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<span class="target" id="index-0"></span><div class="section" id="occ-orbital-optimized-coupled-cluster-and-mo-slashller-plesset-perturbation-theories">
<span id="sec-occ"></span><span id="index-1"></span><h1>OCC: Orbital-Optimized Coupled-Cluster and Møller–Plesset Perturbation Theories<a class="headerlink" href="#occ-orbital-optimized-coupled-cluster-and-mo-slashller-plesset-perturbation-theories" title="Permalink to this headline">¶</a></h1>
<p><em>Code author: Ugur Bozkaya</em></p>
<p><em>Section author: Ugur Bozkaya</em></p>
<p><em>Module:</em> <a class="reference internal" href="autodir_options_c/module__occ.html#apdx-occ"><span>Keywords</span></a>, <a class="reference internal" href="autodir_psivariables/module__occ.html#apdx-occ-psivar"><span>PSI Variables</span></a>, <a class="reference external" href="https://github.com/psi4/psi4public/blob/master/src/bin/occ">OCC</a></p>
<div class="section" id="introduction">
<h2>Introduction<a class="headerlink" href="#introduction" title="Permalink to this headline">¶</a></h2>
<p>Orbital-optimized methods have several advantages over their non-optimized counterparts.
Once the orbitals are optimized, the wave function will obey the Hellmann-Feynman theorem
for orbital rotation parameters. Therefore, there is no need for orbital response terms
in the evaluation of analytic gradients. In other words, it is unnecessary to solve the
first order coupled-perturbed CC and many-body perturbation theory (MBPT) equations.
Further, computation of one-electron properties is easier because there are no response contributions to the particle
density matrices (PDMs). Moreover, active space approximations can be readily incorporated into the CC methods
<a class="reference internal" href="bibliography.html#krylov-2000-vod" id="id1">[Krylov:2000:vod]</a>. Additionally, orbital-optimized coupled-cluster avoids spurious second-order
poles in its response function, and its transition dipole moments are gauge invariant <a class="reference internal" href="bibliography.html#pedersen-1999-od" id="id2">[Pedersen:1999:od]</a>.</p>
<p>Another advantage is that the orbital-optimized methods do not suffer from artifactual symmetry-breaking
instabilities <a class="reference internal" href="bibliography.html#crawford-1997-instability" id="id3">[Crawford:1997:instability]</a>, <a class="reference internal" href="bibliography.html#sherrill-1998-od" id="id4">[Sherrill:1998:od]</a>, <a class="reference internal" href="bibliography.html#bozkaya-2011-omp2" id="id5">[Bozkaya:2011:omp2]</a>, and <a class="reference internal" href="bibliography.html#bozkaya-2011-omp3" id="id6">[Bozkaya:2011:omp3]</a>.
Furthermore, Kurlancheek and Head-Gordon <a class="reference internal" href="bibliography.html#kurlancek-2009" id="id7">[Kurlancek:2009]</a> demonstrated that first order properties such as
forces or dipole moments are discontinuous along nuclear coordinates when such a symmetry breaking occurs.
They also observed that although the energy appears well behaved, the MP2 method can have natural occupation
numbers greater than 2 or less than 0, hence may violate the N-representability condition. They further
discussed that the orbital response equations generally have a singularity problem at the unrestriction point
where spin-restricted orbitals become unstable to unrestriction. This singularity yields to extremely large or
small eigenvalues of the one-particle density matrix (OPDM). These abnormal eigenvalues may lead to unphysical
molecular properties such as vibrational frequencies. However, orbital optimized MP2 (hence Orbital optimized MP3)
will solve this N-representability problem by disregarding orbital response contribution of one-partical
density matrix.</p>
<p>Although the performance of coupled-cluster singles and doubles (CCSD) and orbital-optimized
CCD (OD) is similar, the situation is different in the case of triples corrections, especially at stretched
geometries <a class="reference internal" href="bibliography.html#bozkaya-2012-odtl" id="id8">[Bozkaya:2012:odtl]</a>. Bozkaya and Schaefer demonstrated that orbital-optimized coupled cluster based
triple corrections, especially those of asymmetrics, provide significantly better potential energy curves than
CCSD based triples corrections.</p>
<p><strong>NOTE</strong>: As will be discussed later, all methods with orbital-optimization functionality have non-orbital
optimized counterparts. Consequently, there arise two possible ways to call MP2 and DF-MP2. In most
cases, users should prefer the DF-MP2 code described in the <a class="reference internal" href="dfmp2.html#sec-dfmp2"><span>DF-MP2</span></a> section because it is
faster. If gradients are needed (like in a geometry optimization), then the procedures outlined hereafter
should be followed.</p>
<p>Thus, there arise a few categories of method, each with corresponding input keywords:</p>
<ul>
<li><p class="first">Orbital-optimized MP and CC methods with conventional integrals( <a class="reference internal" href="#sec-occconv"><span>OCC Methods</span></a>)</p>
</li>
<li><p class="first">Non-orbital-optimized MP and CC methods with conventional integrals(<a class="reference internal" href="#sec-convocc"><span>MP/CC</span></a> )</p>
</li>
<li><dl class="first docutils">
<dt>Orbital-optimized MP and CC methods with DF and CD integrals(<a class="reference internal" href="#sec-dfocc"><span>DF/CD</span></a> )</dt>
<dd><ul class="first last simple">
<li>Includes Non-orbital-optimized DF and CD methods</li>
</ul>
</dd>
</dl>
</li>
</ul>
</div>
<div class="section" id="theory">
<h2>Theory<a class="headerlink" href="#theory" title="Permalink to this headline">¶</a></h2>
<p>What follows is a very basic description of orbital-optimized Møller–Plesset perturbation
theory as implemented in <span class="sc">Psi4</span>. We will follow our previous presentations (<a class="reference internal" href="bibliography.html#bozkaya-2011-omp2" id="id9">[Bozkaya:2011:omp2]</a>,
<a class="reference internal" href="bibliography.html#bozkaya-2011-omp3" id="id10">[Bozkaya:2011:omp3]</a>, and <a class="reference internal" href="bibliography.html#bozkaya-2012-odtl" id="id11">[Bozkaya:2012:odtl]</a>)</p>
<p>The orbital variations may be expressed by means of an exponential unitary operator</p>
<div class="math">
<p><img src="_images/math/efc161812242162eaae89d85b9f47bebeb2238b2.png" alt="\widetilde{\hat{p}}^{\dagger} &= e^{\hat{K}} \hat{p}^{\dagger} e^{-\hat{K}}\\
\widetilde{\hat{p}} &= e^{\hat{K}} \ \hat{p} \ e^{-\hat{K}} \\
| \widetilde{p} \rangle &= e^{\hat{K}} \ | p \rangle"/></p>
</div><p>where <img class="math" src="_images/math/a2614acec4a930195ddb2276a49573c70d283c82.png" alt="\hat{K}" style="vertical-align: 0px"/> is the orbital rotation operator</p>
<div class="math">
<p><img src="_images/math/d3030ee3afab6fe21a1a012aa7f78bc4b1440a9a.png" alt="\hat{K} &= \sum_{p,q}^{} K_{pq} \ \hat{E}_{pq} = \sum_{p>q}^{} \kappa_{pq} \ \hat{E}_{pq}^{-} \\
\hat{E}_{pq} &= \hat{p}^{\dagger} \hat{q} \\
\hat{E}_{pq}^{-} &= \hat{E}_{pq} \ - \ \hat{E}_{qp} \\
{\bf K} &= Skew({\bf \kappa})"/></p>
</div><p>The effect of the orbital rotations on the MO coefficients can be written as</p>
<div class="math">
<p><img src="_images/math/166b66815a035d55b2ebd9f2e30c4f77a989921d.png" alt="{\bf C({\bf \kappa})} = {\bf C^{(0)}} \ e^{{\bf K}}"/></p>
</div><p>where <img class="math" src="_images/math/ae3de04517641f256c352a85917fcbda7306612e.png" alt="{\bf C^{(0)}}" style="vertical-align: 0px"/> is the initial MO coefficient matrix and <img class="math" src="_images/math/5f79064cae0d6d14e28a567882089bd92913022b.png" alt="{\bf C({\bf \kappa})}" style="vertical-align: -4px"/> is the new
MO coefficient matrix as a function of <img class="math" src="_images/math/eda8444a7fe009f79723fe9d5c337a229bfa037e.png" alt="{\bf \kappa}" style="vertical-align: 0px"/>.
Now, let us define a variational energy functional (Lagrangian) as a function of <img class="math" src="_images/math/eda8444a7fe009f79723fe9d5c337a229bfa037e.png" alt="{\bf \kappa}" style="vertical-align: 0px"/></p>
<ul class="simple">
<li>OMP2</li>
</ul>
<div class="math">
<p><img src="_images/math/b997e047991d8f589f5a1cfda39bb31058bf4508.png" alt="\widetilde{E}({\bf \kappa}) &= \langle 0| \hat{H}^{\kappa} | 0 \rangle \\
&+ \langle 0| \big(\hat{W}_{N}^{\kappa}\hat{T}_{2}^{(1)}\big)_{c} | 0 \rangle \\
&+ \langle 0| \{\hat{\Lambda}_{2}^{(1)} \ \big(\hat{f}_{N}^{\kappa} \hat{T}_{2}^{(1)}
\ + \ \hat{W}_{N}^{\kappa} \big)_{c}\}_{c} | 0 \rangle"/></p>
</div><ul class="simple">
<li>OMP3</li>
</ul>
<div class="math">
<p><img src="_images/math/2b8940684af2769bed0d0bcc38e671210318fcfd.png" alt="\widetilde{E}({\bf \kappa}) &= \langle 0| \hat{H}^{\kappa} | 0 \rangle \\
&+ \langle 0| \big(\hat{W}_{N}^{\kappa}\hat{T}_{2}^{(1)}\big)_{c} | 0 \rangle
\ + \ \langle 0| \big(\hat{W}_{N}^{\kappa}\hat{T}_{2}^{(2)}\big)_{c} | 0 \rangle \\
&+ \langle 0| \{\hat{\Lambda}_{2}^{(1)} \ \big(\hat{f}_{N}^{\kappa} \hat{T}_{2}^{(1)}
\ + \ \hat{W}_{N}^{\kappa} \big)_{c}\}_{c} | 0 \rangle \\
&+ \langle 0| \{\hat{\Lambda}_{2}^{(1)} \ \big(\hat{f}_{N}^{\kappa} \hat{T}_{2}^{(2)}
\ + \ \hat{W}_{N}^{\kappa}\hat{T}_{2}^{(1)} \big)_{c}\}_{c} | 0 \rangle \\
&+ \langle 0| \{\hat{\Lambda}_{2}^{(2)} \ \big(\hat{f}_{N}^{\kappa} \hat{T}_{2}^{(1)}
\ + \ \hat{W}_{N}^{\kappa} \big)_{c}\}_{c} | 0 \rangle"/></p>
</div><ul class="simple">
<li>OCEPA</li>
</ul>
<div class="math">
<p><img src="_images/math/21c6b95ed4ecb7a0ef6dd8cee36580905ff5dffb.png" alt="\widetilde{E}({\bf \kappa}) &= \langle 0| \hat{H}^{\kappa} | 0 \rangle
\ + \ \langle 0| \big(\hat{W}_{N}^{\kappa}\hat{T}_{2}\big)_{c} | 0 \rangle \\
&+ \langle 0| \{\hat{\Lambda}_{2} \ \big(\hat{W}_{N}^{\kappa} \ + \ \hat{H}_{N}^{\kappa}\hat{T}_{2} \big)_{c}\}_{c} | 0 \rangle"/></p>
</div><p>where subscript c means only connected diagrams are allowed, and
<img class="math" src="_images/math/45024f84836ad2146e2eb0aebcd2c2dc6d9104d7.png" alt="\hat{H}^{\kappa}" style="vertical-align: 0px"/>, <img class="math" src="_images/math/9bcda8a332742e90afba7ee1d6425df47df0bebc.png" alt="\hat{f}_{N}^{\kappa}" style="vertical-align: -5px"/>, and <img class="math" src="_images/math/4a09a78f57dac6c89e3214681be3ecd778955bf4.png" alt="\hat{W}_{N}^{\kappa}" style="vertical-align: -5px"/> defined as</p>
<div class="math">
<p><img src="_images/math/dadc326e8a7f8f8beaafa7cc0425abffb3fa75b6.png" alt="\hat{H}^{\kappa} &= e^{-\hat{K}} \hat{H} e^{\hat{K}} \\
\hat{f}_{N}^{\kappa} &= e^{-\hat{K}} \hat{f}_{N}^{d} e^{\hat{K}} \\
\hat{W}_{N}^{\kappa} &= e^{-\hat{K}} \hat{W}_{N} e^{\hat{K}}"/></p>
</div><p>where <img class="math" src="_images/math/f4de8c089036c2c1431c1a5bad027e40bee0642a.png" alt="\hat{f}_{N}" style="vertical-align: -4px"/>, and <img class="math" src="_images/math/996c82f3f9baf1b88ecefa256dfc38efdfd6c594.png" alt="\hat{W}_{N}" style="vertical-align: -3px"/> are the one- and two-electron components of normal-ordered Hamiltonian. Then,
first and second derivatives of the energy with respect to the <img class="math" src="_images/math/eda8444a7fe009f79723fe9d5c337a229bfa037e.png" alt="{\bf \kappa}" style="vertical-align: 0px"/> parameter at <img class="math" src="_images/math/09132164a880f6c214237b648940e8a84e950029.png" alt="{\bf \kappa} = 0" style="vertical-align: 0px"/></p>
<div class="math">
<p><img src="_images/math/40bb03267d397553383689d1cf57e45a112775cd.png" alt="w_{pq} = \frac{\partial \widetilde{E}}{\partial \kappa_{pq}}"/></p>
</div><div class="math">
<p><img src="_images/math/f84d49f7f696a1043a5548397e39ebc9ca7be83d.png" alt="A_{pq,rs} = \frac{\partial^2 \widetilde{E}}{\partial \kappa_{pq} \partial \kappa_{rs}}"/></p>
</div><p>Then the energy can be expanded up to second-order as follows</p>
<div class="math">
<p><img src="_images/math/c2e98c792352e62d16961dda34b926cbcf2bc7d9.png" alt="\widetilde{E}^{(2)}({\bf \kappa}) = \widetilde{E}^{(0)} + {\bf \kappa^{\dagger} w} + \frac{1}{2}~{\bf \kappa^{\dagger} A \kappa}"/></p>
</div><p>where <img class="math" src="_images/math/a1de58a4e7b4039d752def7ffefe2d98fc05c1a8.png" alt="{\bf w}" style="vertical-align: 0px"/> is the MO gradient vector, <img class="math" src="_images/math/eda8444a7fe009f79723fe9d5c337a229bfa037e.png" alt="{\bf \kappa}" style="vertical-align: 0px"/> is the MO rotation vector,
and <img class="math" src="_images/math/14a7792059fb7789d55742b059d26e66ef311197.png" alt="{\bf A}" style="vertical-align: -1px"/> is the MO Hessian matrix. Therefore, minimizing the energy with respect to <img class="math" src="_images/math/eda8444a7fe009f79723fe9d5c337a229bfa037e.png" alt="{\bf \kappa}" style="vertical-align: 0px"/>
yields</p>
<div class="math">
<p><img src="_images/math/bd85e06a653f664ba10910140c919eeb8f2bf1ca.png" alt="{\bf \kappa} = -{\bf A^{-1}w}"/></p>
</div><p>This final equation corresponds to the usual Newton-Raphson step.</p>
<p>Publications resulting from the use of the OMP2 code should cite the following publications:</p>
<p><a class="reference internal" href="bibliography.html#bozkaya-2011-omp2" id="id12">[Bozkaya:2011:omp2]</a> and <a class="reference internal" href="bibliography.html#bozkaya-2013-omp2grad" id="id13">[Bozkaya:2013:omp2grad]</a>.</p>
<p>Publications resulting from the use of the OMP3 code should cite the following publications:</p>
<p><a class="reference internal" href="bibliography.html#bozkaya-2011-omp3" id="id14">[Bozkaya:2011:omp3]</a> , <a class="reference internal" href="bibliography.html#bozkaya-2013-omp3" id="id15">[Bozkaya:2013:omp3]</a>, and <a class="reference internal" href="bibliography.html#bozkaya-2013-omp3grad" id="id16">[Bozkaya:2013:omp3grad]</a>.</p>
<p>Publications resulting from the use of the OMP2.5 code should cite the following publications:</p>
<p><a class="reference internal" href="bibliography.html#bozkaya-2011-omp3" id="id17">[Bozkaya:2011:omp3]</a>.</p>
<p>Publications resulting from the use of the OCEPA code should cite the following publication(s):</p>
<p><a class="reference internal" href="bibliography.html#bozkaya-2013-ocepa" id="id18">[Bozkaya:2013:ocepa]</a>.</p>
<p>Publications resulting from the use of the CEPA0 code should cite the following publication(s):</p>
<p><a class="reference internal" href="bibliography.html#bozkaya-2013-ocepa" id="id19">[Bozkaya:2013:ocepa]</a>.</p>
</div>
<div class="section" id="convergence-problems">
<h2>Convergence Problems<a class="headerlink" href="#convergence-problems" title="Permalink to this headline">¶</a></h2>
<p>For problematic open-shell systems, we recommend to use the ROHF or DFT orbitals as an initial guess for orbital-optimized methods. Both ROHF and
DFT orbitals may provide better initial guesses than UHF orbitals, hence convergence may be significantly speeded up with ROHF or DFT orbitals.
In order to use ROHF orbitals we can simply use “reference rohf” option. For DFT orbitals one should use “reference uks” and “dft_functional b3lyp” options. Of
course users can use any DFT functional available in Psi4.</p>
</div>
<div class="section" id="methods">
<span id="sec-occconv"></span><h2>Methods<a class="headerlink" href="#methods" title="Permalink to this headline">¶</a></h2>
<p>The conventional (i.e. non-orbital optimized) and orbital-optimized MP2 methods
currently supported in <span class="sc">Psi4</span> are outlined in Table <a class="reference internal" href="#table-omp2-calls"><span>OMP2 Methods</span></a>.</p>
<blockquote>
<div><table border="1" class="docutils" id="table-omp2-calls">
<colgroup>
<col width="19%" />
<col width="48%" />
<col width="7%" />
<col width="8%" />
<col width="18%" />
</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head">Name</th>
<th class="head">Calls Method</th>
<th class="head">Energy</th>
<th class="head">Gradient</th>
<th class="head">Reference</th>
</tr>
</thead>
<tbody valign="top">
<tr class="row-even"><td>conv-mp2</td>
<td>MP2</td>
<td>Y</td>
<td>Y</td>
<td>RHF/ROHF/UHF</td>
</tr>
<tr class="row-odd"><td>omp2</td>
<td>Orbital-Optimized MP2</td>
<td>Y</td>
<td>Y</td>
<td>RHF/ROHF/UHF/RKS/UKS</td>
</tr>
<tr class="row-even"><td>scs-omp2</td>
<td>Spin-Component Scaled Orbital-Optimized MP2</td>
<td>Y</td>
<td>N</td>
<td>RHF/ROHF/UHF/RKS/UKS</td>
</tr>
<tr class="row-odd"><td>sos-omp2</td>
<td>Spin-Opposite Scaled Orbital-Optimized MP2</td>
<td>Y</td>
<td>N</td>
<td>RHF/ROHF/UHF/RKS/UKS</td>
</tr>
<tr class="row-even"><td>scsn-omp2</td>
<td>A special version of SCS-OMP2 for nucleobase interactions</td>
<td>Y</td>
<td>N</td>
<td>RHF/ROHF/UHF/RKS/UKS</td>
</tr>
<tr class="row-odd"><td>scs-omp2-vdw</td>
<td>A special version of SCS-OMP2 (from ethene dimers)</td>
<td>Y</td>
<td>N</td>
<td>RHF/ROHF/UHF/RKS/UKS</td>
</tr>
<tr class="row-even"><td>sos-pi-omp2</td>
<td>A special version of SOS-OMP2 for <img class="math" src="_images/math/2dfc7c4dd47aff2a8de066912cb776bf02f08437.png" alt="\pi" style="vertical-align: 0px"/>-systems</td>
<td>Y</td>
<td>N</td>
<td>RHF/ROHF/UHF/RKS/UKS</td>
</tr>
</tbody>
</table>
</div></blockquote>
<p>The conventional and orbital-optimized MP3 methods currently supported in <span class="sc">Psi4</span> are outlined in Table <a class="reference internal" href="#table-omp3-calls"><span>OMP3 Methods</span></a>.</p>
<blockquote>
<div><table border="1" class="docutils" id="table-omp3-calls">
<colgroup>
<col width="19%" />
<col width="48%" />
<col width="7%" />
<col width="8%" />
<col width="18%" />
</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head">Name</th>
<th class="head">Calls Method</th>
<th class="head">Energy</th>
<th class="head">Gradient</th>
<th class="head">Reference</th>
</tr>
</thead>
<tbody valign="top">
<tr class="row-even"><td>mp3</td>
<td>MP3</td>
<td>Y</td>
<td>Y</td>
<td>RHF/UHF</td>
</tr>
<tr class="row-odd"><td>omp3</td>
<td>Orbital-Optimized MP3</td>
<td>Y</td>
<td>Y</td>
<td>RHF/ROHF/UHF/RKS/UKS</td>
</tr>
<tr class="row-even"><td>scs-omp3</td>
<td>Spin-Component Scaled Orbital-Optimized MP3</td>
<td>Y</td>
<td>N</td>
<td>RHF/ROHF/UHF/RKS/UKS</td>
</tr>
<tr class="row-odd"><td>sos-omp3</td>
<td>Spin-Opposite Scaled Orbital-Optimized MP3</td>
<td>Y</td>
<td>N</td>
<td>RHF/ROHF/UHF/RKS/UKS</td>
</tr>
<tr class="row-even"><td>scsn-omp3</td>
<td>A special version of SCS-OMP3 for nucleobase interactions</td>
<td>Y</td>
<td>N</td>
<td>RHF/ROHF/UHF/RKS/UKS</td>
</tr>
<tr class="row-odd"><td>scs-omp3-vdw</td>
<td>A special version of SCS-OMP3 (from ethene dimers)</td>
<td>Y</td>
<td>N</td>
<td>RHF/ROHF/UHF/RKS/UKS</td>
</tr>
<tr class="row-even"><td>sos-pi-omp3</td>
<td>A special version of SOS-OMP3 for <img class="math" src="_images/math/2dfc7c4dd47aff2a8de066912cb776bf02f08437.png" alt="\pi" style="vertical-align: 0px"/>-systems</td>
<td>Y</td>
<td>N</td>
<td>RHF/ROHF/UHF/RKS/UKS</td>
</tr>
</tbody>
</table>
</div></blockquote>
<p>The conventional and orbital-optimized MP2.5 methods currently supported in <span class="sc">Psi4</span> are outlined in Table <a class="reference internal" href="#table-omp2-5-calls"><span>OMP2.5 Methods</span></a>.</p>
<blockquote>
<div><table border="1" class="docutils" id="table-omp2-5-calls">
<colgroup>
<col width="19%" />
<col width="48%" />
<col width="7%" />
<col width="8%" />
<col width="18%" />
</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head">Name</th>
<th class="head">Calls Method</th>
<th class="head">Energy</th>
<th class="head">Gradient</th>
<th class="head">Reference</th>
</tr>
</thead>
<tbody valign="top">
<tr class="row-even"><td>mp2.5</td>
<td>MP2.5</td>
<td>Y</td>
<td>Y</td>
<td>RHF/UHF</td>
</tr>
<tr class="row-odd"><td>omp2.5</td>
<td>Orbital-Optimized MP2.5</td>
<td>Y</td>
<td>Y</td>
<td>RHF/ROHF/UHF/RKS/UKS</td>
</tr>
</tbody>
</table>
</div></blockquote>
<p>The conventional and orbital-optimized CEPA methods currently supported in <span class="sc">Psi4</span> are outlined in Table <a class="reference internal" href="#table-ocepa-calls"><span>OCEPA Methods</span></a>.</p>
<blockquote>
<div><table border="1" class="docutils" id="table-ocepa-calls">
<colgroup>
<col width="19%" />
<col width="48%" />
<col width="7%" />
<col width="8%" />
<col width="18%" />
</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head">Name</th>
<th class="head">Calls Method</th>
<th class="head">Energy</th>
<th class="head">Gradient</th>
<th class="head">Reference</th>
</tr>
</thead>
<tbody valign="top">
<tr class="row-even"><td>ocepa</td>
<td>Orbital-Optimized CEPA</td>
<td>Y</td>
<td>Y</td>
<td>RHF/ROHF/UHF/RKS/UKS</td>
</tr>
<tr class="row-odd"><td>scs-ocepa</td>
<td>Spin-Component Scaled Orbital-Optimized CEPA</td>
<td>Y</td>
<td>N</td>
<td>RHF/ROHF/UHF/RKS/UKS</td>
</tr>
<tr class="row-even"><td>sos-ocepa</td>
<td>Spin-Opposite Scaled Orbital-Optimized CEPA</td>
<td>Y</td>
<td>N</td>
<td>RHF/ROHF/UHF/RKS/UKS</td>
</tr>
<tr class="row-odd"><td>cepa0</td>
<td>CEPA(0) (identical to Linearized CCD)</td>
<td>Y</td>
<td>Y</td>
<td>RHF/UHF</td>
</tr>
</tbody>
</table>
</div></blockquote>
<span class="target" id="index-2"></span><span class="target" id="index-3"></span><span class="target" id="index-4"></span></div>
<div class="section" id="basic-keywords">
<span id="index-5"></span><h2>Basic Keywords<a class="headerlink" href="#basic-keywords" title="Permalink to this headline">¶</a></h2>
<div class="section" id="e-convergence">
<h3><a class="reference internal" href="autodoc_glossary_options_c.html#term-e-convergence-occ"><span class="xref std std-term">E_CONVERGENCE</span></a><a class="headerlink" href="#e-convergence" title="Permalink to this headline">¶</a></h3>
<blockquote>
<div><p>Convergence criterion for energy. See Table <a class="reference internal" href="scf.html#table-conv-corl"><span>Post-SCF Convergence</span></a> for default convergence criteria for different calculation types.</p>
<ul class="simple">
<li><strong>Type</strong>: <a class="reference internal" href="notes_c.html#op-c-conv"><span>conv double</span></a></li>
<li><strong>Default</strong>: 1e-6</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="r-convergence">
<h3><a class="reference internal" href="autodoc_glossary_options_c.html#term-r-convergence-occ"><span class="xref std std-term">R_CONVERGENCE</span></a><a class="headerlink" href="#r-convergence" title="Permalink to this headline">¶</a></h3>
<blockquote>
<div><p>Convergence criterion for amplitudes (residuals).</p>
<ul class="simple">
<li><strong>Type</strong>: <a class="reference internal" href="notes_c.html#op-c-conv"><span>conv double</span></a></li>
<li><strong>Default</strong>: 1e-5</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="rms-mograd-convergence">
<h3><a class="reference internal" href="autodoc_glossary_options_c.html#term-rms-mograd-convergence-occ"><span class="xref std std-term">RMS_MOGRAD_CONVERGENCE</span></a><a class="headerlink" href="#rms-mograd-convergence" title="Permalink to this headline">¶</a></h3>
<blockquote>
<div><p>Convergence criterion for RMS orbital gradient. Default adjusts depending on <a class="reference internal" href="autodoc_glossary_options_c.html#term-e-convergence-occ"><span class="xref std std-term">E_CONVERGENCE</span></a></p>
<ul class="simple">
<li><strong>Type</strong>: <a class="reference internal" href="notes_c.html#op-c-conv"><span>conv double</span></a></li>
<li><strong>Default</strong>: 1e-6</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="max-mograd-convergence">
<h3><a class="reference internal" href="autodoc_glossary_options_c.html#term-max-mograd-convergence-occ"><span class="xref std std-term">MAX_MOGRAD_CONVERGENCE</span></a><a class="headerlink" href="#max-mograd-convergence" title="Permalink to this headline">¶</a></h3>
<blockquote>
<div><p>Convergence criterion for maximum orbital gradient</p>
<ul class="simple">
<li><strong>Type</strong>: <a class="reference internal" href="notes_c.html#op-c-conv"><span>conv double</span></a></li>
<li><strong>Default</strong>: 1e-3</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="mo-maxiter">
<h3><a class="reference internal" href="autodoc_glossary_options_c.html#term-mo-maxiter-occ"><span class="xref std std-term">MO_MAXITER</span></a><a class="headerlink" href="#mo-maxiter" title="Permalink to this headline">¶</a></h3>
<blockquote>
<div><p>Maximum number of iterations to determine the orbitals</p>
<ul class="simple">
<li><strong>Type</strong>: integer</li>
<li><strong>Default</strong>: 50</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="wfn-type">
<h3><a class="reference internal" href="autodoc_glossary_options_c.html#term-wfn-type-occ"><span class="xref std std-term">WFN_TYPE</span></a><a class="headerlink" href="#wfn-type" title="Permalink to this headline">¶</a></h3>
<blockquote>
<div><p>Type of the wavefunction.</p>
<ul class="simple">
<li><strong>Type</strong>: string</li>
<li><strong>Possible Values</strong>: OMP2, OMP3, OCEPA, OMP2.5</li>
<li><strong>Default</strong>: OMP2</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="orb-opt">
<h3><a class="reference internal" href="autodoc_glossary_options_c.html#term-orb-opt-occ"><span class="xref std std-term">ORB_OPT</span></a><a class="headerlink" href="#orb-opt" title="Permalink to this headline">¶</a></h3>
<blockquote>
<div><p>Do optimize the orbitals?</p>
<ul class="simple">
<li><strong>Type</strong>: <a class="reference internal" href="notes_c.html#op-c-boolean"><span>boolean</span></a></li>
<li><strong>Default</strong>: true</li>
</ul>
</div></blockquote>
</div>
</div>
<div class="section" id="advanced-keywords">
<h2>Advanced Keywords<a class="headerlink" href="#advanced-keywords" title="Permalink to this headline">¶</a></h2>
<div class="section" id="opt-method">
<h3><a class="reference internal" href="autodoc_glossary_options_c.html#term-opt-method-occ"><span class="xref std std-term">OPT_METHOD</span></a><a class="headerlink" href="#opt-method" title="Permalink to this headline">¶</a></h3>
<blockquote>
<div><p>The optimization algorithm. Modified Steepest-Descent (MSD) takes a Newton-Raphson (NR) step with a crude approximation to diagonal elements of the MO Hessian. The ORB_RESP option obtains the orbital rotation parameters by solving the orbital-reponse (coupled-perturbed CC) equations. Additionally, for both methods a DIIS extrapolation will be performed with the DO_DIIS = TRUE option.</p>
<ul class="simple">
<li><strong>Type</strong>: string</li>
<li><strong>Possible Values</strong>: MSD, ORB_RESP</li>
<li><strong>Default</strong>: ORB_RESP</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="mo-diis-num-vecs">
<h3><a class="reference internal" href="autodoc_glossary_options_c.html#term-mo-diis-num-vecs-occ"><span class="xref std std-term">MO_DIIS_NUM_VECS</span></a><a class="headerlink" href="#mo-diis-num-vecs" title="Permalink to this headline">¶</a></h3>
<blockquote>
<div><p>Number of vectors used in orbital DIIS</p>
<ul class="simple">
<li><strong>Type</strong>: integer</li>
<li><strong>Default</strong>: 6</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="lineq-solver">
<h3><a class="reference internal" href="autodoc_glossary_options_c.html#term-lineq-solver-occ"><span class="xref std std-term">LINEQ_SOLVER</span></a><a class="headerlink" href="#lineq-solver" title="Permalink to this headline">¶</a></h3>
<blockquote>
<div><p>The solver will be used for simultaneous linear equations.</p>
<ul class="simple">
<li><strong>Type</strong>: string</li>
<li><strong>Possible Values</strong>: CDGESV, FLIN, POPLE</li>
<li><strong>Default</strong>: CDGESV</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="orth-type">
<h3><a class="reference internal" href="autodoc_glossary_options_c.html#term-orth-type-occ"><span class="xref std std-term">ORTH_TYPE</span></a><a class="headerlink" href="#orth-type" title="Permalink to this headline">¶</a></h3>
<blockquote>
<div><p>The algorithm for orthogonalization of MOs</p>
<ul class="simple">
<li><strong>Type</strong>: string</li>
<li><strong>Possible Values</strong>: GS, MGS</li>
<li><strong>Default</strong>: MGS</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="mp2-os-scale">
<h3><a class="reference internal" href="autodoc_glossary_options_c.html#term-mp2-os-scale-occ"><span class="xref std std-term">MP2_OS_SCALE</span></a><a class="headerlink" href="#mp2-os-scale" title="Permalink to this headline">¶</a></h3>
<blockquote>
<div><p>MP2 opposite-spin scaling value</p>
<ul class="simple">
<li><strong>Type</strong>: double</li>
<li><strong>Default</strong>: 6.0/5.0</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="mp2-ss-scale">
<h3><a class="reference internal" href="autodoc_glossary_options_c.html#term-mp2-ss-scale-occ"><span class="xref std std-term">MP2_SS_SCALE</span></a><a class="headerlink" href="#mp2-ss-scale" title="Permalink to this headline">¶</a></h3>
<blockquote>
<div><p>MP2 same-spin scaling value</p>
<ul class="simple">
<li><strong>Type</strong>: double</li>
<li><strong>Default</strong>: 1.0/3.0</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="mp2-sos-scale">
<h3><a class="reference internal" href="autodoc_glossary_options_c.html#term-mp2-sos-scale-occ"><span class="xref std std-term">MP2_SOS_SCALE</span></a><a class="headerlink" href="#mp2-sos-scale" title="Permalink to this headline">¶</a></h3>
<blockquote>
<div><p>MP2 Spin-opposite scaling (SOS) value</p>
<ul class="simple">
<li><strong>Type</strong>: double</li>
<li><strong>Default</strong>: 1.3</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="mp2-sos-scale2">
<h3><a class="reference internal" href="autodoc_glossary_options_c.html#term-mp2-sos-scale2-occ"><span class="xref std std-term">MP2_SOS_SCALE2</span></a><a class="headerlink" href="#mp2-sos-scale2" title="Permalink to this headline">¶</a></h3>
<blockquote>
<div><p>Spin-opposite scaling (SOS) value for optimized-MP2 orbitals</p>
<ul class="simple">
<li><strong>Type</strong>: double</li>
<li><strong>Default</strong>: 1.2</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="nat-orbs">
<h3><a class="reference internal" href="autodoc_glossary_options_c.html#term-nat-orbs-occ"><span class="xref std std-term">NAT_ORBS</span></a><a class="headerlink" href="#nat-orbs" title="Permalink to this headline">¶</a></h3>
<blockquote>
<div><p>Do compute natural orbitals?</p>
<ul class="simple">
<li><strong>Type</strong>: <a class="reference internal" href="notes_c.html#op-c-boolean"><span>boolean</span></a></li>
<li><strong>Default</strong>: false</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="occ-orbs-print">
<h3><a class="reference internal" href="autodoc_glossary_options_c.html#term-occ-orbs-print-occ"><span class="xref std std-term">OCC_ORBS_PRINT</span></a><a class="headerlink" href="#occ-orbs-print" title="Permalink to this headline">¶</a></h3>
<blockquote>
<div><p>Do print OCC orbital energies?</p>
<ul class="simple">
<li><strong>Type</strong>: <a class="reference internal" href="notes_c.html#op-c-boolean"><span>boolean</span></a></li>
<li><strong>Default</strong>: false</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="tpdm-abcd-type">
<h3><a class="reference internal" href="autodoc_glossary_options_c.html#term-tpdm-abcd-type-occ"><span class="xref std std-term">TPDM_ABCD_TYPE</span></a><a class="headerlink" href="#tpdm-abcd-type" title="Permalink to this headline">¶</a></h3>
<blockquote>
<div><p>How to take care of the TPDM VVVV-block. The COMPUTE option means it will be computed via an IC/OOC algoritm. The DIRECT option (default) means it will not be computed and stored, instead its contribution will be directly added to Generalized-Fock Matrix.</p>
<ul class="simple">
<li><strong>Type</strong>: string</li>
<li><strong>Possible Values</strong>: DIRECT, COMPUTE</li>
<li><strong>Default</strong>: DIRECT</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="do-diis">
<h3><a class="reference internal" href="autodoc_glossary_options_c.html#term-do-diis-occ"><span class="xref std std-term">DO_DIIS</span></a><a class="headerlink" href="#do-diis" title="Permalink to this headline">¶</a></h3>
<blockquote>
<div><p>Do apply DIIS extrapolation?</p>
<ul class="simple">
<li><strong>Type</strong>: <a class="reference internal" href="notes_c.html#op-c-boolean"><span>boolean</span></a></li>
<li><strong>Default</strong>: true</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="do-level-shift">
<h3><a class="reference internal" href="autodoc_glossary_options_c.html#term-do-level-shift-occ"><span class="xref std std-term">DO_LEVEL_SHIFT</span></a><a class="headerlink" href="#do-level-shift" title="Permalink to this headline">¶</a></h3>
<blockquote>
<div><p>Do apply level shifting?</p>
<ul class="simple">
<li><strong>Type</strong>: <a class="reference internal" href="notes_c.html#op-c-boolean"><span>boolean</span></a></li>
<li><strong>Default</strong>: true</li>
</ul>
</div></blockquote>
</div>
</div>
<div class="section" id="conventional-occ-mo-slashller-plesset-perturbation-theories">
<span id="sec-convocc"></span><h2>Conventional OCC Møller–Plesset Perturbation Theories<a class="headerlink" href="#conventional-occ-mo-slashller-plesset-perturbation-theories" title="Permalink to this headline">¶</a></h2>
<p><em>Module:</em> <a class="reference internal" href="autodir_options_c/module__occ.html#apdx-occ"><span>Keywords</span></a>, <a class="reference internal" href="autodir_psivariables/module__occ.html#apdx-occ-psivar"><span>PSI Variables</span></a>, <a class="reference external" href="https://github.com/psi4/psi4public/blob/master/src/bin/occ">OCC</a></p>
<p><span class="sc">Psi4</span> also has a non-density-fitted MP2 algorithm for RHF and UHF
energies and gradients. The
density-fitted module DFMP2 is always the default, so to access the
conventional MP2 code, set <a class="reference internal" href="autodoc_glossary_options_c.html#term-mp2-type-occ"><span class="xref std std-term">MP2_TYPE</span></a> to <code class="docutils literal"><span class="pre">conv</span></code> and call as usual
<code class="docutils literal"><span class="pre">energy('mp2')</span></code>/<code class="docutils literal"><span class="pre">optimize('mp2')</span></code>.</p>
</div>
<div class="section" id="id20">
<h2>Basic Keywords<a class="headerlink" href="#id20" title="Permalink to this headline">¶</a></h2>
<div class="section" id="mp2-type">
<h3><a class="reference internal" href="autodoc_glossary_options_c.html#term-mp2-type-occ"><span class="xref std std-term">MP2_TYPE</span></a><a class="headerlink" href="#mp2-type" title="Permalink to this headline">¶</a></h3>
<blockquote>
<div><p>Algorithm to use for non-OO MP2 computation</p>
<ul class="simple">
<li><strong>Type</strong>: string</li>
<li><strong>Possible Values</strong>: DF, CONV</li>
<li><strong>Default</strong>: DF</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="id21">
<h3><a class="reference internal" href="autodoc_glossary_options_c.html#term-mp2-os-scale-occ"><span class="xref std std-term">MP2_OS_SCALE</span></a><a class="headerlink" href="#id21" title="Permalink to this headline">¶</a></h3>
<blockquote>
<div><p>MP2 opposite-spin scaling value</p>
<ul class="simple">
<li><strong>Type</strong>: double</li>
<li><strong>Default</strong>: 6.0/5.0</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="id22">
<h3><a class="reference internal" href="autodoc_glossary_options_c.html#term-mp2-ss-scale-occ"><span class="xref std std-term">MP2_SS_SCALE</span></a><a class="headerlink" href="#id22" title="Permalink to this headline">¶</a></h3>
<blockquote>
<div><p>MP2 same-spin scaling value</p>
<ul class="simple">
<li><strong>Type</strong>: double</li>
<li><strong>Default</strong>: 1.0/3.0</li>
</ul>
</div></blockquote>
<p>Non-orbital-optimized counterparts to higher order MPn methods are also
available. Summarizing from tables above, the following methods are
available and can be controlled through OCC keywards.</p>
<blockquote>
<div><table border="1" class="docutils" id="table-nonoo">
<colgroup>
<col width="19%" />
<col width="48%" />
<col width="7%" />
<col width="8%" />
<col width="18%" />
</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head">Name</th>
<th class="head">Calls Method</th>
<th class="head">Energy</th>
<th class="head">Gradient</th>
<th class="head">Reference</th>
</tr>
</thead>
<tbody valign="top">
<tr class="row-even"><td>conv-mp2</td>
<td>MP2</td>
<td>Y</td>
<td>Y</td>
<td>RHF/ROHF/UHF</td>
</tr>
<tr class="row-odd"><td>mp3</td>
<td>MP3</td>
<td>Y</td>
<td>Y</td>
<td>RHF/UHF</td>
</tr>
<tr class="row-even"><td>mp2.5</td>
<td>MP2.5</td>
<td>Y</td>
<td>Y</td>
<td>RHF/UHF</td>
</tr>
<tr class="row-odd"><td>cepa0</td>
<td>CEPA(0) (identical to Linearized CCD)</td>
<td>Y</td>
<td>Y</td>
<td>RHF/UHF</td>
</tr>
</tbody>
</table>
</div></blockquote>
</div>
</div>
</div>
<div class="section" id="df-occ-density-fitted-orbital-optimized-coupled-cluster-and-mollerplesset-perturbation-theories">
<span id="sec-dfocc"></span><h1>DF-OCC: Density-Fitted Orbital-Optimized Coupled-Cluster and Møller–Plesset Perturbation Theories<a class="headerlink" href="#df-occ-density-fitted-orbital-optimized-coupled-cluster-and-mollerplesset-perturbation-theories" title="Permalink to this headline">¶</a></h1>
<p>A lot of the functionality in OCC has been enabled with Density Fitting (DF) and Cholesky
Decomposition (CD) techniques, which can greatly speed up calculations and reduce memory
requirements for typically negligible losses in accuracy.</p>
<div class="section" id="id23">
<h2>Methods<a class="headerlink" href="#id23" title="Permalink to this headline">¶</a></h2>
<p>Density-fitted conventional and orbital-optimized CC methods currently supported in <span class="sc">Psi4</span> are outlined in Table <a class="reference internal" href="#table-dfomp2-calls"><span>DF-OMP2 Methods</span></a>.</p>
<blockquote>
<div><table border="1" class="docutils" id="table-dfomp2-calls">
<colgroup>
<col width="19%" />
<col width="48%" />
<col width="7%" />
<col width="8%" />
<col width="18%" />
</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head">Name</th>
<th class="head">Calls Method</th>
<th class="head">Energy</th>
<th class="head">Gradient</th>
<th class="head">Reference</th>
</tr>
</thead>
<tbody valign="top">
<tr class="row-even"><td>ri-mp2</td>
<td>Density-Fitted MP2</td>
<td>Y</td>
<td>Y</td>
<td>RHF/ROHF/UHF</td>
</tr>
<tr class="row-odd"><td>cd-mp2</td>
<td>Cholesky-Decomposed MP2</td>
<td>Y</td>
<td>N</td>
<td>RHF/ROHF/UHF</td>
</tr>
<tr class="row-even"><td>df-omp2</td>
<td>Density-Fitted Orbital-Optimized MP2</td>
<td>Y</td>
<td>Y</td>
<td>RHF/ROHF/UHF/RKS/UKS</td>
</tr>
<tr class="row-odd"><td>cd-omp2</td>
<td>Cholesky-Decomposed Orbital-Optimized MP2</td>
<td>Y</td>
<td>N</td>
<td>RHF/ROHF/UHF/RKS/UKS</td>
</tr>
<tr class="row-even"><td>df-ccsd2</td>
<td>Density-Fitted CCSD</td>
<td>Y</td>
<td>Y</td>
<td>RHF</td>
</tr>
<tr class="row-odd"><td>df-ccd</td>
<td>Density-Fitted CCD</td>
<td>Y</td>
<td>Y</td>
<td>RHF</td>
</tr>
</tbody>
</table>
</div></blockquote>
</div>
<div class="section" id="index-6">
<span id="id24"></span><h2>Basic Keywords<a class="headerlink" href="#index-6" title="Permalink to this headline">¶</a></h2>
<div class="section" id="id25">
<h3><a class="reference internal" href="autodoc_glossary_options_c.html#term-e-convergence-dfocc"><span class="xref std std-term">E_CONVERGENCE</span></a><a class="headerlink" href="#id25" title="Permalink to this headline">¶</a></h3>
<blockquote>
<div><p>Convergence criterion for energy. See Table <a class="reference internal" href="scf.html#table-conv-corl"><span>Post-SCF Convergence</span></a> for default convergence criteria for different calculation types.</p>
<ul class="simple">
<li><strong>Type</strong>: <a class="reference internal" href="notes_c.html#op-c-conv"><span>conv double</span></a></li>
<li><strong>Default</strong>: 1e-6</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="id26">
<h3><a class="reference internal" href="autodoc_glossary_options_c.html#term-r-convergence-dfocc"><span class="xref std std-term">R_CONVERGENCE</span></a><a class="headerlink" href="#id26" title="Permalink to this headline">¶</a></h3>
<blockquote>
<div><p>Convergence criterion for amplitudes (residuals).</p>
<ul class="simple">
<li><strong>Type</strong>: <a class="reference internal" href="notes_c.html#op-c-conv"><span>conv double</span></a></li>
<li><strong>Default</strong>: 1e-5</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="id27">
<h3><a class="reference internal" href="autodoc_glossary_options_c.html#term-rms-mograd-convergence-dfocc"><span class="xref std std-term">RMS_MOGRAD_CONVERGENCE</span></a><a class="headerlink" href="#id27" title="Permalink to this headline">¶</a></h3>
<blockquote>
<div><p>Convergence criterion for RMS orbital gradient. Default adjusts depending on <a class="reference internal" href="autodoc_glossary_options_c.html#term-e-convergence-occ"><span class="xref std std-term">E_CONVERGENCE</span></a></p>
<ul class="simple">
<li><strong>Type</strong>: <a class="reference internal" href="notes_c.html#op-c-conv"><span>conv double</span></a></li>
<li><strong>Default</strong>: 1e-6</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="id28">
<h3><a class="reference internal" href="autodoc_glossary_options_c.html#term-max-mograd-convergence-dfocc"><span class="xref std std-term">MAX_MOGRAD_CONVERGENCE</span></a><a class="headerlink" href="#id28" title="Permalink to this headline">¶</a></h3>
<blockquote>
<div><p>Convergence criterion for maximum orbital gradient</p>
<ul class="simple">
<li><strong>Type</strong>: <a class="reference internal" href="notes_c.html#op-c-conv"><span>conv double</span></a></li>
<li><strong>Default</strong>: 1e-3</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="id29">
<h3><a class="reference internal" href="autodoc_glossary_options_c.html#term-mo-maxiter-dfocc"><span class="xref std std-term">MO_MAXITER</span></a><a class="headerlink" href="#id29" title="Permalink to this headline">¶</a></h3>
<blockquote>
<div><p>Maximum number of iterations to determine the orbitals</p>
<ul class="simple">
<li><strong>Type</strong>: integer</li>
<li><strong>Default</strong>: 50</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="id30">
<h3><a class="reference internal" href="autodoc_glossary_options_c.html#term-orb-opt-dfocc"><span class="xref std std-term">ORB_OPT</span></a><a class="headerlink" href="#id30" title="Permalink to this headline">¶</a></h3>
<blockquote>
<div><p>Do optimize the orbitals?</p>
<ul class="simple">
<li><strong>Type</strong>: <a class="reference internal" href="notes_c.html#op-c-boolean"><span>boolean</span></a></li>
<li><strong>Default</strong>: true</li>
</ul>
</div></blockquote>
</div>
</div>
<div class="section" id="id31">
<h2>Advanced Keywords<a class="headerlink" href="#id31" title="Permalink to this headline">¶</a></h2>
<div class="section" id="id32">
<h3><a class="reference internal" href="autodoc_glossary_options_c.html#term-opt-method-dfocc"><span class="xref std std-term">OPT_METHOD</span></a><a class="headerlink" href="#id32" title="Permalink to this headline">¶</a></h3>
<blockquote>
<div><p>The orbital optimization algorithm. Presently Quasy Newton-Raphson algorithm avaliable with several Hessian options.</p>
<ul class="simple">
<li><strong>Type</strong>: string</li>
<li><strong>Possible Values</strong>: QNR</li>
<li><strong>Default</strong>: QNR</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="hess-type">
<h3><a class="reference internal" href="autodoc_glossary_options_c.html#term-hess-type-dfocc"><span class="xref std std-term">HESS_TYPE</span></a><a class="headerlink" href="#hess-type" title="Permalink to this headline">¶</a></h3>
<blockquote>
<div><p>Type of the MO Hessian matrix</p>
<ul class="simple">
<li><strong>Type</strong>: string</li>
<li><strong>Possible Values</strong>: APPROX_DIAG, APPROX_DIAG_EKT, APPROX_DIAG_HF, HF</li>
<li><strong>Default</strong>: HF</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="id33">
<h3><a class="reference internal" href="autodoc_glossary_options_c.html#term-mo-diis-num-vecs-dfocc"><span class="xref std std-term">MO_DIIS_NUM_VECS</span></a><a class="headerlink" href="#id33" title="Permalink to this headline">¶</a></h3>
<blockquote>
<div><p>Number of vectors used in orbital DIIS</p>
<ul class="simple">
<li><strong>Type</strong>: integer</li>
<li><strong>Default</strong>: 6</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="id34">
<h3><a class="reference internal" href="autodoc_glossary_options_c.html#term-orth-type-dfocc"><span class="xref std std-term">ORTH_TYPE</span></a><a class="headerlink" href="#id34" title="Permalink to this headline">¶</a></h3>
<blockquote>
<div><p>The algorithm for orthogonalization of MOs</p>
<ul class="simple">
<li><strong>Type</strong>: string</li>
<li><strong>Possible Values</strong>: GS, MGS</li>
<li><strong>Default</strong>: MGS</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="id35">
<h3><a class="reference internal" href="autodoc_glossary_options_c.html#term-do-diis-dfocc"><span class="xref std std-term">DO_DIIS</span></a><a class="headerlink" href="#id35" title="Permalink to this headline">¶</a></h3>
<blockquote>
<div><p>Do apply DIIS extrapolation?</p>
<ul class="simple">
<li><strong>Type</strong>: <a class="reference internal" href="notes_c.html#op-c-boolean"><span>boolean</span></a></li>
<li><strong>Default</strong>: true</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="id36">
<h3><a class="reference internal" href="autodoc_glossary_options_c.html#term-do-level-shift-dfocc"><span class="xref std std-term">DO_LEVEL_SHIFT</span></a><a class="headerlink" href="#id36" title="Permalink to this headline">¶</a></h3>
<blockquote>
<div><p>Do apply level shifting?</p>
<ul class="simple">
<li><strong>Type</strong>: <a class="reference internal" href="notes_c.html#op-c-boolean"><span>boolean</span></a></li>
<li><strong>Default</strong>: true</li>
</ul>
</div></blockquote>
<style type="text/css"><!--
.green {color: red;}
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<div class="sphinxsidebarwrapper">
<h3><a href="index.html">Table Of Contents</a></h3>
<ul>
<li><a class="reference internal" href="#">OCC: Orbital-Optimized Coupled-Cluster and Møller–Plesset Perturbation Theories</a><ul>
<li><a class="reference internal" href="#introduction">Introduction</a></li>
<li><a class="reference internal" href="#theory">Theory</a></li>
<li><a class="reference internal" href="#convergence-problems">Convergence Problems</a></li>
<li><a class="reference internal" href="#methods">Methods</a></li>
<li><a class="reference internal" href="#basic-keywords">Basic Keywords</a><ul>
<li><a class="reference internal" href="#e-convergence"><code class="docutils literal"><span class="pre">E_CONVERGENCE</span></code></a></li>
<li><a class="reference internal" href="#r-convergence"><code class="docutils literal"><span class="pre">R_CONVERGENCE</span></code></a></li>
<li><a class="reference internal" href="#rms-mograd-convergence"><code class="docutils literal"><span class="pre">RMS_MOGRAD_CONVERGENCE</span></code></a></li>
<li><a class="reference internal" href="#max-mograd-convergence"><code class="docutils literal"><span class="pre">MAX_MOGRAD_CONVERGENCE</span></code></a></li>
<li><a class="reference internal" href="#mo-maxiter"><code class="docutils literal"><span class="pre">MO_MAXITER</span></code></a></li>
<li><a class="reference internal" href="#wfn-type"><code class="docutils literal"><span class="pre">WFN_TYPE</span></code></a></li>
<li><a class="reference internal" href="#orb-opt"><code class="docutils literal"><span class="pre">ORB_OPT</span></code></a></li>
</ul>
</li>
<li><a class="reference internal" href="#advanced-keywords">Advanced Keywords</a><ul>
<li><a class="reference internal" href="#opt-method"><code class="docutils literal"><span class="pre">OPT_METHOD</span></code></a></li>
<li><a class="reference internal" href="#mo-diis-num-vecs"><code class="docutils literal"><span class="pre">MO_DIIS_NUM_VECS</span></code></a></li>
<li><a class="reference internal" href="#lineq-solver"><code class="docutils literal"><span class="pre">LINEQ_SOLVER</span></code></a></li>
<li><a class="reference internal" href="#orth-type"><code class="docutils literal"><span class="pre">ORTH_TYPE</span></code></a></li>
<li><a class="reference internal" href="#mp2-os-scale"><code class="docutils literal"><span class="pre">MP2_OS_SCALE</span></code></a></li>
<li><a class="reference internal" href="#mp2-ss-scale"><code class="docutils literal"><span class="pre">MP2_SS_SCALE</span></code></a></li>
<li><a class="reference internal" href="#mp2-sos-scale"><code class="docutils literal"><span class="pre">MP2_SOS_SCALE</span></code></a></li>
<li><a class="reference internal" href="#mp2-sos-scale2"><code class="docutils literal"><span class="pre">MP2_SOS_SCALE2</span></code></a></li>
<li><a class="reference internal" href="#nat-orbs"><code class="docutils literal"><span class="pre">NAT_ORBS</span></code></a></li>
<li><a class="reference internal" href="#occ-orbs-print"><code class="docutils literal"><span class="pre">OCC_ORBS_PRINT</span></code></a></li>
<li><a class="reference internal" href="#tpdm-abcd-type"><code class="docutils literal"><span class="pre">TPDM_ABCD_TYPE</span></code></a></li>
<li><a class="reference internal" href="#do-diis"><code class="docutils literal"><span class="pre">DO_DIIS</span></code></a></li>
<li><a class="reference internal" href="#do-level-shift"><code class="docutils literal"><span class="pre">DO_LEVEL_SHIFT</span></code></a></li>
</ul>
</li>
<li><a class="reference internal" href="#conventional-occ-mo-slashller-plesset-perturbation-theories">Conventional OCC Møller–Plesset Perturbation Theories</a></li>
<li><a class="reference internal" href="#id20">Basic Keywords</a><ul>
<li><a class="reference internal" href="#mp2-type"><code class="docutils literal"><span class="pre">MP2_TYPE</span></code></a></li>
<li><a class="reference internal" href="#id21"><code class="docutils literal"><span class="pre">MP2_OS_SCALE</span></code></a></li>
<li><a class="reference internal" href="#id22"><code class="docutils literal"><span class="pre">MP2_SS_SCALE</span></code></a></li>
</ul>
</li>
</ul>
</li>
<li><a class="reference internal" href="#df-occ-density-fitted-orbital-optimized-coupled-cluster-and-mollerplesset-perturbation-theories">DF-OCC: Density-Fitted Orbital-Optimized Coupled-Cluster and Møller–Plesset Perturbation Theories</a><ul>
<li><a class="reference internal" href="#id23">Methods</a></li>
<li><a class="reference internal" href="#index-6">Basic Keywords</a><ul>
<li><a class="reference internal" href="#id25"><code class="docutils literal"><span class="pre">E_CONVERGENCE</span></code></a></li>
<li><a class="reference internal" href="#id26"><code class="docutils literal"><span class="pre">R_CONVERGENCE</span></code></a></li>
<li><a class="reference internal" href="#id27"><code class="docutils literal"><span class="pre">RMS_MOGRAD_CONVERGENCE</span></code></a></li>
<li><a class="reference internal" href="#id28"><code class="docutils literal"><span class="pre">MAX_MOGRAD_CONVERGENCE</span></code></a></li>
<li><a class="reference internal" href="#id29"><code class="docutils literal"><span class="pre">MO_MAXITER</span></code></a></li>
<li><a class="reference internal" href="#id30"><code class="docutils literal"><span class="pre">ORB_OPT</span></code></a></li>
</ul>
</li>
<li><a class="reference internal" href="#id31">Advanced Keywords</a><ul>
<li><a class="reference internal" href="#id32"><code class="docutils literal"><span class="pre">OPT_METHOD</span></code></a></li>
<li><a class="reference internal" href="#hess-type"><code class="docutils literal"><span class="pre">HESS_TYPE</span></code></a></li>
<li><a class="reference internal" href="#id33"><code class="docutils literal"><span class="pre">MO_DIIS_NUM_VECS</span></code></a></li>
<li><a class="reference internal" href="#id34"><code class="docutils literal"><span class="pre">ORTH_TYPE</span></code></a></li>
<li><a class="reference internal" href="#id35"><code class="docutils literal"><span class="pre">DO_DIIS</span></code></a></li>
<li><a class="reference internal" href="#id36"><code class="docutils literal"><span class="pre">DO_LEVEL_SHIFT</span></code></a></li>
</ul>
</li>
</ul>
</li>
</ul>
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