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

TL;DR

This work addresses the inadequacy of local/semilocal RT-TDDFT in describing excitonic dynamics in periodic systems by integrating range-separated hybrid functionals into RT-TDDFT using a numerical-atomic-orbital basis with RI efficiency. It analyzes two regularization schemes for the Coulomb singularity (truncated Coulomb vs auxiliary-function correction) and demonstrates that the auxiliary-function approach provides superior convergence for long-range exchange, particularly in LRCH functionals. To accurately capture excitonic effects under external fields, the authors adopt a hybrid gauge that includes position-dependent phases, improving absorption predictions compared with the velocity gauge. The methodology is validated on Si, monolayer h-BN, and Cs$_2$NaInCl$_6$, showing improved excitonic spectra and band-gap descriptions, and offering a practical route for real-time simulations of excited-state dynamics in extended systems.

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.

Figures (6)

• Figure 1: HF calculations using the Spencer-Alavi and the auxiliary function correction methods are performed to obtain the energy (on the left) and band gap (on the right) variations with respect to the ${\bf k}$-points for Si, AlP, and NaCl. The results are referenced to those obtained with the auxiliary function correction method, using ${\bf k}$-points set to $12 \times 12 \times 12$ ($E_0$/$E_{g0}$).
• Figure 2: LC-PBE calculations using the Spencer-Alavi and the auxiliary function correction methods are performed to obtain the energy (on the left) and band gap (on the right) variations with respect to the ${\bf k}$-points for Si, AlP, and NaCl. The results are referenced to those obtained with the auxiliary function correction method, using ${\bf k}$-points set to $12 \times 12 \times 12$ ($E_0$/$g_0$). When the number of ${\bf k}$-points is insufficient, the Spencer-Alavi method calculations do not converge, and therefore no data points are shown in the figure.
• Figure 3: The variation of the radial functions of different Coulomb potentials with respect to $q$ is shown, where GH refers to the bare Coulomb potential ($\alpha = 1.0$, $\beta = 0.0$), SRCH to the short-range Coulomb potential ($\mu = 0.106$ Bohr$^{-1}$, $\alpha = 0.0$, $\beta = 1.0$), and RSH to the range-separated Coulomb potential ($\mu = 0.106$ Bohr$^{-1}$, $\alpha = 1.0$, $\beta = -0.8$), corresponding to the blue, green, and red solid lines, respectively. The blue and red dashed lines represent the truncated bare Coulomb potential and range-separated Coulomb potential at $R_c = 20$ Bohr, respectively.
• Figure 4: (a) Absorption spectra ($\operatorname{Im}\varepsilon(\omega)$) of Si obtained from RT-TDDFT calculations using different functionals (PBE, SRCH, LRCH), with simulations performed using the hybrid gauge and the external electric field applied along the $z$-direction. (b) A comparison of the Si absorption spectra obtained from RT-LRCH simulations using the hybrid (hyb) and velocity (vel) gauges.
• Figure 5: The current density $j(t)$ and the imaginary part of the dielectric function $\operatorname{Im}\varepsilon(\omega)$ for h-BN calculated using RT-TDDFT with different functionals (PBE, LRCH, GH), are shown.