Dear all,<div><br></div><div>I have been trying to understand the sampling of the Brillouin Zone for integration in the k-space. The method adopted in the automatic generation scheme in Espresso is the Monkhorst-Pack one. I have been reading the file kpoints.f90 in </div>
<div><br></div><div>espresso-5.0/PW/tools/</div><div><br></div><div>and I went through some of the forum archives <a href="http://www.democritos.it/pipermail/pw_forum/2012-February/023321.html">http://www.democritos.it/pipermail/pw_forum/2012-February/023321.html</a> to understand this. </div>
<div><br></div><div>I think the algorithm follows these lines</div><div><br></div><div>1. generate a shifted uniform grid in <i>crystal space</i> of <i>the reciprocal lattice</i> and associating a weight of 1/(total no: of k points)</div>
<div>2. use symmetry of the reciprocal lattice to reduce the list</div><div><div> Here the weights of the eliminated points are accumulated on to the remaining ones</div></div><div><br></div><div>This is what I was hoping to find</div>
<div>a) Some sort of check that ensures that k points fall within the Wigner-Seitz Cell (first Brillouin Zone). </div><div>b) During the generation of the k point mesh, the sampling seems to not extend in all quadrants of the crystal space, i.e., I am not able to find negative crystal vectors. I expect them because the Brillouin zone extends in all quadrants. </div>
<div><br></div><div>Can someone please explain this to me?</div><div><br></div><div>Regards</div><div>Meenakshi Sundaram M</div><div>Grad Student</div><div>Mechanical and Aerospace Engineering </div><div>Ithaca</div><div>
Cornell</div>