Automated mixing of maximally localized Wannier functions into target manifolds

Junfeng Qiao, Giovanni Pizzi & Nicola Marzari

npj Computational Materials9: 206 (2023).

编辑概述：电子结构计算：从MLWFs到MRWFs

最大局域化Wannier函数（MLWFs）是周期晶体电子结构的精确降阶模型。从布洛赫波函数生成MLWFs通常需要选择初始猜测，这些猜测通常是通过化学直觉和试错来进行的。由于低能电子结构通常可以利用原子轨道的紧束缚模型来描述，因此初始猜测通常选择类氢的s、p、d、f轨道。然而，当涉及到仅有价带的情况，或者特别是与更高能带混合的导带的情况，可能难以确定好的初始猜测。但许多物理性质（如电极化）依赖于占据多种的Wannier函数（所有价带Wannier函数的Wannier中心之和）。此外，使用专用的MLWFs意味着可以获得更小的紧束缚模型，在计算时更高效。来自瑞士洛桑联邦理工学院材料理论与模拟中心的Junfeng Qiao等，自动混合最大局域化Wannier函数（MRWFs）到多目标的方法，通过对具有能系的各个子能带（每个k点）构造MLWFs来实现多能带分离。该方法自然适用于多价带和导带的情况，也能自然扩展到任何其他孤立的能带组。作者对硅和二硫化钼的研究结果表明，最终价带/导带MLWFs准确地恢复了成键/反键轨道的化学属性，并准确地再现了多价带/导带混合能带结构的价带/导带。该工作为不同材料的电子结构能带计算提供了新途径。

Editorial Summary: Electronic structure calculations——From MLWFs to MRWFs

Maximally localized Wannier functions (MLWFs) are accurate reduced-order models for the electronic structures of periodic crystals. The generation of MLWFs from Bloch wavefunctions typically requires a choice of initial guesses, which are often conjectured from chemical intuition with trial and error. The initial guesses are usually chosen from the hydrogenic s, p, d, f orbitals, since the low-energy electronic structure can often be well described by a tight-binding model of atomic-like orbitals.However, when it comes to the cases of valence bands (VB) alone, or especially conduction bands (CB) which are mixed with higher-energy bands, it might become difficult to identify good initial guesses. Meanwhile, many physical properties (such as the electric polarization) depend only on the Wannier functions (WFs) of the occupied manifold (sum of Wannier centers of all the valence WFs). Using dedicated MLWFs means that one can obtain smaller tight-binding models that are thus more efficient when computing. In this work, Junfeng Qiao et al. from the Theory and Simulations of Materials, École Polytechnique Fédérale de Lausanne, introduced an automated method (manifold-remixed Wannier functions (MRWF)) to separate band manifolds by constructing MLWFs for the respective submanifolds that have finite energy gaps (at each k-point) between them. The method naturally extends to the case of valence and conduction manifolds, but also to any other case of isolated groups of bands. Results on silicon and MoS₂ suggested that the final valence (conduction) MLWFs restore faithfully chemical intuition for bonding/anti-bonding orbitals, and accurately reproduced the valence/conduction part of the band structure of the valence plus conduction manifold. The proposed approach provides a new avenue for electronic band structure calculations for a variety of materials.