[Pw_forum] Defining an antiferromagnetic graphene nanoribbon

[Stefano de Gironcoli]

Hi Nicola,
     I think that graphite curves in your tests appear smoother that 
the  diamonds one because the 664 grid used for G is  denser  than  the 
444 used in D.
     Increasing the cutoff smooths the curves because the sudden jumps 
become smaller as the basis gets more complete. 
     But E-vs-V becomes also smoother when the k-point sampling is 
increased because each sampled k-point will determine a jump at a 
different volume  (weighted  by 1/Nk) so that for denser grids there are 
more, smaller jumps hence smoother curves.
     Ideally if one were integrating over the full BZ (something 
impossible to do but conceptually useful to establish the trend)  the  
E-vs-V curve would be completely smooth because the PW basis would be 
independent on the volume: only the assignment of a particular basis 
function  to a particular k-point would change with the structure but 
the overall basis would be exactly the same.

    stefano

Nicola Marzari wrote:
> On the second part, I'm a bit more puzzled. I agree that
> discontinuities in the E-vs-V curve appear, especially for
> sparse k-point sampling, due to the sudden increase in
> the number plane waves when the cutoff crosses some critical
> value. Still, those discontinuities would always appear as a
> sudden drop in total energy, since the basis of plane waves has
> discontinuously become larger.
> http://www.pwscf.org/pseudo/1.3/UPF/C.pbe-rrkjus-test-diamond.pdf
> looked a bit different - hence my puzzlement. I though at augmentation
> charges and the existence of fourier oscillations outside the core
> region, due to the multipole representation of the charge, but
> not sure why it would be more relevant in diamond (where the C-C
> distance is longer)