How could one theoretically predict a material's permittivity?

[VortexLattice]

I know experimentally, the permittivity of a material is $\vec D = \epsilon \vec E$, and you can also relate the Polarization to it. So it's basically a response of the material to an applied E field.

But that seems like it would be a fairly complex thing to figure out theoretically. I guess one way would be to, for a given E field applied to a unit cell of the material, see how each atom gets polarized. But that seems like it would be incredibly complicated for unit cells with several atoms and a basis, and each atom having multiple electrons.

So I'm wondering how you could figure out the permittivity of a general crystal, like if you were told its interatomic distances, lattice constants, band structure, etc. Is there a better way than what I described above?

Thanks!

 

[DrDu]

Permittivity can be calculated routinely with programs to calculate band structure. The basic approach is described in the article by Adler:

http://prola.aps.org/abstract/PR/v126/i2/p413_1

 

[VortexLattice]

Permittivity can be calculated routinely with programs to calculate band structure. The basic approach is described in the article by Adler:

http://prola.aps.org/abstract/PR/v126/i2/p413_1

Hi, thank you very much for the reply! However, after a quick glance at this I don't see how to get the permittivity assuming you already know the band structure... I'm sorry if I'm misunderstanding this, but is this what you meant?

 

[DrDu]

Basically you use linear response (i.e. perturbation theory) to calculate the change in charge density due to an applied field. This requires you to know the band structure and Bloch states of the material being studied.