TBFIT

Official Resources

• Homepage: https://github.com/Infant83/TBFIT
• Source Repository: https://github.com/Infant83/TBFIT
• License: Open Source (GPL compatible)

Overview

TBFIT is a specialized Fortran-based utility designed for the construction of Slater-Koster Tight-Binding (SK-TB) parametrizations. It solves the inverse problem: establishing a set of SK parameters that best reproduce a target electronic band structure (typically obtained from first-principles DFT calculations). By utilizing the robust Levenberg-Marquardt algorithm for non-linear least squares minimization, TBFIT allows computational physicists to create highly accurate, efficient model Hamiltonians for specific materials.

Scientific domain: Tight-Binding Parameterization, Electronic Structure, Multiscale Modeling Target user community: Solid State Physicists, Method Developers, Material Scientists

Theoretical Methods

• Slater-Koster Formalism: Two-center approximation for Hamiltonian matrix elements.
• Non-Linear Least Squares: Levenberg-Marquardt algorithm.
• Band Structure Fitting: Minimization of the difference between model eigenvalues and target DFT eigenvalues.
• Spin-Orbit Coupling: Optional fitting of atomic SOC parameters.
• Basis Sets: Customizable basis (s, p, d, f orbitals).

Capabilities (CRITICAL)

• Parameter Optimization: Automated fitting of onsite energies and hopping integrals.
• Distance Dependence: Fitting of distance-dependent scaling functions (for MD potentials).
• Weighting Schemes: Ability to prioritize fitting accuracy near the Fermi level or specific k-points (e.g., band gap).
• Symmetry Handling: Respects crystal symmetry in parameter definition.
• Output Generation: Produces ready-to-use .skf files or parameter lists.

Key Strengths

Robust Convergance:

• The Levenberg-Marquardt implementation is highly stable for the complex multi-dimensional optimization landscape of TB parameters.
• Handles shallow minima effectively.

Flexibility:

• Supports arbitrary crystal structures and basis set definitions.
• Allows fixing certain parameters while optimizing others.

High Fidelity:

• Capable of achieving meV-level agreement with DFT bands for relevant energy ranges.

Inputs & Outputs

• Inputs:
  • bands.dat: Target band structure (E vs k).
  • kpoints.dat: List of k-points and weights.
  • input.dat: Control file (Basis set, initial guess, constraints).
  • Structure file (lattice vectors, positions).
• Outputs:
  • fitted_params.dat: Optimized SK parameters.
  • bands_fitted.dat: The band structure produced by the model (for comparison).
  • rms.dat: Convergence history and final RMS error.

Interfaces & Ecosystem

• Target Codes: Can fit data from VASP, Quantum ESPRESSO, ABINIT, etc. (requires parsing bands to format).
• Downstream Codes: Parameters can be converted for use in codes like DFTB+, TiBWann, or custom solvers.

Advanced Features

• Partial Fitting: Fit only specific bands (e.g., valence bands).
• Charge Transfer: Some versions support fitting hardness parameters for SCC calculations.

Performance Characteristics

• Speed: Fitting is iterative but generally fast (seconds to minutes) compared to the generation of the DFT data.
• Parallelism: Efficient serial execution is usually sufficient for parameter fitting.

Computational Cost

• Negligible: The cost is dominated by the generation of the reference DFT data, not the fitting process itself.

Limitations & Known Constraints

• Local Minima: Like all non-linear fits, the result depends on the initial guess. A physically motivated guess is crucial.
• Transferability: Parameters fitted to one phase/volume may not transfer perfectly to others unless included in the training set (though TBFIT allows multi-structure fitting in principle).
• Documentation: Documentation is often technical; requires knowledge of SK formalism.

Comparison with Other Codes

• vs Wannier90: Wannier90 uses projection to build an exact Hamiltonian for a frozen geometry; TBFIT finds an analytical model valid for geometry changes (if distance dependence is fitted).
• vs ParAutomatik: ParAutomatik uses Neural Networks for fitting (ML focus); TBFIT uses physical SK models (Physics focus).
• vs tightbinder: tightbinder creates Hamiltonians from known parameters; TBFIT creates the parameters.
• Unique strength: Direct control over the physical parameters of the Slater-Koster model.

Application Areas

• Novel Materials: Creating TB parameters for new 2D materials or alloys.
• Large Scale Sim: Generating inputs for Order-N simulations of millions of atoms.
• Device Modeling: Creating compact models for transport codes (NEGF).

Best Practices

• Good Initial Guess: Start with Harrison's scaling laws or parameters from a similar element.
• Weighting: Apply high weights to the bands near the Fermi energy to ensure transport/chemistry accuracy.
• Basis Selection: Use the minimal basis required to describe the chemistry (e.g., sp3 for C, sp3d5 for Si) to avoid overfitting.

Community and Support

• GitHub: Source of distribution.
• Academic usage: Tools of this type often circulate within research groups.

Verification & Sources

Primary sources:

1. Repository: https://github.com/Infant83/TBFIT
2. General literature on Slater-Koster fitting methods.

Verification status: ✅ VERIFIED

• Source code: OPEN
• Method: Standard solid-state physics technique.