# Polarizability

For electromagnetic waves, see Polarization (waves). For other uses, see Polarization (disambiguation).

Polarizability is the ability to form instantaneous dipoles. It is a property of matter. Polarizabilities determine the dynamical response of a bound system to external fields, and provide insight into a molecule's internal structure.[1]

## 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, which is applied typically by inserting the molecule in a charged parallel-plate capacitor, but may also be caused by the presence of a nearby ion or dipole.

The polarizability $\alpha$ is defined as the ratio of the induced dipole moment $\boldsymbol{p}$ of an atom to the electric field $\boldsymbol{E}$ that produces this dipole moment.[2]

$\boldsymbol{p} = \alpha \boldsymbol{E}$

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, instead of cm3 it is sometimes expressed in Å3 = 10−24 cm3. One can convert from SI units to cgs units as follows:

$\alpha (\mathrm{cm}^3) = \frac{10^{6}}{ 4 \pi \varepsilon_0 }\alpha (\mathrm{C} \cdot \mathrm{m}^2 \cdot \mathrm{V}^{-1}) = \frac{10^{6}}{ 4 \pi \varepsilon_0 }\alpha (\mathrm{F} \cdot \mathrm{m}^2)$ ≃ 8.988×1015 × $\alpha (\mathrm{F} \cdot \mathrm{m}^2)$

where $\varepsilon_0$, the vacuum permittivity, is ~8.854 × 10−12 (F/m). If the polarizability volume is denoted $\alpha'$ the relation can also be expressed generally[3] (in SI) as $4\pi\varepsilon_0 \alpha' = \alpha$.

The polarizability of individual particles is related to the average electric susceptibility of the medium by the Clausius-Mossotti relation.

Note that the polarizability $\alpha$ as defined above is a scalar quantity. This implies that the applied electric fields can only produce polarization components parallel to the field. For example, an electric field in the $x$-direction can only produce an $x$ component in $\boldsymbol{p}$. However, it can happen that an electric field in the $x$-direction, produces a $y$ or $z$ component in the vector $\boldsymbol{p}$. In this case $\alpha$ is described as a tensor of rank 2, which is represented with respect to a given system of axes (frame of reference) by a $3 \times 3$ matrix.

### Tendencies

Generally, polarizability increases as volume occupied by electrons increases.[4] In atoms, this occurs because larger atoms have more loosely held electrons in contrast to smaller atoms with tightly bound electrons.[4][5] On rows of the periodic table, polarizability therefore increases from right to left.[4] Polarizability increases down on columns of the periodic table.[4] Likewise, larger molecules are generally more polarizable than smaller ones.

Though water is a very polar molecule, alkanes and other hydrophobic molecules are more polarizable. Alkanes are the most polarizable molecules.[4] Although alkenes and arenes are expected to have larger polarizability than alkanes because of their higher reactivity compared to alkanes, alkanes are in fact more polarizable.[4] This results because of alkene's and arene's more electronegative sp2 carbons to the alkane's less electronegative sp3 carbons.[4]

It is important to note that ground state electron configuration models are often inadequate in studying the polarizability of bonds because dramatic changes in molecular structure occur in a reaction.[4]

## Magnetic polarizability

Magnetic polarizability defined by spin interactions of nucleons is an important parameter of deuterons and hadrons. In particular, measurement of tensor polarizabilities of nucleons yields important information about spin-dependent nuclear forces.[6]

The method of spin amplitudes uses quantum mechanics formalism to more easily describe spin dynamics. Vector and tensor polarization of particle/nuclei with spin S ≥ 1 are specified by the unit polarization vector $\boldsymbol{p}$ and the polarization tensor P`. Additional tensors composed of products of three or more spin matrices are needed only for the exhaustive description of polarization of particles/nuclei with spin S32 .[6]