TBdMM (Tight-Binding d-Band Moment) is a Python package that computes the tight-binding d-band moment (m_n) and the corresponding Hamiltonian matrix (H) for a given site of a material structure. It is useful for analyzing electronic structures in materials modeling, especially in surface chemistry.

• Compute tight-binding d-band moment (m_n) for a selected atomic site. A few low-order moments: d-band center (first moment), d-band width (related to second moment), d-band skewness (standardized third moment) and d-band kurtosis (standardized fourth moment).
• Construct tight-binding Hamiltonian matrix (H) based on user-defined structure.
• Return both (m_n) and (H).
• Command-line interface (CLI) for straightforward usage in shell scripts or remote servers.
• Python API for integration into custom workflows and research pipelines.

You can install TBdMM in several ways:

pip install TBdMM

git clone https://github.com/your_username/TBdMM.git
cd TBdMM
pip install -e .

After installation, TBdMM provides a command-line tool tbdmm. You can run:

tbdmm -i <input_structure> -s <site_index> -n <order> [-o output_file.npy]

Arguments:

• -i, --input-file: Path to your structure file (e.g., POSCAR, CIF, XYZ, etc.).
• -s, --site-index: The site index of the center atom for which to compute the d-band moment.
• -n, --order: The order of the d-band moment.
• -o, --output-h: (Optional) The file path to save the Hamiltonian matrix (H) in NumPy .npy format.

Example:

tbdmm -i POSCAR -s 10 -n 2 -o H_matrix.npy

Sample output:

m_2 = 0.123456   # example result
Hamiltonian saved to H_matrix.npy

You can also import and use TBdMM in Python scripts or Jupyter notebooks:

from ase.io import read
from TBdMM import TBdMM  # or from TBdMM.calculations import TBdMM

atoms = read("POSCAR")  # Load the structure into an ASE Atoms object

m2, H = TBdMM(atoms, site_index=10, n=2)
print("m2 =", m2)
print("Hamiltonian shape:", H.shape)

This returns a tuple (m2, H), where:

• m2 is the second-order d-band moment.
• H is the constructed Hamiltonian as a NumPy 2D array.

If you are using this package, please consider citing the following papers:

• Phys. Rev. B 110, L121404 (2024)
• J. Chem. Phys. 161, 164702 (2024)