation of external fields. We benchmark two schemes for treating the Coulomb singularity - the truncated Coulomb potential and the auxiliary-function correction - and find that the latter shows better convergence behavior and numerical stability for long-range corrected hybrid functions. Additionally, we assess the impact of gauge choice in simulations using numerical atomic orbitals and show that the recently proposed hybrid gauge incorporating position-dependent phases provides a more accurate description of excitonic absorption than the conventional velocity gauge. Our implementation significantly improves the accuracy of RT-TDDFT-RSH for modeling ultrafast excitonic dynamics in periodic systems.