mirror of
https://gitlab.com/scemama/QCaml.git
synced 2024-11-07 14:43:41 +01:00
853 lines
28 KiB
HTML
853 lines
28 KiB
HTML
<?xml version="1.0" encoding="utf-8"?>
|
|
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
|
|
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
|
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
|
<head>
|
|
<!-- 2023-06-17 Sat 00:26 -->
|
|
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
|
<meta name="viewport" content="width=device-width, initial-scale=1" />
|
|
<title>Gaussian Gaussian</title>
|
|
<meta name="generator" content="Org mode" />
|
|
<meta name="author" content="scemama" />
|
|
<style type="text/css">
|
|
<!--/*--><![CDATA[/*><!--*/
|
|
.title { text-align: center;
|
|
margin-bottom: .2em; }
|
|
.subtitle { text-align: center;
|
|
font-size: medium;
|
|
font-weight: bold;
|
|
margin-top:0; }
|
|
.todo { font-family: monospace; color: red; }
|
|
.done { font-family: monospace; color: green; }
|
|
.priority { font-family: monospace; color: orange; }
|
|
.tag { background-color: #eee; font-family: monospace;
|
|
padding: 2px; font-size: 80%; font-weight: normal; }
|
|
.timestamp { color: #bebebe; }
|
|
.timestamp-kwd { color: #5f9ea0; }
|
|
.org-right { margin-left: auto; margin-right: 0px; text-align: right; }
|
|
.org-left { margin-left: 0px; margin-right: auto; text-align: left; }
|
|
.org-center { margin-left: auto; margin-right: auto; text-align: center; }
|
|
.underline { text-decoration: underline; }
|
|
#postamble p, #preamble p { font-size: 90%; margin: .2em; }
|
|
p.verse { margin-left: 3%; }
|
|
pre {
|
|
border: 1px solid #ccc;
|
|
box-shadow: 3px 3px 3px #eee;
|
|
padding: 8pt;
|
|
font-family: monospace;
|
|
overflow: auto;
|
|
margin: 1.2em;
|
|
}
|
|
pre.src {
|
|
position: relative;
|
|
overflow: visible;
|
|
padding-top: 1.2em;
|
|
}
|
|
pre.src:before {
|
|
display: none;
|
|
position: absolute;
|
|
background-color: white;
|
|
top: -10px;
|
|
right: 10px;
|
|
padding: 3px;
|
|
border: 1px solid black;
|
|
}
|
|
pre.src:hover:before { display: inline;}
|
|
/* Languages per Org manual */
|
|
pre.src-asymptote:before { content: 'Asymptote'; }
|
|
pre.src-awk:before { content: 'Awk'; }
|
|
pre.src-C:before { content: 'C'; }
|
|
/* pre.src-C++ doesn't work in CSS */
|
|
pre.src-clojure:before { content: 'Clojure'; }
|
|
pre.src-css:before { content: 'CSS'; }
|
|
pre.src-D:before { content: 'D'; }
|
|
pre.src-ditaa:before { content: 'ditaa'; }
|
|
pre.src-dot:before { content: 'Graphviz'; }
|
|
pre.src-calc:before { content: 'Emacs Calc'; }
|
|
pre.src-emacs-lisp:before { content: 'Emacs Lisp'; }
|
|
pre.src-fortran:before { content: 'Fortran'; }
|
|
pre.src-gnuplot:before { content: 'gnuplot'; }
|
|
pre.src-haskell:before { content: 'Haskell'; }
|
|
pre.src-hledger:before { content: 'hledger'; }
|
|
pre.src-java:before { content: 'Java'; }
|
|
pre.src-js:before { content: 'Javascript'; }
|
|
pre.src-latex:before { content: 'LaTeX'; }
|
|
pre.src-ledger:before { content: 'Ledger'; }
|
|
pre.src-lisp:before { content: 'Lisp'; }
|
|
pre.src-lilypond:before { content: 'Lilypond'; }
|
|
pre.src-lua:before { content: 'Lua'; }
|
|
pre.src-matlab:before { content: 'MATLAB'; }
|
|
pre.src-mscgen:before { content: 'Mscgen'; }
|
|
pre.src-ocaml:before { content: 'Objective Caml'; }
|
|
pre.src-octave:before { content: 'Octave'; }
|
|
pre.src-org:before { content: 'Org mode'; }
|
|
pre.src-oz:before { content: 'OZ'; }
|
|
pre.src-plantuml:before { content: 'Plantuml'; }
|
|
pre.src-processing:before { content: 'Processing.js'; }
|
|
pre.src-python:before { content: 'Python'; }
|
|
pre.src-R:before { content: 'R'; }
|
|
pre.src-ruby:before { content: 'Ruby'; }
|
|
pre.src-sass:before { content: 'Sass'; }
|
|
pre.src-scheme:before { content: 'Scheme'; }
|
|
pre.src-screen:before { content: 'Gnu Screen'; }
|
|
pre.src-sed:before { content: 'Sed'; }
|
|
pre.src-sh:before { content: 'shell'; }
|
|
pre.src-sql:before { content: 'SQL'; }
|
|
pre.src-sqlite:before { content: 'SQLite'; }
|
|
/* additional languages in org.el's org-babel-load-languages alist */
|
|
pre.src-forth:before { content: 'Forth'; }
|
|
pre.src-io:before { content: 'IO'; }
|
|
pre.src-J:before { content: 'J'; }
|
|
pre.src-makefile:before { content: 'Makefile'; }
|
|
pre.src-maxima:before { content: 'Maxima'; }
|
|
pre.src-perl:before { content: 'Perl'; }
|
|
pre.src-picolisp:before { content: 'Pico Lisp'; }
|
|
pre.src-scala:before { content: 'Scala'; }
|
|
pre.src-shell:before { content: 'Shell Script'; }
|
|
pre.src-ebnf2ps:before { content: 'ebfn2ps'; }
|
|
/* additional language identifiers per "defun org-babel-execute"
|
|
in ob-*.el */
|
|
pre.src-cpp:before { content: 'C++'; }
|
|
pre.src-abc:before { content: 'ABC'; }
|
|
pre.src-coq:before { content: 'Coq'; }
|
|
pre.src-groovy:before { content: 'Groovy'; }
|
|
/* additional language identifiers from org-babel-shell-names in
|
|
ob-shell.el: ob-shell is the only babel language using a lambda to put
|
|
the execution function name together. */
|
|
pre.src-bash:before { content: 'bash'; }
|
|
pre.src-csh:before { content: 'csh'; }
|
|
pre.src-ash:before { content: 'ash'; }
|
|
pre.src-dash:before { content: 'dash'; }
|
|
pre.src-ksh:before { content: 'ksh'; }
|
|
pre.src-mksh:before { content: 'mksh'; }
|
|
pre.src-posh:before { content: 'posh'; }
|
|
/* Additional Emacs modes also supported by the LaTeX listings package */
|
|
pre.src-ada:before { content: 'Ada'; }
|
|
pre.src-asm:before { content: 'Assembler'; }
|
|
pre.src-caml:before { content: 'Caml'; }
|
|
pre.src-delphi:before { content: 'Delphi'; }
|
|
pre.src-html:before { content: 'HTML'; }
|
|
pre.src-idl:before { content: 'IDL'; }
|
|
pre.src-mercury:before { content: 'Mercury'; }
|
|
pre.src-metapost:before { content: 'MetaPost'; }
|
|
pre.src-modula-2:before { content: 'Modula-2'; }
|
|
pre.src-pascal:before { content: 'Pascal'; }
|
|
pre.src-ps:before { content: 'PostScript'; }
|
|
pre.src-prolog:before { content: 'Prolog'; }
|
|
pre.src-simula:before { content: 'Simula'; }
|
|
pre.src-tcl:before { content: 'tcl'; }
|
|
pre.src-tex:before { content: 'TeX'; }
|
|
pre.src-plain-tex:before { content: 'Plain TeX'; }
|
|
pre.src-verilog:before { content: 'Verilog'; }
|
|
pre.src-vhdl:before { content: 'VHDL'; }
|
|
pre.src-xml:before { content: 'XML'; }
|
|
pre.src-nxml:before { content: 'XML'; }
|
|
/* add a generic configuration mode; LaTeX export needs an additional
|
|
(add-to-list 'org-latex-listings-langs '(conf " ")) in .emacs */
|
|
pre.src-conf:before { content: 'Configuration File'; }
|
|
|
|
table { border-collapse:collapse; }
|
|
caption.t-above { caption-side: top; }
|
|
caption.t-bottom { caption-side: bottom; }
|
|
td, th { vertical-align:top; }
|
|
th.org-right { text-align: center; }
|
|
th.org-left { text-align: center; }
|
|
th.org-center { text-align: center; }
|
|
td.org-right { text-align: right; }
|
|
td.org-left { text-align: left; }
|
|
td.org-center { text-align: center; }
|
|
dt { font-weight: bold; }
|
|
.footpara { display: inline; }
|
|
.footdef { margin-bottom: 1em; }
|
|
.figure { padding: 1em; }
|
|
.figure p { text-align: center; }
|
|
.inlinetask {
|
|
padding: 10px;
|
|
border: 2px solid gray;
|
|
margin: 10px;
|
|
background: #ffffcc;
|
|
}
|
|
#org-div-home-and-up
|
|
{ text-align: right; font-size: 70%; white-space: nowrap; }
|
|
textarea { overflow-x: auto; }
|
|
.linenr { font-size: smaller }
|
|
.code-highlighted { background-color: #ffff00; }
|
|
.org-info-js_info-navigation { border-style: none; }
|
|
#org-info-js_console-label
|
|
{ font-size: 10px; font-weight: bold; white-space: nowrap; }
|
|
.org-info-js_search-highlight
|
|
{ background-color: #ffff00; color: #000000; font-weight: bold; }
|
|
.org-svg { width: 90%; }
|
|
/*]]>*/-->
|
|
</style>
|
|
<link rel="stylesheet" title="Standard" href="qcaml.css" type="text/css" />
|
|
<link rel="stylesheet" title="Standard" href="qcaml.css" type="text/css" />
|
|
|
|
<script type="text/javascript" src="org-info.js">
|
|
/**
|
|
*
|
|
* @source: org-info.js
|
|
*
|
|
* @licstart The following is the entire license notice for the
|
|
* JavaScript code in org-info.js.
|
|
*
|
|
* Copyright (C) 2012-2018 Free Software Foundation, Inc.
|
|
*
|
|
*
|
|
* The JavaScript code in this tag is free software: you can
|
|
* redistribute it and/or modify it under the terms of the GNU
|
|
* General Public License (GNU GPL) as published by the Free Software
|
|
* Foundation, either version 3 of the License, or (at your option)
|
|
* any later version. The code is distributed WITHOUT ANY WARRANTY;
|
|
* without even the implied warranty of MERCHANTABILITY or FITNESS
|
|
* FOR A PARTICULAR PURPOSE. See the GNU GPL for more details.
|
|
*
|
|
* As additional permission under GNU GPL version 3 section 7, you
|
|
* may distribute non-source (e.g., minimized or compacted) forms of
|
|
* that code without the copy of the GNU GPL normally required by
|
|
* section 4, provided you include this license notice and a URL
|
|
* through which recipients can access the Corresponding Source.
|
|
*
|
|
* @licend The above is the entire license notice
|
|
* for the JavaScript code in org-info.js.
|
|
*
|
|
*/
|
|
</script>
|
|
|
|
<script type="text/javascript">
|
|
|
|
/*
|
|
@licstart The following is the entire license notice for the
|
|
JavaScript code in this tag.
|
|
|
|
Copyright (C) 2012-2018 Free Software Foundation, Inc.
|
|
|
|
The JavaScript code in this tag is free software: you can
|
|
redistribute it and/or modify it under the terms of the GNU
|
|
General Public License (GNU GPL) as published by the Free Software
|
|
Foundation, either version 3 of the License, or (at your option)
|
|
any later version. The code is distributed WITHOUT ANY WARRANTY;
|
|
without even the implied warranty of MERCHANTABILITY or FITNESS
|
|
FOR A PARTICULAR PURPOSE. See the GNU GPL for more details.
|
|
|
|
As additional permission under GNU GPL version 3 section 7, you
|
|
may distribute non-source (e.g., minimized or compacted) forms of
|
|
that code without the copy of the GNU GPL normally required by
|
|
section 4, provided you include this license notice and a URL
|
|
through which recipients can access the Corresponding Source.
|
|
|
|
|
|
@licend The above is the entire license notice
|
|
for the JavaScript code in this tag.
|
|
*/
|
|
|
|
<!--/*--><![CDATA[/*><!--*/
|
|
org_html_manager.set("TOC_DEPTH", "4");
|
|
org_html_manager.set("LINK_HOME", "index.html");
|
|
org_html_manager.set("LINK_UP", "");
|
|
org_html_manager.set("LOCAL_TOC", "1");
|
|
org_html_manager.set("VIEW_BUTTONS", "0");
|
|
org_html_manager.set("MOUSE_HINT", "underline");
|
|
org_html_manager.set("FIXED_TOC", "0");
|
|
org_html_manager.set("TOC", "1");
|
|
org_html_manager.set("VIEW", "info");
|
|
org_html_manager.setup(); // activate after the parameters are set
|
|
/*]]>*///-->
|
|
</script>
|
|
<script type="text/javascript">
|
|
/*
|
|
@licstart The following is the entire license notice for the
|
|
JavaScript code in this tag.
|
|
|
|
Copyright (C) 2012-2018 Free Software Foundation, Inc.
|
|
|
|
The JavaScript code in this tag is free software: you can
|
|
redistribute it and/or modify it under the terms of the GNU
|
|
General Public License (GNU GPL) as published by the Free Software
|
|
Foundation, either version 3 of the License, or (at your option)
|
|
any later version. The code is distributed WITHOUT ANY WARRANTY;
|
|
without even the implied warranty of MERCHANTABILITY or FITNESS
|
|
FOR A PARTICULAR PURPOSE. See the GNU GPL for more details.
|
|
|
|
As additional permission under GNU GPL version 3 section 7, you
|
|
may distribute non-source (e.g., minimized or compacted) forms of
|
|
that code without the copy of the GNU GPL normally required by
|
|
section 4, provided you include this license notice and a URL
|
|
through which recipients can access the Corresponding Source.
|
|
|
|
|
|
@licend The above is the entire license notice
|
|
for the JavaScript code in this tag.
|
|
*/
|
|
<!--/*--><![CDATA[/*><!--*/
|
|
function CodeHighlightOn(elem, id)
|
|
{
|
|
var target = document.getElementById(id);
|
|
if(null != target) {
|
|
elem.cacheClassElem = elem.className;
|
|
elem.cacheClassTarget = target.className;
|
|
target.className = "code-highlighted";
|
|
elem.className = "code-highlighted";
|
|
}
|
|
}
|
|
function CodeHighlightOff(elem, id)
|
|
{
|
|
var target = document.getElementById(id);
|
|
if(elem.cacheClassElem)
|
|
elem.className = elem.cacheClassElem;
|
|
if(elem.cacheClassTarget)
|
|
target.className = elem.cacheClassTarget;
|
|
}
|
|
/*]]>*///-->
|
|
</script>
|
|
<script type="text/x-mathjax-config">
|
|
MathJax.Hub.Config({
|
|
displayAlign: "center",
|
|
displayIndent: "0em",
|
|
|
|
"HTML-CSS": { scale: 100,
|
|
linebreaks: { automatic: "false" },
|
|
webFont: "TeX"
|
|
},
|
|
SVG: {scale: 100,
|
|
linebreaks: { automatic: "false" },
|
|
font: "TeX"},
|
|
NativeMML: {scale: 100},
|
|
TeX: { equationNumbers: {autoNumber: "AMS"},
|
|
MultLineWidth: "85%",
|
|
TagSide: "right",
|
|
TagIndent: ".8em"
|
|
}
|
|
});
|
|
</script>
|
|
<script type="text/javascript"
|
|
src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS_HTML"></script>
|
|
</head>
|
|
<body>
|
|
<div id="org-div-home-and-up">
|
|
<a accesskey="h" href=""> UP </a>
|
|
|
|
|
<a accesskey="H" href="index.html"> HOME </a>
|
|
</div><div id="content">
|
|
<h1 class="title">Gaussian Gaussian</h1>
|
|
<div id="table-of-contents">
|
|
<h2>Table of Contents</h2>
|
|
<div id="text-table-of-contents">
|
|
<ul>
|
|
<li><a href="#org75b028d">1. Summary</a></li>
|
|
<li><a href="#org0603510">2. Atomic shell</a>
|
|
<ul>
|
|
<li><a href="#orgdf52365">2.1. Type</a></li>
|
|
<li><a href="#orgc6225f5">2.2. Access</a></li>
|
|
<li><a href="#org6b8dfa1">2.3. Creation</a></li>
|
|
<li><a href="#orga9e61b8">2.4. Printers</a></li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#orgd615a55">3. Atomic shell pair couple</a>
|
|
<ul>
|
|
<li><a href="#orgda0a937">3.1. Type</a></li>
|
|
<li><a href="#org4991d87">3.2. Access</a></li>
|
|
<li><a href="#orgb976b3f">3.3. Creation</a></li>
|
|
<li><a href="#orgc9cfb8d">3.4. Printers</a></li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#orgc9b4c06">4. Atomic shell pair</a>
|
|
<ul>
|
|
<li><a href="#org2cc8ae6">4.1. Type</a></li>
|
|
<li><a href="#org758a97d">4.2. Access</a></li>
|
|
<li><a href="#orgf49ab7d">4.3. Creation</a></li>
|
|
<li><a href="#org3b5b666">4.4. Printers</a></li>
|
|
</ul>
|
|
</li>
|
|
<li><a href="#orgfc88a58">5. Summary</a></li>
|
|
</ul>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org75b028d" class="outline-2">
|
|
<h2 id="org75b028d"><span class="section-number-2">1</span> Summary</h2>
|
|
</div>
|
|
|
|
<div id="outline-container-org0603510" class="outline-2">
|
|
<h2 id="org0603510"><span class="section-number-2">2</span> Atomic shell</h2>
|
|
<div class="outline-text-2" id="text-2">
|
|
<p>
|
|
Set of contracted Gaussians differing only by the powers of \(x\), \(y\) and \(z\), with a
|
|
constant <code>Angular_momentum.t</code>, all centered on the same point.
|
|
</p>
|
|
|
|
<p>
|
|
In other words, it is the set of all contracted shells sharing the same center.
|
|
</p>
|
|
|
|
\begin{align*}
|
|
\chi_{n_x,n_y,n_z}(r) & = f(n_x,n_y,n_z) \sum_{j=1}^{n} \sum_{i=1}^{m} \mathcal{N}_{ij}\, d_{ij}\, g_{ij\,n_x,n_y,n_z}(r) \\
|
|
& = (x-X_A)^{n_x} (y-Y_A)^{n_y} (z-Z_A)^{n_z} f(n_x,n_y,n_z) \sum_{j=1}^{n} \sum_{i=1}^{m} \mathcal{N}_{ij}\, d_{ij}\, \exp \left( -\alpha_{ij} |r-R_A|^2 \right)
|
|
\end{align*}
|
|
|
|
<p>
|
|
where:
|
|
</p>
|
|
|
|
<ul class="org-ul">
|
|
<li>\(g_{ij\,n_x,n_y,n_z}(r)\) is the $i$-th <code>PrimitiveShell.t</code> of the $j$-th <code>Contracted_shell.t</code></li>
|
|
<li>\(n_x + n_y + n_z = l\), the total angular momentum</li>
|
|
<li>\(\alpha_{ij}\) are the exponents (tabulated) of the $j$-th <code>Contracted_shell.t</code></li>
|
|
<li>\(d_{ij}\) are the contraction coefficients of the $j$-th <code>Contracted_shell.t</code></li>
|
|
<li>\(\mathcal{N}_{ij}\) is the normalization coefficient of the $i$-th primitive shell
|
|
(<code>PrimitiveShell.norm_coef</code>) of the $j$-th <code>Contracted_shell.t</code></li>
|
|
<li>\(f(n_x,n_y,n_z)\) is a scaling factor adjusting the normalization coefficient for the
|
|
particular powers of \(x,y,z\) (<code>PrimitiveShell.norm_coef_scale</code>)</li>
|
|
</ul>
|
|
</div>
|
|
|
|
|
|
<div id="outline-container-orgdf52365" class="outline-3">
|
|
<h3 id="orgdf52365"><span class="section-number-3">2.1</span> Type</h3>
|
|
<div class="outline-text-3" id="text-2-1">
|
|
<div class="org-src-container">
|
|
<pre class="src src-ocaml">type t
|
|
|
|
open Common
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc6225f5" class="outline-3">
|
|
<h3 id="orgc6225f5"><span class="section-number-3">2.2</span> Access</h3>
|
|
<div class="outline-text-3" id="text-2-2">
|
|
<div class="org-src-container">
|
|
<pre class="src src-ocaml">val ang_mom : t -> Angular_momentum.t
|
|
val center : t -> Coordinate.t
|
|
val coefficients : t -> float array array
|
|
val contracted_shells : t -> Contracted_shell.t array
|
|
val exponents : t -> float array array
|
|
val index : t -> int
|
|
val normalizations : t -> float array array
|
|
val norm_scales : t -> float array
|
|
val size_of_shell : t -> int
|
|
val size : t -> int
|
|
</pre>
|
|
</div>
|
|
|
|
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
|
|
|
|
<colgroup>
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
</colgroup>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-left"><code>ang_mom</code></td>
|
|
<td class="org-left">Total angular momentum : \(l = n_x + n_y + n_z\).</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>center</code></td>
|
|
<td class="org-left">Coordinate of the center \(\mathbf{A} = (X_A,Y_A,Z_A)\).</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>coefficients</code></td>
|
|
<td class="org-left">Array of contraction coefficients \(d_{ij}\). The first index is the index of the contracted function, and the second index is the index of the primitive.</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>contracted_shells:</code></td>
|
|
<td class="org-left">Array of contracted gaussians</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>exponents</code></td>
|
|
<td class="org-left">Array of exponents \(\alpha_{ij}\). The first index is the index of the contracted function, and the second index is the index of the primitive.</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>index</code></td>
|
|
<td class="org-left">Index in the basis set, represented as an array of contracted shells.</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>normalizations</code></td>
|
|
<td class="org-left">Normalization coefficients \(\mathcal{N}_{ij}\). The first index is the index of the contracted function, and the second index is the index of the primitive.</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>norm_scales</code></td>
|
|
<td class="org-left">Scaling factors \(f(n_x,n_y,n_z)\), given in the same order as <code>Angular_momentum.zkey_array ang_mom</code>.</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>size</code></td>
|
|
<td class="org-left">Number of contracted functions, \(n\) in the definition.</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>size_of_shell</code></td>
|
|
<td class="org-left">Number of contracted functions in the shell: length of <code>norm_coef_scale</code>.</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
|
|
<pre class="example">
|
|
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org6b8dfa1" class="outline-3">
|
|
<h3 id="org6b8dfa1"><span class="section-number-3">2.3</span> Creation</h3>
|
|
<div class="outline-text-3" id="text-2-3">
|
|
<div class="org-src-container">
|
|
<pre class="src src-ocaml">val make : ?index:int -> Contracted_shell.t array -> t
|
|
|
|
val with_index : t -> int -> t
|
|
</pre>
|
|
</div>
|
|
|
|
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
|
|
|
|
<colgroup>
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
</colgroup>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-left"><code>make</code></td>
|
|
<td class="org-left">Creates a contracted shell from a list of coefficients and primitives.</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>with_index</code></td>
|
|
<td class="org-left">Returns a copy of the contracted shell with a modified index.</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orga9e61b8" class="outline-3">
|
|
<h3 id="orga9e61b8"><span class="section-number-3">2.4</span> Printers</h3>
|
|
<div class="outline-text-3" id="text-2-4">
|
|
<div class="org-src-container">
|
|
<pre class="src src-ocaml">val pp : Format.formatter -> t -> unit
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd615a55" class="outline-2">
|
|
<h2 id="orgd615a55"><span class="section-number-2">3</span> Atomic shell pair couple</h2>
|
|
<div class="outline-text-2" id="text-3">
|
|
<p>
|
|
An atomic shell pair couple is the cartesian product between two sets of functions, one
|
|
set over electron one and one set over electron two. Both sets are atomic shell
|
|
pairs.
|
|
</p>
|
|
|
|
<p>
|
|
These are usually called <i>shell quartets</i> in the literature, but we prefer to use
|
|
<i>pair</i> for two functions with the same electron, and <i>couple</i> for two functions
|
|
acting on different electrons, since they will be coupled by a two-electron operator.
|
|
</p>
|
|
</div>
|
|
|
|
|
|
<div id="outline-container-orgda0a937" class="outline-3">
|
|
<h3 id="orgda0a937"><span class="section-number-3">3.1</span> Type</h3>
|
|
<div class="outline-text-3" id="text-3-1">
|
|
<div class="org-src-container">
|
|
<pre class="src src-ocaml">type t
|
|
|
|
open Common
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org4991d87" class="outline-3">
|
|
<h3 id="org4991d87"><span class="section-number-3">3.2</span> Access</h3>
|
|
<div class="outline-text-3" id="text-3-2">
|
|
<div class="org-src-container">
|
|
<pre class="src src-ocaml">val ang_mom : t -> Angular_momentum.t
|
|
val atomic_shell_a : t -> Atomic_shell.t
|
|
val atomic_shell_b : t -> Atomic_shell.t
|
|
val atomic_shell_c : t -> Atomic_shell.t
|
|
val atomic_shell_d : t -> Atomic_shell.t
|
|
val atomic_shell_pair_p : t -> Atomic_shell_pair.t
|
|
val atomic_shell_pair_q : t -> Atomic_shell_pair.t
|
|
val contracted_shell_pair_couples : t -> Contracted_shell_pair_couple.t list
|
|
val monocentric : t -> bool
|
|
val norm_scales : t -> float array
|
|
val zkey_array : t -> Zkey.t array
|
|
</pre>
|
|
</div>
|
|
|
|
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
|
|
|
|
<colgroup>
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
</colgroup>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-left"><code>ang_mom</code></td>
|
|
<td class="org-left">Total angular momentum of the shell pair couple: sum of the angular momenta of all the shells.</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>atomic_shell_a</code></td>
|
|
<td class="org-left">Returns the first atomic shell of the first shell pair.</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>atomic_shell_b</code></td>
|
|
<td class="org-left">Returns the second atomic shell of the first shell pair.</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>atomic_shell_c</code></td>
|
|
<td class="org-left">Returns the first atomic shell of the second shell pair.</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>atomic_shell_d</code></td>
|
|
<td class="org-left">Returns the second atomic shell of the second shell pair.</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>atomic_shell_pair_p</code></td>
|
|
<td class="org-left">Returns the first atomic shell pair that was used to build the shell pair.</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>atomic_shell_pair_q</code></td>
|
|
<td class="org-left">Returns the second atomic shell pair that was used to build the shell pair.</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>contracted_shell_pair_couples</code></td>
|
|
<td class="org-left">Returns the list of significant contracted shell pair couples.</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>monocentric</code></td>
|
|
<td class="org-left">True if all four atomic shells have the same center.</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>norm_scales</code></td>
|
|
<td class="org-left">Scaling factors of normalization coefficients inside the shell. The ordering is the same as <code>zkey_array</code>.</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>zkey_array</code></td>
|
|
<td class="org-left">Returns the array of <code>Zkey.t</code> relative to the four shells of the shell pair couple.</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgb976b3f" class="outline-3">
|
|
<h3 id="orgb976b3f"><span class="section-number-3">3.3</span> Creation</h3>
|
|
<div class="outline-text-3" id="text-3-3">
|
|
<div class="org-src-container">
|
|
<pre class="src src-ocaml">val make : ?cutoff:float -> Atomic_shell_pair.t -> Atomic_shell_pair.t -> t option
|
|
</pre>
|
|
</div>
|
|
<p>
|
|
Default cutoff is \(\epsilon\).
|
|
</p>
|
|
|
|
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
|
|
|
|
<colgroup>
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
</colgroup>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-left"><code>make</code></td>
|
|
<td class="org-left">Creates an atomic shell pair couple using two atomic shell pairs.</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
|
|
<pre class="example">
|
|
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc9cfb8d" class="outline-3">
|
|
<h3 id="orgc9cfb8d"><span class="section-number-3">3.4</span> Printers</h3>
|
|
<div class="outline-text-3" id="text-3-4">
|
|
<div class="org-src-container">
|
|
<pre class="src src-ocaml">val pp : Format.formatter -> t -> unit
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc9b4c06" class="outline-2">
|
|
<h2 id="orgc9b4c06"><span class="section-number-2">4</span> Atomic shell pair</h2>
|
|
<div class="outline-text-2" id="text-4">
|
|
<p>
|
|
Data structure to represent pairs of atomic shells. The products of
|
|
functions in the shell pair are one-electron functions.
|
|
</p>
|
|
|
|
<p>
|
|
An atomic shell pair is an array of pairs of contracted shells.
|
|
</p>
|
|
</div>
|
|
|
|
<div id="outline-container-org2cc8ae6" class="outline-3">
|
|
<h3 id="org2cc8ae6"><span class="section-number-3">4.1</span> Type</h3>
|
|
<div class="outline-text-3" id="text-4-1">
|
|
<div class="org-src-container">
|
|
<pre class="src src-ocaml">type t
|
|
|
|
open Common
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org758a97d" class="outline-3">
|
|
<h3 id="org758a97d"><span class="section-number-3">4.2</span> Access</h3>
|
|
<div class="outline-text-3" id="text-4-2">
|
|
<div class="org-src-container">
|
|
<pre class="src src-ocaml">val atomic_shell_a : t -> Atomic_shell.t
|
|
val atomic_shell_b : t -> Atomic_shell.t
|
|
val contracted_shell_pairs : t -> Contracted_shell_pair.t list
|
|
val ang_mom : t -> Angular_momentum.t
|
|
val monocentric : t -> bool
|
|
val norm_scales : t -> float array
|
|
val a_minus_b : t -> Coordinate.t
|
|
val a_minus_b_sq : t -> float
|
|
</pre>
|
|
</div>
|
|
|
|
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
|
|
|
|
<colgroup>
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
</colgroup>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-left"><code>atomic_shell_a</code></td>
|
|
<td class="org-left">Returns the first <code>Atomic_shell.t</code> which was used to build the atomic shell pair.</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>atomic_shell_b</code></td>
|
|
<td class="org-left">Returns the second <code>Atomic_shell.t</code> which was used to build the atomic shell pair.</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>contracted_shell_pairs</code></td>
|
|
<td class="org-left">Returns an array of <code>ContractedShellPair.t</code>, containing all the pairs of contracted functions used to build the atomic shell pair.</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>norm_scales</code></td>
|
|
<td class="org-left">norm<sub>coef</sub>.(i) / norm<sub>coef</sub>.(0)</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>ang_mom</code></td>
|
|
<td class="org-left">Total angular Momentum</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>monocentric</code></td>
|
|
<td class="org-left">If true, the two atomic shells have the same center.</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>a_minus_b</code></td>
|
|
<td class="org-left">Returns \(A-B\)</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>a_minus_b_sq</code></td>
|
|
<td class="org-left">Returns \(\vert A-B \vert^2\)</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgf49ab7d" class="outline-3">
|
|
<h3 id="orgf49ab7d"><span class="section-number-3">4.3</span> Creation</h3>
|
|
<div class="outline-text-3" id="text-4-3">
|
|
<div class="org-src-container">
|
|
<pre class="src src-ocaml">val make : ?cutoff:float -> Atomic_shell.t -> Atomic_shell.t -> t option
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Creates an atomic shell pair from two atomic shells.
|
|
</p>
|
|
|
|
<p>
|
|
The contracted shell pairs contains the only pairs of primitives for which
|
|
the norm is greater than <code>cutoff</code>.
|
|
</p>
|
|
|
|
<p>
|
|
If all the contracted shell pairs are not significant, the function returns
|
|
<code>None</code>.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-ocaml">val of_atomic_shell_array : ?cutoff:float -> Atomic_shell.t array -> t option array array
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Creates all possible atomic shell pairs from an array of atomic shells.
|
|
If an atomic shell pair is not significant, sets the value to <code>None</code>.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org3b5b666" class="outline-3">
|
|
<h3 id="org3b5b666"><span class="section-number-3">4.4</span> Printers</h3>
|
|
<div class="outline-text-3" id="text-4-4">
|
|
<div class="org-src-container">
|
|
<pre class="src src-ocaml">val pp : Format.formatter -> t -> unit
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgfc88a58" class="outline-2">
|
|
<h2 id="orgfc88a58"><span class="section-number-2">5</span> Summary</h2>
|
|
</div>
|
|
</div>
|
|
<div id="postamble" class="status">
|
|
<p class="author">Author: scemama</p>
|
|
<p class="date">Created: 2023-06-17 Sat 00:26</p>
|
|
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
|
</div>
|
|
</body>
|
|
</html>
|