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<li class="toctree-l1 current"><a class="current reference internal" href="#">Natural orbitals</a><ul>
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<li class="toctree-l2"><a class="reference internal" href="#summary">Summary</a></li>
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<li class="toctree-l2"><a class="reference internal" href="#extracting-natural-orbitals">Extracting natural orbitals</a></li>
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<div class="section" id="natural-orbitals">
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<h1>Natural orbitals<a class="headerlink" href="#natural-orbitals" title="Permalink to this headline">¶</a></h1>
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<div class="section" id="summary">
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<h2>Summary<a class="headerlink" href="#summary" title="Permalink to this headline">¶</a></h2>
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<p>To produce state-average natural orbitals, run</p>
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<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">qp_run</span> <span class="n">save_natorb</span> <span class="n">file</span><span class="o">.</span><span class="n">ezfio</span>
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</pre></div>
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<p>The MOs will be replaced, so the two-electron integrals and the wave
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function are invalidated as well.</p>
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</div>
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<div class="section" id="extracting-natural-orbitals">
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<h2>Extracting natural orbitals<a class="headerlink" href="#extracting-natural-orbitals" title="Permalink to this headline">¶</a></h2>
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<p>Once obtained the near <abbr title="Full Configuration Interaction">FCI</abbr> wave function, one can obtain many
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Onquantities related to it. e of these quantities are the natural
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Onorbitals which have the properties of diagonalizing the one-body
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Ondensity matrix:</p>
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<blockquote>
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<div><div class="math notranslate nohighlight">
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\[\rho_{ij} = \delta_{ij}\]</div>
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</div></blockquote>
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<p>where the element of the one-body density matrix <span class="math notranslate nohighlight">\(\rho_{ij}\)</span> is
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define as:</p>
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<blockquote>
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<div><div class="math notranslate nohighlight">
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\[\rho_{ij} = \langle \Psi | \left( a^{\dagger}_{j,\alpha} a_{i,\alpha} + a^{\dagger}_{j,\beta} a_{i,\beta} \right) | \Psi \rangle\]</div>
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</div></blockquote>
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<p>These orbitals are in general known to be better than the usual <abbr title="Hartree-Fock">HF</abbr>
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<abbr title="Molecular Orbitals">MOs</abbr> as they are obtained from a correlated wave function. To use these
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orbitals for future calculations, one has to replace the current <abbr title="Molecular Orbitals">MOs</abbr>
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by the natural orbitals. To do so, just run:</p>
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<div class="code highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">qp_run</span> <span class="n">save_natorb</span> <span class="n">file</span><span class="o">.</span><span class="n">ezfio</span>
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</pre></div>
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</div>
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</div>
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<div class="section" id="hands-on">
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<h2>Hands on<a class="headerlink" href="#hands-on" title="Permalink to this headline">¶</a></h2>
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<div class="admonition important">
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<p class="first admonition-title">Important</p>
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<p class="last">As the <abbr title="Molecular Orbitals">MOs</abbr> are changed, for the sake of coherence of future
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calculations, the save_natorb program <em>automatically removes the
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current wave function</em> stored in the <a class="reference external" href="http://gitlab.com/scemama/EZFIO">EZFIO</a> database and replaces
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it by a single Slater determinant corresponding to a <abbr title="Hartree-Fock">HF</abbr> occupation
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of the new spin orbitals. Also, all the keywords to read the one-
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and two-electron integrals on the <abbr title="Molecular Orbital">MO</abbr> basis are set to <code class="docutils literal notranslate"><span class="pre">None</span></code> in
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order to be sure to avoid reading integrals incompatible with the
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current set of <abbr title="Molecular Orbitals">MOs</abbr>.</p>
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</div>
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<div class="admonition seealso">
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<p class="first admonition-title">See also</p>
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<p class="last">The documentation of the <code class="xref c c-func docutils literal notranslate"><span class="pre">save_natorb()</span></code> program.</p>
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