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Bloch's theorem in orbital-density-dependent functionals: band structures from Koopmans spectral functionals

Riccardo De Gennaro1*, Nicola Colonna2,1*, Edward Linscott1*, Nicola Marzari1*

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

2 Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institute, 5232 Villigen PSI, Switzerland

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

Publication date: Nov 19, 2021

How to cite this record

Riccardo De Gennaro, Nicola Colonna, Edward Linscott, Nicola Marzari, Bloch's theorem in orbital-density-dependent functionals: band structures from Koopmans spectral functionals, Materials Cloud Archive 2021.193 (2021),


Koopmans-compliant functionals provide a novel orbital-density-dependent framework for an accurate evaluation of spectral properties; they are obtained by imposing a generalized piecewise-linearity condition on the total energy of the system with respect to the occupation of any orbital. In crystalline materials, due to the orbital-density-dependent nature of the functionals, minimization of the total energy to a ground state provides a set of minimizing variational orbitals that are localized, and thus break the periodicity of the underlying lattice. Despite this, we show that Bloch symmetry can be preserved and it is possible to describe the electronic states with a band-structure picture, thanks to the Wannier-like character of the variational orbitals. We also present a method to unfold and interpolate the electronic bands from supercell (Gamma-point) calculations, which enables us to calculate full band structures with Koopmans-compliant functionals. The results obtained for a set of benchmark semiconductors and insulators show a very good agreement with state-of-the-art many-body perturbation theory and experiments, underscoring the reliability of these spectral functionals in predicting band structures.

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Journal reference


DFT photoemission spectra orbital-density-dependent Koopmans functionals electronic bands electronic structure MARVEL/OSP

Version history:

2022.90 (version v2) Jul 08, 2022 DOI10.24435/materialscloud:vh-mk
2021.193 (version v1) [This version] Nov 19, 2021 DOI10.24435/materialscloud:ee-vg