<div dir="ltr">Hi all,<br><br>this may be a very entry-level question, but please help me understand something that currently confuses me.<br><br>Let's say we want to calculate static energies and forces of a small unit cell (or very few repetitions) of a metallic crystal, much like the "How to Calculate Energy and Forces" howto. I find that there is a large difference between multigrid method and k-point sampling (when parameters of both have been correctly converged). For all systems I tried this on, most individual energy terms are very close, but the "Core Hamiltonian energy" is about 5-10% higher using MGRID than using KPOINTS. From other sources I know the correct cohesive and isolated atom energies, and I find that only k-point sampling returns the correct value.<br><br>Example from 1x1x2 cells Al, basis DZVP-MOLOPT-SR-GTH, potential GTH-PBE-q3, PBE exchange-correlation:<br><div style="background-color: rgb(250, 250, 250); border-color: rgb(187, 187, 187); border-style: solid; border-width: 1px; overflow-wrap: break-word;" class="prettyprint"><code class="prettyprint"><div class="subprettyprint"><span style="color: #000;" class="styled-by-prettify">    </span><span style="color: #660;" class="styled-by-prettify">&</span><span style="color: #000;" class="styled-by-prettify">MGRID<br>      NGRIDS </span><span style="color: #066;" class="styled-by-prettify">4</span><span style="color: #000;" class="styled-by-prettify"><br>      CUTOFF </span><span style="color: #066;" class="styled-by-prettify">300</span><span style="color: #000;" class="styled-by-prettify"><br>      REL_CUTOFF </span><span style="color: #066;" class="styled-by-prettify">50</span><span style="color: #000;" class="styled-by-prettify"><br>    </span><span style="color: #660;" class="styled-by-prettify">&</span><span style="color: #008;" class="styled-by-prettify">END</span><span style="color: #000;" class="styled-by-prettify"> MGRID<br></span></div></code></div><div style="background-color: rgb(250, 250, 250); border-color: rgb(187, 187, 187); border-style: solid; border-width: 1px; overflow-wrap: break-word;" class="prettyprint"><code class="prettyprint"><div class="subprettyprint"><span style="color: #000;" class="styled-by-prettify">  </span><span style="color: #606;" class="styled-by-prettify">Overlap</span><span style="color: #000;" class="styled-by-prettify"> energy of the core charge distribution</span><span style="color: #660;" class="styled-by-prettify">:</span><span style="color: #000;" class="styled-by-prettify">               </span><span style="color: #066;" class="styled-by-prettify">0.00000000001890</span><span style="color: #000;" class="styled-by-prettify"><br>  </span><span style="color: #606;" class="styled-by-prettify">Self</span><span style="color: #000;" class="styled-by-prettify"> energy of the core charge distribution</span><span style="color: #660;" class="styled-by-prettify">:</span><span style="color: #000;" class="styled-by-prettify">                </span><span style="color: #660;" class="styled-by-prettify">-</span><span style="color: #066;" class="styled-by-prettify">45.13516668382051</span><span style="color: #000;" class="styled-by-prettify"><br>  </span><span style="color: #606;" class="styled-by-prettify">Core</span><span style="color: #000;" class="styled-by-prettify"> </span><span style="color: #606;" class="styled-by-prettify">Hamiltonian</span><span style="color: #000;" class="styled-by-prettify"> energy</span><span style="color: #660;" class="styled-by-prettify">:</span><span style="color: #000;" class="styled-by-prettify">                                     </span><span style="color: #066;" class="styled-by-prettify">10.22296505539078</span><span style="color: #000;" class="styled-by-prettify"><br>  </span><span style="color: #606;" class="styled-by-prettify">Hartree</span><span style="color: #000;" class="styled-by-prettify"> energy</span><span style="color: #660;" class="styled-by-prettify">:</span><span style="color: #000;" class="styled-by-prettify">                                              </span><span style="color: #066;" class="styled-by-prettify">25.42600995275711</span><span style="color: #000;" class="styled-by-prettify"><br>  </span><span style="color: #606;" class="styled-by-prettify">Exchange</span><span style="color: #660;" class="styled-by-prettify">-</span><span style="color: #000;" class="styled-by-prettify">correlation energy</span><span style="color: #660;" class="styled-by-prettify">:</span><span style="color: #000;" class="styled-by-prettify">                                 </span><span style="color: #660;" class="styled-by-prettify">-</span><span style="color: #066;" class="styled-by-prettify">6.48331280168588</span><span style="color: #000;" class="styled-by-prettify"><br>  </span><span style="color: #606;" class="styled-by-prettify">Electronic</span><span style="color: #000;" class="styled-by-prettify"> entropic energy</span><span style="color: #660;" class="styled-by-prettify">:</span><span style="color: #000;" class="styled-by-prettify">                                  </span><span style="color: #660;" class="styled-by-prettify">-</span><span style="color: #066;" class="styled-by-prettify">0.00263408295383</span><span style="color: #000;" class="styled-by-prettify"><br>  </span><span style="color: #606;" class="styled-by-prettify">Fermi</span><span style="color: #000;" class="styled-by-prettify"> energy</span><span style="color: #660;" class="styled-by-prettify">:</span><span style="color: #000;" class="styled-by-prettify">                                                 </span><span style="color: #066;" class="styled-by-prettify">0.23983128515630</span><span style="color: #000;" class="styled-by-prettify"><br><br>  </span><span style="color: #606;" class="styled-by-prettify">Total</span><span style="color: #000;" class="styled-by-prettify"> energy</span><span style="color: #660;" class="styled-by-prettify">:</span><span style="color: #000;" class="styled-by-prettify">                                               </span><span style="color: #660;" class="styled-by-prettify">-</span><span style="color: #066;" class="styled-by-prettify">15.97213856029344</span><span style="color: #000;" class="styled-by-prettify"><br></span></div></code></div>vs.<br><div style="background-color: rgb(250, 250, 250); border-color: rgb(187, 187, 187); border-style: solid; border-width: 1px; overflow-wrap: break-word;" class="prettyprint"><code class="prettyprint"><div class="subprettyprint"><span style="color: #000;" class="styled-by-prettify">    </span><span style="color: #660;" class="styled-by-prettify">&</span><span style="color: #000;" class="styled-by-prettify">KPOINTS<br>      SCHEME MONKHORST</span><span style="color: #660;" class="styled-by-prettify">-</span><span style="color: #000;" class="styled-by-prettify">PACK </span><span style="color: #066;" class="styled-by-prettify">17</span><span style="color: #000;" class="styled-by-prettify"> </span><span style="color: #066;" class="styled-by-prettify">17</span><span style="color: #000;" class="styled-by-prettify"> </span><span style="color: #066;" class="styled-by-prettify">34</span><span style="color: #000;" class="styled-by-prettify">    </span><span style="color: #660;" class="styled-by-prettify">!</span><span style="color: #000;" class="styled-by-prettify"> converged to </span><span style="color: #066;" class="styled-by-prettify">5</span><span style="color: #000;" class="styled-by-prettify"> decimals around </span><span style="color: #066;" class="styled-by-prettify">13</span><span style="color: #000;" class="styled-by-prettify"> </span><span style="color: #066;" class="styled-by-prettify">13</span><span style="color: #000;" class="styled-by-prettify"> </span><span style="color: #066;" class="styled-by-prettify">26</span><span style="color: #000;" class="styled-by-prettify"><br>      FULL_GRID T<br>      WAVEFUNCTIONS COMPLEX<br>    </span><span style="color: #660;" class="styled-by-prettify">&</span><span style="color: #008;" class="styled-by-prettify">END</span><span style="color: #000;" class="styled-by-prettify"> KPOINTS</span></div></code></div><div style="background-color: rgb(250, 250, 250); border-color: rgb(187, 187, 187); border-style: solid; border-width: 1px; overflow-wrap: break-word;" class="prettyprint"><code class="prettyprint"><div class="subprettyprint"><span style="color: #000;" class="styled-by-prettify">  </span><span style="color: #606;" class="styled-by-prettify">Overlap</span><span style="color: #000;" class="styled-by-prettify"> energy of the core charge distribution</span><span style="color: #660;" class="styled-by-prettify">:</span><span style="color: #000;" class="styled-by-prettify">               </span><span style="color: #066;" class="styled-by-prettify">0.00000000001890</span><span style="color: #000;" class="styled-by-prettify"><br>  </span><span style="color: #606;" class="styled-by-prettify">Self</span><span style="color: #000;" class="styled-by-prettify"> energy of the core charge distribution</span><span style="color: #660;" class="styled-by-prettify">:</span><span style="color: #000;" class="styled-by-prettify">                </span><span style="color: #660;" class="styled-by-prettify">-</span><span style="color: #066;" class="styled-by-prettify">45.13516668382051</span><span style="color: #000;" class="styled-by-prettify"><br>  </span><span style="color: #606;" class="styled-by-prettify">Core</span><span style="color: #000;" class="styled-by-prettify"> </span><span style="color: #606;" class="styled-by-prettify">Hamiltonian</span><span style="color: #000;" class="styled-by-prettify"> energy</span><span style="color: #660;" class="styled-by-prettify">:</span><span style="color: #000;" class="styled-by-prettify">                                      </span><span style="color: #066;" class="styled-by-prettify">9.67133497320798</span><span style="color: #000;" class="styled-by-prettify"><br>  </span><span style="color: #606;" class="styled-by-prettify">Hartree</span><span style="color: #000;" class="styled-by-prettify"> energy</span><span style="color: #660;" class="styled-by-prettify">:</span><span style="color: #000;" class="styled-by-prettify">                                              </span><span style="color: #066;" class="styled-by-prettify">25.41644035557356</span><span style="color: #000;" class="styled-by-prettify"><br>  </span><span style="color: #606;" class="styled-by-prettify">Exchange</span><span style="color: #660;" class="styled-by-prettify">-</span><span style="color: #000;" class="styled-by-prettify">correlation energy</span><span style="color: #660;" class="styled-by-prettify">:</span><span style="color: #000;" class="styled-by-prettify">                                 </span><span style="color: #660;" class="styled-by-prettify">-</span><span style="color: #066;" class="styled-by-prettify">6.46349454507014</span><span style="color: #000;" class="styled-by-prettify"><br>  </span><span style="color: #606;" class="styled-by-prettify">Electronic</span><span style="color: #000;" class="styled-by-prettify"> entropic energy</span><span style="color: #660;" class="styled-by-prettify">:</span><span style="color: #000;" class="styled-by-prettify">                                  </span><span style="color: #660;" class="styled-by-prettify">-</span><span style="color: #066;" class="styled-by-prettify">0.00027958913223</span><span style="color: #000;" class="styled-by-prettify"><br>  </span><span style="color: #606;" class="styled-by-prettify">Fermi</span><span style="color: #000;" class="styled-by-prettify"> energy</span><span style="color: #660;" class="styled-by-prettify">:</span><span style="color: #000;" class="styled-by-prettify">                                                 </span><span style="color: #066;" class="styled-by-prettify">0.25517849633624</span><span style="color: #000;" class="styled-by-prettify"><br><br>  </span><span style="color: #606;" class="styled-by-prettify">Total</span><span style="color: #000;" class="styled-by-prettify"> energy</span><span style="color: #660;" class="styled-by-prettify">:</span><span style="color: #000;" class="styled-by-prettify">                                               </span><span style="color: #660;" class="styled-by-prettify">-</span><span style="color: #066;" class="styled-by-prettify">16.51116548922202</span></div></code></div><br>The total energy of that particular system should be around -16.51 Ha.<br><br>Why is that? I would very much like to use the multigrid solution, as it is <i>a lot</i> faster for such systems - but obviously I can't if the results are off. I have read one post here that recommended using k-points for such systems, but not why, and where one could place a limit of usefulness between the two methods (if that is possible).<br><br><br>Thanks in advance,<br><br>Sebastian Hütter</div>