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Wien2wannier: From linearized augmented plane waves to maximally localized Wannier functions
Jan Kunes, Ryotaro Arita, Philipp Wissgott, Alessandro Toschi, Hiroaki Ikeda, Karsten Held
TL;DR
The paper addresses the need to construct localized Wannier orbitals from full-potential LAPW electronic structures produced by Wien2K. It develops an interface to wannier90, along with direct-space MLWF generation and visualization tools, and demonstrates the workflow across several materials. The reported applications include accurate compact representations, strongly spin-orbit-coupled orbitals, and localized FeSb2 orbitals spanning a 22-band pd subspace.
Problem
Localized Wannier orbitals are useful for interpreting bonding and modeling local electronic correlations, but a Wien2K-to-wannier90 interface is needed to construct them from full-potential LAPW calculations.
Method
The paper implements a Wien2K–wannier90 interface that computes Bloch-state overlaps, generates MLWFs, and provides direct-space and visualization post-processing.
Results
The interface represents SrVO3 bands with localized orbitals using 4.3 Å spatial cutoffs, while FeSb2 MLWF spreads range from 0.8 Å2 to 1.2 Å2 for Fe-3d and 3.6 Å2 to 5.0 Å2 for Sb-4p orbitals.
Takeaways & Limitations
The implementation supports tight-binding Hamiltonians, band unfolding, visualization, and strongly spin-orbit-coupled Wannier orbitals in Wien2K-based studies.
Takeaways & Limitations
The Bloch-function phases remain arbitrary except for the imposed periodic gauge constraint.
Abstract
from arXiv · showhide
We present an implementaion of interface between the full-potential linearized augmented plane wave package Wien2k and the wannier90 code for the construction of maximally localized Wannier functions. The FORTRAN code and a documentation is made available and results are discussed for SrVO$_3$, Sr$_2$IrO$_4$ (including spin-orbit coupling), LaFeAsO, and FeSb$_2$.
1. Introduction
Wannier functions complement reciprocal-space band-structure calculations by providing localized orbitals useful for bonding, local phenomena, and correlated-electron modeling. The paper introduces a Wien2K–wannier90 interface that constructs and visualizes maximally localized Wannier functions.
- Motivation: Wannier functions provide localized orbitals that complement extended reciprocal-space wave functions used in DFT band-structure calculations.They can offer insight into chemical bonding and describe phenomena with important local aspects.
- Motivation: Wannier-like orbitals restrict beyond-LDA electronic interactions to computationally manageable subspaces such as transition-metal d orbitals.The on-site interaction is typically dominant, while inter-site terms mainly contribute Hartree effects already included in LDA.
- Related methods: Wannier functions are not unique because Bloch-state phases and k-dependent unitary transformations can be chosen to minimize orbital spread.Marzari and Vanderbilt’s procedure and wannier90 implement this construction of maximally localized Wannier functions.
- Contribution: The interface extends MLWF workflows to full-potential LAPW calculations while supporting applications including tight-binding models, band unfolding, visualization, and spin-orbit-coupled orbitals.Earlier implementations and projection alternatives existed for several other DFT/LDA packages, including FLAPW and Wien2K.
- Contribution: The paper presents a Wien2K–wannier90 interface that generates .eig, .mmn, and .amn files, MLWFs in direct space, workflow scripts, documentation, and XCrysSDen visualization output.The FORTRAN90 programs were tested with gfortran and ifort and were not yet parallelized.
2. Theory
The theory defines MLWFs through unitary transformations of Bloch states and evaluates the required overlaps within the LAPW representation. The implementation separates interstitial and muffin-tin contributions and integrates these calculations into a Wien2K-to-wannier90 workflow.
- 2.1. Wannier functions: MLWFs are obtained by applying a k-dependent unitary transformation to Bloch eigenstates and choosing it to minimize the Wannier spread.The Bloch-state phases are arbitrary apart from the periodic gauge constraint.
- 2.1. Wannier functions: The construction requires overlap integrals on a uniform Brillouin-zone k-mesh, including trial-orbital overlaps for disentanglement and initialization.These overlaps provide the quantities used by wannier90 to determine the MLWFs.
- 2.2. Linearized augmented plane-waves: LAPW divides real space into interstitial regions expanded in plane waves and nonoverlapping muffin-tin spheres expanded in partial atomic waves.Both LAPW and APW+lo basis sets can be used with the interface.
- 2.2. Linearized augmented plane-waves: Inside muffin-tin spheres, the radial functions, spherical harmonics, and expansion coefficients determine the LAPW representation used for overlap evaluation.The Bloch function is uniquely specified by plane-wave coefficients because the remaining coefficients follow from continuity at sphere boundaries.
- 2.2. Linearized augmented plane-waves: The Bloch-overlap calculation in the LAPW basis splits naturally into interstitial and muffin-tin contributions.Muffin-tin terms are evaluated using spherical-harmonic and Bessel-function expansions, Gaunt numbers, and radial integrals.
- Implementation workflow: The workflow generates a full-zone uniform k-mesh and eigenstates, evaluates overlap matrices with wien2wannier, constructs MLWFs in wannier90, and post-processes them for bands, hoppings, and plots.With spin-orbit coupling, the two spin components are evaluated separately and their overlap contributions are added.
3. Results
The interface is demonstrated across materials with different orbital characters, energy windows, spin-orbit coupling, and model sizes. Results show that localization and hopping truncation depend on the chosen Wannier subspace, while the constructed models reproduce the relevant electronic bands.
- SrVO3: For SrVO3, choosing only t2g bands or all V-d and O-p bands produces Wannier descriptions with different localization and spatial-cutoff requirements.The two Hilbert-space choices are compared for the partially filled V-d-t2g states.
- Sr2IrO4: For Sr2IrO4, spin-orbit coupling yields J = 1/2 Wannier orbitals with mixed spin projections and an approximately cubic charge density.The optimized orbitals remain essentially J_eff = 1/2 functions, combining a real xy component in one spin channel with a complex (x ± iy)z component in the other.
- Sr2IrO4: Sr2IrO4 tight-binding bands are governed mainly by nearest- and next-nearest-neighbor hoppings and are essentially converged after five coordination spheres.Including out-of-plane hoppings accounts for the z-axis dispersion.
- LaFeAsO: For LaFeAsO, both d and dpp models reproduce the corresponding bands exactly, but their Fe 3d Wannier shapes and spreads differ.The models use Fe 3d orbitals alone or Fe 3d together with pnictogen/chalcogen and oxygen p orbitals.
- FeSb2: For FeSb2, the [-6eV,3.9eV] frozen window describes all 22 bands within ±6eV, with Fe-3d spreads of 0.8–1.2 Å^2 and Sb-4p spreads of 3.6–5.0 Å^2.The fat-band analysis reveals strongly mixed d-p character across the bands, and hoppings retained through 7.3 Å accurately reproduce the LDA bands.
4. Summary
The paper presents a Wien2K–wannier90 interface for constructing maximally localized Wannier functions and demonstrates applications across several electronic-structure tasks and materials.
- The interface connects the FLAPW code Wien2K with wannier90 to construct maximally localized Wannier functions.
- The examples include tight-binding Hamiltonians for complex systems, bandstructure unfolding, and visualization.
- The implementation also treats strongly spin-orbit-coupled Wannier orbitals.
- The overlap matrices can also be used to calculate interactions with an electromagnetic field beyond the dipole approximation.