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Pulay forces in density-functional theory with extended Hubbard functionals: from nonorthogonalized to orthogonalized manifolds

Iurii Timrov1*, Francesco Aquilante1*, Luca Binci1*, Matteo Cococcioni2*, Nicola Marzari1*

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

2 Department of Physics, University of Pavia, via Bassi 6, I-27100 Pavia, Italy

* Corresponding authors emails: iurii.timrov@epfl.ch, francesco.aquilante@epfl.ch, luca.binci@epfl.ch, matteo.cococcioni@unipv.it, nicola.marzari@epfl.ch
DOI10.24435/materialscloud:27-pz [version v1]

Publication date: Oct 27, 2020

How to cite this record

Iurii Timrov, Francesco Aquilante, Luca Binci, Matteo Cococcioni, Nicola Marzari, Pulay forces in density-functional theory with extended Hubbard functionals: from nonorthogonalized to orthogonalized manifolds, Materials Cloud Archive 2020.132 (2020), doi: 10.24435/materialscloud:27-pz.


We present a derivation of the exact expression for Pulay forces in density-functional theory calculations augmented with extended Hubbard functionals, and arising from the use of orthogonalized atomic orbitals as projectors for the Hubbard manifold. The derivative of the inverse square root of the orbital overlap matrix is obtained as a closed-form solution of the associated Lyapunov (Sylvester) equation. The expression for the resulting contribution to the forces is presented in the framework of ultrasoft pseudopotentials and the projector-augmented-wave method, and using a plane wave basis set. We have benchmarked the present implementation with respect to finite differences of total energies for the case of NiO, finding excellent agreement. Owing to the accuracy of Hubbard-corrected density-functional theory calculations - provided the Hubbard parameters are computed for the manifold under consideration - the present work paves the way for systematic studies of solid-state and molecular transition-metal and rare-earth compounds.

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External references

Journal reference
I. Timrov, F. Aquilante, L. Binci, M. Cococcioni, N. Marzari, submitted to Phys. Rev. B (2020).
Preprint (Preprint where the method is described)


Density-functional theory DFT+U DFT+U+V Hubbard corrections Hubbard forces Pulay forces Lowdin orthogonalization method CSCS MARVEL Hubbard parameters Hubbard manifold Self-interaction corrections Orbital overlap matrix Lyapunov equation Sylvester equation

Version history:

2020.132 (version v1) [This version] Oct 27, 2020 DOI10.24435/materialscloud:27-pz