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<div class="section" id="dirac-hartree-fock">
<span id="dhf"></span><h1>Dirac–Hartree–Fock<a class="headerlink" href="#dirac-hartree-fock" 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>The Dirac–Hartree–Fock method performs a self-consistent field orbital optimization and energy calculation within a four-component relativistic framework.
The Dirac–Coulomb, Dirac–Coulomb–Gaunt, or full Dirac–Coulomb–Breit Hamiltonian can be used.
Density fitting is used for the two-electron integrals, and 2-spinor basis functions are generated using restricted kinetic balance (RKB).
External magnetic fields can be applied, in which case the spinor basis functions are generated using restricted magnetic balance (RMB) instead.</p>
<p><strong>Dirac–Hartree–Fock (DHF) should not be run with an odd number of electrons</strong> in the absence of an external magnetic field, due to the Kramers degeneracy.
For open-shell molecules, it is recommended to run relativistic complete active space self-consistent field (ZCASSCF).
Dirac HF can be used to generate guess orbitals by increasing the molecular charge to remove unpaired electrons.</p>
<p>Calculations using DHF can be done using the keyword <code class="docutils literal notranslate"><span class="pre">"title"</span> <span class="pre">:</span> <span class="pre">"dhf"</span></code>.</p>
</div>
<div class="section" id="keywords">
<h2>Keywords<a class="headerlink" href="#keywords" title="Permalink to this headline">¶</a></h2>
<p>The default values are recommended unless mentioned otherwise.</p>
<div class="topic">
<p class="topic-title first"><code class="docutils literal notranslate"><span class="pre">gaunt</span></code></p>
<div class="line-block">
<div class="line"><strong>Description</strong>: Turns on the Gaunt interaction in the Hamiltonian.</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">breit</span></code></p>
<div class="line-block">
<div class="line"><strong>Description</strong>: Turns on the full Breit interaction in the Hamiltonian.</div>
<div class="line"><strong>Datatype</strong>: bool</div>
<div class="line"><strong>Default</strong>: value copied from “gaunt” (if gaunt is true, breit is true)</div>
<div class="line"><strong>Recommendation</strong>: Usually the Breit contribution is not important for molecular properties.</div>
</div>
</div>
<div class="topic">
<p class="topic-title first"><code class="docutils literal notranslate"><span class="pre">robust</span></code></p>
<div class="line-block">
<div class="line"><strong>Description</strong>: Determines whether or not to explicitly symmetrize the exchange matrix for numerical stability.</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">maxiter</span> <span class="pre">(or</span> <span class="pre">maxiter_scf)</span></code></p>
<div class="line-block">
<div class="line"><strong>Description</strong>: Maximum number of iterations, after which the program will terminate if convergence is not reached.</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">conv_ignore</span></code></p>
<div class="line-block">
<div class="line"><strong>Description:</strong> If set to “true,” BAGEL will continue running even if the maximum iterations is reached without convergence.</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">diis_start</span></code></p>
<div class="line-block">
<div class="line"><strong>Description</strong>: After the specified iteration, we will begin using the DIIS algorithm the accelerate the convergence.</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">thresh</span> <span class="pre">(or</span> <span class="pre">thresh_scf)</span></code></p>
<div class="line-block">
<div class="line"><strong>Description</strong>: Convergence threshold for the root mean square of the error vector.</div>
<div class="line"><strong>Datatype</strong>: double</div>
<div class="line"><strong>Default</strong>: 1.0e-8</div>
</div>
</div>
<div class="topic">
<p class="topic-title first"><code class="docutils literal notranslate"><span class="pre">thresh_overlap</span></code></p>
<div class="line-block">
<div class="line"><strong>Description</strong>: Overlap threshold used to identify linear dependancy in the atomic basis set.</div>
<div class="line"><strong>Datatype</strong>: double</div>
<div class="line"><strong>Default</strong>: 1.0e-8</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>: Molecular charge.</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">pop</span></code></p>
<div class="line-block">
<div class="line"><strong>Description</strong>: If set to true, population analysis of the molecular orbitals will be printed to a file named dhf.log.</div>
<div class="line"><strong>Datatype</strong>: bool</div>
<div class="line"><strong>Default</strong>: false</div>
</div>
</div>
</div>
<div class="section" id="example">
<h2>Example<a class="headerlink" href="#example" title="Permalink to this headline">¶</a></h2>
<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">"svp"</span><span class="p">,</span>
<span class="s2">"df_basis"</span> <span class="o">:</span> <span class="s2">"svp-jkfit"</span><span class="p">,</span>
<span class="s2">"angstrom"</span> <span class="o">:</span> <span class="s2">"false"</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">"F"</span><span class="p">,</span> <span class="s2">"xyz"</span> <span class="o">:</span> <span class="p">[</span> <span class="o">-</span><span class="mf">0.000000</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.000000</span><span class="p">,</span> <span class="mf">2.720616</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="o">-</span><span class="mf">0.000000</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.000000</span><span class="p">,</span> <span class="mf">0.305956</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">"dhf"</span><span class="p">,</span>
<span class="s2">"gaunt"</span> <span class="o">:</span> <span class="kc">true</span><span class="p">,</span>
<span class="s2">"breit"</span> <span class="o">:</span> <span class="kc">true</span>
<span class="p">}</span>
<span class="p">]}</span>
</pre></div>
</div>
<p>The non-relativistic SCF calculation converges in 13 iterations to <span class="math notranslate nohighlight">\(-99.84772354\)</span>, and the Dirac HF converges after 9 iterations
to <span class="math notranslate nohighlight">\(-99.92755305\)</span>.</p>
</div>
<div class="section" id="references">
<h2>References<a class="headerlink" href="#references" title="Permalink to this headline">¶</a></h2>
<div class="section" id="bagel-references">
<h3>BAGEL references<a class="headerlink" href="#bagel-references" title="Permalink to this headline">¶</a></h3>
<table border="1" class="docutils">
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<col width="37%" />
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</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head">Description of Reference</th>
<th class="head">Reference</th>
</tr>
</thead>
<tbody valign="top">
<tr class="row-even"><td>Density fitted Dirac–Hartree–Fock method</td>
<td>M. S. Kelley and T. Shiozaki, J. Chem. Phys. <strong>138</strong>, 204113 (2013).</td>
</tr>
<tr class="row-odd"><td>GIAO extension</td>
<td>R. D. Reynolds and T. Shiozaki, Phys. Chem. Chem. Phys. <strong>17</strong>, 14280 (2015).</td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="general-references">
<h3>General references<a class="headerlink" href="#general-references" title="Permalink to this headline">¶</a></h3>
<table border="1" class="docutils">
<colgroup>
<col width="40%" />
<col width="60%" />
</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head">Description of Reference</th>
<th class="head">Reference</th>
</tr>
</thead>
<tbody valign="top">
<tr class="row-even"><td>General text on relativistic electronic
structure, including Dirac–Hartree–Fock.</td>
<td>M. Reiher and A. Wolf, <em>Relativistic Quantum Chemistry</em> (Wiley-VCH,
Weinheim, 2009).</td>
</tr>
</tbody>
</table>
</div>
</div>
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<li class="toctree-l1 current"><a class="reference internal" href="../user-manual.html"><strong>BAGEL user manual</strong></a><ul class="current">
<li class="toctree-l2"><a class="reference internal" href="../quickstart/quickstart.html">First steps with BAGEL</a></li>
<li class="toctree-l2"><a class="reference internal" href="../molecule/molecule-toc.html">Molecule specification</a></li>
<li class="toctree-l2 current"><a class="reference internal" href="scf.html">Self-consistent field</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../multi/multi.html">Multiconfiguration self-consistent field</a></li>
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