Learn from working programs

Read it. Run it.
Follow the source.

Start with four inspectable calculations. Every example names its prerequisites, expected result, runtime class, exact release source, and next guide.

Explore the examples Browse all v0.2.0 source

Runnable, then readable

Small programs, clear outcomes.

The H₂ quickstart uses PyQED 0.3.0; the other examples retain their documented 0.2.0 source. Copy it for a quick inspection, or open the full file when you need its repository context.

01Electronic structure

H₂ in one native RHF calculation

Build a molecule, select PyQED’s built-in integral path, and require a converged restricted Hartree–Fock result.

Prerequisites
PyQED 0.3.0 core install
Typical runtime
Usually seconds on a laptop CPU
Run from repository root
PYTHONPATH=. python examples/quickstart.py
Full source · v0.3.0 Quickstart guide
examples/quickstart.py
from pyqed.qchem import Molecule mol = Molecule(    atom="H 0 0 0; H 0 0 0.74",    unit="angstrom",    basis="sto-3g",)mol.build(eri="auto") mf = mol.RHF().run()if not mf.converged:    raise RuntimeError("The quickstart RHF calculation did not converge.") print(f"RHF energy: {mf.e_tot:.12f} Eh")
ExpectedSTO-3G · 0.74 Å bond length
RHF energy: -1.116759310293 Eh
02Grid dynamics

A harmonic oscillator with Sine DVR

Build the dense Sine DVR Hamiltonian in a few lines and recover the analytic oscillator ladder directly from its eigenvalues.

Prerequisites
PyQED 0.2.0 core install · NumPy
Typical runtime
Usually seconds on a laptop CPU
Run from repository root
PYTHONPATH=. python sine_dvr_harmonic.py
Full source · v0.2.0 DVR guide
sine_dvr_harmonic.py
import numpy as npfrom pyqed.dvr import SineDVR dvr = SineDVR(-8.0, 8.0, 80)hamiltonian = dvr.t() + np.diag(0.5 * dvr.x**2)energies = np.linalg.eigvalsh(hamiltonian)[:4]print(np.array2string(energies, precision=8))
ExpectedFirst four harmonic-oscillator levels
[0.5 1.5 2.5 3.5]
03Open quantum systems

Spin–boson dynamics with HEOM

Define a two-level Hamiltonian, couple it to a Drude bath, and propagate a non-Markovian population observable in one compact calculation.

Prerequisites
PyQED 0.2.0 core install · NumPy · SciPy
Typical runtime
Usually seconds on a laptop CPU
Run from repository root
PYTHONPATH=. python heom_spin_boson.py
Full source · v0.2.0 Open-dynamics guide
heom_spin_boson.py
import numpy as npfrom pyqed import paulifrom pyqed.oqs import HEOMSolver _, sx, _, sz = pauli()H, rho0 = -0.5 * (sx + sz), np.diag([0.0, 1.0])rho = HEOMSolver(H, c_ops=[sz], e_ops=[sz]).run(    rho0, dt=0.02, nt=100, temperature=600,    cutoff=5, reorganization=0.2, nado=5,)print(f"Final <sigma_z>: {rho[0, -1].real:.8f}")
Expected100 steps · five-tier hierarchy
Final <sigma_z>: -0.96907844
04Nonadiabatic dynamics

Shin–Metiu histories with Ehrenfest dynamics

Propagate one two-dimensional trajectory, retain position, population, energy, and norm histories, then render a diagnostic figure.

Prerequisites
PyQED 0.2.0 core install · Matplotlib
Typical runtime
Allow about a minute · 400 steps on a 31×31 grid
Run from repository root
PYTHONPATH=. python examples/namd/ehrenfest_histories.py
Full source · v0.2.0 Dynamics learning path
examples/namd/ehrenfest_histories.py
#!/usr/bin/env python3from pathlib import Path import matplotlib.pyplot as pltimport numpy as np from pyqed import proton_mass as mpfrom pyqed.models.ShinMetiu import ShinMetiu2from pyqed.namd import Ehrenfest  OUT = Path("examples/namd/ehrenfest_histories.png")  def main():    mol = ShinMetiu2()    mol.build(domain=[[-10, 10]] * 2, npts=[31, 31])     ed = Ehrenfest(ndim=mol.ndim, ntraj=1, nstates=mol.nstates, mass=[mp] * 2)    ed.nac_driver = mol.nonadiabatic_coupling    ed.sample(init_state=2, x0=[0.0, 1.3], ax=18.0)    ed.run(dt=0.5, nt=400, nout=2)     populations = np.real(np.diagonal(ed.rho_history, axis1=1, axis2=2))     fig, axes = plt.subplots(3, 1, figsize=(7, 8), sharex=True)     for dim in range(ed.x_history.shape[1]):        axes[0].plot(ed.times, ed.x_history[:, dim], label=f"x[{dim}]")    axes[0].set_ylabel("Position (bohr)")    axes[0].legend(loc="best")     for state in range(populations.shape[1]):        axes[1].plot(ed.times, populations[:, state], label=f"pop[{state}]")    axes[1].set_ylabel("Population")    axes[1].legend(loc="best")     axes[2].plot(ed.times, ed.energy_history, label="Ehrenfest energy")    axes[2].plot(ed.times, ed.norm_history, label="Electronic norm")    axes[2].set_xlabel("Time (a.u.)")    axes[2].legend(loc="best")     fig.tight_layout()    fig.savefig(OUT, dpi=200)    print(f"Saved {OUT}")  if __name__ == "__main__":    main()
ExpectedThree panels: coordinates, populations, energy and norm
Saved examples/namd/ehrenfest_histories.png

Before you scale up

Turn an example into your calculation.

Examples establish a known starting point. Keep the release or commit fixed while you change one physical or numerical choice at a time.

  1. 01
    Pin the software.

    For the H₂ quickstart, install pip install pyqed==0.3.0. For the other examples, install python -m pip install pyqed==0.2.0or work from the v0.2.0 source tag.

  2. 02
    Reproduce the stated result.

    Run from the repository root so relative output paths and local imports resolve as documented.

  3. 03
    Record what changes.

    Preserve units, grids, basis sets, tolerances, optional backends, and convergence checks with your output.