h-orbital 1.5.1

Analytic hydrogen orbital slice visualizer

H-orbital

H-orbital is a small Python package and CLI tool that plots 2D slices of hydrogen atomic orbitals from quantum numbers (n, l, m).

This project is a teaching utility for Zhuang Lin's Structural Chemistry course.

The implementation uses the analytic quantum-mechanical solution:

[ \psi_{n,l,m}(r,\theta,\phi)=R_{n,l}(r)Y_l^m(\theta,\phi) ]

No numerical Schrodinger solver is used.

Features

• CLI input with 1 to 3 quantum numbers: n [l] [m]
• Missing quantum numbers default to zero
• Rendering modes:
  • density for (|\psi|^2)
  • real for (\Re(\psi))
  • imag for (\Im(\psi))
  • real_imag for side-by-side real/imag plots
  • radial_distribution for (r^2|R_{n,l}(r)|^2) vs (r)
  • spherical_harmonic for side-by-side (\Re(Y_l^m)) and (\Im(Y_l^m))
• Smart defaults for plane, value, and range if omitted
• Default color scaling is linear (--scale linear)
• Optional manual slice plane control by CLI:
  • --plane x --value c (plane x=c)
  • --plane y --value c (plane y=c)
  • --plane z --value c (plane z=c)
• Select colormap (--cmap), default is RdYlBu_r
• Optional contour-only line rendering via --line-mode
  • signed fields: positive solid lines and negative dashed lines
  • line colors come from the selected colormap's positive/negative ends
  • density fields: solid contour lines only (no filled surface)
• Density mode uses the positive-value half of the selected colormap, so zero stays near blank and higher values become progressively darker.
• Colorbar toggle: --colorbar / --no-colorbar (default: off)

Install Dependencies

Create and activate a virtual environment, then install:

python -m pip install -e .

This installs required libraries from pyproject.toml.

Usage

Run from repository root:

./H-orbital 2 1 0

GUI Usage

Launch the graphical interface:

./H-orbital-ui

GUI layout:

• Top panel: common parameters (n, l, m, mode, plane, value) and Plot
• Top panel: includes a Colorbar toggle switch
• Advanced dialog: finer controls (points, colormap, scale, Draw nodal lines) with common colormap options and custom Matplotlib names
  • Line mode (contours only) toggle is available below colormap
  • in density mode, symlog is disabled
• Middle area: interactive Matplotlib plot canvas
• Bottom slider: range control in units of a0
• Export button: choose PNG, SVG, or PDF in one save dialog (default PNG)

If you run without arguments, the command prints full help:

./H-orbital

Examples:

# 1s orbital, defaults l=0, m=0
./H-orbital 1

# Real part of 2p(m=0) on z=0 plane
./H-orbital 2 1 0 --mode real --plane z --value 0

# Probability density of 3d(m=1) on y=0.5 a0 plane
./H-orbital 3 2 1 --mode density --plane y --value 0.5 --scale log

# Two-panel real and imaginary parts
./H-orbital 3 2 2 --mode real_imag --plane z --value 0 --cmap RdYlBu_r --scale symlog

# Contour-only line mode with colormap endpoint colors
./H-orbital 4 2 0 --mode real --line-mode --cmap coolwarm

# Radial distribution (independent of plane/value)
./H-orbital 3 0 0 --mode radial_distribution

# Spherical harmonic map (angles only, independent of plane/value)
./H-orbital 3 2 1 --mode spherical_harmonic --scale symlog

Output Naming

If --output is not provided, a filename is generated automatically, e.g.:

orbital_n2_l1_m0_real_z0p0.png

Notes on Units

• Input --value and --range are in units of Bohr radius a0.
• --value means the constant coordinate of the selected slicing plane.
  • Example: --plane x --value 0 means plotting the plane x = 0 * a0.
• If --plane is omitted (default auto), the tool picks a central plane (x=0, y=0, or z=0) that best reveals structure for the selected mode.
• If --value is omitted, the tool uses 0 in the selected plane.
• If --range is omitted, the tool estimates a range from radial probability support and mode-aware heuristics to avoid clipping while preventing excessive zoom-out.
• In radial_distribution and spherical_harmonic modes, --plane and --value are not used.
• If --scale is omitted, the default is linear.
• You can still choose --scale log (good for density) or --scale symlog (good for signed fields).
• Internal wavefunction formulas are evaluated in SI meters.

Development

Run tests:

pytest

Run a single test:

pytest tests/test_quantum_numbers.py::test_parse_single_value_defaults_l_and_m

Version

Current stable version: 1.5.1.

License

This project is distributed under the MIT License. See LICENSE.