Polarizability

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.

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.

[1] 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

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.

[2] "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 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.

in isotropic media is defined as the ratio of the induced dipole moment

If the polarizability volume in cgs units is denoted

is the electronic polarizability, p is the density of molecules, M is the molar mass, and

is the material's relative permittivity or dielectric constant (or in optics, the square of the refractive index).

Polarizability for anisotropic or non-spherical media cannot in general be represented as a scalar quantity.

directions respond in the same way to the applied electric field.

Many crystalline materials have directions that are easier to polarize than others and some even become polarized in directions perpendicular to the applied electric field[citation needed], and the same thing happens with non-spherical bodies.

Some molecules and materials with this sort of anisotropy are optically active, or exhibit linear birefringence of light.

To describe anisotropic media a polarizability rank two tensor or

is defined, so that: The elements describing the response parallel to the applied electric field are those along the diagonal.

Each polarizability measurement along with the refractive index associated with its direction will yield a direction specific density that can be used to develop an accurate three dimensional assessment of molecular stacking in the crystal.

Analyzing a cubic crystal lattice, we can imagine an isotropic spherical region to represent the entire sample.

term giving us We can replace the relative permittivity

The number density can be related to the molecular weight

, adjusting the final form of our equation to include molar refractivity: This equation allows us to relate bulk property (refractive index) to the molecular property (polarizability) as a function of frequency.

[9][10] On rows of the periodic table, polarizability therefore decreases from left to right.

[9] Polarizability increases down on columns of the periodic table.

[9] Likewise, larger molecules are generally more polarizable than smaller ones.

Water with its permanent dipole is less likely to change shape due to an external electric field.

[9] Ground state electron configuration models often describe molecular or bond polarization during chemical reactions poorly, because reactive intermediates may be excited, or be the minor, alternate structures in a chemical equilibrium with the initial reactant.

[9] 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.