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  <span class="target" id="index-0"></span><span class="target" id="index-1"></span><span class="target" id="index-2"></span><div class="section" id="typical-resource-requirements">
<span id="index-3"></span><h1>7. Typical resource requirements<a class="headerlink" href="#typical-resource-requirements" title="Permalink to this headline"></a></h1>
<p>In this section, typical resource requirements for DMRG calculations are discussed. With <span class="math">\(L\)</span> spatial orbitals and <span class="math">\(D\)</span> virtual basis states, the algorithm has a theoretical scaling per sweep of</p>
<ul class="simple">
<li><span class="math">\(\mathcal{O}(L^4D^2 + L^3D^3)\)</span> in CPU time</li>
<li><span class="math">\(\mathcal{O}(L^2D^2)\)</span> in memory</li>
<li><span class="math">\(\mathcal{O}(L^3D^2)\)</span> in disk</li>
</ul>
<p>The block-sparsity and information compression due to the exploitation of symmetry have not been taken into account in these scalings! Ref. <a class="reference internal" href="#timing" id="id1">[TIMING]</a> contains CPU time measurements for polyenes of increasing length, and demonstrates the scaling of CheMPS2 with <span class="math">\(L\)</span>.</p>
<div class="section" id="n2-cc-pvdz">
<h2>7.1. N2/cc-pVDZ<a class="headerlink" href="#n2-cc-pvdz" title="Permalink to this headline"></a></h2>
<p>The nitrogen dimer in the cc-pVDZ basis has an active space of 14 electrons in 28 orbitals. The exploited point group in the calculations was <span class="math">\(\mathsf{d2h}\)</span>, and the targeted state was <span class="math">\(X^1\Sigma_g^+\)</span> at equilibrium bond length: 2.118 a.u. This system was first studied with DMRG in Ref. <a class="reference internal" href="#nitrogen" id="id2">[NITROGEN]</a>. The listed CheMPS2 timings are wall times per sweep (in seconds) on 16 Intel Xeon Sandy Bridge (E5-2670) cores &#64; 2.6 GHz. The calculation was performed with snapshot 045393b439821c81d800328c0b4b8b1732da47f8 from the github repository. OpenMP parallelization on a single node was used, and the calculation needed ~ 6 Gb of memory.</p>
<blockquote>
<div><table border="1" class="docutils">
<colgroup>
<col width="29%" />
<col width="26%" />
<col width="21%" />
<col width="24%" />
</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head"><span class="math">\(D_{\mathsf{SU(2)}}\)</span></th>
<th class="head">Wall time per sweep (s)</th>
<th class="head"><span class="math">\(w_D^{disc}\)</span></th>
<th class="head"><span class="math">\(E_D\)</span> (Hartree)</th>
</tr>
</thead>
<tbody valign="top">
<tr class="row-even"><td>1000</td>
<td>48</td>
<td>9.8027e-07</td>
<td>-109.28209711</td>
</tr>
<tr class="row-odd"><td>1500</td>
<td>113</td>
<td>3.9381e-07</td>
<td>-109.28214593</td>
</tr>
<tr class="row-even"><td>2000</td>
<td>219</td>
<td>1.8910e-07</td>
<td>-109.28216077</td>
</tr>
<tr class="row-odd"><td>2500</td>
<td>371</td>
<td>1.0083e-07</td>
<td>-109.28216667</td>
</tr>
</tbody>
</table>
</div></blockquote>
</div>
<div class="section" id="h2o-roos-ano-dz">
<h2>7.2. H2O/Roos&#8217; ANO DZ<a class="headerlink" href="#h2o-roos-ano-dz" title="Permalink to this headline"></a></h2>
<p>Water in Roos&#8217; ANO DZ basis has an active space of 10 electrons in 41 orbitals. The exploited point group in the calculations was <span class="math">\(\mathsf{c2v}\)</span>, and the targeted state was <span class="math">\(^1A_1\)</span> at equilibrium geometry: O &#64; (0, 0, 0) and H &#64; (± 0.790689766, 0, 0.612217330) Angstrom. This system was first studied with DMRG in Ref. <a class="reference internal" href="#water" id="id3">[WATER]</a>. The listed CheMPS2 timings are wall times per sweep (in seconds) on 20 Intel Xeon Ivy Bridge (E5-2670 v2) cores &#64; 2.5 GHz. The calculation was performed with snapshot 045393b439821c81d800328c0b4b8b1732da47f8 from the github repository. OpenMP parallelization on a single node was used, and the calculation needed ~ 64 Gb of memory.</p>
<blockquote>
<div><table border="1" class="docutils">
<colgroup>
<col width="29%" />
<col width="26%" />
<col width="21%" />
<col width="24%" />
</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head"><span class="math">\(D_{\mathsf{SU(2)}}\)</span></th>
<th class="head">Wall time per sweep (s)</th>
<th class="head"><span class="math">\(w_D^{disc}\)</span></th>
<th class="head"><span class="math">\(E_D\)</span> (Hartree)</th>
</tr>
</thead>
<tbody valign="top">
<tr class="row-even"><td>1000</td>
<td>401</td>
<td>8.7950e-08</td>
<td>-76.31468302</td>
</tr>
<tr class="row-odd"><td>2000</td>
<td>2111</td>
<td>1.1366e-08</td>
<td>-76.31471044</td>
</tr>
<tr class="row-even"><td>3000</td>
<td>5686</td>
<td>2.9114e-09</td>
<td>-76.31471342</td>
</tr>
<tr class="row-odd"><td>4000</td>
<td>10958</td>
<td>6.8011e-10</td>
<td>-76.31471402</td>
</tr>
</tbody>
</table>
</div></blockquote>
<table class="docutils citation" frame="void" id="timing" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id1">[TIMING]</a></td><td><ol class="first last upperalpha simple" start="19">
<li>Wouters and D. Van Neck, <em>European Physical Journal D</em> <strong>68</strong>, 272 (2014), doi: <a class="reference external" href="http://dx.doi.org/10.1140/epjd/e2014-50500-1">10.1140/epjd/e2014-50500-1</a></li>
</ol>
</td></tr>
</tbody>
</table>
<table class="docutils citation" frame="void" id="nitrogen" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id2">[NITROGEN]</a></td><td>G.K.-L. Chan, M. Kallay and J. Gauss, <em>Journal of Chemical Physics</em> <strong>121</strong>, 6110 (2004), doi: <a class="reference external" href="http://dx.doi.org/10.1063/1.1783212">10.1063/1.1783212</a></td></tr>
</tbody>
</table>
<table class="docutils citation" frame="void" id="water" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id3">[WATER]</a></td><td><ol class="first last upperalpha simple" start="7">
<li>K.-L. Chan and M. Head-Gordon, <em>Journal of Chemical Physics</em> <strong>118</strong>, 8551 (2003), doi: <a class="reference external" href="http://dx.doi.org/10.1063/1.1574318">10.1063/1.1574318</a></li>
</ol>
</td></tr>
</tbody>
</table>
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<li><a class="reference internal" href="#">7. Typical resource requirements</a><ul>
<li><a class="reference internal" href="#n2-cc-pvdz">7.1. N2/cc-pVDZ</a></li>
<li><a class="reference internal" href="#h2o-roos-ano-dz">7.2. H2O/Roos&#8217; ANO DZ</a></li>
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