Polarizability usually refers to the tendency of matter, when subjected to an electric field, to acquire an electric dipole moment in proportion to that applied field. It is a property of particles with an electric charge. When subject to an electric field, the negatively charged electrons and positively charged atomic nuclei are subject to opposite forces and undergo charge separation. Polarizability is responsible for a material's dielectric constant and, at high (optical) frequencies, its refractive index. The polarizability of an atom or molecule is defined as the ratio of its induced dipole moment to the local electric field; in a crystalline solid, one considers the dipole moment per unit cell. Note that the local electric field seen by a molecule is generally different from the macroscopic electric field that would be measured externally. This discrepancy is taken into account by the Clausius–Mossotti relation (below) which connects the bulk behaviour (polarization density due to an external electric field according to the electric susceptibility χ = ε r − 1 {\displaystyle \chi =\varepsilon _{\mathrm {r} }-1} ) with the molecular polarizability α {\displaystyle \alpha } due to the local field. Magnetic polarizability likewise refers to the tendency for a magnetic dipole moment to appear in proportion to an external magnetic field. Electric and magnetic polarizabilities determine the dynamical response of a bound system (such as a molecule or crystal) to external fields, and provide insight into a molecule's internal structure. "Polarizability" should not be confused with the intrinsic magnetic or electric dipole moment of an atom, molecule, or bulk substance; these do not depend on the presence of an external field.
Electric polarizability
Definition Electric polarizability is the relative tendency of a charge distribution, like the electron cloud of an atom or molecule, to be distorted from its normal shape by an external electric field. The polarizability α {\displaystyle \alpha } in isotropic media is defined as the ratio of the induced dipole moment p {\displaystyle \mathbf {p} } of an atom to the electric field E {\displaystyle \mathbf {E} } that produces this dipole moment.
α = | p | | E | {\displaystyle \alpha ={\frac {\left|\mathbf {p} \right|}{\left|\mathbf {E} \right|}}}
Polarizability has the SI units of C·m2·V−1 = A2·s4·kg−1 while its cgs unit is cm3. Usually it is expressed in cgs units as a so-called polarizability volume, sometimes expressed in Å3 = 10−24 cm3. One can convert from SI units ( α {\displaystyle \alpha } ) to cgs units ( α ′ {\displaystyle \alpha '} ) as follows:
α ′ ( c m 3 ) = 10 6 4 π ε 0 α ( C ⋅ m 2 ⋅ V − 1 ) = 10 6 4 π ε 0 α ( F ⋅ m 2 ) ≈ 8.988 × 10 15 × α ( F ⋅ m 2 ) {\displaystyle \alpha '(\mathrm {cm} ^{3})={\frac {10^{6}}{4\pi \varepsilon _{0}}}\alpha (\mathrm {C{\cdot }m^{2}{\cdot }V^{-1}} )={\frac {10^{6}}{4\pi \varepsilon _{0}}}\alpha (\mathrm {F{\cdot }m^{2}} )\approx 8.988{\times }{10}^{15}\times \alpha (\mathrm {F{\cdot }m^{2}} )}
where ε 0 {\displaystyle \varepsilon _{0}} , the vacuum permittivity, is ≈8.854 × 10−12 (F/m). If the polarizability volume in cgs units is denoted α ′ {\displaystyle \alpha '} the relation can be expressed generally (in SI) as α = 4 π ε 0 α ′ {\displaystyle \alpha =4\pi \varepsilon _{0}\alpha '} . The polarizability of individual particles is related to the average electric susceptibility of the medium by the Clausius–Mossotti relation:
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