polarizabilities

Polarizability is a property of atoms and molecules describing how easily their electron cloud is distorted by an external electric field. When subjected to a uniform field E, the induced dipole moment p is related by p = α · E, where α is the polarizability tensor. For isotropic or randomly oriented samples, an average scalar polarizability ᾱ can be defined as the mean of the tensor’s diagonal elements. In anisotropic systems, α has components α_xx, α_yy, α_zz and may depend on orientation and symmetry.

Polarizability can be static (frequency-independent) or dynamic (frequency-dependent). The static polarizability α0 describes response to a constant field, while the dynamic polarizability α(ω) describes response to an oscillating field of frequency ω and exhibits dispersion and resonances near electronic transitions. Experimental and computational methods determine α; experiments include dielectric and refractive-index measurements, Stark effect spectroscopy, and dispersion interactions; computations use ab initio and density functional theory, with attention to basis-set completeness and electron correlation.

Polarizability is related to many phenomena and properties: it governs long-range intermolecular forces (London dispersion interactions; C6 coefficients scale with polarizabilities), contributes to optical properties (refractive index via the Lorentz–Lorenz relation), and forms the basis for nonlinear optical responses via higher-order polarizabilities such as hyperpolarizability β and γ.

Applications span materials science, chemistry, and physics, including the design of polarizable materials, dyes, sensors, and nonlinear optical components.