The Functional Formulation of Polarizability

The electric dipole polarizability, a, describes the linear response of the electron cloud of a chemical system to an external electric field that is less 

Quantum Nanochemistry—Volume II Quantum Atoms and Periodicity 

The interaction energy between the induced dipole and the applied field is given by the term  

In general, the electric field is an oscillating ones, but when is constant it correlates with the induced dipole through the static polarizability. Moreover, for atomic systems, assuming the spherical coordinates with the radius r, a given direction of the field E will produces the perturbation potential along the azimuth direction  

By comparison between relations of s it follows the atomic static dipole polarizability to be (Garza Robles, 1993)  

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