Polarizable

Polarizable describes a property of atoms, molecules, or materials that can develop an induced electric dipole moment when exposed to an external electric field. This response arises from the distortion of the electron cloud relative to the nuclei and depends on the electronic structure and the frequency of the applied field. A polarizable object does not necessarily have a permanent dipole; even nonpolar species can polarize in a field.

Mathematically, the induced dipole moment p is related to the external electric field E by p = α · E, where α is the polarizability. For isotropic media α is a scalar, while in general it is a rank-2 tensor to describe direction-dependent response. The static (zero-frequency) polarizability describes response to a constant field, whereas the dynamic polarizability α(ω) describes frequency-dependent response and electronic resonances. In SI units, polarizability has dimensions of C m^2 V^-1; it is often expressed as a volume (for small particles, 1 Å^3 ≈ 1.0×10^-30 m^3) in many chemical contexts.

Polarizability influences many properties: it determines how a substance interacts with light (dispersion and refractive index via relations such as the Lorentz–Lorenz equation), governs van der Waals forces between neutral species, and affects Raman and infrared scattering signatures. Anisotropic molecules exhibit different polarizability components along different axes, leading to orientation-dependent optical responses.

Measurement and calculation of polarizability are central in chemistry and materials science. It can be inferred from refractive index measurements, Stark spectroscopy, or molecular beam experiments, and is also computed from quantum-chemical methods to predict molecular interactions and optical properties.