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<div class="section" id="full-configuration-interaction-fci">
<span id="fci"></span><h1>Full configuration interaction (FCI)<a class="headerlink" href="#full-configuration-interaction-fci" title="Permalink to this headline">¶</a></h1>
<div class="section" id="description">
<h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
<p>FCI exactly diagonalizes the molecular Hamiltonian within the space spanned by all of the Slater determinants.
This FCI section is closely related to that for the <a class="reference internal" href="../multi/casscf.html#casscf"><span class="std std-ref">Complete active space self-consistent field (CASSCF)</span></a> method.</p>
</div>
<div class="section" id="prerequisites">
<h2>Prerequisites<a class="headerlink" href="#prerequisites" title="Permalink to this headline">¶</a></h2>
<p>A reference wavefunction generated by a <a class="reference internal" href="../scf/hf.html#hf"><span class="std std-ref">HF</span></a> or <a class="reference internal" href="../multi/casscf.html#casscf"><span class="std std-ref">CASSCF</span></a> calculation.</p>
</div>
<div class="section" id="keywords">
<h2>Keywords<a class="headerlink" href="#keywords" title="Permalink to this headline">¶</a></h2>
<div class="topic">
<p class="topic-title first"><code class="docutils literal notranslate"><span class="pre">maxiter</span> <span class="pre">(or</span> <span class="pre">maxiter_fci)</span></code></p>
<div class="line-block">
<div class="line"><strong>Description:</strong> Maximum number of iterations in the FCI algorithm.</div>
<div class="line"><strong>Datatype:</strong> int</div>
<div class="line"><strong>Default:</strong> 100</div>
</div>
</div>
<div class="topic">
<p class="topic-title first"><code class="docutils literal notranslate"><span class="pre">thresh</span> <span class="pre">(or</span> <span class="pre">thresh_fci)</span></code></p>
<div class="line-block">
<div class="line"><strong>Description:</strong> Threshold for the convergence of the selected CI algorithm.</div>
<div class="line"><strong>Datatype:</strong> double</div>
<div class="line"><strong>Default:</strong> 1.0e-10</div>
</div>
</div>
<div class="topic">
<p class="topic-title first"><code class="docutils literal notranslate"><span class="pre">algorithm</span></code></p>
<div class="line-block">
<div class="line"><strong>Description:</strong> FCI algorithm to be used.</div>
<div class="line"><strong>Datatype:</strong> string</div>
<div class="line"><strong>Values:</strong></div>
<div class="line-block">
<div class="line"><code class="docutils literal notranslate"><span class="pre">KH,</span> <span class="pre">Knowles,</span> <span class="pre">Handy</span></code>: Use the Knowles–Handy algorithm.</div>
<div class="line"><code class="docutils literal notranslate"><span class="pre">HZ,</span> <span class="pre">Harrison,</span> <span class="pre">Zarrabian</span></code>: Use the Harrison–Zarrabian algorithm.</div>
<div class="line"><code class="docutils literal notranslate"><span class="pre">Dist,</span> <span class="pre">parallel</span></code>: Use a parallel algorithm based on HZ.</div>
</div>
<div class="line"><strong>Default:</strong> KH or Dist depending on the size of the calculation and the number of MPI processes.</div>
</div>
</div>
<div class="topic">
<p class="topic-title first"><code class="docutils literal notranslate"><span class="pre">frozen</span></code></p>
<div class="line-block">
<div class="line"><strong>Description:</strong> Use of the freeze core approximation.</div>
<div class="line"><strong>Datatype:</strong> bool</div>
<div class="line"><strong>Default:</strong> false</div>
</div>
</div>
<div class="topic">
<p class="topic-title first"><code class="docutils literal notranslate"><span class="pre">ncore</span></code></p>
<div class="line-block">
<div class="line"><strong>Description:</strong> Number of frozen core orbitals. <code class="docutils literal notranslate"><span class="pre">ncore</span></code> overides <code class="docutils literal notranslate"><span class="pre">frozen</span></code>.</div>
<div class="line"><strong>Datatype:</strong> int</div>
<div class="line"><strong>Default:</strong> If <code class="docutils literal notranslate"><span class="pre">frozen</span></code> is true, subvalence orbitals are frozen. If false, zero.</div>
</div>
</div>
<div class="topic">
<p class="topic-title first"><code class="docutils literal notranslate"><span class="pre">norb</span></code></p>
<div class="line-block">
<div class="line"><strong>Description:</strong> Number of correlated orbitals. Any high-energy orbitals in excess of this number will be excluded.</div>
<div class="line"><strong>Datatype:</strong> int</div>
<div class="line"><strong>Default:</strong> All molecular orbitals except those excluded using ncore.</div>
</div>
</div>
<div class="topic">
<p class="topic-title first"><code class="docutils literal notranslate"><span class="pre">active</span></code></p>
<div class="line-block">
<div class="line"><strong>Description:</strong> Orbital indices for the orbitals to be included. Note that orbital numbers start from 1.</div>
<div class="line"><strong>Datatype:</strong> vector<int></div>
<div class="line"><strong>Default:</strong> Frontier orbitals are used.</div>
</div>
</div>
<div class="topic">
<p class="topic-title first"><code class="docutils literal notranslate"><span class="pre">charge</span></code></p>
<div class="line-block">
<div class="line"><strong>Description:</strong> The total charge of the system.</div>
<div class="line"><strong>Datatype:</strong> int</div>
<div class="line"><strong>Default:</strong> 0</div>
</div>
</div>
<div class="topic">
<p class="topic-title first"><code class="docutils literal notranslate"><span class="pre">nspin</span></code></p>
<div class="line-block">
<div class="line"><strong>Description:</strong> The number associated with the spin states: 0 for singlet, 1 for doublet, 2 for triplet, etc.</div>
<div class="line"><strong>Datatype:</strong> int</div>
<div class="line"><strong>Default:</strong> 0</div>
</div>
</div>
<div class="topic">
<p class="topic-title first"><code class="docutils literal notranslate"><span class="pre">nstate</span></code></p>
<div class="line-block">
<div class="line"><strong>Description:</strong> Number of states to be calculated.</div>
<div class="line"><strong>Datatype:</strong> int</div>
<div class="line"><strong>Default:</strong> 1</div>
</div>
</div>
<div class="topic">
<p class="topic-title first"><code class="docutils literal notranslate"><span class="pre">davidson_subspace</span></code></p>
<div class="line-block">
<div class="line"><strong>Description:</strong> Number of vectors retained in the limited-memory Davidson algorithm.</div>
<div class="line"><strong>Datatype:</strong> int</div>
<div class="line"><strong>Default:</strong> 20</div>
<div class="line"><strong>Recommendation:</strong> Reduce if an insufficient amount of memory is available (do not reduce to a value lower than 3).</div>
</div>
</div>
<div class="topic">
<p class="topic-title first"><code class="docutils literal notranslate"><span class="pre">nguess</span></code></p>
<div class="line-block">
<div class="line"><strong>Description:</strong> Number of guess configurations</div>
<div class="line"><strong>Datatype:</strong> int</div>
<div class="line"><strong>Default:</strong> <code class="docutils literal notranslate"><span class="pre">nstate</span></code></div>
</div>
</div>
<div class="topic">
<p class="topic-title first"><code class="docutils literal notranslate"><span class="pre">only_ints</span></code></p>
<div class="line-block">
<div class="line"><strong>Description:</strong> If true, calculates integrals and dumps to a file. This is used to interface BAGEL to an external program.</div>
<div class="line"><strong>Datatype:</strong> bool</div>
<div class="line"><strong>Default:</strong> false</div>
</div>
</div>
<div class="topic">
<p class="topic-title first"><code class="docutils literal notranslate"><span class="pre">dipoles</span></code></p>
<div class="line-block">
<div class="line"><strong>Description:</strong> Calculate dipoles</div>
<div class="line"><strong>Datatype:</strong> bool</div>
<div class="line"><strong>Default:</strong> false</div>
</div>
</div>
<div class="topic">
<p class="topic-title first"><code class="docutils literal notranslate"><span class="pre">restart</span></code></p>
<div class="line-block">
<div class="line"><strong>Description:</strong> Generate binary archive files that can be used to restart a calculation.</div>
<div class="line"><strong>Datatype:</strong> bool</div>
<div class="line"><strong>Default:</strong> false</div>
</div>
</div>
<div class="topic">
<p class="topic-title first"><code class="docutils literal notranslate"><span class="pre">print_thresh</span></code></p>
<div class="line-block">
<div class="line"><strong>Description:</strong> Threshold below which CI coefficients are not printed</div>
<div class="line"><strong>Datatype:</strong> double</div>
<div class="line"><strong>Default:</strong> 0.05</div>
</div>
</div>
</div>
<div class="section" id="example">
<h2>Example<a class="headerlink" href="#example" title="Permalink to this headline">¶</a></h2>
<p>A Hartree–Fock and FCI calculation on an oxygen molecule with an elongated bond. The HF calculation is a references for the FCI calculation. Please refer to <a class="reference internal" href="../miscellaneous/molden.html#molden"><span class="std std-ref">MOLDEN</span></a> for more information on the print input block.</p>
<div class="section" id="sample-input">
<h3>Sample input<a class="headerlink" href="#sample-input" title="Permalink to this headline">¶</a></h3>
<div class="highlight-javascript notranslate"><div class="highlight"><pre><span></span><span class="p">{</span> <span class="s2">"bagel"</span> <span class="o">:</span> <span class="p">[</span>
<span class="p">{</span>
<span class="s2">"title"</span> <span class="o">:</span> <span class="s2">"molecule"</span><span class="p">,</span>
<span class="s2">"basis"</span> <span class="o">:</span> <span class="s2">"sto-3g"</span><span class="p">,</span>
<span class="s2">"df_basis"</span> <span class="o">:</span> <span class="s2">"cc-pvdz-jkfit"</span><span class="p">,</span>
<span class="s2">"angstrom"</span> <span class="o">:</span> <span class="kc">true</span><span class="p">,</span>
<span class="s2">"geometry"</span> <span class="o">:</span> <span class="p">[</span>
<span class="p">{</span> <span class="s2">"atom"</span> <span class="o">:</span> <span class="s2">"H"</span><span class="p">,</span> <span class="s2">"xyz"</span> <span class="o">:</span> <span class="p">[</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">1.5</span> <span class="p">]},</span>
<span class="p">{</span> <span class="s2">"atom"</span> <span class="o">:</span> <span class="s2">"F"</span><span class="p">,</span> <span class="s2">"xyz"</span> <span class="o">:</span> <span class="p">[</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span> <span class="p">]}</span>
<span class="p">]</span>
<span class="p">},</span>
<span class="p">{</span>
<span class="s2">"title"</span> <span class="o">:</span> <span class="s2">"hf"</span>
<span class="p">},</span>
<span class="p">{</span>
<span class="s2">"title"</span> <span class="o">:</span> <span class="s2">"fci"</span><span class="p">,</span>
<span class="s2">"thresh"</span> <span class="o">:</span> <span class="mf">1.0e-6</span><span class="p">,</span>
<span class="s2">"nstate"</span> <span class="o">:</span> <span class="mi">2</span>
<span class="p">}</span>
<span class="p">]}</span>
</pre></div>
</div>
<p>from which one obtains</p>
<div class="highlight-javascript notranslate"><div class="highlight"><pre><span></span><span class="o">---------------------------</span>
<span class="nx">FCI</span> <span class="nx">calculation</span>
<span class="o">---------------------------</span>
<span class="nx">Performs</span> <span class="nx">exactly</span> <span class="nx">the</span> <span class="nx">same</span> <span class="nx">way</span> <span class="nx">as</span> <span class="nx">Knowles</span> <span class="o">&</span> <span class="nx">Handy</span> <span class="mi">1984</span> <span class="nx">CPL</span>
<span class="nx">o</span> <span class="nx">alpha</span><span class="o">-</span><span class="nx">beta</span> <span class="nx">strings</span>
<span class="nx">length</span><span class="o">:</span> <span class="mi">12</span>
<span class="nx">o</span> <span class="nx">size</span> <span class="k">of</span> <span class="nx">the</span> <span class="nx">space</span>
<span class="nx">determinant</span> <span class="nx">space</span><span class="o">:</span> <span class="mi">36</span>
<span class="nx">spin</span><span class="o">-</span><span class="nx">adapted</span> <span class="nx">space</span><span class="o">:</span> <span class="mi">21</span>
<span class="nx">o</span> <span class="nx">single</span> <span class="nx">displacement</span> <span class="nx">lists</span> <span class="p">(</span><span class="nx">alpha</span><span class="p">)</span>
<span class="nx">length</span><span class="o">:</span> <span class="mi">60</span>
<span class="nx">o</span> <span class="nx">single</span> <span class="nx">displacement</span> <span class="nx">lists</span> <span class="p">(</span><span class="nx">beta</span><span class="p">)</span>
<span class="nx">length</span><span class="o">:</span> <span class="mi">60</span>
<span class="o">*</span> <span class="nx">Integral</span> <span class="nx">transformation</span> <span class="nx">done</span><span class="p">.</span> <span class="nx">Elapsed</span> <span class="nx">time</span><span class="o">:</span> <span class="mf">0.00</span>
<span class="nx">guess</span> <span class="mi">0</span><span class="o">:</span> <span class="nx">closed</span> <span class="mf">11111.</span> <span class="nx">open</span> <span class="p">......</span>
<span class="nx">guess</span> <span class="mi">1</span><span class="o">:</span> <span class="nx">closed</span> <span class="mf">111.1</span><span class="p">.</span> <span class="nx">open</span> <span class="p">...</span><span class="mf">1.1</span>
<span class="o">===</span> <span class="nx">FCI</span> <span class="nx">iteration</span> <span class="o">===</span>
<span class="mi">0</span> <span class="mi">0</span> <span class="o">-</span><span class="mf">98.41480561</span> <span class="mf">4.76e-02</span> <span class="mf">0.00</span>
<span class="mi">0</span> <span class="mi">1</span> <span class="o">-</span><span class="mf">98.26379090</span> <span class="mf">4.50e-02</span> <span class="mf">0.00</span>
<span class="mi">1</span> <span class="mi">0</span> <span class="o">-</span><span class="mf">98.51664721</span> <span class="mf">1.09e-02</span> <span class="mf">0.00</span>
<span class="mi">1</span> <span class="mi">1</span> <span class="o">-</span><span class="mf">98.41322803</span> <span class="mf">1.00e-02</span> <span class="mf">0.00</span>
<span class="mi">2</span> <span class="mi">0</span> <span class="o">-</span><span class="mf">98.51931832</span> <span class="mf">1.71e-03</span> <span class="mf">0.00</span>
<span class="mi">2</span> <span class="mi">1</span> <span class="o">-</span><span class="mf">98.41524119</span> <span class="mf">1.91e-04</span> <span class="mf">0.00</span>
<span class="mi">3</span> <span class="mi">0</span> <span class="o">-</span><span class="mf">98.51940404</span> <span class="mf">3.13e-04</span> <span class="mf">0.00</span>
<span class="mi">3</span> <span class="mi">1</span> <span class="o">*</span> <span class="o">-</span><span class="mf">98.41524124</span> <span class="mf">2.55e-14</span> <span class="mf">0.00</span>
<span class="mi">4</span> <span class="mi">0</span> <span class="o">-</span><span class="mf">98.51940654</span> <span class="mf">4.91e-05</span> <span class="mf">0.00</span>
<span class="mi">4</span> <span class="mi">1</span> <span class="o">*</span> <span class="o">-</span><span class="mf">98.41524124</span> <span class="mf">2.80e-14</span> <span class="mf">0.00</span>
<span class="mi">5</span> <span class="mi">0</span> <span class="o">-</span><span class="mf">98.51940660</span> <span class="mf">2.62e-06</span> <span class="mf">0.00</span>
<span class="mi">5</span> <span class="mi">1</span> <span class="o">*</span> <span class="o">-</span><span class="mf">98.41524124</span> <span class="mf">1.86e-14</span> <span class="mf">0.00</span>
<span class="mi">6</span> <span class="mi">0</span> <span class="o">*</span> <span class="o">-</span><span class="mf">98.51940660</span> <span class="mf">1.96e-07</span> <span class="mf">0.00</span>
<span class="mi">6</span> <span class="mi">1</span> <span class="o">*</span> <span class="o">-</span><span class="mf">98.41524124</span> <span class="mf">2.02e-14</span> <span class="mf">0.00</span>
<span class="o">*</span> <span class="nx">ci</span> <span class="nx">vector</span><span class="p">,</span> <span class="nx">state</span> <span class="mi">0</span><span class="p">,</span> <span class="o"><</span><span class="nx">S</span><span class="o">^</span><span class="mi">2</span><span class="o">></span> <span class="o">=</span> <span class="mf">0.0000</span>
<span class="mf">22222.</span> <span class="o">-</span><span class="mf">0.9320921105</span>
<span class="mf">2222.2</span> <span class="mf">0.3574718122</span>
<span class="o">*</span> <span class="nx">ci</span> <span class="nx">vector</span><span class="p">,</span> <span class="nx">state</span> <span class="mi">1</span><span class="p">,</span> <span class="o"><</span><span class="nx">S</span><span class="o">^</span><span class="mi">2</span><span class="o">></span> <span class="o">=</span> <span class="o">-</span><span class="mf">0.0000</span>
<span class="mi">222</span><span class="nx">a2b</span> <span class="mf">0.6167681811</span>
<span class="mi">222</span><span class="nx">b2a</span> <span class="mf">0.6167681811</span>
<span class="mi">222</span><span class="nx">ab2</span> <span class="o">-</span><span class="mf">0.3441653374</span>
<span class="mi">222</span><span class="nx">ba2</span> <span class="o">-</span><span class="mf">0.3441653374</span>
<span class="o">*</span> <span class="nx">METHOD</span><span class="o">:</span> <span class="nx">FCI</span> <span class="mf">0.00</span>
</pre></div>
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<h2>References<a class="headerlink" href="#references" title="Permalink to this headline">¶</a></h2>
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<th class="head">Reference</th>
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<tbody valign="top">
<tr class="row-even"><td>Efficient calculation of sigma vectors (KH)</td>
<td>P. J. Knowles and N. C. Handy, Chem. Phys. Lett. <strong>111</strong>, 315 (1984).</td>
</tr>
<tr class="row-odd"><td>Efficient calculation of sigma vectors (HZ)</td>
<td>R. J. Harrison and S. Zarrabian, Chem. Phys. Lett. <strong>158</strong>, 393 (1989).</td>
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