<div dir="ltr"><div><div><div><div><div><div><div><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>
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<td align="LEFT" height="16">K-point mesh</td>
<td align="LEFT">Total Energy (Ry)<br></td>
<td colspan="2" valign="MIDDLE" align="CENTER">Total magnetization (uB)<br></td>
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<td align="LEFT" height="16">16x16</td>
<td align="LEFT">-355.586</td>
<td align="RIGHT">1.29</td>
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<td align="LEFT" height="16">20x20</td>
<td align="LEFT">-355.586</td>
<td align="RIGHT">1.21</td>
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<td align="LEFT" height="16">24x24</td>
<td align="LEFT">-355.586</td>
<td align="RIGHT">1.25</td>
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<td align="LEFT" height="16">32x32</td>
<td align="LEFT">-355.586</td>
<td align="RIGHT">1.27</td>
<td align="LEFT"><br></td>
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<td align="LEFT" height="16">36x36</td>
<td align="LEFT">-355.586</td>
<td align="RIGHT">1.27</td>
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<br></div>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><div><div><div><div><div><div><br></div><div>Thank you.<br><br></div><div>Haricharan Padmanabhan<br><br></div><div>Indian Institute of Technology Madras<br></div></div></div></div></div></div></div>