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Atomic shell in org
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Atomic shell in org
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</head>
<body>
<div id="content">
<h1 class="title">Gaussian</h1>
Atomic shell in org
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<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#orgab17fb9">1. Atomic shell</a>
<ul>
<li><a href="#org0ac793c">1.1. Type</a></li>
<li><a href="#org25b631d">1.2. Access</a></li>
<li><a href="#org6a770e6">1.3. Creation</a></li>
<li><a href="#orgfd4aeac">1.4. Printers</a></li>
</ul>
</li>
</ul>
</div>
</div>
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<div class="org-src-container">
Atomic shell in org
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<pre class="src src-ocaml" id="orgbe48c1b"><span class="org-string">"Gaussian basis sets"</span>
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</pre>
</div>
Atomic shell in org
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<div id="outline-container-orgab17fb9" class="outline-2">
<h2 id="orgab17fb9"><span class="section-number-2">1</span> Atomic shell</h2>
<div class="outline-text-2" id="text-1">
<p>
Set of contracted Gaussians differing only by the powers of \(x\), \(y\) and \(z\), with a
constant <code>Angular_momentum.t</code>, all centered on the same point.
</p>
<p>
In other words, it is the set of all contracted shells sharing the same center.
</p>
\begin{align*}
\chi_{n_x,n_y,n_z}(r) & = f(n_x,n_y,n_z) \sum_{j=1}^{n} \sum_{i=1}^{m} \mathcal{N}_{ij}\, d_{ij}\, g_{ij\,n_x,n_y,n_z}(r) \\
& = (x-X_A)^{n_x} (y-Y_A)^{n_y} (z-Z_A)^{n_z} f(n_x,n_y,n_z) \sum_{j=1}^{n} \sum_{i=1}^{m} \mathcal{N}_{ij}\, d_{ij}\, \exp \left( -\alpha_{ij} |r-R_A|^2 \right)
\end{align*}
<p>
where:
</p>
<ul class="org-ul">
<li>\(g_{ij\,n_x,n_y,n_z}(r)\) is the $i$-th <code>PrimitiveShell.t</code> of the $j$-th <code>Contracted_shell.t</code></li>
<li>\(n_x + n_y + n_z = l\), the total angular momentum</li>
<li>\(\alpha_{ij}\) are the exponents (tabulated) of the $j$-th <code>Contracted_shell.t</code></li>
<li>\(d_{ij}\) are the contraction coefficients of the $j$-th <code>Contracted_shell.t</code></li>
<li>\(\mathcal{N}_{ij}\) is the normalization coefficient of the $i$-th primitive shell
(<code>PrimitiveShell.norm_coef</code>) of the $j$-th <code>Contracted_shell.t</code></li>
<li>\(f(n_x,n_y,n_z)\) is a scaling factor adjusting the normalization coefficient for the
particular powers of \(x,y,z\) (<code>PrimitiveShell.norm_coef_scale</code>)</li>
</ul>
</div>
<div id="outline-container-org0ac793c" class="outline-3">
<h3 id="org0ac793c"><span class="section-number-3">1.1</span> Type</h3>
<div class="outline-text-3" id="text-1-1">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">type</span> <span class="org-type">t</span>
<span class="org-tuareg-font-lock-governing">open </span><span class="org-tuareg-font-lock-module">Common</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-org25b631d" class="outline-3">
<h3 id="org25b631d"><span class="section-number-3">1.2</span> Access</h3>
<div class="outline-text-3" id="text-1-2">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">index</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> int
<span class="org-doc">(** Index in the basis set, represented as an array of contracted shells. *)</span>
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">center</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-tuareg-font-lock-module">Coordinate.</span>t
<span class="org-doc">(** Coordinate of the center {% $\mathbf{A} = (X_A,Y_A,Z_A)$ %}. *)</span>
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">ang_mom</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-tuareg-font-lock-module">Angular_momentum.</span>t
<span class="org-doc">(** Total angular momentum : {% $l = n_x + n_y + n_z$ %}. *)</span>
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">size</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> int
<span class="org-doc">(** Number of contracted functions, {% $n$ %} in the definition. *)</span>
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">contracted_shells</span><span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-tuareg-font-lock-module">Contracted_shell.</span>t array
<span class="org-doc">(** Array of contracted gaussians *)</span>
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">exponents</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> float array array
<span class="org-doc">(** Array of exponents {% $\alpha_{ij}$ %}. The first index is the index of</span>
<span class="org-doc"> the contracted function, and the second index is the index of the primitive.</span>
<span class="org-doc">*)</span>
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">coefficients</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> float array array
<span class="org-doc">(** Array of contraction coefficients {% $d_{ij}$ %}. The first index is the index of</span>
<span class="org-doc"> the contracted function, and the second index is the index of the primitive.</span>
<span class="org-doc">*)</span>
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">normalizations</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> float array array
<span class="org-doc">(** Normalization coefficients {% $\mathcal{N}_{ij}$ %}. The first index is the index of</span>
<span class="org-doc"> the contracted function, and the second index is the index of the primitive.</span>
<span class="org-doc">*)</span>
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">norm_scales</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> float array
<span class="org-doc">(** Scaling factors {% $f(n_x,n_y,n_z)$ %}, given in the same order as</span>
<span class="org-doc"> [Angular_momentum.zkey_array ang_mom]. *)</span>
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">size_of_shell</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> int
<span class="org-doc">(** Number of contracted functions in the shell: length of {!norm_coef_scale}. *)</span>
</pre>
</div>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<tbody>
<tr>
<td class="org-left"><code>index</code></td>
<td class="org-left">Index in the basis set, represented as an array of contracted shells.</td>
</tr>
<tr>
<td class="org-left"><code>center</code></td>
<td class="org-left">Coordinate of the center \(\mathbf{A} = (X_A,Y_A,Z_A)\).</td>
</tr>
<tr>
<td class="org-left"><code>ang_mom</code></td>
<td class="org-left">Total angular momentum : \(l = n_x + n_y + n_z\).</td>
</tr>
<tr>
<td class="org-left"><code>size</code></td>
<td class="org-left">Number of contracted functions, \(n\) in the definition.</td>
</tr>
<tr>
<td class="org-left"><code>contracted_shells:</code></td>
<td class="org-left">Array of contracted gaussians</td>
</tr>
<tr>
<td class="org-left"><code>exponents</code></td>
<td class="org-left">Array of exponents \(\alpha_{ij}\). The first index is the index of the contracted function, and the second index is the index of the primitive.</td>
</tr>
<tr>
<td class="org-left"><code>coefficients</code></td>
<td class="org-left">Array of contraction coefficients \(d_{ij}\). The first index is the index of the contracted function, and the second index is the index of the primitive.</td>
</tr>
<tr>
<td class="org-left"><code>normalizations</code></td>
<td class="org-left">Normalization coefficients \(\mathcal{N}_{ij}\). The first index is the index of the contracted function, and the second index is the index of the primitive.</td>
</tr>
<tr>
<td class="org-left"><code>norm_scales</code></td>
<td class="org-left">Scaling factors \(f(n_x,n_y,n_z)\), given in the same order as <code>Angular_momentum.zkey_array ang_mom</code>.</td>
</tr>
<tr>
<td class="org-left"><code>size_of_shell</code></td>
<td class="org-left">Number of contracted functions in the shell: length of <code>norm_coef_scale</code>.</td>
</tr>
</tbody>
</table>
<pre class="example" id="org32dc57a">
</pre>
</div>
</div>
<div id="outline-container-org6a770e6" class="outline-3">
<h3 id="org6a770e6"><span class="section-number-3">1.3</span> Creation</h3>
<div class="outline-text-3" id="text-1-3">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">make</span> <span class="org-tuareg-font-lock-operator">:</span> <span class="org-tuareg-font-lock-label">?index</span><span class="org-tuareg-font-lock-operator">:</span>int <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-tuareg-font-lock-module">Contracted_shell.</span>t array <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-doc">(** Creates a contracted shell from a list of coefficients and primitives. *)</span>
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">with_index</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> int <span class="org-tuareg-font-lock-operator">-&gt;</span> t
<span class="org-doc">(** Returns a copy of the contracted shell with a modified index. *)</span>
</pre>
</div>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<tbody>
<tr>
<td class="org-left"><code>make</code></td>
<td class="org-left">Creates a contracted shell from a list of coefficients and primitives.</td>
</tr>
<tr>
<td class="org-left"><code>with_index</code></td>
<td class="org-left">Returns a copy of the contracted shell with a modified index.</td>
</tr>
</tbody>
</table>
<pre class="example" id="orgcab2544">
</pre>
</div>
</div>
<div id="outline-container-orgfd4aeac" class="outline-3">
<h3 id="orgfd4aeac"><span class="section-number-3">1.4</span> Printers</h3>
<div class="outline-text-3" id="text-1-4">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">pp</span> <span class="org-tuareg-font-lock-operator">:</span> <span class="org-tuareg-font-lock-module">Format.</span>formatter <span class="org-tuareg-font-lock-operator">-&gt;</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> unit
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MP2 OK
2021-01-01 16:39:33 +01:00
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<p class="author">Author: Anthony Scemama</p>
Atomic shell in org
2021-01-06 09:03:26 +01:00
<p class="date">Created: 2021-01-06 Wed 09:02</p>
MP2 OK
2021-01-01 16:39:33 +01:00
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
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