[Pw_forum] Defining an antiferromagnetic graphene nanoribbon

[Stefano Baroni]

On May 11, 2008, at 3:49 PM, Nicola Marzari wrote:

> The convergence tests for ultrasoft carbon are actually posted on the
> webpage:
>
> http://www.quantum-espresso.org/pseudo/upfdetails.php?upf=C.pbe-rrkjus.UPF
>
> Interesting, sp2 carbon (graphite) looks a bit smoother than
> sp3 carbon (diamond) (I do wonder why) but roughly the cutoffs
> are the same.

The energy gain in going form one cutoff to the next is very similar  
in the two plots, reflecting the same effective number of p electrons  
in graphite and carbon. If this number was different, I would expect  
the energy difference between two cutoffs to depend on the structure,  
because the s-channel potential should be softer than the p-channel  
one. For instance, I would expect the energy per atom in diamond to  
behave similarly as for an isolated atom in a sp3 configuration, but  
differently from an s2p2 atom (the energy of the latter should depend  
less on the cutoff). This is just a guess. Has anybody evidence of this?

In the specific case, the main difference between the convergence  
tests reported for diamond and graphite is not the absolute  
convergence, which is quite similar in the two cases, but rather that,  
for lower cutoffs, the E-vs-V curve looks more rugged for diamond than  
for graphite. Couldn't this be simply a consequence of the smaller  
number of k-points used for the former than for the latter?  
Discontinuities in the E-vs-V curve are due to the sudden increase in  
the number plane waves when the cutoff crosses some critical values  
(when an infinitesimal increase of the volume of the reciprocal-space  
sphere of radius \sqrt{ecut} lets one or more G vectors be included in  
the sphere). This critical values depend on the k-point around which  
the sphere is centered. Using more k-points usually has a compensating  
effect on the discontinuities. That's why the more the k-points, the  
less rugged the E-vs.V curves usually look. Of course, this does not  
indicate that the convergence is faster the larger the number of k- 
points, but only that the E-vs-V smoothness, by itself, is not a good  
indicator of cutoff convergence.

Am I wrong?

Stefano

---
Stefano Baroni - SISSA  &  DEMOCRITOS National Simulation Center -  
Trieste
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