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<div class="section" id="nuclear-gradient-and-derivative-coupling">
<span id="force"></span><h1>Nuclear gradient and derivative coupling<a class="headerlink" href="#nuclear-gradient-and-derivative-coupling" 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 force section can be used to compute the analytical gradient (force), the numerical gradient by finite difference, or the non-adiabatic coupling matrix elements (NACME). Analytical gradients are implemented for unrestricted Hartree–Fock (UHF), restricted open-shell Hartree–Fock (ROHF), restricted Hartree–Fock (RHF), Dirac–Hartree–Fock (DHF), Møller–Plesset perturbation theory (MP2), complete active space self consistent field (CASSCF), and multireference perturbation theory (CASPT2). For CASSCF and CASPT2, it is also possible to perform multiple evaluations of the gradients without repeating the energy calculations.
In addition, the relaxed density in MP2, SA-CASSCF, and CASPT2 calculations can be printed in the Gaussian Cube format.</p>
</div>
<div class="section" id="keywords">
<h2>Keywords<a class="headerlink" href="#keywords" title="Permalink to this headline">¶</a></h2>
<div class="section" id="required-keywords">
<h3>Required Keywords<a class="headerlink" href="#required-keywords" title="Permalink to this headline">¶</a></h3>
<div class="topic">
<p class="topic-title first"><code class="docutils literal"><span class="pre">title</span></code></p>
<div class="line-block">
<div class="line"><strong>Description:</strong> The title of the type of gradient calculation being performed.</div>
<div class="line"><strong>Datatype:</strong> string</div>
<div class="line"><strong>Values:</strong> (force, nacme, dgrad, forces)</div>
<div class="line-block">
<div class="line"><code class="docutils literal"><span class="pre">force</span></code>: Calculates the gradient (force)</div>
<div class="line"><code class="docutils literal"><span class="pre">nacme</span></code>: Calculates the non-adiabatic coupling matrix elements</div>
<div class="line"><code class="docutils literal"><span class="pre">dgrad</span></code>: Difference gradient (only available for CASSCF)</div>
<div class="line"><code class="docutils literal"><span class="pre">forces</span></code>: Calculates many gradients [available for multi-state methods, such as SA-CASSCF and (X)MS-CASPT2]</div>
</div>
<div class="line"><strong>Default:</strong> N/A</div>
</div>
</div>
<div class="topic">
<p class="topic-title first"><code class="docutils literal"><span class="pre">method</span></code></p>
<div class="line-block">
<div class="line"><strong>Description:</strong> The method input block allows the user to specify one or more methods to be used in the gradient calculation. See section on input structure for more information.</div>
</div>
</div>
<div class="topic">
<p class="topic-title first"><code class="docutils literal"><span class="pre">grads</span></code></p>
<div class="line-block">
<div class="line"><strong>Description:</strong> The grads input block allows the user to specify one or more gradients to be calculated. The keywords <code class="docutils literal"><span class="pre">title</span></code>, <code class="docutils literal"><span class="pre">target</span></code>, <code class="docutils literal"><span class="pre">target2</span></code>, <code class="docutils literal"><span class="pre">nacmtype</span></code>, <code class="docutils literal"><span class="pre">maxziter</span></code> can be specified for each gradient evaluation. See below for example.</div>
</div>
</div>
<div class="topic">
<p class="topic-title first"><code class="docutils literal"><span class="pre">nacmtype</span></code></p>
<div class="line-block">
<div class="line"><strong>Description:</strong> Type of non-adiabatic coupling matrix element to be computed</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"><span class="pre">full</span></code>: Full non-adiabatic coupling</div>
<div class="line"><code class="docutils literal"><span class="pre">interstate</span></code>: Interstate coupling</div>
<div class="line"><code class="docutils literal"><span class="pre">etf</span></code>: Non-adiabtic coupling with built-in electronic translational factor (ETF)</div>
<div class="line"><code class="docutils literal"><span class="pre">noweight</span></code>: Interstate coupling without weighting it by energy gap</div>
</div>
<div class="line"><strong>Default:</strong> full.</div>
</div>
</div>
</div>
<div class="section" id="optional-keywords">
<h3>Optional Keywords<a class="headerlink" href="#optional-keywords" title="Permalink to this headline">¶</a></h3>
<div class="topic">
<p class="topic-title first"><code class="docutils literal"><span class="pre">numerical</span></code></p>
<div class="line-block">
<div class="line"><strong>Description:</strong> The gradients will be computed by finite difference.</div>
<div class="line"><strong>Datatype:</strong> bool</div>
<div class="line"><strong>Values:</strong></div>
<div class="line-block">
<div class="line"><code class="docutils literal"><span class="pre">true</span></code>: Uses finite difference</div>
<div class="line"><code class="docutils literal"><span class="pre">false</span></code> : Uses analytical gradient</div>
</div>
<div class="line"><strong>Default:</strong> false</div>
<div class="line"><strong>Recommendation:</strong> If available, use analytical gradient. If analytical gradient is not available, BAGEL automatically switches to numerical gradient.</div>
</div>
</div>
<div class="topic">
<p class="topic-title first"><code class="docutils literal"><span class="pre">dx</span></code></p>
<div class="line-block">
<div class="line"><strong>Description:</strong> The step size used in the displacements in the finite difference calculations. The units are bohr.</div>
<div class="line"><strong>Datatype:</strong> double precision</div>
<div class="line"><strong>Default:</strong> 1.0e-3</div>
</div>
</div>
<div class="topic">
<p class="topic-title first"><code class="docutils literal"><span class="pre">target</span></code></p>
<div class="line-block">
<div class="line"><strong>Description:</strong> The target state for the energy and gradient evaluation (e.g. which state in a state-averaged CASSCF calculation)</div>
<div class="line"><strong>Datatype:</strong> int</div>
<div class="line"><strong>Values:</strong></div>
<div class="line-block">
<div class="line"><code class="docutils literal"><span class="pre">int</span></code>: ground state = 0</div>
</div>
<div class="line"><strong>Default:</strong> 0</div>
</div>
</div>
<div class="topic">
<p class="topic-title first"><code class="docutils literal"><span class="pre">target2</span></code></p>
<div class="line-block">
<div class="line"><strong>Description:</strong> In an NACME or DGRAD calculation, target2 designates the target state for the second state.</div>
<div class="line"><strong>Datatype:</strong> int</div>
<div class="line"><strong>Values:</strong></div>
<div class="line-block">
<div class="line"><code class="docutils literal"><span class="pre">int</span></code>: first exited state = 1</div>
</div>
<div class="line"><strong>Default:</strong> 1</div>
</div>
</div>
<div class="topic">
<p class="topic-title first"><code class="docutils literal"><span class="pre">dipole</span></code></p>
<div class="line-block">
<div class="line"><strong>Description:</strong> Calculate unrelaxed (transition) dipole moments, available in SA-CASSCF and XMS-CASPT2.</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"><span class="pre">export</span></code></p>
<div class="line-block">
<div class="line"><strong>Description:</strong> This option will export the nuclear gradient to a text file.</div>
<div class="line"><strong>Datatype:</strong> bool</div>
<div class="line"><strong>Default:</strong> false</div>
<div class="line"><strong>Recommendation:</strong> This is used to interface with the QM/MM program. See section on non-adiabatic dynamics.</div>
</div>
</div>
<div class="topic">
<p class="topic-title first"><code class="docutils literal"><span class="pre">export_single</span></code></p>
<div class="line-block">
<div class="line"><strong>Description:</strong> This option will export the nuclear gradient to a text file for a single state.</div>
<div class="line"><strong>Datatype:</strong> bool</div>
<div class="line"><strong>Default:</strong> false</div>
<div class="line"><strong>Recommendation:</strong> This is used to interface with the QM/MM program. See section on non-adiabatic dynamics.</div>
</div>
</div>
<div class="topic">
<p class="topic-title first"><code class="docutils literal"><span class="pre">maxziter</span></code></p>
<div class="line-block">
<div class="line"><strong>Description:</strong> Maximum number of Z-vector iterations for gradient evaluation. Applies to SA-CASSCF, CASPT2, and MP2 calculations.</div>
<div class="line"><strong>Datatype:</strong> int</div>
<div class="line"><strong>Default:</strong> 100</div>
<div class="line"><strong>Recommendation:</strong> Increase the value when Z-vector equation does not converge.</div>
</div>
</div>
<div class="topic">
<p class="topic-title first"><code class="docutils literal"><span class="pre">nproc</span></code></p>
<div class="line-block">
<div class="line"><strong>Description:</strong> The numerical gradient code is embarrassingly parallelized so that the displacements in the finite difference calculations can be run at the same time. The nproc keyword allows the user to specify the number of MPI processes to be used for each energy calculation.</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"><span class="pre">density_print</span></code></p>
<div class="line-block">
<div class="line"><strong>Description:</strong> Print relaxed densities in the Gaussian Cube format. Applies to SA-CASSCF, CASPT2, and MP2 calculations. The options for density printing can be specified in <code class="docutils literal"><span class="pre">moprint</span></code> block (see below for example and <a class="reference internal" href="../miscellaneous/moprint.html#moprint"><span class="std std-ref">here</span></a> for the keywords).</div>
<div class="line"><strong>Datatype:</strong> bool</div>
<div class="line"><strong>Default:</strong> false</div>
</div>
</div>
</div>
</div>
<div class="section" id="example">
<h2>Example<a class="headerlink" href="#example" title="Permalink to this headline">¶</a></h2>
<p>The benzophenone molecule</p>
<div class="align-center figure" id="id1">
<a class="reference internal image-reference" href="../_images/benzophenone.png"><img alt="alternate text" src="../_images/benzophenone.png" style="width: 200px;" /></a>
<p class="caption"><span class="caption-text">The benzophenone molecule with carbon atoms in grey, oxygen in red, and hydrogen in white.</span></p>
</div>
<div class="section" id="sample-input-force">
<h3>Sample input: force<a class="headerlink" href="#sample-input-force" title="Permalink to this headline">¶</a></h3>
<div class="highlight-javascript"><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="kc">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">"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">2.002493</span><span class="p">,</span> <span class="o">-</span><span class="mf">2.027773</span><span class="p">,</span> <span class="mf">0.004882</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">2.506057</span><span class="p">,</span> <span class="o">-</span><span class="mf">4.613700</span><span class="p">,</span> <span class="mf">0.009896</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">0.536515</span><span class="p">,</span> <span class="o">-</span><span class="mf">1.276360</span><span class="p">,</span> <span class="mf">0.003515</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">0.558724</span><span class="p">,</span> <span class="o">-</span><span class="mf">6.375134</span><span class="p">,</span> <span class="mf">0.013503</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">4.396140</span><span class="p">,</span> <span class="o">-</span><span class="mf">5.341490</span><span class="p">,</span> <span class="mf">0.011057</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">2.478233</span><span class="p">,</span> <span class="o">-</span><span class="mf">3.024614</span><span class="p">,</span> <span class="mf">0.007049</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">0.959539</span><span class="p">,</span> <span class="mf">0.714937</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.000292</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">1.936441</span><span class="p">,</span> <span class="o">-</span><span class="mf">5.592475</span><span class="p">,</span> <span class="mf">0.012127</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">1.012481</span><span class="p">,</span> <span class="o">-</span><span class="mf">8.367883</span><span class="p">,</span> <span class="mf">0.017419</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">4.418042</span><span class="p">,</span> <span class="o">-</span><span class="mf">2.380738</span><span class="p">,</span> <span class="mf">0.005919</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">3.448750</span><span class="p">,</span> <span class="o">-</span><span class="mf">6.968581</span><span class="p">,</span> <span class="mf">0.014980</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">6.758666</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.057378</span><span class="p">,</span> <span class="mf">0.001157</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">8.231109</span><span class="p">,</span> <span class="o">-</span><span class="mf">2.241648</span><span class="p">,</span> <span class="mf">0.000224</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">8.022986</span><span class="p">,</span> <span class="mf">2.269249</span><span class="p">,</span> <span class="mf">0.001194</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">10.853532</span><span class="p">,</span> <span class="o">-</span><span class="mf">2.110536</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.000769</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">7.410047</span><span class="p">,</span> <span class="o">-</span><span class="mf">4.093049</span><span class="p">,</span> <span class="mf">0.000224</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">10.632155</span><span class="p">,</span> <span class="mf">2.405932</span><span class="p">,</span> <span class="mf">0.000369</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">6.913797</span><span class="p">,</span> <span class="mf">3.976253</span><span class="p">,</span> <span class="mf">0.001805</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">12.064741</span><span class="p">,</span> <span class="mf">0.207004</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.000695</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">11.941318</span><span class="p">,</span> <span class="o">-</span><span class="mf">3.840822</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.001614</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">11.548963</span><span class="p">,</span> <span class="mf">4.232744</span><span class="p">,</span> <span class="mf">0.000447</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">14.107194</span><span class="p">,</span> <span class="mf">0.302907</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.001460</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">3.892311</span><span class="p">,</span> <span class="mf">0.136360</span><span class="p">,</span> <span class="mf">0.001267</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">"O"</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">3.026383</span><span class="p">,</span> <span class="mf">2.227189</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.001563</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">"force"</span><span class="p">,</span>
<span class="s2">"method"</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">"hf"</span><span class="p">,</span>
<span class="s2">"thresh"</span> <span class="o">:</span> <span class="mf">1.0e-12</span>
<span class="p">}</span> <span class="p">]</span>
<span class="p">}</span>
<span class="p">]}</span>
</pre></div>
</div>
<p>Using the same molecule block, a XMS-CASPT2 analytical gradient calculation can be performed.
In this particular example as is often the case, the active keyword is used to select the orbitals for the active space that includes 4 electrons and 3 orbitals.
Three sets of <span class="math">\(\pi\)</span> and <span class="math">\(\pi^*\)</span> orbitals localized on the phenyl rings are included along with one non-bonding orbital (oxygen lone pair).
The CASSCF orbitals are state-averaged over two states.</p>
<div class="highlight-javascript"><div class="highlight"><pre><span></span><span class="p">{</span>
<span class="s2">"title"</span> <span class="o">:</span> <span class="s2">"casscf"</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="s2">"nclosed"</span> <span class="o">:</span> <span class="mi">46</span><span class="p">,</span>
<span class="s2">"nact"</span> <span class="o">:</span> <span class="mi">3</span><span class="p">,</span>
<span class="s2">"active"</span> <span class="o">:</span> <span class="p">[</span><span class="mi">37</span><span class="p">,</span> <span class="mi">44</span><span class="p">,</span> <span class="mi">49</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">"force"</span><span class="p">,</span>
<span class="s2">"target"</span> <span class="o">:</span> <span class="mi">0</span><span class="p">,</span>
<span class="s2">"method"</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">"caspt2"</span><span class="p">,</span>
<span class="s2">"smith"</span> <span class="o">:</span> <span class="p">{</span>
<span class="s2">"method"</span> <span class="o">:</span> <span class="s2">"caspt2"</span><span class="p">,</span>
<span class="s2">"ms"</span> <span class="o">:</span> <span class="s2">"true"</span><span class="p">,</span>
<span class="s2">"xms"</span> <span class="o">:</span> <span class="s2">"true"</span><span class="p">,</span>
<span class="s2">"sssr"</span> <span class="o">:</span> <span class="s2">"true"</span><span class="p">,</span>
<span class="s2">"shift"</span> <span class="o">:</span> <span class="mf">0.2</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="s2">"nstate"</span> <span class="o">:</span> <span class="mi">2</span><span class="p">,</span>
<span class="s2">"nact"</span> <span class="o">:</span> <span class="mi">3</span><span class="p">,</span>
<span class="s2">"nclosed"</span> <span class="o">:</span> <span class="mi">46</span>
<span class="p">}</span> <span class="p">]</span>
<span class="p">}</span>
</pre></div>
</div>
</div>
<div class="section" id="sample-input-nacme-and-dgrad">
<h3>Sample input: NACME and DGRAD<a class="headerlink" href="#sample-input-nacme-and-dgrad" title="Permalink to this headline">¶</a></h3>
<div class="highlight-javascript"><div class="highlight"><pre><span></span><span class="p">{</span>
<span class="s2">"title"</span> <span class="o">:</span> <span class="s2">"nacme"</span><span class="p">,</span>
<span class="s2">"target"</span> <span class="o">:</span> <span class="mi">0</span><span class="p">,</span>
<span class="s2">"target2"</span> <span class="o">:</span> <span class="mi">1</span><span class="p">,</span>
<span class="s2">"method"</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">"caspt2"</span><span class="p">,</span>
<span class="s2">"smith"</span> <span class="o">:</span> <span class="p">{</span>
<span class="s2">"method"</span> <span class="o">:</span> <span class="s2">"caspt2"</span><span class="p">,</span>
<span class="s2">"ms"</span> <span class="o">:</span> <span class="s2">"true"</span><span class="p">,</span>
<span class="s2">"xms"</span> <span class="o">:</span> <span class="s2">"true"</span><span class="p">,</span>
<span class="s2">"sssr"</span> <span class="o">:</span> <span class="s2">"true"</span><span class="p">,</span>
<span class="s2">"shift"</span> <span class="o">:</span> <span class="mf">0.2</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="s2">"nstate"</span> <span class="o">:</span> <span class="mi">3</span><span class="p">,</span>
<span class="s2">"nact"</span> <span class="o">:</span> <span class="mi">7</span><span class="p">,</span>
<span class="s2">"nclosed"</span> <span class="o">:</span> <span class="mi">44</span>
<span class="p">}</span> <span class="p">]</span>
<span class="p">}</span>
</pre></div>
</div>
<p>Using the keyword <code class="docutils literal"><span class="pre">forces</span></code>, you can run multiple gradient or derivative coupling calculations without repeating the energy calculations. The example below evaluates the nuclear gradient of the energy of the ground state, the first excited state, and the interstate coupling vector (<code class="docutils literal"><span class="pre">nacmtype</span></code> is <code class="docutils literal"><span class="pre">interstate</span></code>) between these two states.</p>
<div class="highlight-javascript"><div class="highlight"><pre><span></span><span class="p">{</span>
<span class="s2">"title"</span> <span class="o">:</span> <span class="s2">"forces"</span><span class="p">,</span>
<span class="s2">"grads"</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">"force"</span><span class="p">,</span> <span class="s2">"target"</span> <span class="o">:</span> <span class="mi">0</span> <span class="p">},</span>
<span class="p">{</span> <span class="s2">"title"</span> <span class="o">:</span> <span class="s2">"force"</span><span class="p">,</span> <span class="s2">"target"</span> <span class="o">:</span> <span class="mi">1</span> <span class="p">},</span>
<span class="p">{</span> <span class="s2">"title"</span> <span class="o">:</span> <span class="s2">"nacme"</span><span class="p">,</span> <span class="s2">"target"</span> <span class="o">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"target2"</span> <span class="o">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">"nacmtype"</span> <span class="o">:</span> <span class="s2">"interstate"</span> <span class="p">}</span>
<span class="p">],</span>
<span class="s2">"method"</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">"caspt2"</span><span class="p">,</span>
<span class="s2">"smith"</span> <span class="o">:</span> <span class="p">{</span>
<span class="s2">"method"</span> <span class="o">:</span> <span class="s2">"caspt2"</span><span class="p">,</span>
<span class="s2">"ms"</span> <span class="o">:</span> <span class="s2">"true"</span><span class="p">,</span>
<span class="s2">"xms"</span> <span class="o">:</span> <span class="s2">"true"</span><span class="p">,</span>
<span class="s2">"sssr"</span> <span class="o">:</span> <span class="s2">"true"</span><span class="p">,</span>
<span class="s2">"shift"</span> <span class="o">:</span> <span class="mf">0.2</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="s2">"nstate"</span> <span class="o">:</span> <span class="mi">3</span><span class="p">,</span>
<span class="s2">"nact"</span> <span class="o">:</span> <span class="mi">7</span><span class="p">,</span>
<span class="s2">"nclosed"</span> <span class="o">:</span> <span class="mi">44</span>
<span class="p">}</span> <span class="p">]</span>
<span class="p">}</span>
</pre></div>
</div>
</div>
<div class="section" id="sample-input-printing-relaxed-density">
<h3>Sample input: Printing relaxed density<a class="headerlink" href="#sample-input-printing-relaxed-density" title="Permalink to this headline">¶</a></h3>
<p>The relaxed density in MP2, SA-CASSCF, and CASPT2 gradient calculations can be printed in the Gaussian Cube format (<code class="docutils literal"><span class="pre">density.cub</span></code> file) by setting the keyword <code class="docutils literal"><span class="pre">density_print</span></code> to true
(see the example below).</p>
<div class="highlight-javascript"><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">"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">"Li"</span><span class="p">,</span> <span class="s2">"xyz"</span> <span class="o">:</span> <span class="p">[</span> <span class="mf">0.000000</span><span class="p">,</span> <span class="mf">0.000000</span><span class="p">,</span> <span class="mf">6.000000</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">"F"</span><span class="p">,</span> <span class="s2">"xyz"</span> <span class="o">:</span> <span class="p">[</span> <span class="mf">0.000000</span><span class="p">,</span> <span class="mf">0.000000</span><span class="p">,</span> <span class="mf">0.000000</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">"force"</span><span class="p">,</span>
<span class="s2">"target"</span> <span class="o">:</span> <span class="mi">0</span><span class="p">,</span>
<span class="s2">"density_print"</span> <span class="o">:</span> <span class="kc">true</span><span class="p">,</span>
<span class="s2">"moprint"</span> <span class="o">:</span> <span class="p">{</span>
<span class="s2">"inc_size"</span> <span class="o">:</span> <span class="p">[</span> <span class="mf">0.20</span><span class="p">,</span> <span class="mf">0.20</span><span class="p">,</span> <span class="mf">0.20</span><span class="p">]</span>
<span class="p">},</span>
<span class="s2">"method"</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">"caspt2"</span><span class="p">,</span>
<span class="s2">"smith"</span> <span class="o">:</span> <span class="p">{</span>
<span class="s2">"method"</span> <span class="o">:</span> <span class="s2">"caspt2"</span><span class="p">,</span>
<span class="s2">"shift"</span> <span class="o">:</span> <span class="mf">0.2</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="s2">"nstate"</span> <span class="o">:</span> <span class="mi">4</span><span class="p">,</span>
<span class="s2">"nact"</span> <span class="o">:</span> <span class="mi">4</span><span class="p">,</span>
<span class="s2">"nclosed"</span> <span class="o">:</span> <span class="mi">3</span>
<span class="p">}</span> <span class="p">]</span>
<span class="p">}</span>
<span class="p">]}</span>
</pre></div>
</div>
<p>Using the keyword <code class="docutils literal"><span class="pre">forces</span></code>, you can print multiple relaxed densities without repeating the energy calculations.
The example below prints all the XMS-CASPT2 relaxed densities.</p>
<div class="highlight-javascript"><div class="highlight"><pre><span></span><span class="p">{</span>
<span class="s2">"title"</span> <span class="o">:</span> <span class="s2">"forces"</span><span class="p">,</span>
<span class="s2">"grads"</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">"force"</span><span class="p">,</span> <span class="s2">"target"</span> <span class="o">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"density_print"</span> <span class="o">:</span> <span class="kc">true</span><span class="p">,</span> <span class="s2">"moprint"</span> <span class="o">:</span> <span class="p">{</span> <span class="s2">"density_filename"</span> <span class="o">:</span> <span class="s2">"density_0"</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">"force"</span><span class="p">,</span> <span class="s2">"target"</span> <span class="o">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">"density_print"</span> <span class="o">:</span> <span class="kc">true</span><span class="p">,</span> <span class="s2">"moprint"</span> <span class="o">:</span> <span class="p">{</span> <span class="s2">"density_filename"</span> <span class="o">:</span> <span class="s2">"density_1"</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">"force"</span><span class="p">,</span> <span class="s2">"target"</span> <span class="o">:</span> <span class="mi">2</span><span class="p">,</span> <span class="s2">"density_print"</span> <span class="o">:</span> <span class="kc">true</span><span class="p">,</span> <span class="s2">"moprint"</span> <span class="o">:</span> <span class="p">{</span> <span class="s2">"density_filename"</span> <span class="o">:</span> <span class="s2">"density_2"</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">"force"</span><span class="p">,</span> <span class="s2">"target"</span> <span class="o">:</span> <span class="mi">3</span><span class="p">,</span> <span class="s2">"density_print"</span> <span class="o">:</span> <span class="kc">true</span><span class="p">,</span> <span class="s2">"moprint"</span> <span class="o">:</span> <span class="p">{</span> <span class="s2">"density_filename"</span> <span class="o">:</span> <span class="s2">"density_3"</span> <span class="p">}</span> <span class="p">}</span>
<span class="p">],</span>
<span class="s2">"method"</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">"caspt2"</span><span class="p">,</span>
<span class="s2">"smith"</span> <span class="o">:</span> <span class="p">{</span>
<span class="s2">"method"</span> <span class="o">:</span> <span class="s2">"caspt2"</span><span class="p">,</span>
<span class="s2">"ms"</span> <span class="o">:</span> <span class="s2">"true"</span><span class="p">,</span>
<span class="s2">"xms"</span> <span class="o">:</span> <span class="s2">"true"</span><span class="p">,</span>
<span class="s2">"sssr"</span> <span class="o">:</span> <span class="s2">"true"</span><span class="p">,</span>
<span class="s2">"shift"</span> <span class="o">:</span> <span class="mf">0.2</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="s2">"nstate"</span> <span class="o">:</span> <span class="mi">4</span><span class="p">,</span>
<span class="s2">"nact"</span> <span class="o">:</span> <span class="mi">4</span><span class="p">,</span>
<span class="s2">"nclosed"</span> <span class="o">:</span> <span class="mi">3</span>
<span class="p">}</span> <span class="p">]</span>
<span class="p">}</span>
</pre></div>
</div>
</div>
</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">
<colgroup>
<col width="37%" />
<col width="63%" />
</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>SS-CASPT2 gradient</td>
<td>M. K. MacLeod and T. Shiozaki, J. Chem. Phys. <strong>142</strong>, 051103 (2015).</td>
</tr>
<tr class="row-odd"><td>(X)MS-CASPT2 gradient</td>
<td>B. Vlaisavljevich and T. Shiozaki, J. Chem. Theory Comput. <strong>12</strong>, 3781 (2016).</td>
</tr>
<tr class="row-even"><td>(X)MS-CASPT2 derivative coupling</td>
<td>J. W. Park and T. Shiozaki, J. Chem. Theory Comput. <strong>13</strong>, 2561 (2017).</td>
</tr>
<tr class="row-odd"><td>Current (X)MS-CASPT2 gradient algorithm</td>
<td>J. W. Park and T. Shiozaki, J. Chem. Theory Comput. <strong>13</strong>, 3676 (2017).</td>
</tr>
</tbody>
</table>
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<th class="head">Reference</th>
</tr>
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<tbody valign="top">
<tr class="row-even"><td>General review of gradient methods</td>
<td>P. Pulay, WIREs Comput. Mol. Sci. <strong>4</strong>, 169-181 (2014).</td>
</tr>
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