Flaviano José dos Santos^1,2*, Nicola Marzari^1,2*

1 Theory and Simulation 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, 5232 Villigen PSI, Switzerland

* Corresponding authors emails: flaviano.dossantos@psi.ch, nicola.marzari@epfl.ch

DOI10.24435/materialscloud:4q-zx [version v1]

Publication date: Mar 20, 2023

How to cite this record

Flaviano José dos Santos, Nicola Marzari, Fermi energy determination for advanced smearing techniques, Materials Cloud Archive 2023.46 (2023), https://doi.org/10.24435/materialscloud:4q-zx

Description

Smearing techniques are widely used in first-principles calculations of metallic and magnetic materials, where they improve the accuracy of Brillouin zone sampling and lessen the impact of level-crossing instabilities. Smearing introduces a fictitious electronic temperature that smooths the discontinuities of the integrands; consequently, a corresponding fictitious entropic term arises and needs to be considered in the total free energy functional. Advanced smearing techniques – such as Methfessel-Paxton and cold smearing – have been introduced to guarantee that the system’s total free energy remains independent of the smearing temperature at least up to the second order. In doing so, they give rise to non-monotonic occupation functions (and, for Methfessel-Paxton, non-positive definite), which can result in the chemical potential not being uniquely defined. We explore this shortcoming in detail and introduce a numerical protocol utilizing Newton’s minimization method that is able to identify the desired Fermi energy. We validate the method by calculating the Fermi energy of ~20,000 materials and comparing it with the results of standard bisection approaches. In passing, we also highlight how traditional approaches, based on Fermi-Dirac or Gaussian smearing, are actually equivalent for all practical purposes, provided the smearing width is appropriately renormalized by a factor ~2.565. This data set contains the AiiDA databases, scripts, and other data necessary for the reproduction of our results.

Materials Cloud sections using this data

Files

File name	Size	Description
README MD5md5:22755e794ba14d43b341edad3515a1f1	2.9 KiB	README file describe the content of the other files.
bulkAl_Fig2.aiida MD5md5:9513647274239cb9915e241a1b9250ff Open this AiiDA archive on renkulab.io (https://renkulab.io/)	16.8 MiB	AiiDA database for Fig 2
bulkAl_Fig3c.aiida MD5md5:f073cd93c0d1f9882b991557caa514fc Open this AiiDA archive on renkulab.io (https://renkulab.io/)	18.1 MiB	AiiDA database for Fig 3c
bulkAl_Fig4a.aiida MD5md5:acd6ae3ccc1d47597f3b1b3c5462f55d Open this AiiDA archive on renkulab.io (https://renkulab.io/)	2.0 GiB	AiiDA database for Fig 4a
bulkAl_Fig4b.aiida MD5md5:c83f9633fea9c5c0bd66d53b052bae38 Open this AiiDA archive on renkulab.io (https://renkulab.io/)	19.1 MiB	AiiDA database for Fig 4b
new_Fermi_energy_relax_Fig8.aiida MD5md5:55c1a832e8109598c8bdc50435c884e3 Open this AiiDA archive on renkulab.io (https://renkulab.io/)	2.4 GiB	AiiDA database used for Fig 8
aiida_3dd_final_scf.aiida.zip MD5md5:d39e60cd472ede30680f3577bacedce0 Open this AiiDA archive on renkulab.io (https://renkulab.io/)	6.3 GiB	AiiDA database used for the high-throughput study
launch_plot_Figs2-3-4.ipynb MD5md5:2328486f0a8970b47ecbdbafc4eb42fe	703.5 KiB	Jupyter notebook for Figs 2, 3, and 4
fermi_energy_3dd_M-P_Fig5a.ipynb MD5md5:ad36adc44c855f36d903a4f2afd5437e	155.3 KiB	Jupyter notebook for Fig 5a
fermi_energy_3dd_Cold_Fig5b.ipynb MD5md5:3a80efaaffd23d5754f75c9731ebaa5e	321.5 KiB	Jupyter notebook for Fig 5b
analysis_selected_structures_Fig8.ipynb MD5md5:a6675ae792ba1195cfbf1d8a198328cf	567.7 KiB	Jupyter notebook for Fig 8
fermi_energy_3dd_24842struct_SecIIIB.json MD5md5:16f32a0b0871b43362aa759a9c973754	13.4 MiB	Parsed data in JSON format
analysis_selected_structure_HT3_Fig8.json MD5md5:5c0ccbb4b2271bff6fa43d04a2e3f578	195.0 KiB	Parsed data in JSON format
QE_subs.zip MD5md5:ee93af0eaa06367768bd4a2516ec21e4	35.0 KiB	Fortran subroutine to compute the number of electrons

License

Files and data are licensed under the terms of the following license: Creative Commons Attribution 4.0 International.
Metadata, except for email addresses, are licensed under the Creative Commons Attribution Share-Alike 4.0 International license.

External references

Keywords

smearing Fermi energy MARVEL Intersect semiconductors insulators