Automated Workflow for Non-Empirical Wannier-Localized Optimal Tuning of Range-Separated Hybrid Functionals

TL;DR

This work presents a fully automated, non-empirical workflow for Wannier-localized optimally tuned screened range-separated hybrids (WOT-SRSH) to predict band gaps and spectroscopic properties. By leveraging a cheap, robust parameter selection strategy that enforces dielectric screening and an ionization-potential-like constraint, the workflow determines the SRSH parameters $(\alpha,\beta,\gamma)$ with typically 3–5 energy evaluations. Implemented in Jobflow with VASP and Wannier90, the method is validated on 23 semiconductors and insulators, achieving a mean absolute error around $0.1$ eV relative to experiment and comparable to prior benchmarks while reducing tuning cost and human input. This automated approach enables scalable, high-throughput applications of WOT-SRSH and sets the stage for future ML-assisted acceleration and broader material scope.

Abstract

We introduce an automated workflow for generating non-empirical Wannier-localized optimally-tuned screened range-separated hybrid (WOT-SRSH) functionals. WOT-SRSH functionals have been shown to yield highly accurate fundamental band gaps, band structures, and optical spectra for bulk and 2D semiconductors and insulators. Our workflow automatically and efficiently determines the WOT-SRSH functional parameters for a given crystal structure and composition, approximately enforcing the correct screened long-range Coulomb interaction and an ionization potential ansatz. In contrast to previous manual tuning approaches, our tuning procedure relies on a new search algorithm that only requires a few hybrid functional calculations with minimal user input. We demonstrate our workflow on 23 previously studied semiconductors and insulators, reporting the same high level of accuracy. By automating the tuning process and improving its computational efficiency, the approach outlined here enables applications of the WOT-SRSH functional to compute spectroscopic and optoelectronic properties for a wide range of materials.

Figures (2)

• Figure 1: $\Delta I$ tuning landscape for LiF (left) and Si (right). Panels (a)-(b) illustrate the near‐linear dependence of $\Delta I$ on $\alpha$ in the non-range-separated limit ($\beta=0$ and/or $\gamma=0$). Panels (c)-(f) fix $\alpha + \beta = 1 / \varepsilon_{\infty}$, and panels (c)-(d) show $\Delta I$ as a function of the range-separation parameter, $\gamma$, for fixed values of $\alpha$. All curves converging to the common asymptote $\Delta I_{LR}$ as $\gamma\to\infty$. Zero crossings, where $\Delta I=0$, are highlighted by black circles. Panels (e)-(f) collect these zero‐crossings to show the one‐dimensional manifolds in $(\alpha,\gamma)$ space where the optimal tuning constraints are satisfied. The terminations of these curves at $\gamma=0$ indicate a critical value of $\alpha$, below or above which zero crossing will not occur.
• Figure 2: Automated WOT‑SRSH workflow. (a) Schematic of the seven step procedure: perform an SCF unit cell calculation; compute the clamped‐ion dielectric constant $\varepsilon_\infty$; build a cubic supercell, generate maximally localized Wannier functions, and select the highest energy valence Wannier orbital, $\phi_w$; determine the optimal exact‐exchange fraction $\alpha^{\rm opt}$ by two simultaneous non-range-separated hybrid $\Delta I$ calculations, at $\alpha=0.25$ and $0.50$, and a linear fit (green diamonds in panel b); fix $\alpha=\alpha^{\rm opt}$ and $\beta=1/\varepsilon_\infty-\alpha^{\rm opt}$, sample $\Delta I$ at an initial $\gamma$ and test $|\Delta I|<\delta^{\max}$; if un-converged, fit $\Delta I(\gamma)$ using Eq. (\ref{['eq:fit_func']}), predict a new $\gamma$, and iterate; once $|\Delta I|<\delta^{\max}$, finalize $(\alpha,\beta,\gamma)$ and proceed to band structure calculations. (b) Illustration of step four for LiF: green markers denote the two non-range-separated hybrid $\Delta I$ points, the dashed line is the linear fit, the orange square is $-\Delta I_{LR}$, and the purple diamond is the $\Delta I_{LR}$ asymptote; the crossing of the fit with $\Delta I=0$ yields $\alpha^{\rm opt}$. (c) Example of the $\gamma$‐tuning loop (steps 5-6): the blue curve is the erf fit through $\Delta I_1$ and $\Delta I_3$, and successive green markers show $\Delta I(\gamma)$ evaluations (steps 3-5) until convergence.