dipolemoment

Dipole moment is a measure of the separation of positive and negative electric charges in a system, most commonly used to describe the polarity of a molecule. In chemistry, it is a vector quantity that reflects the asymmetry of the charge distribution; it points from the negative to the positive charge.

For a discrete set of charges, the dipole moment is defined as μ = ∑_i q_i r_i, where q_i is the charge and r_i the position vector with respect to a chosen origin. In a simple diatomic molecule with charges +q and -q separated by a distance r, |μ| = q r and the direction is from the negative to the positive nucleus. In molecules without net charge, the dipole moment magnitude depends on geometry and the electronic structure.

The unit most commonly used is the debye (D); 1 D ≈ 3.33564 × 10^-30 C·m. A nonpolar molecule has μ ≈ 0; polar molecules have μ greater than zero, with water around 1.85 D, HCl about 1.08 D, CO about 0.11 D in the gas phase.

Experimentally, dipole moments are inferred from rotational or microwave spectra and from dielectric measurements, and they influence properties such as solubility, boiling points, and solvent interactions. In quantum chemistry, the dipole moment is the expectation value μ = ⟨Ψ|μ̂|Ψ⟩ of the dipole moment operator, dependent on the electronic wavefunction and molecular geometry; it can be computed to assess polarity and interpret spectroscopy.