Polarizability

Polarizability is a property that describes how readily the electron cloud of an atom, molecule, or ion is distorted by an external electric field. The distortion produces an induced dipole moment p, which in the simplest isotropic case is proportional to the field: p = α E, where α is the polarizability. For anisotropic systems, the response is described by a polarizability tensor α_ij, and the induced dipole components obey p_i = α_ij E_j. The scalar ᾱ = (α_xx+α_yy+α_zz)/3 gives the average polarizability.

Dynamic polarizability α(ω) generalizes this to oscillating fields of frequency ω and underpins optical dispersion and many spectroscopic phenomena. Values depend on the frequency of the applied field and the electronic structure; they can be computed with quantum‑chemical linear response methods or measured indirectly through optical data such as refractive indices and scattering.

In SI units, α has dimensions of C m^2/V, but it is often quoted in cubic ångströms (Å^3) in chemistry. A useful relation connects α to the macroscopic refractive index via the Lorentz–Lorenz equation: (n^2−1)/(n^2+2) = N α/(3 ε0), where N is the number density and ε0 is the vacuum permittivity. For liquids and solids, this yields estimates of molar refractivity.

Polarizability influences many properties: it governs van der Waals dispersion forces (C6 coefficients scale with α_A α_B), affects dielectric constants and refractive indices, and determines the intensity of Raman scattering through its derivatives with respect to normal modes. It is a central quantity in molecular physics and physical chemistry.