HP - A code for the calculation of Hubbard parameters using density-functional perturbation theory

We introduce HP, an implementation of density-functional perturbation theory, designed to compute Hubbard parameters (on-site U and inter-site V ) in the framework of DFT+U and DFT+U+V. The code does not require the use of computationally expensive supercells of the traditional linear-response approach; instead, unit cells are used with monochromatic perturbations that significantly reduce the computational cost of determining Hubbard parameters. HP is an open-source software distributed under the terms of the GPL as a component of QUANTUM ESPRESSO. As with other components, HP is optimized to run on a variety of different platforms, from laptops to massively parallel architectures, using native mathematical libraries (LAPACK and FFTW) and a hierarchy of custom parallelization layers built on top of MPI. The effectiveness of the code is showcased by computing Hubbard parameters self-consistently for the phospho-olivine LixMn1/2Fe1/2PO4 (x = 0, 1/2, 1) and by highlighting the accuracy of predictions of the geometry and Li intercalation voltages. Program summaryProgram Title: HP CPC Library link to program files: https://doi .org /10 .17632 /xsbtkpknf7 .1 Licensing provisions: GNU General Public License v 2.0 Programming language: Fortran 95 External routines: HP is a tightly integrated component of the QUANTUM ESPRESSO distribution and requires the standard libraries linked by it: BLAS, LAPACK, FFTW, MPI.Nature of problem: Calculation of Hubbard interaction parameters for DFT+U and DFT+U+V.Solution method: Hubbard parameters are expressed in terms of the inverse response matrices to localized perturbations of the atomic occupations. The response matrices are computed using densityfunctional perturbation theory to first order (linear-response theory) in the reciprocal space, that allows to reconstruct the response to a localized perturbation (obtained from calculations in an appropriately sized supercell) as the superposition of the responses to a series of monochromatic perturbations in a primitive unit cell, thus reducing significantly the computational cost. The response matrices are computed via a self-consistent solution of the static Sternheimer equation, whose implementation does not require the calculation of any virtual states. Pseudopotentials (norm-conserving, ultrasoft, projector augmented wave) are used in conjunction with plane-wave basis sets and periodic boundary conditions. Additional comments including restrictions and unusual features: Local and semi-local exchange-correlation kernels only. Noncollinear spin-polarized formalism is not supported, only collinear spin-polarized or non-spin-polarized cases can be treated. Spin-orbit coupling cannot be used. Calculation of Hund's J is not supported. Multiple Hubbard channels per atom are not supported. The Hubbard manifold can be only constructed on atomic orbitals, both orthogonalized and non-orthogonalized, while Wannier functions (as well as other localized basis sets) are not supported. The linear-response approach we adopt here typically results in Hubbard parameters that are unphysically large for closed shell states [1]. No virtual orbitals are used, nor even calculated.The distribution file of this program can be downloaded from the QUANTUM ESPRESSO website: http:// www.quantum -espresso .org/, and the development version of this program can be downloaded via Git from the GitLab website: https://gitlab .com /QEF /q-e. Interactions with end users of the HP code happen via a mailing-list forum of QUANTUM ESPRESSO: https://www.quantum -espresso .org /forum. Documentation of the HP code is tightly coupled with the code and is done via standard code comments; different subroutines that implement different equations of the DFPT formalism contain references to the two main papers [2,3] describing in detail theory behind the implementation.(c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).