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Projectability disentanglement for accurate and automated electronic-structure Hamiltonians

Junfeng Qiao1*, Giovanni Pizzi1,2*, Nicola Marzari1,2*

1 Theory and Simulations of Materials (THEOS), and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland

2 Laboratory for Materials Simulations (LMS), Paul Scherrer Institut (PSI), CH-5232 Villigen PSI, Switzerland

* Corresponding authors emails:,,
DOI10.24435/materialscloud:v4-e9 [version v1]

Publication date: Mar 17, 2023

How to cite this record

Junfeng Qiao, Giovanni Pizzi, Nicola Marzari, Projectability disentanglement for accurate and automated electronic-structure Hamiltonians, Materials Cloud Archive 2023.44 (2023), doi: 10.24435/materialscloud:v4-e9.


Maximally-localized Wannier functions (MLWFs) are a powerful and broadly used tool to characterize the electronic structure of materials, from chemical bonding to dielectric response to topological properties. Most generally, one can construct MLWFs that describe isolated band manifolds, e.g. for the valence bands of insulators, or entangled band manifolds, e.g. in metals or describing both the valence and the conduction manifolds in insulators. Obtaining MLWFs that describe a target manifold accurately and with the most compact representation often requires chemical intuition and trial and error, a challenging step even for experienced researchers and a roadblock for automated high-throughput calculations. Here, we present a very natural and powerful approach that provides automatically MLWFs spanning the occupied bands and their natural complement for the empty states, resulting in WÎannier Hamiltonian models that provide a tight-binding picture of optimized atomic orbitals in crystals. Key to the success of the algorithm is the introduction of a projectability measure for each Bloch state onto atomic orbitals (here, chosen from the pseudopotential projectors) that determines if that state should be kept identically, discarded, or mixed into a disentangling algorithm. We showcase the accuracy of our method by comparing a reference test set of 200 materials against the selected-columns-of-the-density-matrix (SCDM) algorithm, and its reliability by Wannierizing 21 737 materials from the Materials Cloud.

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File name Size Description
5.7 KiB Descriptions of files
43.4 KiB List of AiiDA calculations for 200 structures
6.4 KiB List of AiiDA calculations for 4 testing materials
Open this AiiDA archive on (
15.2 GiB AiiDA database containing all the calculations


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Wannier functions high-throughput Wannierization MARVEL SNSF

Version history:

2023.117 (version v2) Jul 27, 2023 DOI10.24435/materialscloud:x0-yf
2023.44 (version v1) [This version] Mar 17, 2023 DOI10.24435/materialscloud:v4-e9