10
1
mirror of https://gitlab.com/scemama/QCaml.git synced 2024-12-23 04:43:32 +01:00
QCaml/docs/ao.html

676 lines
32 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>
<!-- 2021-01-07 Thu 09:10 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Atomic Orbitals</title>
<meta name="generator" content="Org mode" />
<meta name="author" content="Anthony 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: auto;
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; }
.equation-container {
display: table;
text-align: center;
width: 100%;
}
.equation {
vertical-align: middle;
}
.equation-label {
display: table-cell;
text-align: right;
vertical-align: middle;
}
.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" type="text/css" href="https://fniessen.github.io/org-html-themes/src/readtheorg_theme/css/htmlize.css"/>
<link rel="stylesheet" type="text/css" href="https://fniessen.github.io/org-html-themes/src/readtheorg_theme/css/readtheorg.css"/>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.3/jquery.min.js"></script>
<script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.4/js/bootstrap.min.js"></script>
<script type="text/javascript" src="https://fniessen.github.io/org-html-themes/src/lib/js/jquery.stickytableheaders.min.js"></script>
<script type="text/javascript" src="https://fniessen.github.io/org-html-themes/src/readtheorg_theme/js/readtheorg.js"></script>
<script type="text/javascript">
// @license magnet:?xt=urn:btih:e95b018ef3580986a04669f1b5879592219e2a7a&dn=public-domain.txt Public Domain
<!--/*--><![CDATA[/*><!--*/
function CodeHighlightOn(elem, id)
{
var target = document.getElementById(id);
if(null != target) {
elem.classList.add("code-highlighted");
target.classList.add("code-highlighted");
}
}
function CodeHighlightOff(elem, id)
{
var target = document.getElementById(id);
if(null != target) {
elem.classList.remove("code-highlighted");
target.classList.remove("code-highlighted");
}
}
/*]]>*///-->
// @license-end
</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="content">
<h1 class="title">Atomic Orbitals</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org2a03573">1. Gaussian basis</a>
<ul>
<li><a href="#orge0b8bc4">1.1. Type</a></li>
<li><a href="#orgcc77f3c">1.2. Access</a></li>
<li><a href="#orgcf498d9">1.3. Computation</a></li>
<li><a href="#org2055d70">1.4. Creation</a></li>
<li><a href="#orge0a9e0f">1.5. Printers</a></li>
</ul>
</li>
<li><a href="#org7d95757">2. Basis</a>
<ul>
<li><a href="#org9729ac2">2.1. Dimensions&#xa0;&#xa0;&#xa0;<span class="tag"><span class="noexports">noexports</span></span></a></li>
<li><a href="#org9a18f6b">2.2. Polymorphic types</a></li>
<li><a href="#org959a3bc">2.3. Types</a></li>
<li><a href="#org9986f87">2.4. Conversions</a></li>
<li><a href="#org825a4be">2.5. Access</a></li>
<li><a href="#org657865c">2.6. Printers</a></li>
</ul>
</li>
</ul>
</div>
</div>
<div class="org-src-container">
<pre class="src src-ocaml" id="org5676495"><span class="org-string">"Atomic basis set"</span>
</pre>
</div>
<div id="outline-container-org2a03573" class="outline-2">
<h2 id="org2a03573"><span class="section-number-2">1</span> Gaussian basis</h2>
<div class="outline-text-2" id="text-1">
<p>
Data structure for Gaussian Atomic Orbitals:
</p>
<p>
\[
\chi_i(\mathbf{r}) = P_i(\mathbf{r}) \sum_k c_k \exp\left( -\alpha_k (\mathbf{r-R_A})^2 \right)
\]
</p>
<p>
where the polynomial $P<sub>Ai</sub> and the Gaussian part are both centered on
nucleus \(A\).
</p>
</div>
<div id="outline-container-orge0b8bc4" class="outline-3">
<h3 id="orge0b8bc4"><span class="section-number-3">1.1</span> Type</h3>
<div class="outline-text-3" id="text-1-1">
<div class="org-src-container">
<pre class="src src-ocaml" id="org576c159"><span class="org-tuareg-font-lock-governing">open </span><span class="org-tuareg-font-lock-module">Common</span>
<span class="org-tuareg-font-lock-governing">open </span><span class="org-tuareg-font-lock-module">Particles</span>
<span class="org-tuareg-font-lock-governing">open </span><span class="org-tuareg-font-lock-module">Linear_algebra</span>
<span class="org-tuareg-font-lock-governing">open </span><span class="org-tuareg-font-lock-module">Gaussian_integrals</span>
<span class="org-tuareg-font-lock-governing">open </span><span class="org-tuareg-font-lock-module">Operators</span>
<span class="org-tuareg-font-lock-governing">type</span> <span class="org-type">t</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-orgcc77f3c" class="outline-3">
<h3 id="orgcc77f3c"><span class="section-number-3">1.2</span> Access</h3>
<div class="outline-text-3" id="text-1-2">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">basis</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-tuareg-font-lock-module">Gaussian.Basis.</span>t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">cartesian</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> bool
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">ee_ints</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-tuareg-font-lock-module">Eri.</span>t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">ee_lr_ints</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-tuareg-font-lock-module">Eri_long_range.</span>t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">eN_ints</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-tuareg-font-lock-module">Electron_nucleus.</span>t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">f12_ints</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-tuareg-font-lock-module">F12.</span>t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">f12_over_r12_ints</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-tuareg-font-lock-module">Screened_eri.</span>t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">kin_ints</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-tuareg-font-lock-module">Kinetic.</span>t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">multipole</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-tuareg-font-lock-module">Multipole.</span>t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">ortho</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-tuareg-font-lock-module">Orthonormalization.</span>t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">overlap</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-tuareg-font-lock-module">Overlap.</span>t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">size</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> int
</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>basis</code></td>
<td class="org-left">One-electron basis set</td>
</tr>
<tr>
<td class="org-left"><code>cartesian</code></td>
<td class="org-left">If true, use cartesian Gaussians (6d, 10f, &#x2026;)</td>
</tr>
<tr>
<td class="org-left"><code>ee_ints</code></td>
<td class="org-left">Electron-electron potential integrals</td>
</tr>
<tr>
<td class="org-left"><code>ee_lr_ints</code></td>
<td class="org-left">Electron-electron long-range potential integrals</td>
</tr>
<tr>
<td class="org-left"><code>eN_ints</code></td>
<td class="org-left">Electron-nucleus potential integrals</td>
</tr>
<tr>
<td class="org-left"><code>f12_ints</code></td>
<td class="org-left">Electron-electron potential integrals</td>
</tr>
<tr>
<td class="org-left"><code>f12_over_r12_ints</code></td>
<td class="org-left">Electron-electron potential integrals</td>
</tr>
<tr>
<td class="org-left"><code>kin_ints</code></td>
<td class="org-left">Kinetic energy integrals</td>
</tr>
<tr>
<td class="org-left"><code>multipole</code></td>
<td class="org-left">Multipole matrices</td>
</tr>
<tr>
<td class="org-left"><code>ortho</code></td>
<td class="org-left">Orthonormalization matrix of the overlap</td>
</tr>
<tr>
<td class="org-left"><code>overlap</code></td>
<td class="org-left">Overlap matrix</td>
</tr>
<tr>
<td class="org-left"><code>size</code></td>
<td class="org-left">Number of atomic orbitals</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-orgcf498d9" class="outline-3">
<h3 id="orgcf498d9"><span class="section-number-3">1.3</span> Computation</h3>
<div class="outline-text-3" id="text-1-3">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">values</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-tuareg-font-lock-module">Coordinate.</span>t <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-tuareg-font-lock-module">Gaussian.Basis.</span>t <span class="org-tuareg-font-lock-module">Vector.</span>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>values</code></td>
<td class="org-left">Returns the values of all the AOs evaluated at a given point</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-org2055d70" class="outline-3">
<h3 id="org2055d70"><span class="section-number-3">1.4</span> Creation</h3>
<div class="outline-text-3" id="text-1-4">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">make</span> <span class="org-tuareg-font-lock-operator">:</span> <span class="org-tuareg-font-lock-label">basis</span><span class="org-tuareg-font-lock-operator">:</span><span class="org-tuareg-font-lock-module">Gaussian.Basis.</span>t <span class="org-tuareg-font-lock-operator">-&gt;</span>
<span class="org-tuareg-font-lock-label">?operators</span><span class="org-tuareg-font-lock-operator">:</span><span class="org-tuareg-font-lock-module">Operator.</span>t list <span class="org-tuareg-font-lock-operator">-&gt;</span>
<span class="org-tuareg-font-lock-label">?cartesian</span><span class="org-tuareg-font-lock-operator">:</span>bool <span class="org-tuareg-font-lock-operator">-&gt;</span>
<span class="org-tuareg-font-lock-module">Nuclei.</span>t <span class="org-tuareg-font-lock-operator">-&gt;</span> t
</pre>
</div>
<p>
Creates the data structure for atomic orbitals from a Gaussian basis and the
molecular geometry <code>Nuclei.t</code>.
</p>
<p>
Defaults:
</p>
<ul class="org-ul">
<li><code>operators</code> : <code>[]</code></li>
<li><code>cartesian</code> : <code>false</code></li>
</ul>
<pre class="example" id="org9015ed3">
let b = Ao.Basis_gaussian.make ~basis nuclei ;;
val b : Ao.Basis_gaussian.t = Gaussian Basis, spherical, 15 AOs
</pre>
</div>
</div>
<div id="outline-container-orge0a9e0f" class="outline-3">
<h3 id="orge0a9e0f"><span class="section-number-3">1.5</span> Printers</h3>
<div class="outline-text-3" id="text-1-5">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">pp</span> <span class="org-tuareg-font-lock-operator">:</span> <span class="org-tuareg-font-lock-module">Format.</span>formatter <span class="org-tuareg-font-lock-operator">-&gt;</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> unit
</pre>
</div>
</div>
</div>
</div>
<div id="outline-container-org7d95757" class="outline-2">
<h2 id="org7d95757"><span class="section-number-2">2</span> Basis</h2>
<div class="outline-text-2" id="text-2">
<p>
Data structure for Atomic Orbitals.
</p>
</div>
<div id="outline-container-org9729ac2" class="outline-3">
<h3 id="org9729ac2"><span class="section-number-3">2.1</span> Dimensions&#xa0;&#xa0;&#xa0;<span class="tag"><span class="noexports">noexports</span></span></h3>
</div>
<div id="outline-container-org9a18f6b" class="outline-3">
<h3 id="org9a18f6b"><span class="section-number-3">2.2</span> Polymorphic types</h3>
<div class="outline-text-3" id="text-2-2">
<div class="org-src-container">
<pre class="src src-ocaml" id="org99746e4"><span class="org-tuareg-font-lock-governing">type</span> <span class="org-type">t</span> <span class="org-tuareg-font-lock-operator">=</span>
<span class="org-tuareg-font-lock-operator">|</span> <span class="org-tuareg-font-lock-constructor">Unknown</span>
<span class="org-tuareg-font-lock-operator">|</span> <span class="org-tuareg-font-lock-constructor">Gaussian</span> <span class="org-keyword">of</span> <span class="org-tuareg-font-lock-module">Basis_gaussian.</span>t
</pre>
</div>
</div>
</div>
<div id="outline-container-org959a3bc" class="outline-3">
<h3 id="org959a3bc"><span class="section-number-3">2.3</span> Types</h3>
<div class="outline-text-3" id="text-2-3">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">type</span> <span class="org-type">t</span>
<span class="org-tuareg-font-lock-governing">type</span> <span class="org-type">ao</span> <span class="org-tuareg-font-lock-operator">=</span> <span class="org-tuareg-font-lock-module">Ao_dim.</span>t
<span class="org-tuareg-font-lock-governing">open </span><span class="org-tuareg-font-lock-module">Common</span>
<span class="org-tuareg-font-lock-governing">open </span><span class="org-tuareg-font-lock-module">Particles</span>
<span class="org-tuareg-font-lock-governing">open </span><span class="org-tuareg-font-lock-module">Operators</span>
<span class="org-tuareg-font-lock-governing">open </span><span class="org-tuareg-font-lock-module">Linear_algebra</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-org9986f87" class="outline-3">
<h3 id="org9986f87"><span class="section-number-3">2.4</span> Conversions</h3>
<div class="outline-text-3" id="text-2-4">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">of_nuclei_and_basis_filename</span> <span class="org-tuareg-font-lock-operator">:</span>
<span class="org-tuareg-font-lock-label">?kind</span><span class="org-tuareg-font-lock-operator">:[&gt;</span> <span class="org-tuareg-font-lock-constructor">`Gaussian</span> <span class="org-tuareg-font-lock-operator">]</span> <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-tuareg-font-lock-label">?operators</span><span class="org-tuareg-font-lock-operator">:</span><span class="org-tuareg-font-lock-module">Operator.</span>t list <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-tuareg-font-lock-label">?cartesian</span><span class="org-tuareg-font-lock-operator">:</span>bool <span class="org-tuareg-font-lock-operator">-&gt;</span>
<span class="org-tuareg-font-lock-label">nuclei</span><span class="org-tuareg-font-lock-operator">:</span><span class="org-tuareg-font-lock-module">Nuclei.</span>t <span class="org-tuareg-font-lock-operator">-&gt;</span> string <span class="org-tuareg-font-lock-operator">-&gt;</span> 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>of_nuclei_and_basis_filename</code></td>
<td class="org-left">Creates the data structure for the atomic orbitals basis from a molecule <code>Nuclei.t</code> and the name of the basis-set file</td>
</tr>
</tbody>
</table>
<p>
Defaults:
</p>
<ul class="org-ul">
<li><code>kind</code> : <code>`Gaussian</code></li>
<li><code>operators</code> : <code>[]</code></li>
<li><code>cartesian</code> : <code>false</code></li>
</ul>
<pre class="example" id="orgd8b19e0">
let b = Ao.Basis.of_nuclei_and_basis_filename ~nuclei filename;;
val b : Ao.Basis.t = Gaussian Basis, spherical, 15 AOs
</pre>
</div>
</div>
<div id="outline-container-org825a4be" class="outline-3">
<h3 id="org825a4be"><span class="section-number-3">2.5</span> Access</h3>
<div class="outline-text-3" id="text-2-5">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">size</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> int
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">ao_basis</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-tuareg-font-lock-module">Basis_poly.</span>t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">overlap</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-tuareg-font-lock-operator">(</span>ao<span class="org-tuareg-font-lock-operator">,</span>ao<span class="org-tuareg-font-lock-operator">)</span> <span class="org-tuareg-font-lock-module">Matrix.</span>t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">multipole</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> string <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-tuareg-font-lock-operator">(</span>ao<span class="org-tuareg-font-lock-operator">,</span>ao<span class="org-tuareg-font-lock-operator">)</span> <span class="org-tuareg-font-lock-module">Matrix.</span>t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">ortho</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-tuareg-font-lock-operator">(</span>ao<span class="org-tuareg-font-lock-operator">,</span>'a<span class="org-tuareg-font-lock-operator">)</span> <span class="org-tuareg-font-lock-module">Matrix.</span>t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">eN_ints</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-tuareg-font-lock-operator">(</span>ao<span class="org-tuareg-font-lock-operator">,</span>ao<span class="org-tuareg-font-lock-operator">)</span> <span class="org-tuareg-font-lock-module">Matrix.</span>t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">kin_ints</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-tuareg-font-lock-operator">(</span>ao<span class="org-tuareg-font-lock-operator">,</span>ao<span class="org-tuareg-font-lock-operator">)</span> <span class="org-tuareg-font-lock-module">Matrix.</span>t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">ee_ints</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> ao <span class="org-tuareg-font-lock-module">Four_idx_storage.</span>t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">ee_lr_ints</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> ao <span class="org-tuareg-font-lock-module">Four_idx_storage.</span>t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">f12_ints</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> ao <span class="org-tuareg-font-lock-module">Four_idx_storage.</span>t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">f12_over_r12_ints</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> ao <span class="org-tuareg-font-lock-module">Four_idx_storage.</span>t
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">cartesian</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> bool
<span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">values</span> <span class="org-tuareg-font-lock-operator">:</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> <span class="org-tuareg-font-lock-module">Coordinate.</span>t <span class="org-tuareg-font-lock-operator">-&gt;</span> ao <span class="org-tuareg-font-lock-module">Vector.</span>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>size</code></td>
<td class="org-left">Number of atomic orbitals in the AO basis set</td>
</tr>
<tr>
<td class="org-left"><code>ao_basis</code></td>
<td class="org-left">One-electron basis set</td>
</tr>
<tr>
<td class="org-left"><code>overlap</code></td>
<td class="org-left">Overlap matrix</td>
</tr>
<tr>
<td class="org-left"><code>multipole</code></td>
<td class="org-left">Multipole matrices</td>
</tr>
<tr>
<td class="org-left"><code>ortho</code></td>
<td class="org-left">Orthonormalization matrix of the overlap</td>
</tr>
<tr>
<td class="org-left"><code>eN_ints</code></td>
<td class="org-left">Electron-nucleus potential integrals</td>
</tr>
<tr>
<td class="org-left"><code>kin_ints</code></td>
<td class="org-left">Kinetic energy integrals</td>
</tr>
<tr>
<td class="org-left"><code>ee_ints</code></td>
<td class="org-left">Electron-electron potential integrals</td>
</tr>
<tr>
<td class="org-left"><code>ee_lr_ints</code></td>
<td class="org-left">Electron-electron long-range potential integrals</td>
</tr>
<tr>
<td class="org-left"><code>f12_ints</code></td>
<td class="org-left">Electron-electron potential integrals</td>
</tr>
<tr>
<td class="org-left"><code>f12_over_r12_ints</code></td>
<td class="org-left">Electron-electron potential integrals</td>
</tr>
<tr>
<td class="org-left"><code>cartesian</code></td>
<td class="org-left">If true, use cartesian Gaussians (6d, 10f, &#x2026;)</td>
</tr>
<tr>
<td class="org-left"><code>values</code></td>
<td class="org-left">Values of the AOs evaluated at a given point</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-org657865c" class="outline-3">
<h3 id="org657865c"><span class="section-number-3">2.6</span> Printers</h3>
<div class="outline-text-3" id="text-2-6">
<div class="org-src-container">
<pre class="src src-ocaml"><span class="org-tuareg-font-lock-governing">val</span> <span class="org-function-name">pp</span> <span class="org-tuareg-font-lock-operator">:</span> <span class="org-tuareg-font-lock-module">Format.</span>formatter <span class="org-tuareg-font-lock-operator">-&gt;</span> t <span class="org-tuareg-font-lock-operator">-&gt;</span> unit
</pre>
</div>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Anthony Scemama</p>
<p class="date">Created: 2021-01-07 Thu 09:10</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
</body>
</html>