UVextract

UVextract extracts effective Hubbard interaction parameters (U) and inter-site interactions (V) for a DFT+U+V Hamiltonian by mapping hybrid-functional calculations onto semilocal DFT within a common Wannier-function basis.

The implementation follows the methodology described in:

Parameterizing DFT+U+V from Hybrid Functionals: A Wannier-Function-Based Approach for Strongly Correlated Materials (http://arxiv.org/abs/2602.20814).

Overview

Hybrid density functionals often provide significantly improved electronic structure compared to semilocal DFT approximations, but their computational cost limits applications to large systems and systematic studies.

UVextract transfers hybrid-functional information into an effective low-cost model by constructing interaction parameters (U) and (V) such that a corrected Hamiltonian

$$H^{\mathrm{DFT+U+V}}$$

reproduces the hybrid-functional Hamiltonian in a localized Wannier representation.

The resulting parameters can be directly used in standard DFT+U+V simulations.

Physical Idea

Both hybrid and semilocal DFT calculations are projected onto the same Wannier basis.
Their difference is interpreted as an effective interaction correction.

Parameters are obtained from the condition

$$ H^{\mathrm{hyb}} \approx H^{\mathrm{DFT}} + H^{U+V}. $$

The correction contains:

• on-site interactions $U(0.5I - n_{ii}),$

• inter-site interactions $-V n_{ij},$

where $n_{ij}$ are Wannier occupation matrices.

Fitting is performed inside a finite real-space cluster surrounding a selected atom.

Algorithmic Workflow

The implemented procedure consists of:

1. Reading crystal structure, Wannier basis data, Hamiltonians, and occupation matrices from .am files.

2. Constructing a real-space cluster around an origin atom using a spherical cutoff (in units of alat).

3. Projecting k-resolved Hamiltonians and occupations onto the cluster using k-point weights and phase factors.

4. Grouping Wannier orbitals into angular-momentum shells (s, p, d, f).

5. Building on-site and intersite interaction corrections.

6. Determining optimal (U) and (V) parameters by minimizing the squared mismatch between hybrid and corrected DFT Hamiltonians (upper-triangle elements summed over spins).

Requirements

• Python ≥ 3.9
• numpy
• scipy
• pymatgen

Example setup:

python3 -m venv .venv
source .venv/bin/activate
pip install numpy scipy pymatgen

Required Input Files

The working directory must contain:

system.am
dft_hamilt.am
dft_occm.am
hyb_hamilt.am
hyb_occm.am

File presence is automatically validated at startup.

Generating Hamitonian and occupation matrices in Wanneir functions basis

Wannier Hamiltonian and occupation matrices (*.am) compatible with this workflow can be generated using wannier_ham.x distributed with Quantum ESPRESSO.

Methodological reference:

Dm. Korotin et al.,
Eur. Phys. J. B 65, 91 (2008)
https://doi.org/10.1140/epjb/e2008-00326-3

Usage

python uvextract.py \
    -o ORIGIN_INDEX \
    -d DISTANCE_ALAT \
    [--verbose]
    [--dft-fermi E]
    [--hyb-fermi E]

Options

Option Description

---

-o, --origin Origin atom index (0-based) -d, --distance Cluster radius in units of alat --verbose Print diagnostic matrices --dft-fermi Energy shift subtracted from DFT Hamiltonian --hyb-fermi Energy shift subtracted from hybrid Hamiltonian

Typical Output

The program prints:

• selected cluster atoms,
• projected Hamiltonian and occupation matrices,
• fitted correction matrix,
• corrected Hamiltonian,
• hybrid vs corrected eigenvalues,
• final fitted parameters, e.g.

    U Mg-s = 4.25 eV
    U O-p  = 2.49 eV
    V Mg-s <-> O-p = 1.96 eV
    (distance = 0.50 alat = 2.10 Å)

Citation

If you use UVextract in scientific work, please cite:

Dmitry M. Korotin, Anna A. Anisimova, Vladimir I. Anisimov. Parameterizing DFT+U+V from Hybrid Functionals: A Wannier-Function-Based Approach for Strongly Correlated Materials (http://arxiv.org/abs/2602.20814)