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kthpanor committed Mar 22, 2024
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15 changes: 12 additions & 3 deletions _sources/docs/spec_prop/hf_param_energy.ipynb
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"source": [
"In order, we have introduced:\n",
"\n",
"1. The Hermitian electronic Hessian\n",
"The Hermitian electronic Hessian\n",
"\n",
"$$\n",
"\\mathbf{E}^{[2]} = \n",
"\\begin{pmatrix}\n",
"\\mathbf{A} & \\mathbf{B} \\\\\n",
"\\mathbf{B}^* & \\mathbf{A}^* \\\\\n",
"\\end{pmatrix}\n",
"$$\n",
"\n",
"with blocks\n",
"\n",
"$$\n",
"A_{mn} =\n",
"\\left.\n",
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"tags": []
},
"source": [
"2. The (unknown) response vector\n",
"The (unknown) response vector\n",
"\n",
"$$\n",
"\\mathbf{N} =\n",
"\\begin{pmatrix}\n",
"\\mathbf{Z} \\\\\n",
"\\mathbf{Z}^*\n",
"\\end{pmatrix}\n",
"$$\n",
"\n",
"with \n",
"\n",
"$$\n",
"Z_n = \n",
"\\left.\n",
Expand All @@ -239,15 +245,18 @@
"tags": []
},
"source": [
"3. And the property gradient\n",
"And the property gradient\n",
"\n",
"$$\n",
"\\mathbf{B}^{[1]} =\n",
"\\begin{pmatrix}\n",
"\\mathbf{g} \\\\\n",
"\\mathbf{g}^* \\\\\n",
"\\end{pmatrix}\n",
"$$\n",
"\n",
"with\n",
"\n",
"$$\n",
"g_m = \n",
"\\left.\n",
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12 changes: 6 additions & 6 deletions _sources/docs/tutorials/vib_ir_exercises.ipynb
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Expand Up @@ -417,11 +417,11 @@
"# Either optimize the geometries\n",
"# Uncomment below\n",
"# ethene_opt_drv.ostream.unmute()\n",
"# opt_ethene = ethene_opt_drv.compute(ethene, ethene_basis, ethene_scf_drv)\n",
"# opt_ethene = ethene_opt_drv.compute(ethene, ethene_basis)\n",
"# fluoroethene_opt_drv.ostream.unmute()\n",
"# opt_fluoroethene = fluoroethene_opt_drv.compute(fluoroethene, fluoroethene_basis, fluoroethene_scf_drv)\n",
"# opt_fluoroethene = fluoroethene_opt_drv.compute(fluoroethene, fluoroethene_basis)\n",
"# chloroethene_opt_drv.ostream.unmute()\n",
"# opt_chloroethene = chloroethene_opt_drv.compute(chloroethene, chloroethene_basis, chloroethene_scf_drv)\n",
"# opt_chloroethene = chloroethene_opt_drv.compute(chloroethene, chloroethene_basis)\n",
"\n",
"# Or read them from file if already calculated\n",
"opt_ethene = vlx.Molecule.read_xyz_file(\"../../data/ir_raman/opt_ethene.xyz\")\n",
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"chloroethene_hessian_drv.update_settings(method_settings, hessian_settings)\n",
"\n",
"# Calculate\n",
"# ethene_hessian_drv.compute(ethene, ethene_basis, ethene_scf_drv)\n",
"# fluoroethene_hessian_drv.compute(fluoroethene, fluoroethene_basis, fluoroethene_scf_drv)\n",
"# chloroethene_hessian_drv.compute(chloroethene, chloroethene_basis, chloroethene_scf_drv)\n",
"# ethene_hessian_drv.compute(ethene, ethene_basis)\n",
"# fluoroethene_hessian_drv.compute(fluoroethene, fluoroethene_basis)\n",
"# chloroethene_hessian_drv.compute(chloroethene, chloroethene_basis)\n",
"\n",
"# Or read from file:\n",
"import h5py\n",
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72 changes: 33 additions & 39 deletions docs/spec_prop/hf_param_energy.html
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Expand Up @@ -738,75 +738,69 @@ <h2>Linear response equation<a class="headerlink" href="#linear-response-equatio
\mathbf{E}^{[2]} \mathbf{N} = - \mathbf{B}^{[1]}
\]</div>
<p>In order, we have introduced:</p>
<ol class="arabic simple">
<li><p>The Hermitian electronic Hessian
$$
\mathbf{E}^{[2]} =</p></li>
</ol>
<div class="amsmath math notranslate nohighlight" id="equation-a8aaed93-e2f5-4d1b-bcc6-aae2a9e90ac2">
<span class="eqno">()<a class="headerlink" href="#equation-a8aaed93-e2f5-4d1b-bcc6-aae2a9e90ac2" title="Permalink to this equation">#</a></span>\[\begin{pmatrix}
<p>The Hermitian electronic Hessian</p>
<div class="math notranslate nohighlight">
\[\begin{split}
\mathbf{E}^{[2]} =
\begin{pmatrix}
\mathbf{A} &amp; \mathbf{B} \\
\mathbf{B}^* &amp; \mathbf{A}^* \\
\end{pmatrix}\]</div>
\end{pmatrix}
\end{split}\]</div>
<p>with blocks</p>
<div class="math notranslate nohighlight">
\[
with blocks
\]</div>
<p>A_{mn} =
A_{mn} =
\left.
\frac{
\partial^2 E(\kappa, F)
}{
\partial \kappa_{m}^* \partial \kappa_{n}
}
\right|<em>{F = 0} ; \qquad
B</em>{mn} =
\right|_{F = 0} ; \qquad
B_{mn} =
\left.
\frac{
\partial^2 E(\kappa, F)
}{
\partial \kappa_{m}^* \partial \kappa_{n}^*
}
\right|_{F = 0}
$$</p>
<ol class="arabic simple" start="2">
<li><p>The (unknown) response vector
$$
\mathbf{N} =</p></li>
</ol>
<div class="amsmath math notranslate nohighlight" id="equation-9e312e1a-5c9c-4cef-a3b0-9611a179f1a9">
<span class="eqno">()<a class="headerlink" href="#equation-9e312e1a-5c9c-4cef-a3b0-9611a179f1a9" title="Permalink to this equation">#</a></span>\[\begin{pmatrix}
\right|_{F = 0}
\]</div>
<p>The (unknown) response vector</p>
<div class="math notranslate nohighlight">
\[\begin{split}
\mathbf{N} =
\begin{pmatrix}
\mathbf{Z} \\
\mathbf{Z}^*
\end{pmatrix}\]</div>
\end{pmatrix}
\end{split}\]</div>
<p>with</p>
<div class="math notranslate nohighlight">
\[
with
\]</div>
<p>Z_n =
Z_n =
\left.
\frac{d \kappa_n}{d F_\alpha}
\right|_{F=0}
$$</p>
<ol class="arabic simple" start="3">
<li><p>And the property gradient
$$
\mathbf{B}^{[1]} =</p></li>
</ol>
<div class="amsmath math notranslate nohighlight" id="equation-bf74af34-6dc3-4de8-aa64-cd125585bd6f">
<span class="eqno">()<a class="headerlink" href="#equation-bf74af34-6dc3-4de8-aa64-cd125585bd6f" title="Permalink to this equation">#</a></span>\[\begin{pmatrix}
\]</div>
<p>And the property gradient</p>
<div class="math notranslate nohighlight">
\[\begin{split}
\mathbf{B}^{[1]} =
\begin{pmatrix}
\mathbf{g} \\
\mathbf{g}^* \\
\end{pmatrix}\]</div>
\end{pmatrix}
\end{split}\]</div>
<p>with</p>
<div class="math notranslate nohighlight">
\[
with
\]</div>
<p>g_m =
g_m =
\left.
\frac{\partial^2 E(\kappa, F)}{\partial \kappa_{m}^* \partial F_\alpha}
\right|_{F=0}
$$</p>
\]</div>
</section>
<section id="bakercampbellhausdorff-expansion">
<h2>Baker–Campbell–Hausdorff expansion<a class="headerlink" href="#bakercampbellhausdorff-expansion" title="Link to this heading">#</a></h2>
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2 changes: 1 addition & 1 deletion docs/tutorials/vib_ir.html
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