Atomic Term Symbol Calculator

A Python package for calculating all possible atomic term symbols from electron configurations. This tool uses quantum mechanical principles to determine microstates and derive term symbols including J-coupling.

Features

• Calculate total number of microstates for any electron configuration
• Generate all possible term symbols from electron configurations
• Support for s, p, d, and f orbitals
• Handles multiple electron shells and mixed configurations
• Applies Pauli exclusion principle and Hund's rules
• Calculates J quantum numbers using Russell-Saunders coupling
• Flexible input format (space or dot separated orbitals)

Installation

From Source

1. Clone the repository:

git clone https://github.com/ccheung93/atomic-term-symbol-calculator.git
cd atomic-term-symbol-calculator

2. Create a virtual environment (recommended):

python -m venv venv
source venv/bin/activate  # On Windows: venv\Scripts\activate

3. Install the package in development mode:

pip install -e .

4. To install with testing dependencies:

pip install -e .[test]

Requirements

• Python ≥ 3.8
• numpy
• pandas
• fractions (built-in)
• itertools (built-in)
• re (built-in)

Usage

As a Python Module

from atomic_term_symbol_calculator.terms import calc_term_symbols, calc_microstates

# Calculate term symbols for carbon (2p2)
terms = calc_term_symbols("2p2")
print(terms)
# Output: ['3P0', '3P1', '3P2', '1D2', '1S0']

# Calculate microstates for p2 configuration
microstates = calc_microstates(6, 2)  # 6 positions, 2 electrons
print(microstates)
# Output: 15

# Mixed orbital configurations
terms = calc_term_symbols("2s1.2p1")
print(terms)
# Output: ['3P0', '3P1', '3P2', '1P1']

# d orbital configurations
terms = calc_term_symbols("3d2")
print(terms)

Command Line Usage

python -m atomic_term_symbol_calculator.terms
# Enter configuration when prompted: 2p3

Input Format

Electron configurations can be specified in two formats:

1. Dot separated: 2s1.2p3.3d2
2. Space separated: 2s1 2p3 3d2

The occupancy number can be omitted if it's 1:

• 2p1 is equivalent to 2p
• 3d1 is equivalent to 3d

Examples

Configuration	Description	Example Terms
1s1	Hydrogen	2S1/2
2p1	Boron	2P1/2, 2P3/2
2p2	Carbon	3P0, 3P1, 3P2, 1D2, 1S0
2p3	Nitrogen	4S3/2, 2D3/2, 2D5/2, 2P1/2, 2P3/2
3d1	Sc²⁺	2D3/2, 2D5/2
3d5	Mn²⁺	Multiple terms (high-spin d5)

Testing

Run the test suite:

pytest

Run tests with verbose output:

pytest -v

Run tests for a specific file:

pytest tests/test_terms.py

Run tests with coverage:

pytest --cov=atomic_term_symbol_calculator

Development

Project Structure

atomic-term-symbol-calculator/
├── src/
│   └── atomic_term_symbol_calculator/
│       ├── __init__.py          # Version info
│       └── terms.py             # Main calculation functions
├── tests/
│   └── test_terms.py           # Comprehensive test suite
├── pyproject.toml              # Project configuration
├── README.md                   # This file
└── CLAUDE.md                   # Development guidance

Algorithm Overview

The calculator follows these steps:

1. Parse Configuration: Extract orbital types and electron counts
2. Generate Microstates: Create all possible electron arrangements
3. Apply Quantum Rules: Filter using Pauli exclusion principle
4. Tabulate States: Create ML vs MS quantum number table
5. Extract Terms: Systematically remove term symbols from table
6. Calculate J Values: Apply |L-S| ≤ J ≤ |L+S| coupling rules

Contributing

1. Fork the repository
2. Create a feature branch
3. Add tests for new functionality
4. Ensure all tests pass
5. Submit a pull request

License

MIT License - see LICENSE file for details.

References

• Term Symbols Notes
• Russell-Saunders coupling theory
• Quantum mechanical principles of atomic structure

Author

Charles Cheung (ccheung@udel.edu)