Official Resources
- Homepage: https://koopmans-functionals.org/
- Documentation: https://koopmans.readthedocs.io/
- Source Repository: https://github.com/koopmans-functionals/koopmans
- License: GNU General Public License v3.0
Overview
Koopmans is a spectral functional code designed to predict accurate electronic structures, particularly band gaps and ionization potentials, by enforcing the Generalized Koopmans' Theorem (GKT). It serves as a wrapper and extension around Quantum ESPRESSO, using Wannier90 to construct localized orbitals on which Koopmans-compliant corrections are applied. The code addresses the band gap problem in standard DFT by ensuring that orbital energies correspond directly to charged excitation energies, achieving accuracy comparable to high-level GW calculations but at a significantly lower computational cost.
Scientific domain: Band structure theory, Spectroscopy, Insulators and Semiconductors, Photovoltaics
Target user community: Researchers needing accurate band gaps and spectral properties without the cost of GW
Theoretical Methods
- Generalized Koopmans' Theorem (GKT): Enforces linear behavior of energy with respect to fractional particle number.
- Koopmans-Compliant Functionals:
- KI (Koopmans Integral): Removes curvature in energy vs. occupation.
- KIPZ (Koopmans Integral + Perdew-Zunger): Includes screened self-interaction correction.
- KIER (Koopmans Integral + External Relaxed): accounts for orbital relaxation.
- Screening Parameters: Calculated ab initio via linear response or predicted via Machine Learning.
- Orbital Minimization: Variational optimization of orbital densities.
- Wannier Localization: Uses Wannier functions (from Wannier90) as the variational basis for corrections.
Capabilities
- Spectral Properties:
- Accurate Band Gaps
- Ionization Potentials
- Electron Affinities
- Photoemission Spectra
- Band-edge alignments
- Automated Workflows:
- Automatic determination of screening parameters.
- End-to-end calculation from DFT ground state to spectral properties.
- Machine Learning Integration: Accelerates screening parameter prediction for large systems.
- System Types:
- Molecules (finite systems)
- Crystals (periodic systems)
- Disordered solids and liquids
Key Strengths
- Accuracy vs. Cost: Delivers GW-level accuracy for band gaps at a computational cost comparable to standard DFT (or hybrid functionals).
- Physical Insight: Provides a clear orbital-based picture of excitations using Wannier functions.
- Automation: Streamlines the complex process of calculating screening and corrections.
- Integration: Seamlessly works with the widely used Quantum ESPRESSO and Wannier90 ecosystems.
Inputs & Outputs
- Inputs:
- Quantum ESPRESSO input files (pw.x)
- Wannier90 input files (wannier90.win)
- JSON-based workflow configuration
- Outputs:
- Corrected Band Structures (interpolated)
- Density of States (DOS)
- Screening parameters
- Optimized Wannier orbitals
Interfaces & Ecosystem
- Quantum ESPRESSO: Functions as a driver/wrapper around QE (
pw.x, ph.x).
- Wannier90: Tightly coupled for orbital localization and interpolation.
- ASE: Compatible with Atomic Simulation Environment workflows.
- Python API: Provides a scriptable interface for advanced users.
Performance Characteristics
- Speed: Significantly faster than GW (Many-Body Perturbation Theory). Roughly 2-10x cost of standard DFT depending on functional.
- Scaling: Linear-scaling characteristics arising from the localization of Wannier functions.
- Parallelization: Inherits MPI/OpenMP scalability from Quantum ESPRESSO engines.
Limitations & Known Constraints
- Metals: Primarily designed for systems with a band gap (insulators, semiconductors, molecules); application to metals is non-trivial.
- Dependence on Wannierization: Quality of results depends on obtaining good Maximally Localized Wannier Functions (MLWFs).
- Memory: Can be memory-intensive for large supercells when calculating screening.
Comparison with Other Codes
- vs. GW (Yambo, BerkeleyGW): Koopmans is faster and avoids convergence issues with empty states/frequency integration, though GW is more general for metals.
- vs. Hybrid Functionals (HSE06): Koopmans theory is non-empirical and often yields more accurate gaps than standard hybrids which rely on fixed mixing parameters.
- vs. DFT+U: DFT+U corrects local errors but doesn't guarantee correct spectral properties; Koopmans enforces the correct physical condition for charged excitations.
Application Areas
- Photovoltaics: Accurate band alignment and gap prediction for solar cell materials.
- Catalysis: Correct placement of orbital levels in surface reactions.
- Molecular Electronics: Transport gaps in organic semiconductors.
- Spectroscopy: Interpretation of photoemission experiments.
Community and Support
- Development: Led by the THEOS group (EPFL) and MARVEL NCCR.
- Documentation: Comprehensive ReadTheDocs with tutorials.
- Forum: Support via Quantum ESPRESSO forums and GitHub issues.
Verification & Sources