[Pw_forum] G-vectors

Stefano de Gironcoli degironc at sissa.it
Sun May 22 11:24:44 CEST 2011

On 05/22/2011 05:57 AM, S. D. Wang wrote:
> Dear developers:
> In scf.out file, it has 'G cutoff =  122.3770  (  89195 G-vectors)     FFT
> grid: ( 24, 40,216)' , I want to kown the relation of cutoff and G-vectors.
> How can I understand the 122.3770 and 89195
G = b1*n1+b2*n2+b3*n3: where b1,b2,b3 are fundamental lattice vectors of
the reciprocal lattice.

All G such that G^2 < Ecut_rho are included in the G vector list. G
cutoff is just Ecut_rho in unit of (2pi/a)^2 (or maybe the sqrt of it).
The number of G in the cutoff sphere is in your case 89195.

the FFT grid dimensions are set in such a way that the sphere is
contained in it. FFT grid contains 24*40*216= 207360 which is about
twice the number of G in the list. It is the expected ratio as the
volume between a sphere and the cube containing it is pi/6


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