Dipole Moments

The molecular dipole moment $\overrightarrow{\mu }$ measures the overall polarity of a molecule. sci-form computes it from partial charges and atomic positions.

Dipole Calculation

Formula

The molecular dipole moment is computed as the charge-weighted sum of atomic positions:

$$\overrightarrow{\mu }=\sum _A{q}_A{\overrightarrow{R}}_A$$

where $q_A$ is the partial charge on atom $A$ (from Mulliken or Löwdin analysis) and ${\overrightarrow{R}}_A$ is the Cartesian position of atom $A$.

Unit Conversion

The raw dipole is in atomic units (e·Å). Conversion to Debye (the standard unit for molecular dipoles):

$$|\overrightarrow{\mu }{|}_{\text{Debye}}=|\overrightarrow{\mu }{|}_{\text{a.u.}}\times 4.80321$$

Component Form

The dipole has three Cartesian components:

$${\mu }_x=\sum _A{q}_A{x}_A,{\mu }_y=\sum _A{q}_A{y}_A,{\mu }_z=\sum _A{q}_A{z}_A$$

The magnitude is:

$$|\overrightarrow{\mu }|=\sqrt{{\mu }_x^2+{\mu }_y^2+{\mu }_z^2}$$

Physical Interpretation

• Nonpolar molecules: $|\overrightarrow{\mu }|\approx 0$ D — symmetric charge distribution (CO₂, CH₄, H₂)
• Polar molecules: $|\overrightarrow{\mu }|>0$ — asymmetric charge distribution
  • H₂O ≈ 1.85 D
  • HF ≈ 1.83 D
  • NH₃ ≈ 1.47 D
• Direction: Points from the center of negative charge toward the center of positive charge

Conformer Dependence

The dipole moment depends on the 3D geometry. Different conformers of the same molecule can have different dipole magnitudes and orientations. sci-form computes the dipole for whatever conformer geometry is provided.

API

Rust

use sci_form::compute_dipole;

let result = compute_dipole("O", None);
// result.components: [f64; 3] — (μx, μy, μz)
// result.magnitude: f64 — |μ| in Debye

CLI

sci-form dipole "O"
# Output: JSON with components and magnitude

Python

import sci_form
result = sci_form.dipole("O")
print(result.magnitude)    # ~1.85 D for water
print(result.components)   # [μx, μy, μz]

Validation

• H₂O: magnitude in range 1.5–2.5 D
• H₂: magnitude ≈ 0 D (symmetric)
• CH₄: magnitude ≈ 0 D (tetrahedral symmetry)
• HF: dipole points from H toward F (more electronegative)
• Consistency: $|\overrightarrow{\mu }|=\sqrt{{\mu }_x^2+{\mu }_y^2+{\mu }_z^2}$ always holds