Tutorials

These tutorials show the practical usage of PySCIVR step by step.

The first five tutorials, from 1. Single Point Calculation to 5. Spectrum Calculation, go through the whole procedure of an SC-IVR calculation: potentials, constrained dynamics, Hessians and monodromy matrices, direct dynamics in curvilinear coordinates, and spectra. They use simple examples that run in a short time.

The following tutorials, from 6. Rotational Spectra of Hydrogen, compute the spectra of actual molecules with the phase-space sampling, reproducing the calculations in the paper.

The advanced tutorials show calculations not covered in the paper, and how to extend PySCIVR to other coordinates and molecules.

• 10. Pyramidal Inversion Spectra of Ammonia defines custom coordinates (the out-of-plane angle and the differences of bond angles) by register_kind, constructs a one-dimensional Hamiltonian by the rigid scan, and compares the levels with the exact results of the discrete variable representation.

• 11. Ro-vibrational Spectra of Methane uses the normal mode coordinate in the body frame together with the rotation, which describes the rovibrational motion without constructing the rovibrational Hamiltonian.

• 12. Spectra with Custom Initial States uses the DVR eigenstates obtained in the ammonia tutorial as the initial states by defining their overlap with the coherent states, and examines the accuracy of the semiclassical propagation level by level.

Running the tutorials

The tutorials are Jupyter notebooks in docs/notebooks. Move to this directory

and start Jupyter Lab in the virtual environment of PySCIVR:

cd docs/notebooks
uv run --with jupyterlab jupyter lab

Alternatively, open the notebooks in VS Code and select .venv/bin/python in the repository as the kernel.

Precomputed data, such as the trajectories of butane and the spectra computed in the tutorials, are available at Zenodo (https://doi.org/10.5281/zenodo.22639777). Download them as needed and place them in docs/notebooks.

Basics

• 1. Single Point Calculation
• 2. Constrained Dynamics
• 3. Hessian and Variation
• 4. Direct Dynamics in Curvilinear Coordinates
• 5. Spectrum Calculation

Examples

• 6. Rotational Spectra of Hydrogen
• 7. Ro-vibrational Spectra of Hydrogen
• 8. Rotational Spectra of Methane
• 9. Torsional Spectra of Butane

Advanced

• 10. Pyramidal Inversion Spectra of Ammonia
• 11. Ro-vibrational Spectra of Methane
• 12. Spectra with Custom Initial States