2021-03-19 13:49:11 +01:00
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2021-05-18 12:33:38 +02:00
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2021-03-19 13:49:11 +01:00
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<title>Atomic Orbitals</title>
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2021-04-30 01:35:52 +02:00
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2021-03-19 13:49:11 +01:00
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2021-04-30 01:35:52 +02:00
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* JavaScript code in org-info.js.
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*
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* Copyright (C) 2012-2019 Free Software Foundation, Inc.
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*
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*
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* The JavaScript code in this tag is free software: you can
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* redistribute it and/or modify it under the terms of the GNU
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* General Public License (GNU GPL) as published by the Free Software
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* Foundation, either version 3 of the License, or (at your option)
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* any later version. The code is distributed WITHOUT ANY WARRANTY;
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* without even the implied warranty of MERCHANTABILITY or FITNESS
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* FOR A PARTICULAR PURPOSE. See the GNU GPL for more details.
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*
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* As additional permission under GNU GPL version 3 section 7, you
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* may distribute non-source (e.g., minimized or compacted) forms of
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* that code without the copy of the GNU GPL normally required by
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* section 4, provided you include this license notice and a URL
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* through which recipients can access the Corresponding Source.
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*
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* @licend The above is the entire license notice
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* for the JavaScript code in org-info.js.
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*
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<script type="text/javascript">
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/*
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@licstart The following is the entire license notice for the
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JavaScript code in this tag.
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Copyright (C) 2012-2019 Free Software Foundation, Inc.
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The JavaScript code in this tag is free software: you can
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redistribute it and/or modify it under the terms of the GNU
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General Public License (GNU GPL) as published by the Free Software
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Foundation, either version 3 of the License, or (at your option)
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any later version. The code is distributed WITHOUT ANY WARRANTY;
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without even the implied warranty of MERCHANTABILITY or FITNESS
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FOR A PARTICULAR PURPOSE. See the GNU GPL for more details.
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As additional permission under GNU GPL version 3 section 7, you
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may distribute non-source (e.g., minimized or compacted) forms of
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that code without the copy of the GNU GPL normally required by
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section 4, provided you include this license notice and a URL
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through which recipients can access the Corresponding Source.
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@licend The above is the entire license notice
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for the JavaScript code in this tag.
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*/
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/*]]>*///-->
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</script>
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2021-03-19 13:49:11 +01:00
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<script type="text/javascript">
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/*
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@licstart The following is the entire license notice for the
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JavaScript code in this tag.
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Copyright (C) 2012-2019 Free Software Foundation, Inc.
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The JavaScript code in this tag is free software: you can
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redistribute it and/or modify it under the terms of the GNU
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General Public License (GNU GPL) as published by the Free Software
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Foundation, either version 3 of the License, or (at your option)
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any later version. The code is distributed WITHOUT ANY WARRANTY;
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without even the implied warranty of MERCHANTABILITY or FITNESS
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FOR A PARTICULAR PURPOSE. See the GNU GPL for more details.
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As additional permission under GNU GPL version 3 section 7, you
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may distribute non-source (e.g., minimized or compacted) forms of
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that code without the copy of the GNU GPL normally required by
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section 4, provided you include this license notice and a URL
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through which recipients can access the Corresponding Source.
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@licend The above is the entire license notice
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for the JavaScript code in this tag.
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*/
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<!--/*--><![CDATA[/*><!--*/
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</head>
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<body>
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<div id="org-div-home-and-up">
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<a accesskey="h" href=""> UP </a>
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<a accesskey="H" href="index.html"> HOME </a>
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</div><div id="content">
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2021-03-19 13:49:11 +01:00
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<h1 class="title">Atomic Orbitals</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="#org863b0d4">1. Context</a>
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<ul>
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<li><a href="#org3dd1c32">1.1. Data structure</a></li>
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<li><a href="#org9d91b4a">1.2. Access functions</a></li>
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<li><a href="#org4607a3d">1.3. Initialization functions</a></li>
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<li><a href="#org70b0e20">1.4. <span class="todo TODO">TODO</span> Fortran interfaces</a></li>
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</ul>
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</li>
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2021-05-18 12:33:38 +02:00
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<li><a href="#orgf5f4b46">2. Polynomial part</a>
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<ul>
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2021-05-18 12:33:38 +02:00
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<li><a href="#orge5c06eb">2.1. Powers of \(x-X_i\)</a>
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<ul>
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<li><a href="#org9087143">2.1.1. Requirements</a></li>
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<li><a href="#orge43dd13">2.1.2. C Header</a></li>
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<li><a href="#orgf7c150c">2.1.3. Source</a></li>
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<li><a href="#org69a0758">2.1.4. C interface</a></li>
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<li><a href="#org7b89bd3">2.1.5. Fortran interface</a></li>
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<li><a href="#org6bc139e">2.1.6. Test</a></li>
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2021-04-21 00:01:53 +02:00
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</ul>
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</li>
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2021-05-18 12:33:38 +02:00
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<li><a href="#org0caea4a">2.2. Value, Gradient and Laplacian of a polynomial</a>
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<ul>
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2021-05-18 12:33:38 +02:00
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<li><a href="#org73fe6fb">2.2.1. Requirements</a></li>
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<li><a href="#org4ec074f">2.2.2. C Header</a></li>
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<li><a href="#orgd7ade7f">2.2.3. Source</a></li>
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<li><a href="#org3a56acc">2.2.4. C interface</a></li>
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<li><a href="#org6227e9d">2.2.5. Fortran interface</a></li>
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<li><a href="#org8c26478">2.2.6. Test</a></li>
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2021-04-21 00:01:53 +02:00
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</ul>
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</li>
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</ul>
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</li>
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2021-05-18 12:33:38 +02:00
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<li><a href="#orgc8ad16a">3. Radial part</a>
|
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<ul>
|
2021-05-18 12:33:38 +02:00
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<li><a href="#org8a338ee">3.1. Gaussian basis functions</a></li>
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<li><a href="#org320ff80">3.2. <span class="todo TODO">TODO</span> Slater basis functions</a></li>
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<li><a href="#org2309ef2">3.3. <span class="todo TODO">TODO</span> Radial functions on a grid</a></li>
|
2021-04-21 00:01:53 +02:00
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</ul>
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</li>
|
2021-05-18 12:33:38 +02:00
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<li><a href="#orgdbf8f98">4. Combining radial and polynomial parts</a></li>
|
2021-03-19 13:49:11 +01:00
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</ul>
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</div>
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</div>
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2021-05-18 12:33:38 +02:00
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<div id="outline-container-org863b0d4" class="outline-2">
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<h2 id="org863b0d4"><span class="section-number-2">1</span> Context</h2>
|
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<div class="outline-text-2" id="text-1">
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<p>
|
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The following arrays are stored in the context:
|
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</p>
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2021-04-21 00:01:53 +02:00
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<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<tbody>
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<tr>
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<td class="org-left"><code>type</code></td>
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<td class="org-left"> </td>
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<td class="org-left">Gaussian (<code>'G'</code>) or Slater (<code>'S'</code>)</td>
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</tr>
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<tr>
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<td class="org-left"><code>shell_num</code></td>
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<td class="org-left"> </td>
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<td class="org-left">Number of shells</td>
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</tr>
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<tr>
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<td class="org-left"><code>prim_num</code></td>
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<td class="org-left"> </td>
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<td class="org-left">Total number of primitives</td>
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</tr>
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<tr>
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<td class="org-left"><code>shell_center</code></td>
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<td class="org-left"><code>[shell_num]</code></td>
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<td class="org-left">Id of the nucleus on which each shell is centered</td>
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</tr>
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<tr>
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<td class="org-left"><code>shell_ang_mom</code></td>
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<td class="org-left"><code>[shell_num]</code></td>
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<td class="org-left">Angular momentum of each shell</td>
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</tr>
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<tr>
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<td class="org-left"><code>shell_prim_num</code></td>
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<td class="org-left"><code>[shell_num]</code></td>
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<td class="org-left">Number of primitives in each shell</td>
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</tr>
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<tr>
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<td class="org-left"><code>shell_prim_index</code></td>
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<td class="org-left"><code>[shell_num]</code></td>
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<td class="org-left">Address of the first primitive of each shell in the <code>EXPONENT</code> array</td>
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</tr>
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<tr>
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<td class="org-left"><code>shell_factor</code></td>
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<td class="org-left"><code>[shell_num]</code></td>
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<td class="org-left">Normalization factor for each shell</td>
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</tr>
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<tr>
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<td class="org-left"><code>exponent</code></td>
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<td class="org-left"><code>[prim_num]</code></td>
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<td class="org-left">Array of exponents</td>
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</tr>
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<tr>
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<td class="org-left"><code>coefficient</code></td>
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|
<td class="org-left"><code>[prim_num]</code></td>
|
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|
|
<td class="org-left">Array of coefficients</td>
|
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</tr>
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</tbody>
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</table>
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2021-03-19 13:49:11 +01:00
|
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<p>
|
2021-04-21 00:01:53 +02:00
|
|
|
For H<sub>2</sub> with the following basis set,
|
2021-03-19 13:49:11 +01:00
|
|
|
</p>
|
|
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|
|
2021-04-21 00:01:53 +02:00
|
|
|
<pre class="example">
|
|
|
|
|
HYDROGEN
|
|
|
|
|
S 5
|
|
|
|
|
1 3.387000E+01 6.068000E-03
|
|
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|
|
2 5.095000E+00 4.530800E-02
|
|
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|
|
3 1.159000E+00 2.028220E-01
|
|
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|
|
4 3.258000E-01 5.039030E-01
|
|
|
|
|
5 1.027000E-01 3.834210E-01
|
|
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|
|
S 1
|
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|
|
1 3.258000E-01 1.000000E+00
|
|
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S 1
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|
1 1.027000E-01 1.000000E+00
|
|
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P 1
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|
|
1 1.407000E+00 1.000000E+00
|
|
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|
|
P 1
|
|
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|
|
1 3.880000E-01 1.000000E+00
|
|
|
|
|
D 1
|
|
|
|
|
1 1.057000E+00 1.0000000
|
|
|
|
|
</pre>
|
|
|
|
|
|
2021-03-19 13:49:11 +01:00
|
|
|
<p>
|
2021-04-21 00:01:53 +02:00
|
|
|
we have:
|
2021-03-19 13:49:11 +01:00
|
|
|
</p>
|
|
|
|
|
|
2021-04-21 00:01:53 +02:00
|
|
|
<pre class="example">
|
|
|
|
|
type = 'G'
|
|
|
|
|
shell_num = 12
|
|
|
|
|
prim_num = 20
|
|
|
|
|
shell_center = [1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2]
|
|
|
|
|
shell_ang_mom = ['S', 'S', 'S', 'P', 'P', 'D', 'S', 'S', 'S', 'P', 'P', 'D']
|
|
|
|
|
shell_factor = [ 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.]
|
|
|
|
|
shell_prim_num = [5, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1]
|
|
|
|
|
shell_prim_index = [1, 6, 7, 8, 9, 10, 11, 16, 17, 18, 19, 20]
|
|
|
|
|
exponent = [ 33.87, 5.095, 1.159, 0.3258, 0.1027, 0.3258, 0.1027,
|
|
|
|
|
1.407, 0.388, 1.057, 33.87, 5.095, 1.159, 0.3258, 0.1027,
|
|
|
|
|
0.3258, 0.1027, 1.407, 0.388, 1.057]
|
|
|
|
|
coefficient = [ 0.006068, 0.045308, 0.202822, 0.503903, 0.383421,
|
|
|
|
|
1.0, 1.0, 1.0, 1.0, 1.0, 0.006068, 0.045308, 0.202822,
|
|
|
|
|
0.503903, 0.383421, 1.0, 1.0, 1.0, 1.0, 1.0]
|
|
|
|
|
</pre>
|
|
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|
|
</div>
|
|
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|
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|
2021-05-18 12:33:38 +02:00
|
|
|
<div id="outline-container-org3dd1c32" class="outline-3">
|
|
|
|
|
<h3 id="org3dd1c32"><span class="section-number-3">1.1</span> Data structure</h3>
|
2021-04-21 00:01:53 +02:00
|
|
|
<div class="outline-text-3" id="text-1-1">
|
|
|
|
|
<div class="org-src-container">
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|
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|
|
<pre class="src src-c"><span style="color: #a020f0;">typedef</span> <span style="color: #a020f0;">struct</span> <span style="color: #228b22;">qmckl_ao_basis_struct</span> {
|
|
|
|
|
<span style="color: #228b22;">int32_t</span> <span style="color: #a0522d;">uninitialized</span>;
|
|
|
|
|
<span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">shell_num</span>;
|
|
|
|
|
<span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">prim_num</span>;
|
|
|
|
|
<span style="color: #228b22;">int64_t</span> * <span style="color: #a0522d;">shell_center</span>;
|
|
|
|
|
<span style="color: #228b22;">char</span> * <span style="color: #a0522d;">shell_ang_mom</span>;
|
|
|
|
|
<span style="color: #228b22;">int64_t</span> * <span style="color: #a0522d;">shell_prim_num</span>;
|
|
|
|
|
<span style="color: #228b22;">int64_t</span> * <span style="color: #a0522d;">shell_prim_index</span>;
|
|
|
|
|
<span style="color: #228b22;">double</span> * <span style="color: #a0522d;">shell_factor</span>;
|
|
|
|
|
<span style="color: #228b22;">double</span> * <span style="color: #a0522d;">exponent</span> ;
|
|
|
|
|
<span style="color: #228b22;">double</span> * <span style="color: #a0522d;">coefficient</span> ;
|
2021-04-21 01:58:32 +02:00
|
|
|
<span style="color: #228b22;">bool</span> <span style="color: #a0522d;">provided</span>;
|
2021-04-21 00:01:53 +02:00
|
|
|
<span style="color: #228b22;">char</span> <span style="color: #a0522d;">type</span>;
|
|
|
|
|
} <span style="color: #228b22;">qmckl_ao_basis_struct</span>;
|
|
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
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|
2021-03-19 13:49:11 +01:00
|
|
|
<p>
|
2021-04-21 00:01:53 +02:00
|
|
|
The <code>uninitialized</code> integer contains one bit set to one for each
|
|
|
|
|
initialization function which has not bee called. It becomes equal
|
|
|
|
|
to zero after all initialization functions have been called. The
|
2021-04-21 01:58:32 +02:00
|
|
|
struct is then initialized and <code>provided == true</code>.
|
2021-03-19 13:49:11 +01:00
|
|
|
</p>
|
2021-04-21 00:01:53 +02:00
|
|
|
</div>
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</div>
|
2021-03-19 13:49:11 +01:00
|
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|
2021-05-18 12:33:38 +02:00
|
|
|
<div id="outline-container-org9d91b4a" class="outline-3">
|
|
|
|
|
<h3 id="org9d91b4a"><span class="section-number-3">1.2</span> Access functions</h3>
|
2021-04-21 00:01:53 +02:00
|
|
|
<div class="outline-text-3" id="text-1-2">
|
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|
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|
<p>
|
2021-04-21 13:01:35 +02:00
|
|
|
When all the data for the AOs have been provided, the following
|
|
|
|
|
function returns <code>true</code>.
|
2021-03-19 13:49:11 +01:00
|
|
|
</p>
|
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|
2021-04-21 00:01:53 +02:00
|
|
|
<div class="org-src-container">
|
2021-04-21 01:58:32 +02:00
|
|
|
<pre class="src src-c"><span style="color: #228b22;">bool</span> <span style="color: #0000ff;">qmckl_ao_basis_provided</span> (<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>);
|
2021-04-21 00:01:53 +02:00
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
|
2021-05-18 12:33:38 +02:00
|
|
|
<div id="outline-container-org4607a3d" class="outline-3">
|
|
|
|
|
<h3 id="org4607a3d"><span class="section-number-3">1.3</span> Initialization functions</h3>
|
2021-04-21 00:01:53 +02:00
|
|
|
<div class="outline-text-3" id="text-1-3">
|
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|
|
|
<p>
|
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|
|
|
To set the basis set, all the following functions need to be
|
|
|
|
|
called. When
|
2021-03-19 13:49:11 +01:00
|
|
|
</p>
|
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|
2021-04-21 00:01:53 +02:00
|
|
|
<div class="org-src-container">
|
|
|
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_set_ao_basis_type</span> (<span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>, <span style="color: #a020f0;">const</span> <span style="color: #228b22;">char</span> <span style="color: #a0522d;">t</span>);
|
|
|
|
|
<span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_set_ao_basis_shell_num</span> (<span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>, <span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">shell_num</span>);
|
|
|
|
|
<span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_set_ao_basis_prim_num</span> (<span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>, <span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">prim_num</span>);
|
|
|
|
|
<span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_set_ao_basis_shell_prim_index</span> (<span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>, <span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> * <span style="color: #a0522d;">shell_prim_index</span>);
|
|
|
|
|
<span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_set_ao_basis_shell_center</span> (<span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>, <span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> * <span style="color: #a0522d;">shell_center</span>);
|
|
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|
|
<span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_set_ao_basis_shell_ang_mom</span> (<span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>, <span style="color: #a020f0;">const</span> <span style="color: #228b22;">char</span> * <span style="color: #a0522d;">shell_ang_mom</span>);
|
|
|
|
|
<span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_set_ao_basis_shell_prim_num</span> (<span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>, <span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> * <span style="color: #a0522d;">shell_prim_num</span>);
|
|
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|
|
<span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_set_ao_basis_shell_factor</span> (<span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>, <span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> * <span style="color: #a0522d;">shell_factor</span>);
|
|
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|
|
<span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_set_ao_basis_exponent</span> (<span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>, <span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> * <span style="color: #a0522d;">exponent</span>);
|
|
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|
|
<span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_set_ao_basis_coefficient</span> (<span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>, <span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> * <span style="color: #a0522d;">coefficient</span>);
|
|
|
|
|
</pre>
|
2021-03-19 13:49:11 +01:00
|
|
|
</div>
|
2021-04-21 00:01:53 +02:00
|
|
|
</div>
|
|
|
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|
</div>
|
|
|
|
|
|
2021-05-18 12:33:38 +02:00
|
|
|
<div id="outline-container-org70b0e20" class="outline-3">
|
|
|
|
|
<h3 id="org70b0e20"><span class="section-number-3">1.4</span> <span class="todo TODO">TODO</span> Fortran interfaces</h3>
|
2021-04-21 00:01:53 +02:00
|
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|
</div>
|
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|
</div>
|
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|
2021-05-18 12:33:38 +02:00
|
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|
<div id="outline-container-orgf5f4b46" class="outline-2">
|
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|
|
|
<h2 id="orgf5f4b46"><span class="section-number-2">2</span> Polynomial part</h2>
|
2021-04-21 00:01:53 +02:00
|
|
|
<div class="outline-text-2" id="text-2">
|
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|
|
</div>
|
2021-05-18 12:33:38 +02:00
|
|
|
<div id="outline-container-orge5c06eb" class="outline-3">
|
|
|
|
|
<h3 id="orge5c06eb"><span class="section-number-3">2.1</span> Powers of \(x-X_i\)</h3>
|
2021-04-21 00:01:53 +02:00
|
|
|
<div class="outline-text-3" id="text-2-1">
|
2021-03-19 13:49:11 +01:00
|
|
|
<p>
|
|
|
|
|
The <code>qmckl_ao_power</code> function computes all the powers of the <code>n</code>
|
|
|
|
|
input data up to the given maximum value given in input for each of
|
|
|
|
|
the \(n\) points:
|
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|
|
|
</p>
|
|
|
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|
|
|
|
|
|
<p>
|
|
|
|
|
\[ P_{ik} = X_i^k \]
|
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|
|
|
</p>
|
|
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|
|
|
2021-05-18 12:33:38 +02:00
|
|
|
<table id="orga189a72" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
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|
|
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|
<colgroup>
|
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|
<col class="org-left" />
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|
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|
<col class="org-left" />
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|
2021-04-21 00:01:53 +02:00
|
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<col class="org-left" />
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|
2021-03-19 13:49:11 +01:00
|
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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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|
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|
<td class="org-left">qmckl<sub>context</sub></td>
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|
<td class="org-left">context</td>
|
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|
|
<td class="org-left">in</td>
|
2021-03-19 13:49:11 +01:00
|
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|
<td class="org-left">Global state</td>
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</tr>
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<tr>
|
2021-04-21 00:01:53 +02:00
|
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|
<td class="org-left">int64<sub>t</sub></td>
|
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|
|
<td class="org-left">n</td>
|
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|
<td class="org-left">in</td>
|
2021-03-19 13:49:11 +01:00
|
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|
<td class="org-left">Number of values</td>
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</tr>
|
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|
<tr>
|
2021-04-21 00:01:53 +02:00
|
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|
<td class="org-left">double</td>
|
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|
<td class="org-left">X[n]</td>
|
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|
|
<td class="org-left">in</td>
|
2021-03-19 13:49:11 +01:00
|
|
|
<td class="org-left">Array containing the input values</td>
|
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|
|
</tr>
|
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|
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|
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|
|
<tr>
|
2021-04-21 00:01:53 +02:00
|
|
|
<td class="org-left">int32<sub>t</sub></td>
|
|
|
|
|
<td class="org-left">LMAX[n]</td>
|
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|
|
<td class="org-left">in</td>
|
2021-03-19 13:49:11 +01:00
|
|
|
<td class="org-left">Array containing the maximum power for each value</td>
|
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|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
2021-04-21 00:01:53 +02:00
|
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|
<td class="org-left">double</td>
|
|
|
|
|
<td class="org-left">P[n][ldp]</td>
|
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|
|
<td class="org-left">out</td>
|
2021-03-19 13:49:11 +01:00
|
|
|
<td class="org-left">Array containing all the powers of <code>X</code></td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
2021-04-21 00:01:53 +02:00
|
|
|
<td class="org-left">int64<sub>t</sub></td>
|
|
|
|
|
<td class="org-left">ldp</td>
|
|
|
|
|
<td class="org-left">in</td>
|
2021-03-19 13:49:11 +01:00
|
|
|
<td class="org-left">Leading dimension of array <code>P</code></td>
|
|
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|
|
</tr>
|
|
|
|
|
</tbody>
|
|
|
|
|
</table>
|
2021-04-21 00:01:53 +02:00
|
|
|
</div>
|
2021-03-19 13:49:11 +01:00
|
|
|
|
2021-05-18 12:33:38 +02:00
|
|
|
<div id="outline-container-org9087143" class="outline-4">
|
|
|
|
|
<h4 id="org9087143"><span class="section-number-4">2.1.1</span> Requirements</h4>
|
2021-04-21 00:01:53 +02:00
|
|
|
<div class="outline-text-4" id="text-2-1-1">
|
2021-03-19 13:49:11 +01:00
|
|
|
<ul class="org-ul">
|
|
|
|
|
<li><code>context</code> is not <code>QMCKL_NULL_CONTEXT</code></li>
|
|
|
|
|
<li><code>n</code> > 0</li>
|
|
|
|
|
<li><code>X</code> is allocated with at least \(n \times 8\) bytes</li>
|
|
|
|
|
<li><code>LMAX</code> is allocated with at least \(n \times 4\) bytes</li>
|
|
|
|
|
<li><code>P</code> is allocated with at least \(n \times \max_i \text{LMAX}_i \times 8\) bytes</li>
|
|
|
|
|
<li><code>LDP</code> >= \(\max_i\) <code>LMAX[i]</code></li>
|
|
|
|
|
</ul>
|
2021-04-21 00:01:53 +02:00
|
|
|
</div>
|
|
|
|
|
</div>
|
2021-03-19 13:49:11 +01:00
|
|
|
|
2021-05-18 12:33:38 +02:00
|
|
|
<div id="outline-container-orge43dd13" class="outline-4">
|
|
|
|
|
<h4 id="orge43dd13"><span class="section-number-4">2.1.2</span> C Header</h4>
|
2021-04-21 00:01:53 +02:00
|
|
|
<div class="outline-text-4" id="text-2-1-2">
|
2021-03-19 13:49:11 +01:00
|
|
|
<div class="org-src-container">
|
2021-04-21 00:01:53 +02:00
|
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_ao_power</span> (
|
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">n</span>,
|
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">X</span>,
|
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int32_t</span>* <span style="color: #a0522d;">LMAX</span>,
|
|
|
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">const</span> <span style="color: #a0522d;">P</span>,
|
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">ldp</span> );
|
2021-03-19 13:49:11 +01:00
|
|
|
</pre>
|
|
|
|
|
</div>
|
2021-04-21 00:01:53 +02:00
|
|
|
</div>
|
|
|
|
|
</div>
|
2021-03-19 13:49:11 +01:00
|
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|
2021-05-18 12:33:38 +02:00
|
|
|
<div id="outline-container-orgf7c150c" class="outline-4">
|
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|
<h4 id="orgf7c150c"><span class="section-number-4">2.1.3</span> Source</h4>
|
2021-04-21 00:01:53 +02:00
|
|
|
<div class="outline-text-4" id="text-2-1-3">
|
2021-03-19 13:49:11 +01:00
|
|
|
<div class="org-src-container">
|
|
|
|
|
<pre class="src src-f90"><span style="color: #228b22;">integer </span><span style="color: #a020f0;">function</span><span style="color: #a0522d;"> </span><span style="color: #0000ff;">qmckl_ao_power_f</span><span style="color: #000000; background-color: #ffffff;">(context, n, X, LMAX, P, ldp) result(info)</span>
|
|
|
|
|
<span style="color: #a020f0;">use</span> <span style="color: #0000ff;">qmckl</span>
|
|
|
|
|
<span style="color: #a020f0;">implicit</span> <span style="color: #228b22;">none</span>
|
|
|
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|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> context</span>
|
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|
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|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> n</span>
|
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|
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|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> X(n)</span>
|
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|
<span style="color: #228b22;">integer</span> , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> LMAX(n)</span>
|
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|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">intent</span>(out) ::<span style="color: #a0522d;"> P(ldp,n)</span>
|
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|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> ldp</span>
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|
<span style="color: #228b22;">integer</span>*8 ::<span style="color: #a0522d;"> i,k</span>
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|
info = QMCKL_SUCCESS
|
|
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|
|
|
|
|
|
|
<span style="color: #a020f0;">if</span> (context == QMCKL_NULL_CONTEXT) <span style="color: #a020f0;">then</span>
|
|
|
|
|
info = QMCKL_INVALID_CONTEXT
|
|
|
|
|
<span style="color: #a020f0;">return</span>
|
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|
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|
<span style="color: #a020f0;">endif</span>
|
|
|
|
|
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|
<span style="color: #a020f0;">if</span> (n <= ldp) <span style="color: #a020f0;">then</span>
|
|
|
|
|
info = QMCKL_INVALID_ARG_2
|
|
|
|
|
<span style="color: #a020f0;">return</span>
|
|
|
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
|
|
|
|
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|
k = <span style="color: #a020f0;">MAXVAL</span>(LMAX)
|
|
|
|
|
<span style="color: #a020f0;">if</span> (LDP < k) <span style="color: #a020f0;">then</span>
|
|
|
|
|
info = QMCKL_INVALID_ARG_6
|
|
|
|
|
<span style="color: #a020f0;">return</span>
|
|
|
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
|
|
|
|
|
|
<span style="color: #a020f0;">if</span> (k <= 0) <span style="color: #a020f0;">then</span>
|
|
|
|
|
info = QMCKL_INVALID_ARG_4
|
|
|
|
|
<span style="color: #a020f0;">return</span>
|
|
|
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
|
|
|
|
|
|
<span style="color: #a020f0;">do</span> i=1,n
|
|
|
|
|
P(1,i) = X(i)
|
|
|
|
|
<span style="color: #a020f0;">do</span> k=2,LMAX(i)
|
2021-04-30 01:28:23 +02:00
|
|
|
P(k,i) = P(k-1,i) * X(i)
|
2021-03-19 13:49:11 +01:00
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|
<span style="color: #a020f0;">end do</span>
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|
<span style="color: #a020f0;">end do</span>
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|
<span style="color: #a020f0;">end function</span> <span style="color: #0000ff;">qmckl_ao_power_f</span>
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|
|
</pre>
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|
|
</div>
|
2021-04-21 00:01:53 +02:00
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|
</div>
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|
</div>
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2021-05-18 12:33:38 +02:00
|
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<div id="outline-container-org69a0758" class="outline-4">
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<h4 id="org69a0758"><span class="section-number-4">2.1.4</span> C interface</h4>
|
2021-04-21 00:01:53 +02:00
|
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|
</div>
|
2021-05-18 12:33:38 +02:00
|
|
|
<div id="outline-container-org7b89bd3" class="outline-4">
|
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|
<h4 id="org7b89bd3"><span class="section-number-4">2.1.5</span> Fortran interface</h4>
|
2021-04-21 00:01:53 +02:00
|
|
|
</div>
|
2021-03-19 13:49:11 +01:00
|
|
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|
2021-05-18 12:33:38 +02:00
|
|
|
<div id="outline-container-org6bc139e" class="outline-4">
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|
<h4 id="org6bc139e"><span class="section-number-4">2.1.6</span> Test</h4>
|
2021-04-21 00:01:53 +02:00
|
|
|
<div class="outline-text-4" id="text-2-1-6">
|
2021-03-19 13:49:11 +01:00
|
|
|
<div class="org-src-container">
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|
<pre class="src src-f90"><span style="color: #228b22;">integer</span>(<span style="color: #008b8b;">c_int32_t</span>) <span style="color: #a020f0;">function</span> <span style="color: #0000ff;">test_qmckl_ao_power</span>(context) <span style="color: #a020f0;">bind</span>(C)
|
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|
<span style="color: #a020f0;">use</span> <span style="color: #0000ff;">qmckl</span>
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<span style="color: #a020f0;">implicit</span> <span style="color: #228b22;">none</span>
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|
2021-04-21 00:01:53 +02:00
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<span style="color: #228b22;">integer</span>(qmckl_context), <span style="color: #a020f0;">intent</span>(in), <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> context</span>
|
2021-03-19 13:49:11 +01:00
|
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|
2021-04-30 01:28:23 +02:00
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<span style="color: #228b22;">integer</span>*8 ::<span style="color: #a0522d;"> n, LDP</span>
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<span style="color: #228b22;">integer</span>, <span style="color: #a020f0;">allocatable</span> ::<span style="color: #a0522d;"> LMAX(:)</span>
|
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|
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<span style="color: #228b22;">double precision</span>, <span style="color: #a020f0;">allocatable</span> ::<span style="color: #a0522d;"> X(:), P(:,:)</span>
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<span style="color: #228b22;">integer</span>*8 ::<span style="color: #a0522d;"> i,j</span>
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<span style="color: #228b22;">double precision</span> ::<span style="color: #a0522d;"> epsilon</span>
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|
2021-04-21 00:01:53 +02:00
|
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epsilon = qmckl_get_numprec_epsilon(context)
|
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|
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|
|
n = 100;
|
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|
|
LDP = 10;
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|
|
<span style="color: #a020f0;">allocate</span>(X(n), P(LDP,n), LMAX(n))
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|
<span style="color: #a020f0;">do</span> j=1,n
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|
X(j) = -5.d0 + 0.1d0 * <span style="color: #a020f0;">dble</span>(j)
|
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|
|
LMAX(j) = 1 + <span style="color: #a020f0;">int</span>(<span style="color: #a020f0;">mod</span>(j, 5),4)
|
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|
<span style="color: #a020f0;">end do</span>
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|
|
2021-04-30 01:28:23 +02:00
|
|
|
test_qmckl_ao_power = qmckl_ao_power(context, n, X, LMAX, P, LDP)
|
2021-04-21 00:01:53 +02:00
|
|
|
<span style="color: #a020f0;">if</span> (test_qmckl_ao_power /= QMCKL_SUCCESS) <span style="color: #a020f0;">return</span>
|
2021-03-19 13:49:11 +01:00
|
|
|
|
2021-04-21 00:01:53 +02:00
|
|
|
test_qmckl_ao_power = QMCKL_FAILURE
|
2021-03-19 13:49:11 +01:00
|
|
|
|
|
|
|
|
<span style="color: #a020f0;">do</span> j=1,n
|
|
|
|
|
<span style="color: #a020f0;">do</span> i=1,LMAX(j)
|
|
|
|
|
<span style="color: #a020f0;">if</span> ( X(j)**i == 0.d0 ) <span style="color: #a020f0;">then</span>
|
|
|
|
|
<span style="color: #a020f0;">if</span> ( P(i,j) /= 0.d0) <span style="color: #a020f0;">return</span>
|
|
|
|
|
<span style="color: #a020f0;">else</span>
|
|
|
|
|
<span style="color: #a020f0;">if</span> ( dabs(1.d0 - P(i,j) / (X(j)**i)) > epsilon ) <span style="color: #a020f0;">return</span>
|
|
|
|
|
<span style="color: #a020f0;">end if</span>
|
|
|
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
|
|
2021-04-21 00:01:53 +02:00
|
|
|
test_qmckl_ao_power = QMCKL_SUCCESS
|
2021-03-19 13:49:11 +01:00
|
|
|
<span style="color: #a020f0;">deallocate</span>(X,P,LMAX)
|
|
|
|
|
<span style="color: #a020f0;">end function</span> <span style="color: #0000ff;">test_qmckl_ao_power</span>
|
|
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
2021-04-21 00:01:53 +02:00
|
|
|
</div>
|
2021-03-19 13:49:11 +01:00
|
|
|
|
2021-05-18 12:33:38 +02:00
|
|
|
<div id="outline-container-org0caea4a" class="outline-3">
|
|
|
|
|
<h3 id="org0caea4a"><span class="section-number-3">2.2</span> Value, Gradient and Laplacian of a polynomial</h3>
|
2021-04-21 00:01:53 +02:00
|
|
|
<div class="outline-text-3" id="text-2-2">
|
2021-03-19 13:49:11 +01:00
|
|
|
<p>
|
|
|
|
|
A polynomial is centered on a nucleus \(\mathbf{R}_i\)
|
|
|
|
|
</p>
|
|
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
\[
|
2021-04-30 01:28:23 +02:00
|
|
|
P_l(\mathbf{r},\mathbf{R}_i) = (x-X_i)^a (y-Y_i)^b (z-Z_i)^c
|
2021-03-19 13:49:11 +01:00
|
|
|
\]
|
|
|
|
|
</p>
|
|
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
The gradients with respect to electron coordinates are
|
|
|
|
|
</p>
|
|
|
|
|
|
2021-04-30 01:28:23 +02:00
|
|
|
\begin{eqnarray*}
|
2021-03-19 13:49:11 +01:00
|
|
|
\frac{\partial }{\partial x} P_l\left(\mathbf{r},\mathbf{R}_i \right) &
|
|
|
|
|
= & a (x-X_i)^{a-1} (y-Y_i)^b (z-Z_i)^c \\
|
|
|
|
|
\frac{\partial }{\partial y} P_l\left(\mathbf{r},\mathbf{R}_i \right) &
|
|
|
|
|
= & b (x-X_i)^a (y-Y_i)^{b-1} (z-Z_i)^c \\
|
|
|
|
|
\frac{\partial }{\partial z} P_l\left(\mathbf{r},\mathbf{R}_i \right) &
|
|
|
|
|
= & c (x-X_i)^a (y-Y_i)^b (z-Z_i)^{c-1} \\
|
2021-04-30 01:28:23 +02:00
|
|
|
\end{eqnarray*}
|
2021-03-19 13:49:11 +01:00
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
and the Laplacian is
|
|
|
|
|
</p>
|
|
|
|
|
|
2021-04-30 01:28:23 +02:00
|
|
|
\begin{eqnarray*}
|
|
|
|
|
\left( \frac{\partial }{\partial x^2} +
|
|
|
|
|
\frac{\partial }{\partial y^2} +
|
2021-03-19 13:49:11 +01:00
|
|
|
\frac{\partial }{\partial z^2} \right) P_l
|
2021-04-30 01:28:23 +02:00
|
|
|
\left(\mathbf{r},\mathbf{R}_i \right) & = &
|
2021-03-19 13:49:11 +01:00
|
|
|
a(a-1) (x-X_i)^{a-2} (y-Y_i)^b (z-Z_i)^c + \\
|
|
|
|
|
&& b(b-1) (x-X_i)^a (y-Y_i)^{b-1} (z-Z_i)^c + \\
|
|
|
|
|
&& c(c-1) (x-X_i)^a (y-Y_i)^b (z-Z_i)^{c-1}.
|
|
|
|
|
\end{eqnarray*}
|
|
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
<code>qmckl_ao_polynomial_vgl</code> computes the values, gradients and
|
|
|
|
|
Laplacians at a given point in space, of all polynomials with an
|
|
|
|
|
angular momentum up to <code>lmax</code>.
|
|
|
|
|
</p>
|
|
|
|
|
|
2021-05-18 12:33:38 +02:00
|
|
|
<table id="org79789d9" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
2021-03-19 13:49:11 +01:00
|
|
|
|
|
|
|
|
|
|
|
|
|
<colgroup>
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
2021-04-21 00:01:53 +02:00
|
|
|
<col class="org-left" />
|
|
|
|
|
|
2021-03-19 13:49:11 +01:00
|
|
|
<col class="org-left" />
|
|
|
|
|
</colgroup>
|
|
|
|
|
<tbody>
|
|
|
|
|
<tr>
|
2021-04-21 00:01:53 +02:00
|
|
|
<td class="org-left">qmckl<sub>context</sub></td>
|
|
|
|
|
<td class="org-left">context</td>
|
|
|
|
|
<td class="org-left">in</td>
|
2021-03-19 13:49:11 +01:00
|
|
|
<td class="org-left">Global state</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
2021-04-21 00:01:53 +02:00
|
|
|
<td class="org-left">double</td>
|
|
|
|
|
<td class="org-left">X[3]</td>
|
|
|
|
|
<td class="org-left">in</td>
|
2021-03-19 13:49:11 +01:00
|
|
|
<td class="org-left">Array containing the coordinates of the points</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
2021-04-21 00:01:53 +02:00
|
|
|
<td class="org-left">double</td>
|
|
|
|
|
<td class="org-left">R[3]</td>
|
|
|
|
|
<td class="org-left">in</td>
|
2021-03-19 13:49:11 +01:00
|
|
|
<td class="org-left">Array containing the x,y,z coordinates of the center</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
2021-04-21 00:01:53 +02:00
|
|
|
<td class="org-left">int32<sub>t</sub></td>
|
|
|
|
|
<td class="org-left">lmax</td>
|
|
|
|
|
<td class="org-left">in</td>
|
2021-03-19 13:49:11 +01:00
|
|
|
<td class="org-left">Maximum angular momentum</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
2021-04-21 00:01:53 +02:00
|
|
|
<td class="org-left">int64<sub>t</sub></td>
|
|
|
|
|
<td class="org-left">n</td>
|
|
|
|
|
<td class="org-left">inout</td>
|
2021-03-19 13:49:11 +01:00
|
|
|
<td class="org-left">Number of computed polynomials</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
2021-04-21 00:01:53 +02:00
|
|
|
<td class="org-left">int32<sub>t</sub></td>
|
|
|
|
|
<td class="org-left">L[n][ldl]</td>
|
|
|
|
|
<td class="org-left">out</td>
|
2021-03-19 13:49:11 +01:00
|
|
|
<td class="org-left">Contains a,b,c for all <code>n</code> results</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
2021-04-21 00:01:53 +02:00
|
|
|
<td class="org-left">int64<sub>t</sub></td>
|
|
|
|
|
<td class="org-left">ldl</td>
|
|
|
|
|
<td class="org-left">in</td>
|
2021-03-19 13:49:11 +01:00
|
|
|
<td class="org-left">Leading dimension of <code>L</code></td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
2021-04-21 00:01:53 +02:00
|
|
|
<td class="org-left">double</td>
|
|
|
|
|
<td class="org-left">VGL[n][ldv]</td>
|
|
|
|
|
<td class="org-left">out</td>
|
2021-03-19 13:49:11 +01:00
|
|
|
<td class="org-left">Value, gradients and Laplacian of the polynomials</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
2021-04-21 00:01:53 +02:00
|
|
|
<td class="org-left">int64<sub>t</sub></td>
|
|
|
|
|
<td class="org-left">ldv</td>
|
|
|
|
|
<td class="org-left">in</td>
|
2021-03-19 13:49:11 +01:00
|
|
|
<td class="org-left">Leading dimension of array <code>VGL</code></td>
|
|
|
|
|
</tr>
|
|
|
|
|
</tbody>
|
|
|
|
|
</table>
|
2021-04-21 00:01:53 +02:00
|
|
|
</div>
|
2021-03-19 13:49:11 +01:00
|
|
|
|
2021-05-18 12:33:38 +02:00
|
|
|
<div id="outline-container-org73fe6fb" class="outline-4">
|
|
|
|
|
<h4 id="org73fe6fb"><span class="section-number-4">2.2.1</span> Requirements</h4>
|
2021-04-21 00:01:53 +02:00
|
|
|
<div class="outline-text-4" id="text-2-2-1">
|
2021-03-19 13:49:11 +01:00
|
|
|
<ul class="org-ul">
|
|
|
|
|
<li><code>context</code> is not <code>QMCKL_NULL_CONTEXT</code></li>
|
|
|
|
|
<li><code>n</code> > 0</li>
|
|
|
|
|
<li><code>lmax</code> >= 0</li>
|
|
|
|
|
<li><code>ldl</code> >= 3</li>
|
|
|
|
|
<li><code>ldv</code> >= 5</li>
|
|
|
|
|
<li><code>X</code> is allocated with at least \(3 \times 8\) bytes</li>
|
|
|
|
|
<li><code>R</code> is allocated with at least \(3 \times 8\) bytes</li>
|
|
|
|
|
<li><code>n</code> >= <code>(lmax+1)(lmax+2)(lmax+3)/6</code></li>
|
|
|
|
|
<li><code>L</code> is allocated with at least \(3 \times n \times 4\) bytes</li>
|
|
|
|
|
<li><code>VGL</code> is allocated with at least \(5 \times n \times 8\) bytes</li>
|
|
|
|
|
<li>On output, <code>n</code> should be equal to <code>(lmax+1)(lmax+2)(lmax+3)/6</code></li>
|
|
|
|
|
<li>On output, the powers are given in the following order (l=a+b+c):
|
|
|
|
|
<ul class="org-ul">
|
|
|
|
|
<li>Increasing values of <code>l</code></li>
|
|
|
|
|
<li>Within a given value of <code>l</code>, alphabetical order of the
|
|
|
|
|
string made by a*"x" + b*"y" + c*"z" (in Python notation).
|
|
|
|
|
For example, with a=0, b=2 and c=1 the string is "yyz"</li>
|
|
|
|
|
</ul></li>
|
|
|
|
|
</ul>
|
2021-04-21 00:01:53 +02:00
|
|
|
</div>
|
|
|
|
|
</div>
|
2021-03-19 13:49:11 +01:00
|
|
|
|
2021-05-18 12:33:38 +02:00
|
|
|
<div id="outline-container-org4ec074f" class="outline-4">
|
|
|
|
|
<h4 id="org4ec074f"><span class="section-number-4">2.2.2</span> C Header</h4>
|
2021-04-21 00:01:53 +02:00
|
|
|
<div class="outline-text-4" id="text-2-2-2">
|
2021-03-19 13:49:11 +01:00
|
|
|
<div class="org-src-container">
|
2021-04-21 00:01:53 +02:00
|
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_ao_polynomial_vgl</span> (
|
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">X</span>,
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<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">R</span>,
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<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int32_t</span> <span style="color: #a0522d;">lmax</span>,
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<span style="color: #228b22;">int64_t</span>* <span style="color: #a0522d;">n</span>,
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<span style="color: #228b22;">int32_t</span>* <span style="color: #a020f0;">const</span> <span style="color: #a0522d;">L</span>,
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<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">ldl</span>,
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<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">const</span> <span style="color: #a0522d;">VGL</span>,
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<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">ldv</span> );
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2021-03-19 13:49:11 +01:00
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</pre>
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</div>
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2021-04-21 00:01:53 +02:00
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</div>
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</div>
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2021-03-19 13:49:11 +01:00
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2021-05-18 12:33:38 +02:00
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<div id="outline-container-orgd7ade7f" class="outline-4">
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<h4 id="orgd7ade7f"><span class="section-number-4">2.2.3</span> Source</h4>
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2021-04-21 00:01:53 +02:00
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<div class="outline-text-4" id="text-2-2-3">
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2021-03-19 13:49:11 +01:00
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<div class="org-src-container">
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<pre class="src src-f90"><span style="color: #228b22;">integer </span><span style="color: #a020f0;">function</span><span style="color: #a0522d;"> </span><span style="color: #0000ff;">qmckl_ao_polynomial_vgl_f</span><span style="color: #000000; background-color: #ffffff;">(context, X, R, lmax, n, L, ldl, VGL, ldv) result(info)</span>
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<span style="color: #a020f0;">use</span> <span style="color: #0000ff;">qmckl</span>
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<span style="color: #a020f0;">implicit</span> <span style="color: #228b22;">none</span>
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<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> context</span>
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<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> X(3), R(3)</span>
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<span style="color: #228b22;">integer</span> , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> lmax</span>
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<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(out) ::<span style="color: #a0522d;"> n</span>
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<span style="color: #228b22;">integer</span> , <span style="color: #a020f0;">intent</span>(out) ::<span style="color: #a0522d;"> L(ldl,(lmax+1)*(lmax+2)*(lmax+3)/6)</span>
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<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> ldl</span>
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<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">intent</span>(out) ::<span style="color: #a0522d;"> VGL(ldv,(lmax+1)*(lmax+2)*(lmax+3)/6)</span>
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<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> ldv</span>
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<span style="color: #228b22;">integer</span>*8 ::<span style="color: #a0522d;"> i,j</span>
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<span style="color: #228b22;">integer</span> ::<span style="color: #a0522d;"> a,b,c,d</span>
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<span style="color: #228b22;">real</span>*8 ::<span style="color: #a0522d;"> Y(3)</span>
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<span style="color: #228b22;">integer</span> ::<span style="color: #a0522d;"> lmax_array(3)</span>
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<span style="color: #228b22;">real</span>*8 ::<span style="color: #a0522d;"> pows(-2:lmax,3)</span>
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<span style="color: #228b22;">integer</span>, <span style="color: #a020f0;">external</span> ::<span style="color: #a0522d;"> qmckl_ao_power_f</span>
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<span style="color: #228b22;">double precision</span> ::<span style="color: #a0522d;"> xy, yz, xz</span>
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<span style="color: #228b22;">double precision</span> ::<span style="color: #a0522d;"> da, db, dc, dd</span>
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info = 0
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<span style="color: #a020f0;">if</span> (context == QMCKL_NULL_CONTEXT) <span style="color: #a020f0;">then</span>
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info = QMCKL_INVALID_CONTEXT
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<span style="color: #a020f0;">return</span>
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<span style="color: #a020f0;">endif</span>
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2021-03-19 23:17:37 +01:00
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<span style="color: #a020f0;">if</span> (lmax < 0) <span style="color: #a020f0;">then</span>
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2021-03-19 13:49:11 +01:00
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info = QMCKL_INVALID_ARG_4
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<span style="color: #a020f0;">return</span>
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<span style="color: #a020f0;">endif</span>
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<span style="color: #a020f0;">if</span> (ldl < 3) <span style="color: #a020f0;">then</span>
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info = QMCKL_INVALID_ARG_7
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<span style="color: #a020f0;">return</span>
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<span style="color: #a020f0;">endif</span>
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<span style="color: #a020f0;">if</span> (ldv < 5) <span style="color: #a020f0;">then</span>
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info = QMCKL_INVALID_ARG_9
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<span style="color: #a020f0;">return</span>
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<span style="color: #a020f0;">endif</span>
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<span style="color: #a020f0;">do</span> i=1,3
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Y(i) = X(i) - R(i)
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<span style="color: #a020f0;">end do</span>
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lmax_array(1:3) = lmax
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<span style="color: #a020f0;">if</span> (lmax == 0) <span style="color: #a020f0;">then</span>
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VGL(1,1) = 1.d0
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vgL(2:5,1) = 0.d0
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l(1:3,1) = 0
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n=1
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<span style="color: #a020f0;">else if</span> (lmax > 0) <span style="color: #a020f0;">then</span>
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pows(-2:0,1:3) = 1.d0
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<span style="color: #a020f0;">do</span> i=1,lmax
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2021-04-30 01:28:23 +02:00
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pows(i,1) = pows(i-1,1) * Y(1)
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pows(i,2) = pows(i-1,2) * Y(2)
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pows(i,3) = pows(i-1,3) * Y(3)
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2021-03-19 13:49:11 +01:00
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<span style="color: #a020f0;">end do</span>
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VGL(1:5,1:4) = 0.d0
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l (1:3,1:4) = 0
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VGL(1 ,1 ) = 1.d0
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vgl(1:5,2:4) = 0.d0
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l (1,2) = 1
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vgl(1,2) = pows(1,1)
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vgL(2,2) = 1.d0
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l (2,3) = 1
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vgl(1,3) = pows(1,2)
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vgL(3,3) = 1.d0
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l (3,4) = 1
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vgl(1,4) = pows(1,3)
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vgL(4,4) = 1.d0
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n=4
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<span style="color: #a020f0;">endif</span>
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! <span style="color: #b22222;">l>=2</span>
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dd = 2.d0
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<span style="color: #a020f0;">do</span> d=2,lmax
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da = dd
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<span style="color: #a020f0;">do</span> a=d,0,-1
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db = dd-da
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<span style="color: #a020f0;">do</span> b=d-a,0,-1
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c = d - a - b
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dc = dd - da - db
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n = n+1
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l(1,n) = a
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l(2,n) = b
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l(3,n) = c
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xy = pows(a,1) * pows(b,2)
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yz = pows(b,2) * pows(c,3)
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xz = pows(a,1) * pows(c,3)
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vgl(1,n) = xy * pows(c,3)
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xy = dc * xy
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xz = db * xz
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yz = da * yz
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vgl(2,n) = pows(a-1,1) * yz
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vgl(3,n) = pows(b-1,2) * xz
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vgl(4,n) = pows(c-1,3) * xy
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vgl(5,n) = <span style="color: #a020f0;">&</span>
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(da-1.d0) * pows(a-2,1) * yz + <span style="color: #a020f0;">&</span>
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(db-1.d0) * pows(b-2,2) * xz + <span style="color: #a020f0;">&</span>
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(dc-1.d0) * pows(c-2,3) * xy
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db = db - 1.d0
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<span style="color: #a020f0;">end do</span>
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da = da - 1.d0
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<span style="color: #a020f0;">end do</span>
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dd = dd + 1.d0
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<span style="color: #a020f0;">end do</span>
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info = QMCKL_SUCCESS
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<span style="color: #a020f0;">end function</span> <span style="color: #0000ff;">qmckl_ao_polynomial_vgl_f</span>
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</pre>
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</div>
|
2021-04-21 00:01:53 +02:00
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</div>
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</div>
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2021-05-18 12:33:38 +02:00
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<div id="outline-container-org3a56acc" class="outline-4">
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<h4 id="org3a56acc"><span class="section-number-4">2.2.4</span> C interface</h4>
|
2021-04-21 00:01:53 +02:00
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</div>
|
2021-03-19 13:49:11 +01:00
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2021-05-18 12:33:38 +02:00
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<div id="outline-container-org6227e9d" class="outline-4">
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<h4 id="org6227e9d"><span class="section-number-4">2.2.5</span> Fortran interface</h4>
|
2021-04-21 00:01:53 +02:00
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</div>
|
2021-03-19 13:49:11 +01:00
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2021-05-18 12:33:38 +02:00
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<div id="outline-container-org8c26478" class="outline-4">
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<h4 id="org8c26478"><span class="section-number-4">2.2.6</span> Test</h4>
|
2021-04-21 00:01:53 +02:00
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<div class="outline-text-4" id="text-2-2-6">
|
2021-03-19 13:49:11 +01:00
|
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<div class="org-src-container">
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<pre class="src src-f90"><span style="color: #228b22;">integer</span>(<span style="color: #008b8b;">c_int32_t</span>) <span style="color: #a020f0;">function</span> <span style="color: #0000ff;">test_qmckl_ao_polynomial_vgl</span>(context) <span style="color: #a020f0;">bind</span>(C)
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<span style="color: #a020f0;">use</span> <span style="color: #0000ff;">qmckl</span>
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<span style="color: #a020f0;">implicit</span> <span style="color: #228b22;">none</span>
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<span style="color: #228b22;">integer</span>(<span style="color: #008b8b;">c_int64_t</span>), <span style="color: #a020f0;">intent</span>(in), <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> context</span>
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<span style="color: #228b22;">integer</span> ::<span style="color: #a0522d;"> lmax, d, i</span>
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<span style="color: #228b22;">integer</span>, <span style="color: #a020f0;">allocatable</span> ::<span style="color: #a0522d;"> L(:,:)</span>
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<span style="color: #228b22;">integer</span>*8 ::<span style="color: #a0522d;"> n, ldl, ldv, j</span>
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<span style="color: #228b22;">double precision</span> ::<span style="color: #a0522d;"> X(3), R(3), Y(3)</span>
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<span style="color: #228b22;">double precision</span>, <span style="color: #a020f0;">allocatable</span> ::<span style="color: #a0522d;"> VGL(:,:)</span>
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<span style="color: #228b22;">double precision</span> ::<span style="color: #a0522d;"> w</span>
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<span style="color: #228b22;">double precision</span> ::<span style="color: #a0522d;"> epsilon</span>
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2021-04-21 00:01:53 +02:00
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epsilon = qmckl_get_numprec_epsilon(context)
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2021-03-19 13:49:11 +01:00
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X = (/ 1.1 , 2.2 , 3.3 /)
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R = (/ 0.1 , 1.2 , -2.3 /)
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Y(:) = X(:) - R(:)
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lmax = 4;
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ldl = 3;
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ldv = 100;
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d = (lmax+1)*(lmax+2)*(lmax+3)/6
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<span style="color: #a020f0;">allocate</span> (L(ldl,d), VGL(ldv,d))
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test_qmckl_ao_polynomial_vgl = <span style="color: #a020f0;">&</span>
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qmckl_ao_polynomial_vgl(context, X, R, lmax, n, L, ldl, VGL, ldv)
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<span style="color: #a020f0;">if</span> (test_qmckl_ao_polynomial_vgl /= QMCKL_SUCCESS) <span style="color: #a020f0;">return</span>
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<span style="color: #a020f0;">if</span> (n /= d) <span style="color: #a020f0;">return</span>
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<span style="color: #a020f0;">do</span> j=1,n
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test_qmckl_ao_polynomial_vgl = QMCKL_FAILURE
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<span style="color: #a020f0;">do</span> i=1,3
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<span style="color: #a020f0;">if</span> (L(i,j) < 0) <span style="color: #a020f0;">return</span>
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<span style="color: #a020f0;">end do</span>
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test_qmckl_ao_polynomial_vgl = QMCKL_FAILURE
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<span style="color: #a020f0;">if</span> (dabs(1.d0 - VGL(1,j) / (<span style="color: #a020f0;">&</span>
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Y(1)**L(1,j) * Y(2)**L(2,j) * Y(3)**L(3,j) <span style="color: #a020f0;">&</span>
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)) > epsilon ) <span style="color: #a020f0;">return</span>
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test_qmckl_ao_polynomial_vgl = QMCKL_FAILURE
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<span style="color: #a020f0;">if</span> (L(1,j) < 1) <span style="color: #a020f0;">then</span>
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<span style="color: #a020f0;">if</span> (VGL(2,j) /= 0.d0) <span style="color: #a020f0;">return</span>
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<span style="color: #a020f0;">else</span>
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<span style="color: #a020f0;">if</span> (dabs(1.d0 - VGL(2,j) / (<span style="color: #a020f0;">&</span>
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|
L(1,j) * Y(1)**(L(1,j)-1) * Y(2)**L(2,j) * Y(3)**L(3,j) <span style="color: #a020f0;">&</span>
|
|
|
|
|
)) > epsilon ) <span style="color: #a020f0;">return</span>
|
|
|
|
|
<span style="color: #a020f0;">end if</span>
|
|
|
|
|
|
|
|
|
|
test_qmckl_ao_polynomial_vgl = QMCKL_FAILURE
|
|
|
|
|
<span style="color: #a020f0;">if</span> (L(2,j) < 1) <span style="color: #a020f0;">then</span>
|
|
|
|
|
<span style="color: #a020f0;">if</span> (VGL(3,j) /= 0.d0) <span style="color: #a020f0;">return</span>
|
|
|
|
|
<span style="color: #a020f0;">else</span>
|
|
|
|
|
<span style="color: #a020f0;">if</span> (dabs(1.d0 - VGL(3,j) / (<span style="color: #a020f0;">&</span>
|
|
|
|
|
L(2,j) * Y(1)**L(1,j) * Y(2)**(L(2,j)-1) * Y(3)**L(3,j) <span style="color: #a020f0;">&</span>
|
|
|
|
|
)) > epsilon ) <span style="color: #a020f0;">return</span>
|
|
|
|
|
<span style="color: #a020f0;">end if</span>
|
|
|
|
|
|
|
|
|
|
test_qmckl_ao_polynomial_vgl = QMCKL_FAILURE
|
|
|
|
|
<span style="color: #a020f0;">if</span> (L(3,j) < 1) <span style="color: #a020f0;">then</span>
|
|
|
|
|
<span style="color: #a020f0;">if</span> (VGL(4,j) /= 0.d0) <span style="color: #a020f0;">return</span>
|
|
|
|
|
<span style="color: #a020f0;">else</span>
|
|
|
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|
<span style="color: #a020f0;">if</span> (dabs(1.d0 - VGL(4,j) / (<span style="color: #a020f0;">&</span>
|
|
|
|
|
L(3,j) * Y(1)**L(1,j) * Y(2)**L(2,j) * Y(3)**(L(3,j)-1) <span style="color: #a020f0;">&</span>
|
|
|
|
|
)) > epsilon ) <span style="color: #a020f0;">return</span>
|
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|
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|
<span style="color: #a020f0;">end if</span>
|
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|
test_qmckl_ao_polynomial_vgl = QMCKL_FAILURE
|
|
|
|
|
w = 0.d0
|
|
|
|
|
<span style="color: #a020f0;">if</span> (L(1,j) > 1) <span style="color: #a020f0;">then</span>
|
2021-04-30 01:28:23 +02:00
|
|
|
w = w + L(1,j) * (L(1,j)-1) * Y(1)**(L(1,j)-2) * Y(2)**L(2,j) * Y(3)**L(3,j)
|
2021-03-19 13:49:11 +01:00
|
|
|
<span style="color: #a020f0;">end if</span>
|
|
|
|
|
<span style="color: #a020f0;">if</span> (L(2,j) > 1) <span style="color: #a020f0;">then</span>
|
2021-04-30 01:28:23 +02:00
|
|
|
w = w + L(2,j) * (L(2,j)-1) * Y(1)**L(1,j) * Y(2)**(L(2,j)-2) * Y(3)**L(3,j)
|
2021-03-19 13:49:11 +01:00
|
|
|
<span style="color: #a020f0;">end if</span>
|
|
|
|
|
<span style="color: #a020f0;">if</span> (L(3,j) > 1) <span style="color: #a020f0;">then</span>
|
2021-04-30 01:28:23 +02:00
|
|
|
w = w + L(3,j) * (L(3,j)-1) * Y(1)**L(1,j) * Y(2)**L(2,j) * Y(3)**(L(3,j)-2)
|
2021-03-19 13:49:11 +01:00
|
|
|
<span style="color: #a020f0;">end if</span>
|
|
|
|
|
<span style="color: #a020f0;">if</span> (dabs(1.d0 - VGL(5,j) / w) > epsilon ) <span style="color: #a020f0;">return</span>
|
|
|
|
|
<span style="color: #a020f0;">end do</span>
|
|
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|
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|
|
|
|
test_qmckl_ao_polynomial_vgl = QMCKL_SUCCESS
|
|
|
|
|
|
|
|
|
|
<span style="color: #a020f0;">deallocate</span>(L,VGL)
|
|
|
|
|
<span style="color: #a020f0;">end function</span> <span style="color: #0000ff;">test_qmckl_ao_polynomial_vgl</span>
|
|
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
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|
<div class="org-src-container">
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|
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<pre class="src src-c"><span style="color: #228b22;">int</span> <span style="color: #0000ff;">test_qmckl_ao_polynomial_vgl</span>(<span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>);
|
2021-05-12 02:37:06 +02:00
|
|
|
assert(0 == test_qmckl_ao_polynomial_vgl(context));
|
2021-03-19 13:49:11 +01:00
|
|
|
</pre>
|
|
|
|
|
</div>
|
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|
</div>
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|
</div>
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</div>
|
2021-04-21 00:01:53 +02:00
|
|
|
</div>
|
2021-03-19 13:49:11 +01:00
|
|
|
|
2021-05-18 12:33:38 +02:00
|
|
|
<div id="outline-container-orgc8ad16a" class="outline-2">
|
|
|
|
|
<h2 id="orgc8ad16a"><span class="section-number-2">3</span> Radial part</h2>
|
2021-04-21 00:01:53 +02:00
|
|
|
<div class="outline-text-2" id="text-3">
|
|
|
|
|
</div>
|
2021-05-18 12:33:38 +02:00
|
|
|
<div id="outline-container-org8a338ee" class="outline-3">
|
|
|
|
|
<h3 id="org8a338ee"><span class="section-number-3">3.1</span> Gaussian basis functions</h3>
|
2021-04-21 00:01:53 +02:00
|
|
|
<div class="outline-text-3" id="text-3-1">
|
2021-03-19 13:49:11 +01:00
|
|
|
<p>
|
|
|
|
|
<code>qmckl_ao_gaussian_vgl</code> computes the values, gradients and
|
|
|
|
|
Laplacians at a given point of <code>n</code> Gaussian functions centered at
|
|
|
|
|
the same point:
|
|
|
|
|
</p>
|
|
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
\[ v_i = \exp(-a_i |X-R|^2) \]
|
|
|
|
|
\[ \nabla_x v_i = -2 a_i (X_x - R_x) v_i \]
|
|
|
|
|
\[ \nabla_y v_i = -2 a_i (X_y - R_y) v_i \]
|
|
|
|
|
\[ \nabla_z v_i = -2 a_i (X_z - R_z) v_i \]
|
|
|
|
|
\[ \Delta v_i = a_i (4 |X-R|^2 a_i - 6) v_i \]
|
|
|
|
|
</p>
|
|
|
|
|
|
|
|
|
|
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<colgroup>
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
</colgroup>
|
|
|
|
|
<tbody>
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>context</code></td>
|
|
|
|
|
<td class="org-left">input</td>
|
|
|
|
|
<td class="org-left">Global state</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>X(3)</code></td>
|
|
|
|
|
<td class="org-left">input</td>
|
|
|
|
|
<td class="org-left">Array containing the coordinates of the points</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>R(3)</code></td>
|
|
|
|
|
<td class="org-left">input</td>
|
|
|
|
|
<td class="org-left">Array containing the x,y,z coordinates of the center</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>n</code></td>
|
|
|
|
|
<td class="org-left">input</td>
|
2021-03-29 01:18:41 +02:00
|
|
|
<td class="org-left">Number of computed Gaussians</td>
|
2021-03-19 13:49:11 +01:00
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>A(n)</code></td>
|
|
|
|
|
<td class="org-left">input</td>
|
|
|
|
|
<td class="org-left">Exponents of the Gaussians</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>VGL(ldv,5)</code></td>
|
|
|
|
|
<td class="org-left">output</td>
|
|
|
|
|
<td class="org-left">Value, gradients and Laplacian of the Gaussians</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>ldv</code></td>
|
|
|
|
|
<td class="org-left">input</td>
|
|
|
|
|
<td class="org-left">Leading dimension of array <code>VGL</code></td>
|
|
|
|
|
</tr>
|
|
|
|
|
</tbody>
|
|
|
|
|
</table>
|
|
|
|
|
|
|
|
|
|
<p>
|
2021-04-21 12:45:07 +02:00
|
|
|
Requirements
|
2021-03-19 13:49:11 +01:00
|
|
|
</p>
|
|
|
|
|
|
|
|
|
|
<ul class="org-ul">
|
|
|
|
|
<li><code>context</code> is not 0</li>
|
|
|
|
|
<li><code>n</code> > 0</li>
|
|
|
|
|
<li><code>ldv</code> >= 5</li>
|
|
|
|
|
<li><code>A(i)</code> > 0 for all <code>i</code></li>
|
|
|
|
|
<li><code>X</code> is allocated with at least \(3 \times 8\) bytes</li>
|
|
|
|
|
<li><code>R</code> is allocated with at least \(3 \times 8\) bytes</li>
|
|
|
|
|
<li><code>A</code> is allocated with at least \(n \times 8\) bytes</li>
|
|
|
|
|
<li><code>VGL</code> is allocated with at least \(n \times 5 \times 8\) bytes</li>
|
|
|
|
|
</ul>
|
|
|
|
|
|
|
|
|
|
<div class="org-src-container">
|
|
|
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span>
|
|
|
|
|
<span style="color: #0000ff;">qmckl_ao_gaussian_vgl</span>(<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> *<span style="color: #a0522d;">X</span>,
|
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> *<span style="color: #a0522d;">R</span>,
|
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> *<span style="color: #a0522d;">n</span>,
|
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> *<span style="color: #a0522d;">A</span>,
|
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> *<span style="color: #a0522d;">VGL</span>,
|
|
|
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">ldv</span>);
|
|
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
|
|
|
|
|
|
<div class="org-src-container">
|
|
|
|
|
<pre class="src src-f90"><span style="color: #228b22;">integer </span><span style="color: #a020f0;">function</span><span style="color: #a0522d;"> </span><span style="color: #0000ff;">qmckl_ao_gaussian_vgl_f</span><span style="color: #000000; background-color: #ffffff;">(context, X, R, n, A, VGL, ldv) result(info)</span>
|
|
|
|
|
<span style="color: #a020f0;">use</span> <span style="color: #0000ff;">qmckl</span>
|
|
|
|
|
<span style="color: #a020f0;">implicit</span> <span style="color: #228b22;">none</span>
|
|
|
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> context</span>
|
|
|
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> X(3), R(3)</span>
|
|
|
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> n</span>
|
|
|
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> A(n)</span>
|
|
|
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">intent</span>(out) ::<span style="color: #a0522d;"> VGL(ldv,5)</span>
|
|
|
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> ldv</span>
|
|
|
|
|
|
|
|
|
|
<span style="color: #228b22;">integer</span>*8 ::<span style="color: #a0522d;"> i,j</span>
|
|
|
|
|
<span style="color: #228b22;">real</span>*8 ::<span style="color: #a0522d;"> Y(3), r2, t, u, v</span>
|
|
|
|
|
|
|
|
|
|
info = QMCKL_SUCCESS
|
|
|
|
|
|
|
|
|
|
<span style="color: #a020f0;">if</span> (context == QMCKL_NULL_CONTEXT) <span style="color: #a020f0;">then</span>
|
|
|
|
|
info = QMCKL_INVALID_CONTEXT
|
|
|
|
|
<span style="color: #a020f0;">return</span>
|
|
|
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
|
|
|
|
|
|
<span style="color: #a020f0;">if</span> (n <= 0) <span style="color: #a020f0;">then</span>
|
|
|
|
|
info = QMCKL_INVALID_ARG_4
|
|
|
|
|
<span style="color: #a020f0;">return</span>
|
|
|
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
|
|
|
|
|
|
<span style="color: #a020f0;">if</span> (ldv < n) <span style="color: #a020f0;">then</span>
|
|
|
|
|
info = QMCKL_INVALID_ARG_7
|
|
|
|
|
<span style="color: #a020f0;">return</span>
|
|
|
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<span style="color: #a020f0;">do</span> i=1,3
|
|
|
|
|
Y(i) = X(i) - R(i)
|
|
|
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
|
r2 = Y(1)*Y(1) + Y(2)*Y(2) + Y(3)*Y(3)
|
|
|
|
|
|
|
|
|
|
<span style="color: #a020f0;">do</span> i=1,n
|
|
|
|
|
VGL(i,1) = dexp(-A(i) * r2)
|
|
|
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
|
|
|
|
|
|
<span style="color: #a020f0;">do</span> i=1,n
|
|
|
|
|
VGL(i,5) = A(i) * VGL(i,1)
|
|
|
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
|
|
|
|
|
|
t = -2.d0 * ( X(1) - R(1) )
|
|
|
|
|
u = -2.d0 * ( X(2) - R(2) )
|
|
|
|
|
v = -2.d0 * ( X(3) - R(3) )
|
|
|
|
|
|
|
|
|
|
<span style="color: #a020f0;">do</span> i=1,n
|
|
|
|
|
VGL(i,2) = t * VGL(i,5)
|
|
|
|
|
VGL(i,3) = u * VGL(i,5)
|
|
|
|
|
VGL(i,4) = v * VGL(i,5)
|
|
|
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
|
|
|
|
|
|
t = 4.d0 * r2
|
|
|
|
|
<span style="color: #a020f0;">do</span> i=1,n
|
|
|
|
|
VGL(i,5) = (t * A(i) - 6.d0) * VGL(i,5)
|
|
|
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
|
|
|
|
|
|
<span style="color: #a020f0;">end function</span> <span style="color: #0000ff;">qmckl_ao_gaussian_vgl_f</span>
|
|
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
|
|
|
|
|
|
<div class="org-src-container">
|
|
|
|
|
<pre class="src src-f90"><span style="color: #228b22;">integer</span>(<span style="color: #008b8b;">c_int32_t</span>) <span style="color: #a020f0;">function</span> <span style="color: #0000ff;">test_qmckl_ao_gaussian_vgl</span>(context) <span style="color: #a020f0;">bind</span>(C)
|
|
|
|
|
<span style="color: #a020f0;">use</span> <span style="color: #0000ff;">qmckl</span>
|
|
|
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<span style="color: #a020f0;">implicit</span> <span style="color: #228b22;">none</span>
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<span style="color: #228b22;">integer</span>(<span style="color: #008b8b;">c_int64_t</span>), <span style="color: #a020f0;">intent</span>(in), <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> context</span>
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<span style="color: #228b22;">integer</span>*8 ::<span style="color: #a0522d;"> n, ldv, j, i</span>
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<span style="color: #228b22;">double precision</span> ::<span style="color: #a0522d;"> X(3), R(3), Y(3), r2</span>
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<span style="color: #228b22;">double precision</span>, <span style="color: #a020f0;">allocatable</span> ::<span style="color: #a0522d;"> VGL(:,:), A(:)</span>
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<span style="color: #228b22;">double precision</span> ::<span style="color: #a0522d;"> epsilon</span>
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2021-04-21 00:01:53 +02:00
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epsilon = qmckl_get_numprec_epsilon(context)
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2021-03-19 13:49:11 +01:00
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X = (/ 1.1 , 2.2 , 3.3 /)
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R = (/ 0.1 , 1.2 , -2.3 /)
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Y(:) = X(:) - R(:)
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r2 = Y(1)**2 + Y(2)**2 + Y(3)**2
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n = 10;
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ldv = 100;
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<span style="color: #a020f0;">allocate</span> (A(n), VGL(ldv,5))
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<span style="color: #a020f0;">do</span> i=1,n
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A(i) = 0.0013 * <span style="color: #a020f0;">dble</span>(<span style="color: #a020f0;">ishft</span>(1,i))
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<span style="color: #a020f0;">end do</span>
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test_qmckl_ao_gaussian_vgl = <span style="color: #a020f0;">&</span>
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qmckl_ao_gaussian_vgl(context, X, R, n, A, VGL, ldv)
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<span style="color: #a020f0;">if</span> (test_qmckl_ao_gaussian_vgl /= 0) <span style="color: #a020f0;">return</span>
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test_qmckl_ao_gaussian_vgl = -1
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<span style="color: #a020f0;">do</span> i=1,n
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test_qmckl_ao_gaussian_vgl = -11
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<span style="color: #a020f0;">if</span> (dabs(1.d0 - VGL(i,1) / (<span style="color: #a020f0;">&</span>
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dexp(-A(i) * r2) <span style="color: #a020f0;">&</span>
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)) > epsilon ) <span style="color: #a020f0;">return</span>
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test_qmckl_ao_gaussian_vgl = -12
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<span style="color: #a020f0;">if</span> (dabs(1.d0 - VGL(i,2) / (<span style="color: #a020f0;">&</span>
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-2.d0 * A(i) * Y(1) * dexp(-A(i) * r2) <span style="color: #a020f0;">&</span>
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)) > epsilon ) <span style="color: #a020f0;">return</span>
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test_qmckl_ao_gaussian_vgl = -13
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<span style="color: #a020f0;">if</span> (dabs(1.d0 - VGL(i,3) / (<span style="color: #a020f0;">&</span>
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-2.d0 * A(i) * Y(2) * dexp(-A(i) * r2) <span style="color: #a020f0;">&</span>
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)) > epsilon ) <span style="color: #a020f0;">return</span>
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test_qmckl_ao_gaussian_vgl = -14
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<span style="color: #a020f0;">if</span> (dabs(1.d0 - VGL(i,4) / (<span style="color: #a020f0;">&</span>
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-2.d0 * A(i) * Y(3) * dexp(-A(i) * r2) <span style="color: #a020f0;">&</span>
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)) > epsilon ) <span style="color: #a020f0;">return</span>
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test_qmckl_ao_gaussian_vgl = -15
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<span style="color: #a020f0;">if</span> (dabs(1.d0 - VGL(i,5) / (<span style="color: #a020f0;">&</span>
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A(i) * (4.d0*r2*A(i) - 6.d0) * dexp(-A(i) * r2) <span style="color: #a020f0;">&</span>
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)) > epsilon ) <span style="color: #a020f0;">return</span>
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<span style="color: #a020f0;">end do</span>
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test_qmckl_ao_gaussian_vgl = 0
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<span style="color: #a020f0;">deallocate</span>(VGL)
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<span style="color: #a020f0;">end function</span> <span style="color: #0000ff;">test_qmckl_ao_gaussian_vgl</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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2021-05-18 12:33:38 +02:00
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<div id="outline-container-org320ff80" class="outline-3">
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<h3 id="org320ff80"><span class="section-number-3">3.2</span> <span class="todo TODO">TODO</span> Slater basis functions</h3>
|
2021-04-21 00:01:53 +02:00
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</div>
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2021-05-18 12:33:38 +02:00
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<div id="outline-container-org2309ef2" class="outline-3">
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<h3 id="org2309ef2"><span class="section-number-3">3.3</span> <span class="todo TODO">TODO</span> Radial functions on a grid</h3>
|
2021-04-21 00:01:53 +02:00
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</div>
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</div>
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2021-05-18 12:33:38 +02:00
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<div id="outline-container-orgdbf8f98" class="outline-2">
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<h2 id="orgdbf8f98"><span class="section-number-2">4</span> Combining radial and polynomial parts</h2>
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2021-03-19 13:49:11 +01:00
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</div>
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</div>
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<div id="postamble" class="status">
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2021-04-30 01:35:52 +02:00
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<p class="author">Author: TREX CoE</p>
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2021-05-18 12:33:38 +02:00
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<p class="date">Created: 2021-05-18 Tue 10:33</p>
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2021-03-19 13:49:11 +01:00
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<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
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</div>
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</body>
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</html>
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