ReciprocalXtal

This repository accompanies the manuscript Crystal Representation in the Reciprocal Space.

@misc{ridwan2026crystalrepresentationreciprocalspace,
      title={Crystal Representation in the Reciprocal Space}, 
      author={Osman Goni Ridwan and Hongfei Xue and Youxing Chen and Harish Cherukuri and Qiang Zhu},
      year={2026},
      eprint={2601.17981},
      archivePrefix={arXiv},
      primaryClass={cond-mat.mtrl-sci},
      url={https://arxiv.org/abs/2601.17981}, 
}

It contains scripts used to generate the figures and demonstrations in the manuscript, focusing on a rotation- and translation-invariant crystal representation built in reciprocal space.

Repository Structure

.
├── reciprocal.py        # Core routines for reciprocal-space representation and P_nl computation
├── rdf_real.py          # Real-space RDF Calculation
├── README.md
├── Fig-4_Pnl_calc/
│   ├── compute_and_plot__Pnl.py   # Computes and visualizes the power spectrum P_nl
├── Fig-5_noise_stability/
│   ├── plot_diamond_noise_robustness.py   # Noise-robustness test (diamond)
└── Fig-6_reconstruction/                   # Reconstruct from noisy structure
    ├── diamond/
    └── quartz/

What This Code Does

• Builds a four-dimensional reciprocal-space representation from structure factors.
• Converts it into a rotationally invariant power spectrum using spherical harmonics.
• Demonstrates:
  • Power-spectrum calculation (Fig. 4),
  • Robustness against noise and symmetry-equivalent perturbations (Fig. 5),
  • Symmetry-constrained reconstruction of crystal structures (Fig. 6).

The scripts are intentionally lightweight and meant to illustrate the core ideas rather than provide a full production framework.

Set Up Conda Environment

We recommend using a dedicated Conda environment to reproduce the results.

conda create -n xtal python=3.10.8
conda activate xtal

# Install PyXtal 
pip install --upgrade git+https://github.com/MaterSim/PyXtal.git@master

This setup provides the minimal environment required to run the example scripts in this repository.