Simplified Range-Separation Tuning as a Practical Starting Point for G0W0 and Bethe-Salpeter Calculations

TL;DR

This work introduces a simplified, density-based range-separation tuning via the effective parameter $\omega_{\mathrm{eff}}$ as a universal starting point for $G_0W_0$ and BSE calculations. By testing on the GW100 IP benchmark, Thiel excitation benchmarks, and hydrogenated silicon quantum dots, the authors show that $\omega_{\mathrm{eff}}$ delivers IPs and excitation energies in close agreement with high-level references, while avoiding the computational overhead of multi-step optimally tuned RSH procedures. The $G_0W_0$ corrections largely remove KS-DFT starting-point biases, and BSE spectra remain competitive with the best-tuned starting points. The results demonstrate that $\omega_{\mathrm{eff}}$ is a practical, black-box starting point suitable for large-scale and high-throughput studies of excited-state properties in molecules and nanostructures, with potential extensions to broader material systems and charge-transfer scenarios.

Abstract

The accuracy of one-shot $G_0W_0$ and the Bethe-Salpeter equation (BSE) is well known to be highly sensitive to the choice of the starting-point eigensystem, typically obtained from mean-field theory. A highly effective method explored is the use of density functional approximation (DFA) with a range-separated hybrid (RSH) approach. In this work, we evaluate the performance of $G_0W_0$ in predicting ionization potentials and the BSE for describing neutral excitations, employing a recently proposed, broadly applicable, and computationally efficient range-separation tuning scheme [Singh \textit{et. al.}, Journal of Physical Chemistry Letters, 16, 32, 8198-8208, (2025)]. Our results demonstrate that this simplified tuning protocol provides an accurate starting point for many-body perturbation theory, thereby eliminating the need for conventional, multi-step optimally tuned RSH optimization procedure. The resulting quasiparticle energies from $G_0W_0$ closely reproduce reference ionization potentials, while BSE calculations based on the same tuned RSH orbitals yield quantitatively accurate optical absorption spectra and excitonic properties across a range of molecular systems and clusters.

Figures (5)

• Figure 1: The figure shows the results of the tuning procedure from Eq. \ref{['eq:omega_form']}, with all parameters given in bohr$^{-1}$. Results for the GW100 test set are in the top panel, and those for Thiel's set are in the bottom panel. The numbering on the x-axis aligns with the system order listed in Tables S1-S3 of the SIsupplementary.
• Figure 2: An illustration of how the variation of omega impacts IP's, we also present the cases where $\omega_{OTRSH}$ overestimates the result but $\omega_{eff}$ and $\omega_{HOMO}$ alings well with the reference.
• Figure 3: Visualization of the frontier molecular orbitals (HOMO and LUMO) for Uracil and Butadiene. The plots illustrate the outcomes from three different tuned variants: $GKS$ ($\omega_{eff}$) (A $\&$ D), $GKS$ ($\omega_{OTRSH}$) (B $\&$ E) and $GKS$ ($\omega_{HOMO}$) (C $\&$ F). The def2-TZVPP basis set was used throughout.
• Figure 4: The range separation parameters $\omega$ for few hydrogenated silicon quantum dots (Si$_n$H$_m$). The complete data is available in Table S4 of the SIsupplementary.
• Figure 5: A comparison of the photoabsorption spectra for silicon clusters calculated with TDDFT (left panel) and the many-body BSE (right panel). The simulations were performed with the LC-$\omega$PBEh functional, considering all RS tuning parameters. The calculations have been performed with TZVP basis set.