As a test, I use Castep module to calculate the polarizability of Si crystal.
The parameters and corresponding results are as follows:
1，Based on conventional cell. 8 Si atoms, Volume: 160.165, Density: 2.329,
I got the following results:
===============================================================================
Optical Permittivity (f->infinity) DC Permittivity (f=0)
---------------------------------- ---------------------
13.14345 0.00000 0.00000 13.14345 0.00000 0.00000
0.00000 13.14345 0.00000 0.00000 13.14345 0.00000
0.00000 0.00000 13.14345 0.00000 0.00000 13.14345
===============================================================================
===============================================================================
Polarisabilities (A**3)
Optical (f->infinity) Static (f=0)
--------------------- -------------
154.77456 0.00000 0.00000 154.77456 0.00000 0.00000
0.00000 154.77456 0.00000 0.00000 154.77456 0.00000
0.00000 0.00000 154.77456 0.00000 0.00000 154.77456
===============================================================================
2，Based on primitive cell, 2 Si atoms，Volume: 40.08，Density: 2.329
I got the following results.
===============================================================================
Optical Permittivity (f->infinity) DC Permittivity (f=0)
---------------------------------- ---------------------
12.42772 0.00000 0.00000 12.42772 0.00000 0.00000
0.00000 12.42772 0.00000 0.00000 12.42772 0.00000
0.00000 0.00000 12.42772 0.00000 0.00000 12.42772
===============================================================================
===============================================================================
Polarisabilities (A**3)
Optical (f->infinity) Static (f=0)
--------------------- -------------
36.41307 0.00000 0.00000 36.41307 0.00000 0.00000
0.00000 36.41307 0.00000 0.00000 36.41307 0.00000
0.00000 0.00000 36.41307 0.00000 0.00000 36.41307
===============================================================================
My Questions:
1，How to relate the permittivity to the polarizability? I try the Clausius-Mossotti relationship alpha = [(Permitivity-1)/(Permitivity+2)]*3*V/(4*PI), but fail.
2，How to understand the defference between Permittivities based on the conventional and primitive cell.
3，How to obtain the polarizability in A**3/atom unit.
For example, for 36.41307, I get 36.413/2 = 18.41 which is much larger than many refered values such as 3.71 A**3/atom based on Clausius_Mossotti relationship.
Best regards.
Lyzhao
