Add dipole electrostatic potential and field functions

[rahulbalaji13]

Implements dipole_potential() and dipole_field() following the same vectorized NumPy pattern as the monopole functions. Includes proper handling of edge cases (r->0) and comprehensive docstrings with physics formulas.

Builds on PR #2 to extend electrostatics module toward full multipole support.

Context

This PR addresses issue #1 (GSoC 2026: Electrostatics beyond the atomic charges) by implementing the dipole contribution to the multipole electrostatics module.

Implementation Details

• dipole_potential(p, r_vec): Computes V = (p · r̂) / r² in atomic units
• dipole_field(p, r_vec): Computes E = (1/r³)[3(p·r̂)r̂ - p] in atomic units
• Follows the same vectorized NumPy pattern as monopole functions (PR Add monopole electrostatic potential and field with unit tests #2)
• Handles edge cases: r → 0 returns 0.0/zeros safely
• Supports both single positions and arrays
• Comprehensive docstrings with physics formulas

Next Steps

After this PR is reviewed, I plan to:

1. Implement quadrupole functions
2. Create unified multipole interface
3. Add comprehensive unit tests for dipole functions
4. Build analysis utilities (field projection, comparison metrics)

Related

• Builds on Add monopole electrostatic potential and field with unit tests #2 (monopole implementation by @chinmaybhardwaj711)
• Addresses GSOC 2026: Electrostatics beyond the atomic charges #1 (GSoC 2026 issue)