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Dear Haricharan Padmanabhan<br>
<br>
The magnetization asociated with a vacancy is known to converge very slowly. As you will see in the following detailed study: PHYSICAL REVIEW B 85, 245443 (2012)<br>
the 6x6 supercell in in fact very small... if you want to get your magnetization converged.<br>
<br>
2d systems can have some advantages but also some serious drawbacks due to the very slow convergence of certain quantities related to the bi-dimensionality. This is also why tight-binding is very popular in graphene :-)<br>
<br>
good luck<br>
<br>
Cyrille<br>
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<div style="font-family:Tahoma; font-size:13px"><font size="2"><span style="background-color:white; font-family:Times New Roman"><font color="black"><span dir="ltr" style="font-size:10pt"><span style="font-size:16px"></span></span></font></span><font face="Times New Roman"><b>Cyrille
Barreteau</b><br>
CEA Saclay<span style="background-color:white"></span></font><font face="Times New Roman">,
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<font face="Times New Roman">DTU Nanotech<br>
Ørsteds Plads, building 345E<br>
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</font><font face="Times New Roman"><font face="Times New Roman"><font face="Times New Roman">+33 1 69 08 29 51 /</font></font></font><font face="Times New Roman">
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(Dk)<br>
<font face="Times New Roman">email: cyrille.barreteau@cea.fr /</font><font face="Times New Roman"> cyrbar@nanotech.dtu.dk
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Web: <a href="http://iramis.cea.fr/Pisp/cyrille.barreteau/" tabindex="0">http://iramis.cea.fr/Pisp/cyrille.barreteau/</a>
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<div style="direction: ltr;" id="divRpF611152"><font size="2" color="#000000" face="Tahoma"><b>De :</b> pw_forum-bounces@pwscf.org [pw_forum-bounces@pwscf.org] de la part de Haricharan Padmanabhan [hari00968@gmail.com]<br>
<b>Envoyé :</b> mardi 21 octobre 2014 10:43<br>
<b>À :</b> pw_forum@pwscf.org<br>
<b>Objet :</b> [Pw_forum] Convergence of Magnetization in Graphene Monovacancy Supercell<br>
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<div>Dear Quantum ESPRESSO users,<br>
<br>
</div>
I am attempting to estimate the value of the magnetism in Graphene with a mono-vacancy, using supercells of different sizes.<br>
<br>
</div>
<div>Some background - <br>
</div>
<div><br>
</div>
- One would expect (from literature) the magnetism to converge to around 1.5 bohr magnetons (uB) as the supercell size is increased.
<br>
<br>
</div>
- Since vacancies result in localized states at the Fermi level (flat bands, or peaks in the DOS), a dense k-point mesh is usually required to accurately estimate (N.up - N.down), and hence the magnetism.<br>
<br>
</div>
I first obtained convergence with respect to k-point sampling, for a 4x4 supercell (31 atoms + 1 vacancy)
<br>
<br>
<table cols="4" border="0" cellspacing="0">
<colgroup width="240"></colgroup><colgroup width="140"></colgroup><colgroup span="2" width="85">
</colgroup>
<tbody>
<tr>
<td align="LEFT" height="16">K-point mesh</td>
<td align="LEFT">Total Energy (Ry)<br>
</td>
<td colspan="2" align="CENTER" valign="MIDDLE">Total magnetization (uB)<br>
</td>
</tr>
<tr>
<td align="LEFT" height="16">16x16</td>
<td align="LEFT">-355.586</td>
<td align="RIGHT">1.29</td>
<td align="LEFT"><br>
</td>
</tr>
<tr>
<td align="LEFT" height="16">20x20</td>
<td align="LEFT">-355.586</td>
<td align="RIGHT">1.21</td>
<td align="LEFT"><br>
</td>
</tr>
<tr>
<td align="LEFT" height="16">24x24</td>
<td align="LEFT">-355.586</td>
<td align="RIGHT">1.25</td>
<td align="LEFT"><br>
</td>
</tr>
<tr>
<td align="LEFT" height="16">32x32</td>
<td align="LEFT">-355.586</td>
<td align="RIGHT">1.27</td>
<td align="LEFT"><br>
</td>
</tr>
<tr>
<td align="LEFT" height="16">36x36</td>
<td align="LEFT">-355.586</td>
<td align="RIGHT">1.27</td>
<td align="LEFT"><br>
</td>
</tr>
</tbody>
</table>
<br>
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A larger 6x6 supercell (71 atoms + 1 vacancy), by conventional wisdom, would require a less dense k-point mesh for convergence. However, even with a dense 32x32 k-point mesh, I get a non-converged value of 0.59 uB for the magnetism. Different calculations with
different k-point meshes give me values that oscillate between 0.59 and 1.45 uB, with no apparent pattern. It does not make sense to me to further increase the k-point mesh density.<br>
<br>
</div>
Clearly, the flat bands at the Fermi level are causing trouble depending on whether they've been bumped slightly above or below the Fermi level, due to inadequate k-point sampling in different calculations. How can I fix this problem? Will doing a manual k-point
sampling help? <br>
<br>
</div>
<br>
<br>
A part of the input file - <br>
<br>
<br>
&system<br>
ibrav= 4, celldm(1) =27.9, celldm(3) = 1, nat= 71, ntyp= 1,<br>
ecutwfc =30.0,<br>
ecutrho = 250.0,<br>
occupations='smearing', smearing='gaussian', degauss=0.001<br>
nspin = 2, starting_magnetization(1)=0.7<br>
/<br>
&electrons<br>
diagonalization='cg'<br>
mixing_mode = 'plain'<br>
mixing_beta = 0.1<br>
conv_thr = 1.0d-6<br>
electron_maxstep = 200<br>
/<br>
<br>
ATOMIC_SPECIES<br>
C 12.011 c_pbe_v1.2.uspp.F.UPF<br>
<br>
K_POINTS {automatic}<br>
32 32 1 0 0 0<br>
<br>
</div>
<br>
A part of the output file - <br>
<br>
<br>
the Fermi energy is -1.9682 ev<br>
<br>
total energy = -815.17816366 Ry<br>
Harris-Foulkes estimate = -815.17815922 Ry<br>
estimated scf accuracy < 0.00000077 Ry<br>
<br>
The total energy is the sum of the following terms:<br>
<br>
one-electron contribution = -5427.83442348 Ry<br>
hartree contribution = 2763.25828072 Ry<br>
xc contribution = -257.55564014 Ry<br>
ewald contribution = 2106.95386447 Ry<br>
smearing contrib. (-TS) = -0.00024524 Ry<br>
<br>
total magnetization = 0.59 Bohr mag/cell<br>
absolute magnetization = 0.79 Bohr mag/cell<br>
<br>
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<div><br>
</div>
<div>Thank you.<br>
<br>
</div>
<div>Haricharan Padmanabhan<br>
<br>
</div>
<div>Indian Institute of Technology Madras<br>
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