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<div class="section" id="moller-plesset-perturbation-theory-mp2">
<span id="mp2"></span><h1>Møller–Plesset perturbation theory (MP2)<a class="headerlink" href="#moller-plesset-perturbation-theory-mp2" 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>Second-order Møller–Plesset perturbation theory (MP2) calculations are performed with density fitting using
the keyword <code class="docutils literal notranslate"><span class="pre">"title"</span> <span class="pre">:</span> <span class="pre">"mp2"</span></code>.</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">frozen</span></code></p>
<div class="line-block">
<div class="line"><strong>Description</strong>: to have frozen orbitals or not</div>
<div class="line"><strong>Datatype</strong>: bool</div>
<div class="line"><strong>Default</strong>: true</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>: manually specify number of frozen orbitals, used when ‘frozen’ is turned on</div>
<div class="line"><strong>Datatype</strong>: int</div>
</div>
</div>
<div class="topic">
<p class="topic-title first"><code class="docutils literal notranslate"><span class="pre">aux_basis</span></code></p>
<div class="line-block">
<div class="line"><strong>Description</strong>: specify an auxiliary basis set for MP2</div>
<div class="line"><strong>Datatype</strong>: string</div>
<div class="line"><strong>Default</strong>: use the same density fitting basis as in <a class="reference internal" href="../molecule/molecule.html#molecule"><span class="std std-ref">Required keywords</span></a></div>
<div class="line"><strong>Recommendation</strong>: use MP2-fit auxiliary basis (auxiliary basis ends with ‘ri’)</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">"cc-pvdz"</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="s2">"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">"C"</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">1.20433891360</span><span class="p">,</span> <span class="mf">0.54285096106</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.04748199659</span><span class="p">]</span> <span class="p">},</span>
<span class="p">{</span> <span class="s2">"atom"</span> <span class="o">:</span> <span class="s2">"C"</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">1.20543291352</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.83826393986</span><span class="p">,</span> <span class="mf">0.12432899108</span><span class="p">]</span> <span class="p">},</span>
<span class="p">{</span> <span class="s2">"atom"</span> <span class="o">:</span> <span class="s2">"C"</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">0.00000600000</span><span class="p">,</span> <span class="o">-</span><span class="mf">1.52953889027</span><span class="p">,</span> <span class="mf">0.20833398505</span><span class="p">]</span> <span class="p">},</span>
<span class="p">{</span> <span class="s2">"atom"</span> <span class="o">:</span> <span class="s2">"C"</span><span class="p">,</span> <span class="s2">"xyz"</span> <span class="o">:</span> <span class="p">[</span> <span class="mf">1.20544091352</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.83825393987</span><span class="p">,</span> <span class="mf">0.12432799108</span><span class="p">]</span> <span class="p">},</span>
<span class="p">{</span> <span class="s2">"atom"</span> <span class="o">:</span> <span class="s2">"C"</span><span class="p">,</span> <span class="s2">"xyz"</span> <span class="o">:</span> <span class="p">[</span> <span class="mf">1.20433091360</span><span class="p">,</span> <span class="mf">0.54284396106</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.04748099659</span><span class="p">]</span> <span class="p">},</span>
<span class="p">{</span> <span class="s2">"atom"</span> <span class="o">:</span> <span class="s2">"C"</span><span class="p">,</span> <span class="s2">"xyz"</span> <span class="o">:</span> <span class="p">[</span> <span class="mf">0.00000400000</span><span class="p">,</span> <span class="mf">1.23314191154</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.13372399041</span><span class="p">]</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">2.13410484690</span><span class="p">,</span> <span class="mf">1.07591192282</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.12500499103</span><span class="p">]</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">2.13651384673</span><span class="p">,</span> <span class="o">-</span><span class="mf">1.37179190159</span><span class="p">,</span> <span class="mf">0.18742198655</span><span class="p">]</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">0.00000000000</span><span class="p">,</span> <span class="o">-</span><span class="mf">2.59646181374</span><span class="p">,</span> <span class="mf">0.33932597566</span><span class="p">]</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">2.13651384673</span><span class="p">,</span> <span class="o">-</span><span class="mf">1.37179290159</span><span class="p">,</span> <span class="mf">0.18742198655</span><span class="p">]</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">2.13410684690</span><span class="p">,</span> <span class="mf">1.07591292282</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.12500599103</span><span class="p">]</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">0.00000000000</span><span class="p">,</span> <span class="mf">2.29608983528</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.28688797942</span><span class="p">]</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">"mp2"</span><span class="p">,</span>
<span class="s2">"aux_basis"</span> <span class="o">:</span> <span class="s2">"cc-pvdz-ri"</span><span class="p">,</span>
<span class="s2">"frozen"</span> <span class="o">:</span> <span class="kc">true</span>
<span class="p">}</span>
<span class="p">]}</span>
</pre></div>
</div>
<p>The SCF calculation should converge after 11 iterations with energy -230.72159477. The DF-MP2 output is as follows:</p>
<div class="highlight-javascript notranslate"><div class="highlight"><pre><span></span><span class="o">===</span> <span class="nx">DF</span><span class="o">-</span><span class="nx">MP2</span> <span class="nx">calculation</span> <span class="o">===</span>
<span class="o">*</span> <span class="nx">freezing</span> <span class="mi">6</span> <span class="nx">orbitals</span>
<span class="nb">Number</span> <span class="k">of</span> <span class="nx">auxiliary</span> <span class="nx">basis</span> <span class="nx">functions</span><span class="o">:</span> <span class="mi">420</span>
<span class="nx">Since</span> <span class="nx">a</span> <span class="nx">DF</span> <span class="nx">basis</span> <span class="nx">is</span> <span class="nx">specified</span><span class="p">,</span> <span class="nx">we</span> <span class="nx">compute</span> <span class="mi">2</span><span class="o">-</span> <span class="nx">and</span> <span class="mi">3</span><span class="o">-</span><span class="nx">index</span> <span class="nx">integrals</span><span class="o">:</span>
<span class="nx">o</span> <span class="nx">Being</span> <span class="nx">stored</span> <span class="nx">without</span> <span class="nx">compression</span><span class="p">.</span> <span class="nx">Storage</span> <span class="nx">requirement</span> <span class="nx">is</span> <span class="mf">0.044</span> <span class="nx">GB</span>
<span class="o">-</span> <span class="mi">3</span><span class="o">-</span><span class="nx">index</span> <span class="nx">ints</span> <span class="nx">prep</span> <span class="mf">0.00</span>
<span class="o">-</span> <span class="mi">3</span><span class="o">-</span><span class="nx">index</span> <span class="nx">ints</span> <span class="mf">0.06</span>
<span class="o">-</span> <span class="mi">2</span><span class="o">-</span><span class="nx">index</span> <span class="nx">ints</span> <span class="mf">0.00</span>
<span class="o">-</span> <span class="nx">computing</span> <span class="nx">inverse</span> <span class="mf">0.02</span>
<span class="nx">elapsed</span> <span class="nx">time</span><span class="o">:</span> <span class="mf">0.09</span> <span class="nx">sec</span><span class="p">.</span>
<span class="nb">Number</span> <span class="k">of</span> <span class="nx">basis</span> <span class="nx">functions</span><span class="o">:</span> <span class="mi">114</span>
<span class="nb">Number</span> <span class="k">of</span> <span class="nx">electrons</span> <span class="o">:</span> <span class="mi">42</span>
<span class="o">*</span> <span class="mi">3</span><span class="o">-</span><span class="nx">index</span> <span class="nx">integral</span> <span class="nx">transformation</span> <span class="nx">done</span>
<span class="o">*</span> <span class="nx">ncache</span> <span class="o">=</span> <span class="mi">20</span>
<span class="o">*</span> <span class="nx">assembly</span> <span class="nx">done</span>
<span class="nx">MP2</span> <span class="nx">correlation</span> <span class="nx">energy</span><span class="o">:</span> <span class="o">-</span><span class="mf">0.7813195576</span> <span class="mf">0.19</span>
<span class="nx">MP2</span> <span class="nx">total</span> <span class="nx">energy</span><span class="o">:</span> <span class="o">-</span><span class="mf">231.5029143295</span>
<span class="o">*</span> <span class="nx">METHOD</span><span class="o">:</span> <span class="nx">MP2</span> <span class="mf">0.34</span>
</pre></div>
</div>
</div>
<div class="section" id="references">
<h2>References<a class="headerlink" href="#references" title="Permalink to this headline">¶</a></h2>
<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>Original reference for MP2</td>
<td>C. Møller and M. S. Plesset, Phys. Rev. <strong>46</strong>, 618 (1934).</td>
</tr>
</tbody>
</table>
</div>
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