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Atomic shell in org
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<!-- 2021-01-04 Mon 23:32 -->
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<meta name="viewport" content="width=device-width, initial-scale=1" />
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<title>Gaussian</title>
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/*]]>*///-->
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// @license-end
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</head>
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<body>
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<div id="content">
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<h1 class="title">Gaussian</h1>
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<div id="table-of-contents">
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<ul>
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<li><a href="#orgab17fb9">1. Atomic shell</a>
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<ul>
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<li><a href="#org0ac793c">1.1. Type</a></li>
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<li><a href="#org25b631d">1.2. Access</a></li>
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<li><a href="#org6a770e6">1.3. Creation</a></li>
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<li><a href="#orgfd4aeac">1.4. Printers</a></li>
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</ul>
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</li>
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</ul>
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</div>
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</div>
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<div class="org-src-container">
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<pre class="src src-ocaml" id="org0a27d10"><span class="org-string">"Gaussian basis sets"</span>
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<pre class="src src-ocaml" id="orgbe48c1b"><span class="org-string">"Gaussian basis sets"</span>
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</pre>
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</div>
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<div id="outline-container-orgab17fb9" class="outline-2">
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<h2 id="orgab17fb9"><span class="section-number-2">1</span> Atomic shell</h2>
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<div class="outline-text-2" id="text-1">
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<p>
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Set of contracted Gaussians differing only by the powers of \(x\), \(y\) and \(z\), with a
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constant <code>Angular_momentum.t</code>, all centered on the same point.
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</p>
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<p>
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In other words, it is the set of all contracted shells sharing the same center.
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</p>
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\begin{align*}
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\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) \\
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& = (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)
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\end{align*}
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<p>
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where:
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</p>
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<ul class="org-ul">
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<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>
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<li>\(n_x + n_y + n_z = l\), the total angular momentum</li>
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<li>\(\alpha_{ij}\) are the exponents (tabulated) of the $j$-th <code>Contracted_shell.t</code></li>
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<li>\(d_{ij}\) are the contraction coefficients of the $j$-th <code>Contracted_shell.t</code></li>
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<li>\(\mathcal{N}_{ij}\) is the normalization coefficient of the $i$-th primitive shell
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(<code>PrimitiveShell.norm_coef</code>) of the $j$-th <code>Contracted_shell.t</code></li>
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<li>\(f(n_x,n_y,n_z)\) is a scaling factor adjusting the normalization coefficient for the
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particular powers of \(x,y,z\) (<code>PrimitiveShell.norm_coef_scale</code>)</li>
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</ul>
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</div>
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<div id="outline-container-org0ac793c" class="outline-3">
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<h3 id="org0ac793c"><span class="section-number-3">1.1</span> Type</h3>
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<div class="outline-text-3" id="text-1-1">
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<div class="org-src-container">
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<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">type</span> <span class="org-type">t</span>
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<span class="org-tuareg-font-lock-governing">open </span><span class="org-tuareg-font-lock-module">Common</span>
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</pre>
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</div>
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</div>
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</div>
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<div id="outline-container-org25b631d" class="outline-3">
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<h3 id="org25b631d"><span class="section-number-3">1.2</span> Access</h3>
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<div class="outline-text-3" id="text-1-2">
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<div class="org-src-container">
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<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">-></span> int
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<span class="org-doc">(** Index in the basis set, represented as an array of contracted shells. *)</span>
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<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">-></span> <span class="org-tuareg-font-lock-module">Coordinate.</span>t
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<span class="org-doc">(** Coordinate of the center {% $\mathbf{A} = (X_A,Y_A,Z_A)$ %}. *)</span>
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<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">-></span> <span class="org-tuareg-font-lock-module">Angular_momentum.</span>t
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<span class="org-doc">(** Total angular momentum : {% $l = n_x + n_y + n_z$ %}. *)</span>
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<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">-></span> int
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<span class="org-doc">(** Number of contracted functions, {% $n$ %} in the definition. *)</span>
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<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">-></span> <span class="org-tuareg-font-lock-module">Contracted_shell.</span>t array
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<span class="org-doc">(** Array of contracted gaussians *)</span>
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<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">-></span> float array array
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<span class="org-doc">(** Array of exponents {% $\alpha_{ij}$ %}. The first index is the index of</span>
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<span class="org-doc"> the contracted function, and the second index is the index of the primitive.</span>
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<span class="org-doc">*)</span>
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<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">-></span> float array array
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<span class="org-doc">(** Array of contraction coefficients {% $d_{ij}$ %}. The first index is the index of</span>
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<span class="org-doc"> the contracted function, and the second index is the index of the primitive.</span>
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<span class="org-doc">*)</span>
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<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">-></span> float array array
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<span class="org-doc">(** Normalization coefficients {% $\mathcal{N}_{ij}$ %}. The first index is the index of</span>
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<span class="org-doc"> the contracted function, and the second index is the index of the primitive.</span>
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<span class="org-doc">*)</span>
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<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">-></span> float array
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<span class="org-doc">(** Scaling factors {% $f(n_x,n_y,n_z)$ %}, given in the same order as</span>
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<span class="org-doc"> [Angular_momentum.zkey_array ang_mom]. *)</span>
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<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">-></span> int
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<span class="org-doc">(** Number of contracted functions in the shell: length of {!norm_coef_scale}. *)</span>
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</pre>
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</div>
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<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<colgroup>
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<col class="org-left" />
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<col class="org-left" />
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</colgroup>
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<tbody>
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<tr>
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<td class="org-left"><code>index</code></td>
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<td class="org-left">Index in the basis set, represented as an array of contracted shells.</td>
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</tr>
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<tr>
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<td class="org-left"><code>center</code></td>
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<td class="org-left">Coordinate of the center \(\mathbf{A} = (X_A,Y_A,Z_A)\).</td>
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</tr>
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<tr>
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<td class="org-left"><code>ang_mom</code></td>
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<td class="org-left">Total angular momentum : \(l = n_x + n_y + n_z\).</td>
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</tr>
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<tr>
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<td class="org-left"><code>size</code></td>
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<td class="org-left">Number of contracted functions, \(n\) in the definition.</td>
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</tr>
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<tr>
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<td class="org-left"><code>contracted_shells:</code></td>
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<td class="org-left">Array of contracted gaussians</td>
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</tr>
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<tr>
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<td class="org-left"><code>exponents</code></td>
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<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>
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</tr>
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<tr>
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<td class="org-left"><code>coefficients</code></td>
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<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>
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</tr>
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<tr>
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<td class="org-left"><code>normalizations</code></td>
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<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>
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</tr>
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<tr>
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<td class="org-left"><code>norm_scales</code></td>
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<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>
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</tr>
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<tr>
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<td class="org-left"><code>size_of_shell</code></td>
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<td class="org-left">Number of contracted functions in the shell: length of <code>norm_coef_scale</code>.</td>
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</tr>
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</tbody>
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</table>
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<pre class="example" id="org32dc57a">
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</pre>
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</div>
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</div>
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<div id="outline-container-org6a770e6" class="outline-3">
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<h3 id="org6a770e6"><span class="section-number-3">1.3</span> Creation</h3>
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<div class="outline-text-3" id="text-1-3">
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<div class="org-src-container">
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<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">-></span> <span class="org-tuareg-font-lock-module">Contracted_shell.</span>t array <span class="org-tuareg-font-lock-operator">-></span> t
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<span class="org-doc">(** Creates a contracted shell from a list of coefficients and primitives. *)</span>
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<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">-></span> int <span class="org-tuareg-font-lock-operator">-></span> t
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<span class="org-doc">(** Returns a copy of the contracted shell with a modified index. *)</span>
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</pre>
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</div>
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<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<colgroup>
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<col class="org-left" />
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<col class="org-left" />
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</colgroup>
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<tbody>
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<tr>
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<td class="org-left"><code>make</code></td>
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<td class="org-left">Creates a contracted shell from a list of coefficients and primitives.</td>
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</tr>
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<tr>
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<td class="org-left"><code>with_index</code></td>
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<td class="org-left">Returns a copy of the contracted shell with a modified index.</td>
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</tr>
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</tbody>
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</table>
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<pre class="example" id="orgcab2544">
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</pre>
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</div>
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</div>
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<div id="outline-container-orgfd4aeac" class="outline-3">
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<h3 id="orgfd4aeac"><span class="section-number-3">1.4</span> Printers</h3>
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<div class="outline-text-3" id="text-1-4">
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<div class="org-src-container">
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<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">-></span> t <span class="org-tuareg-font-lock-operator">-></span> unit
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</pre>
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</div>
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</div>
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</div>
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</div>
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</div>
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<div id="postamble" class="status">
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<p class="author">Author: Anthony Scemama</p>
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<p class="date">Created: 2021-01-04 Mon 23:32</p>
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<p class="date">Created: 2021-01-06 Wed 09:02</p>
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<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
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</div>
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</body>
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@ -3,7 +3,7 @@
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<head>
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<!-- 2021-01-04 Mon 23:51 -->
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<!-- 2021-01-06 Wed 09:03 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<meta name="viewport" content="width=device-width, initial-scale=1" />
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<title>Top-level</title>
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@ -226,13 +226,13 @@
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<div id="content">
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<h1 class="title">Top-level</h1>
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<div class="org-src-container">
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<pre class="src src-ocaml" id="org6a155c1"><span class="org-string">"Installs pretty printers for top-level."</span>
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<pre class="src src-ocaml" id="org6726456"><span class="org-string">"Installs pretty printers for top-level."</span>
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</pre>
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</div>
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</div>
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<div id="postamble" class="status">
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<p class="author">Author: Anthony Scemama</p>
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<p class="date">Created: 2021-01-04 Mon 23:51</p>
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<p class="date">Created: 2021-01-06 Wed 09:03</p>
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<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
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</div>
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</body>
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217
gaussian/atomic_shell.org
Normal file
217
gaussian/atomic_shell.org
Normal file
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#+begin_src elisp tangle: no :results none :exports none
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(setq pwd (file-name-directory buffer-file-name))
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(setq name (file-name-nondirectory (substring buffer-file-name 0 -4)))
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(setq lib (concat pwd "lib/"))
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(setq testdir (concat pwd "test/"))
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(setq mli (concat lib name ".mli"))
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(setq ml (concat lib name ".ml"))
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(setq test-ml (concat testdir name ".ml"))
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(org-babel-tangle)
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#+end_src
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* Atomic shell
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||||
:PROPERTIES:
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:header-args: :noweb yes :comments both
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:END:
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||||
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||||
Set of contracted Gaussians differing only by the powers of $x$, $y$ and $z$, with a
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constant ~Angular_momentum.t~, all centered on the same point.
|
||||
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||||
In other words, it is the set of all contracted shells sharing the same center.
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||||
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\begin{align*}
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||||
\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) \\
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& = (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)
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\end{align*}
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where:
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|
||||
- $g_{ij\,n_x,n_y,n_z}(r)$ is the $i$-th ~PrimitiveShell.t~ of the $j$-th ~Contracted_shell.t~
|
||||
- $n_x + n_y + n_z = l$, the total angular momentum
|
||||
- $\alpha_{ij}$ are the exponents (tabulated) of the $j$-th ~Contracted_shell.t~
|
||||
- $d_{ij}$ are the contraction coefficients of the $j$-th ~Contracted_shell.t~
|
||||
- $\mathcal{N}_{ij}$ is the normalization coefficient of the $i$-th primitive shell
|
||||
(~PrimitiveShell.norm_coef~) of the $j$-th ~Contracted_shell.t~
|
||||
- $f(n_x,n_y,n_z)$ is a scaling factor adjusting the normalization coefficient for the
|
||||
particular powers of $x,y,z$ (~PrimitiveShell.norm_coef_scale~)
|
||||
|
||||
|
||||
** Type
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
type t
|
||||
|
||||
open Common
|
||||
#+end_src
|
||||
|
||||
#+begin_src ocaml :tangle (eval ml) :exports none
|
||||
open Common
|
||||
|
||||
type t = {
|
||||
expo : float array array;
|
||||
coef : float array array;
|
||||
norm_coef : float array array;
|
||||
norm_coef_scale : float array;
|
||||
contr : Contracted_shell.t array;
|
||||
index : int;
|
||||
center : Coordinate.t;
|
||||
ang_mom : Angular_momentum.t;
|
||||
}
|
||||
|
||||
module Am = Angular_momentum
|
||||
module Co = Coordinate
|
||||
module Cs = Contracted_shell
|
||||
#+end_src
|
||||
|
||||
** Access
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val index : t -> int
|
||||
(** Index in the basis set, represented as an array of contracted shells. *)
|
||||
|
||||
val center : t -> Coordinate.t
|
||||
(** Coordinate of the center {% $\mathbf{A} = (X_A,Y_A,Z_A)$ %}. *)
|
||||
|
||||
val ang_mom : t -> Angular_momentum.t
|
||||
(** Total angular momentum : {% $l = n_x + n_y + n_z$ %}. *)
|
||||
|
||||
val size : t -> int
|
||||
(** Number of contracted functions, {% $n$ %} in the definition. *)
|
||||
|
||||
val contracted_shells: t -> Contracted_shell.t array
|
||||
(** Array of contracted gaussians *)
|
||||
|
||||
val exponents : t -> float array array
|
||||
(** 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.
|
||||
*)
|
||||
|
||||
val coefficients : t -> float array array
|
||||
(** 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.
|
||||
*)
|
||||
|
||||
val normalizations : t -> float array array
|
||||
(** 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.
|
||||
*)
|
||||
|
||||
val norm_scales : t -> float array
|
||||
(** Scaling factors {% $f(n_x,n_y,n_z)$ %}, given in the same order as
|
||||
[Angular_momentum.zkey_array ang_mom]. *)
|
||||
|
||||
val size_of_shell : t -> int
|
||||
(** Number of contracted functions in the shell: length of {!norm_coef_scale}. *)
|
||||
|
||||
#+end_src
|
||||
|
||||
| ~index~ | Index in the basis set, represented as an array of contracted shells. |
|
||||
| ~center~ | Coordinate of the center $\mathbf{A} = (X_A,Y_A,Z_A)$. |
|
||||
| ~ang_mom~ | Total angular momentum : $l = n_x + n_y + n_z$. |
|
||||
| ~size~ | Number of contracted functions, $n$ in the definition. |
|
||||
| ~contracted_shells:~ | Array of contracted gaussians |
|
||||
| ~exponents~ | 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. |
|
||||
| ~coefficients~ | 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. |
|
||||
| ~normalizations~ | 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. |
|
||||
| ~norm_scales~ | Scaling factors $f(n_x,n_y,n_z)$, given in the same order as ~Angular_momentum.zkey_array ang_mom~. |
|
||||
| ~size_of_shell~ | Number of contracted functions in the shell: length of ~norm_coef_scale~. |
|
||||
|
||||
#+begin_example
|
||||
|
||||
#+end_example
|
||||
|
||||
#+begin_src ocaml :tangle (eval ml) :exports none
|
||||
let exponents x = x.expo
|
||||
|
||||
let coefficients x = x.coef
|
||||
|
||||
let center x = x.center
|
||||
|
||||
let ang_mom x = x.ang_mom
|
||||
|
||||
let size x = Array.length x.contr
|
||||
|
||||
let normalizations x = x.norm_coef
|
||||
|
||||
let norm_scales x = x.norm_coef_scale
|
||||
|
||||
let index x = x.index
|
||||
|
||||
let size_of_shell x = Array.length x.norm_coef_scale
|
||||
|
||||
let contracted_shells x = x.contr
|
||||
#+end_src
|
||||
|
||||
** Creation
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val make : ?index:int -> Contracted_shell.t array -> t
|
||||
(** Creates a contracted shell from a list of coefficients and primitives. *)
|
||||
|
||||
val with_index : t -> int -> t
|
||||
(** Returns a copy of the contracted shell with a modified index. *)
|
||||
#+end_src
|
||||
|
||||
| ~make~ | Creates a contracted shell from a list of coefficients and primitives. |
|
||||
| ~with_index~ | Returns a copy of the contracted shell with a modified index. |
|
||||
|
||||
#+begin_example
|
||||
|
||||
#+end_example
|
||||
|
||||
#+begin_src ocaml :tangle (eval ml) :exports none
|
||||
let make ?(index=0) contr =
|
||||
assert (Array.length contr > 0);
|
||||
|
||||
let coef = Array.map Cs.coefficients contr
|
||||
and expo = Array.map Cs.exponents contr
|
||||
in
|
||||
|
||||
let center = Cs.center contr.(0) in
|
||||
let rec unique_center = function
|
||||
| 0 -> true
|
||||
| i -> if Cs.center contr.(i) = center then (unique_center [@tailcall]) (i-1) else false
|
||||
in
|
||||
if not (unique_center (Array.length contr - 1)) then
|
||||
invalid_arg "ContractedAtomicShell.make Coordinate.t differ";
|
||||
|
||||
let ang_mom = Cs.ang_mom contr.(0) in
|
||||
let rec unique_angmom = function
|
||||
| 0 -> true
|
||||
| i -> if Cs.ang_mom contr.(i) = ang_mom then (unique_angmom [@tailcall]) (i-1) else false
|
||||
in
|
||||
if not (unique_angmom (Array.length contr - 1)) then
|
||||
invalid_arg "Contracted_shell.make: Angular_momentum.t differ";
|
||||
|
||||
let norm_coef =
|
||||
Array.map Cs.normalizations contr
|
||||
in
|
||||
let norm_coef_scale = Cs.norm_scales contr.(0)
|
||||
in
|
||||
{ index ; expo ; coef ; center ; ang_mom ; norm_coef ;
|
||||
norm_coef_scale ; contr }
|
||||
|
||||
|
||||
let with_index a i =
|
||||
{ a with index = i }
|
||||
#+end_src
|
||||
|
||||
|
||||
** Printers
|
||||
|
||||
#+begin_src ocaml :tangle (eval mli)
|
||||
val pp : Format.formatter -> t -> unit
|
||||
#+end_src
|
||||
|
||||
#+begin_src ocaml :tangle (eval ml) :exports none
|
||||
let pp ppf s =
|
||||
let open Format in
|
||||
fprintf ppf "@[%3d-%-3d@]" (s.index+1) (s.index+ (size_of_shell s)*(size s));
|
||||
fprintf ppf "@[%a@ %a@] @[" Am.pp_string s.ang_mom Co.pp s.center;
|
||||
Array.iter2 (fun e_arr c_arr -> fprintf ppf "@[<v>";
|
||||
Array.iter2 (fun e c -> fprintf ppf "@[%16.8e %16.8e@]@;" e c)
|
||||
e_arr c_arr;
|
||||
fprintf ppf "@;@]") s.expo s.coef;
|
||||
fprintf ppf "@]"
|
||||
#+end_src
|
||||
|
||||
@ -1,3 +1,4 @@
|
||||
(* [[file:~/QCaml/gaussian/atomic_shell.org::*Type][Type:2]] *)
|
||||
open Common
|
||||
|
||||
type t = {
|
||||
@ -14,8 +15,59 @@ type t = {
|
||||
module Am = Angular_momentum
|
||||
module Co = Coordinate
|
||||
module Cs = Contracted_shell
|
||||
(* Type:2 ends here *)
|
||||
|
||||
|
||||
|
||||
(* | ~index~ | Index in the basis set, represented as an array of contracted shells. |
|
||||
* | ~center~ | Coordinate of the center $\mathbf{A} = (X_A,Y_A,Z_A)$. |
|
||||
* | ~ang_mom~ | Total angular momentum : $l = n_x + n_y + n_z$. |
|
||||
* | ~size~ | Number of contracted functions, $n$ in the definition. |
|
||||
* | ~contracted_shells:~ | Array of contracted gaussians |
|
||||
* | ~exponents~ | 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. |
|
||||
* | ~coefficients~ | 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. |
|
||||
* | ~normalizations~ | 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. |
|
||||
* | ~norm_scales~ | Scaling factors $f(n_x,n_y,n_z)$, given in the same order as ~Angular_momentum.zkey_array ang_mom~. |
|
||||
* | ~size_of_shell~ | Number of contracted functions in the shell: length of ~norm_coef_scale~. |
|
||||
*
|
||||
* #+begin_example
|
||||
*
|
||||
* #+end_example *)
|
||||
|
||||
|
||||
(* [[file:~/QCaml/gaussian/atomic_shell.org::*Access][Access:2]] *)
|
||||
let exponents x = x.expo
|
||||
|
||||
let coefficients x = x.coef
|
||||
|
||||
let center x = x.center
|
||||
|
||||
let ang_mom x = x.ang_mom
|
||||
|
||||
let size x = Array.length x.contr
|
||||
|
||||
let normalizations x = x.norm_coef
|
||||
|
||||
let norm_scales x = x.norm_coef_scale
|
||||
|
||||
let index x = x.index
|
||||
|
||||
let size_of_shell x = Array.length x.norm_coef_scale
|
||||
|
||||
let contracted_shells x = x.contr
|
||||
(* Access:2 ends here *)
|
||||
|
||||
|
||||
|
||||
(* | ~make~ | Creates a contracted shell from a list of coefficients and primitives. |
|
||||
* | ~with_index~ | Returns a copy of the contracted shell with a modified index. |
|
||||
*
|
||||
* #+begin_example
|
||||
*
|
||||
* #+end_example *)
|
||||
|
||||
|
||||
(* [[file:~/QCaml/gaussian/atomic_shell.org::*Creation][Creation:2]] *)
|
||||
let make ?(index=0) contr =
|
||||
assert (Array.length contr > 0);
|
||||
|
||||
@ -50,47 +102,11 @@ let make ?(index=0) contr =
|
||||
|
||||
let with_index a i =
|
||||
{ a with index = i }
|
||||
(* Creation:2 ends here *)
|
||||
|
||||
|
||||
let exponents x = x.expo
|
||||
|
||||
let coefficients x = x.coef
|
||||
|
||||
let center x = x.center
|
||||
|
||||
let ang_mom x = x.ang_mom
|
||||
|
||||
let size x = Array.length x.contr
|
||||
|
||||
let normalizations x = x.norm_coef
|
||||
|
||||
let norm_scales x = x.norm_coef_scale
|
||||
|
||||
let index x = x.index
|
||||
|
||||
let size_of_shell x = Array.length x.norm_coef_scale
|
||||
|
||||
let contracted_shells x = x.contr
|
||||
|
||||
|
||||
(** {2 Printers} *)
|
||||
|
||||
open Format
|
||||
|
||||
(*
|
||||
let pp_debug ppf x =
|
||||
fprintf ppf "@[<2>{@ ";
|
||||
fprintf ppf "@[<2>expo =@ %a ;@]@ " pp_float_2darray_size x.expo;
|
||||
fprintf ppf "@[<2>coef =@ %a ;@]@ " pp_float_2darray_size x.coef;
|
||||
fprintf ppf "@[<2>center =@ %a ;@]@ " Co.pp_angstrom x.center;
|
||||
fprintf ppf "@[<2>ang_mom =@ %a ;@]@ " Am.pp_string x.ang_mom;
|
||||
fprintf ppf "@[<2>norm_coef =@ %a ;@]@ " pp_float_2darray_size x.norm_coef;
|
||||
fprintf ppf "@[<2>norm_coef_scale =@ %a ;@]@ " pp_float_array_size x.norm_coef_scale;
|
||||
fprintf ppf "@[<2>index =@ %d ;@]@ " x.index;
|
||||
fprintf ppf "}@,@]"
|
||||
*)
|
||||
|
||||
(* [[file:~/QCaml/gaussian/atomic_shell.org::*Printers][Printers:2]] *)
|
||||
let pp ppf s =
|
||||
let open Format in
|
||||
fprintf ppf "@[%3d-%-3d@]" (s.index+1) (s.index+ (size_of_shell s)*(size s));
|
||||
fprintf ppf "@[%a@ %a@] @[" Am.pp_string s.ang_mom Co.pp s.center;
|
||||
Array.iter2 (fun e_arr c_arr -> fprintf ppf "@[<v>";
|
||||
@ -98,6 +114,4 @@ let pp ppf s =
|
||||
e_arr c_arr;
|
||||
fprintf ppf "@;@]") s.expo s.coef;
|
||||
fprintf ppf "@]"
|
||||
|
||||
|
||||
|
||||
(* Printers:2 ends here *)
|
||||
|
||||
@ -1,43 +1,16 @@
|
||||
(** Set of contracted Gaussians differing only by the powers of x, y and z, with a
|
||||
constant {!Angular_momentum.t}, all centered on the same center.
|
||||
(* Type *)
|
||||
|
||||
In other words, it is the set of all contracted shells sharing the same center.
|
||||
|
||||
{%
|
||||
\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*}
|
||||
%}
|
||||
|
||||
where:
|
||||
|
||||
- {% $g_{ij\,n_x,n_y,n_z}(r)$ %} is the i-th {!PrimitiveShell.t} of the j-th {!Contracted_shell.t}
|
||||
|
||||
- {% $n_x + n_y + n_z = l$ %}, the total angular momentum
|
||||
|
||||
- {% $\alpha_{ij}$ %} are the exponents (tabulated) of the j-th {!Contracted_shell.t}
|
||||
|
||||
- {% $d_{ij}$ %} are the contraction coefficients of the j-th {!Contracted_shell.t}
|
||||
|
||||
- {% $\mathcal{N}_{ij}$ %} is the normalization coefficient of the i-th primitive shell
|
||||
({!PrimitiveShell.norm_coef}) of the j-th {!Contracted_shell.t}
|
||||
|
||||
- {% $f(n_x,n_y,n_z)$ %} is a scaling factor adjusting the normalization coefficient for the
|
||||
particular powers of {% $x,y,z$ %} ({!PrimitiveShell.norm_coef_scale})
|
||||
|
||||
*)
|
||||
|
||||
type t
|
||||
(* [[file:~/QCaml/gaussian/atomic_shell.org::*Type][Type:1]] *)
|
||||
type t
|
||||
|
||||
open Common
|
||||
|
||||
val make : ?index:int -> Contracted_shell.t array -> t
|
||||
(** Creates a contracted shell from a list of coefficients and primitives. *)
|
||||
(* Type:1 ends here *)
|
||||
|
||||
val with_index : t -> int -> t
|
||||
(** Returns a copy of the contracted shell with a modified index. *)
|
||||
(* Access *)
|
||||
|
||||
|
||||
(* [[file:~/QCaml/gaussian/atomic_shell.org::*Access][Access:1]] *)
|
||||
val index : t -> int
|
||||
(** Index in the basis set, represented as an array of contracted shells. *)
|
||||
|
||||
@ -74,9 +47,22 @@ val norm_scales : t -> float array
|
||||
|
||||
val size_of_shell : t -> int
|
||||
(** Number of contracted functions in the shell: length of {!norm_coef_scale}. *)
|
||||
(* Access:1 ends here *)
|
||||
|
||||
(* Creation *)
|
||||
|
||||
|
||||
(** {2 Printers} *)
|
||||
(* [[file:~/QCaml/gaussian/atomic_shell.org::*Creation][Creation:1]] *)
|
||||
val make : ?index:int -> Contracted_shell.t array -> t
|
||||
(** Creates a contracted shell from a list of coefficients and primitives. *)
|
||||
|
||||
val with_index : t -> int -> t
|
||||
(** Returns a copy of the contracted shell with a modified index. *)
|
||||
(* Creation:1 ends here *)
|
||||
|
||||
(* Printers *)
|
||||
|
||||
|
||||
(* [[file:~/QCaml/gaussian/atomic_shell.org::*Printers][Printers:1]] *)
|
||||
val pp : Format.formatter -> t -> unit
|
||||
|
||||
(* Printers:1 ends here *)
|
||||
|
||||
@ -11,6 +11,7 @@ let printers =
|
||||
"Common.Range.pp" ;
|
||||
"Common.Spin.pp" ;
|
||||
"Common.Zkey.pp" ;
|
||||
"Gaussian.Atomic_shell.pp" ;
|
||||
"Mo.Frozen_core.pp" ;
|
||||
"Particles.Electrons.pp" ;
|
||||
"Particles.Element.pp" ;
|
||||
|
||||
Loading…
Reference in New Issue
Block a user