2021-06-18 12:05:06 +02:00
|
|
|
<?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>
|
2021-06-22 22:32:47 +02:00
|
|
|
<!-- 2021-06-22 Tue 20:32 -->
|
2021-06-18 12:05:06 +02:00
|
|
|
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
|
|
|
|
<meta name="viewport" content="width=device-width, initial-scale=1" />
|
|
|
|
|
<title>TREX Configuration file</title>
|
|
|
|
|
<meta name="generator" content="Org mode" />
|
2021-06-18 12:11:36 +02:00
|
|
|
<meta name="author" content="TREX-CoE" />
|
2021-06-18 12:05:06 +02:00
|
|
|
<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>
|
2021-06-18 12:11:36 +02:00
|
|
|
<link rel="stylesheet" title="Standard" href="trexio.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) 2012-2019 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) 2012-2019 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>
|
2021-06-18 12:05:06 +02:00
|
|
|
<script type="text/javascript">
|
|
|
|
|
/*
|
|
|
|
|
@licstart The following is the entire license notice for the
|
|
|
|
|
JavaScript code in this tag.
|
|
|
|
|
|
|
|
|
|
Copyright (C) 2012-2019 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>
|
2021-06-18 12:11:36 +02:00
|
|
|
<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">
|
2021-06-18 12:05:06 +02:00
|
|
|
<h1 class="title">TREX Configuration file</h1>
|
|
|
|
|
<div id="table-of-contents">
|
|
|
|
|
<h2>Table of Contents</h2>
|
|
|
|
|
<div id="text-table-of-contents">
|
|
|
|
|
<ul>
|
2021-06-22 22:32:47 +02:00
|
|
|
<li><a href="#orgc08a996">1. Metadata</a></li>
|
|
|
|
|
<li><a href="#orgfc6802e">2. Electron</a></li>
|
|
|
|
|
<li><a href="#org89ad5cd">3. Nucleus</a></li>
|
|
|
|
|
<li><a href="#orgb4ac0b7">4. <span class="todo TODO">TODO</span> Effective core potentials</a></li>
|
|
|
|
|
<li><a href="#org86016e6">5. Basis set</a></li>
|
|
|
|
|
<li><a href="#org96b16b7">6. Atomic orbitals</a>
|
2021-06-18 12:05:06 +02:00
|
|
|
<ul>
|
|
|
|
|
<li><a href="#ao_one_e">6.1. One-electron integrals</a></li>
|
|
|
|
|
<li><a href="#ao_two_e">6.2. Two-electron integrals</a></li>
|
|
|
|
|
</ul>
|
|
|
|
|
</li>
|
2021-06-22 22:32:47 +02:00
|
|
|
<li><a href="#org2f3ed38">7. Molecular orbitals</a>
|
2021-06-18 12:05:06 +02:00
|
|
|
<ul>
|
2021-06-22 22:32:47 +02:00
|
|
|
<li><a href="#org72bc6af">7.1. One-electron integrals</a></li>
|
|
|
|
|
<li><a href="#orgd1fde5a">7.2. Two-electron integrals</a></li>
|
2021-06-18 12:05:06 +02:00
|
|
|
</ul>
|
|
|
|
|
</li>
|
2021-06-22 22:32:47 +02:00
|
|
|
<li><a href="#org22ac68f">8. <span class="todo TODO">TODO</span> Slater determinants</a></li>
|
|
|
|
|
<li><a href="#org177ee41">9. <span class="todo TODO">TODO</span> Reduced density matrices</a></li>
|
|
|
|
|
<li><a href="#orgbbdb680">10. Appendix</a>
|
2021-06-18 12:05:06 +02:00
|
|
|
<ul>
|
2021-06-22 22:32:47 +02:00
|
|
|
<li><a href="#orgca98b95">10.1. Python script from table to json</a></li>
|
2021-06-18 12:05:06 +02:00
|
|
|
</ul>
|
|
|
|
|
</li>
|
|
|
|
|
</ul>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
<p>
|
|
|
|
|
All the quantities are saved in atomic units.
|
|
|
|
|
The dimensions of the arrays in the tables below are given in
|
|
|
|
|
column-major order (as in Fortran), and the ordering of the dimensions
|
|
|
|
|
is reversed in the produces JSON configuration file as the library is
|
|
|
|
|
written in C.
|
|
|
|
|
</p>
|
|
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
In Fortran, the arrays are 1-based and in most other languages the
|
|
|
|
|
arrays are 0-base. Hence, we introduce the <code>index</code> type which is an
|
|
|
|
|
1-based <code>int</code> in the Fortran interface and 0-based otherwise.
|
|
|
|
|
</p>
|
|
|
|
|
|
|
|
|
|
<div class="org-src-container">
|
|
|
|
|
<pre class="src src-python">{
|
|
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
|
|
2021-06-22 22:32:47 +02:00
|
|
|
<div id="outline-container-orgc08a996" class="outline-2">
|
|
|
|
|
<h2 id="orgc08a996"><span class="section-number-2">1</span> Metadata</h2>
|
2021-06-18 12:05:06 +02:00
|
|
|
<div class="outline-text-2" id="text-1">
|
|
|
|
|
<p>
|
|
|
|
|
As we expect our files to be archived in open-data repositories, we
|
|
|
|
|
need to give the possibility to the users to store some metadata
|
|
|
|
|
inside the files. We propose to store the list of names of the codes
|
|
|
|
|
which have participated to the creation of the file, a list of
|
|
|
|
|
authors of the file, and a textual description.
|
|
|
|
|
</p>
|
|
|
|
|
|
2021-06-22 22:32:47 +02:00
|
|
|
<table id="orgee436b4" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
2021-06-18 12:05:06 +02:00
|
|
|
|
|
|
|
|
|
|
|
|
|
<colgroup>
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
</colgroup>
|
|
|
|
|
<tbody>
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>code_num</code></td>
|
|
|
|
|
<td class="org-left"><code>int</code></td>
|
|
|
|
|
<td class="org-left"> </td>
|
|
|
|
|
<td class="org-left">Number of codes used to produce the file</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>code</code></td>
|
|
|
|
|
<td class="org-left"><code>str</code></td>
|
|
|
|
|
<td class="org-left"><code>(metadata.code_num)</code></td>
|
|
|
|
|
<td class="org-left">Names of the codes used</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>author_num</code></td>
|
|
|
|
|
<td class="org-left"><code>int</code></td>
|
|
|
|
|
<td class="org-left"> </td>
|
|
|
|
|
<td class="org-left">Number of authors of the file</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>author</code></td>
|
|
|
|
|
<td class="org-left"><code>str</code></td>
|
|
|
|
|
<td class="org-left"><code>(metadata.author_num)</code></td>
|
|
|
|
|
<td class="org-left">Names of the authors of the file</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>description</code></td>
|
|
|
|
|
<td class="org-left"><code>str</code></td>
|
|
|
|
|
<td class="org-left"> </td>
|
|
|
|
|
<td class="org-left">Text describing the content of file</td>
|
|
|
|
|
</tr>
|
|
|
|
|
</tbody>
|
|
|
|
|
</table>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
|
2021-06-22 22:32:47 +02:00
|
|
|
<div id="outline-container-orgfc6802e" class="outline-2">
|
|
|
|
|
<h2 id="orgfc6802e"><span class="section-number-2">2</span> Electron</h2>
|
2021-06-18 12:05:06 +02:00
|
|
|
<div class="outline-text-2" id="text-2">
|
|
|
|
|
<p>
|
|
|
|
|
We consider wave functions expressed in the spin-free formalism, where
|
|
|
|
|
the number of ↑ and ↓ electrons is fixed.
|
|
|
|
|
</p>
|
|
|
|
|
|
2021-06-22 22:32:47 +02:00
|
|
|
<table id="orgee69920" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
2021-06-18 12:05:06 +02:00
|
|
|
|
|
|
|
|
|
|
|
|
|
<colgroup>
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
</colgroup>
|
|
|
|
|
<tbody>
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>up_num</code></td>
|
|
|
|
|
<td class="org-left"><code>int</code></td>
|
|
|
|
|
<td class="org-left"> </td>
|
|
|
|
|
<td class="org-left">Number of ↑-spin electrons</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>dn_num</code></td>
|
|
|
|
|
<td class="org-left"><code>int</code></td>
|
|
|
|
|
<td class="org-left"> </td>
|
|
|
|
|
<td class="org-left">Number of ↓-spin electrons</td>
|
|
|
|
|
</tr>
|
|
|
|
|
</tbody>
|
|
|
|
|
</table>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
|
2021-06-22 22:32:47 +02:00
|
|
|
<div id="outline-container-org89ad5cd" class="outline-2">
|
|
|
|
|
<h2 id="org89ad5cd"><span class="section-number-2">3</span> Nucleus</h2>
|
2021-06-18 12:05:06 +02:00
|
|
|
<div class="outline-text-2" id="text-3">
|
|
|
|
|
<p>
|
|
|
|
|
The nuclei are considered as fixed point charges. Coordinates are
|
|
|
|
|
given in Cartesian \((x,y,z)\) format.
|
|
|
|
|
</p>
|
|
|
|
|
|
2021-06-22 22:32:47 +02:00
|
|
|
<table id="org9732f69" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
2021-06-18 12:05:06 +02:00
|
|
|
|
|
|
|
|
|
|
|
|
|
<colgroup>
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
</colgroup>
|
|
|
|
|
<tbody>
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>num</code></td>
|
|
|
|
|
<td class="org-left"><code>int</code></td>
|
|
|
|
|
<td class="org-left"> </td>
|
|
|
|
|
<td class="org-left">Number of nuclei</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>charge</code></td>
|
|
|
|
|
<td class="org-left"><code>float</code></td>
|
|
|
|
|
<td class="org-left"><code>(nucleus.num)</code></td>
|
|
|
|
|
<td class="org-left">Charges of the nuclei</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>coord</code></td>
|
|
|
|
|
<td class="org-left"><code>float</code></td>
|
|
|
|
|
<td class="org-left"><code>(3,nucleus.num)</code></td>
|
|
|
|
|
<td class="org-left">Coordinates of the atoms</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>label</code></td>
|
|
|
|
|
<td class="org-left"><code>str</code></td>
|
|
|
|
|
<td class="org-left"><code>(nucleus.num)</code></td>
|
|
|
|
|
<td class="org-left">Atom labels</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>point_group</code></td>
|
|
|
|
|
<td class="org-left"><code>str</code></td>
|
|
|
|
|
<td class="org-left"> </td>
|
|
|
|
|
<td class="org-left">Symmetry point group</td>
|
|
|
|
|
</tr>
|
|
|
|
|
</tbody>
|
|
|
|
|
</table>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
|
2021-06-22 22:32:47 +02:00
|
|
|
<div id="outline-container-orgb4ac0b7" class="outline-2">
|
|
|
|
|
<h2 id="orgb4ac0b7"><span class="section-number-2">4</span> <span class="todo TODO">TODO</span> Effective core potentials</h2>
|
2021-06-18 12:05:06 +02:00
|
|
|
<div class="outline-text-2" id="text-4">
|
|
|
|
|
<p>
|
|
|
|
|
An effective core potential (ECP) \(V_A^{\text{pp}}\) replacing the
|
|
|
|
|
core electrons of atom \(A\) is the sum of a local component
|
|
|
|
|
\(V_A^{\text{l}}\) and a non-local component \(V_A^{\text{nl}}\).
|
|
|
|
|
The local component is given by
|
|
|
|
|
</p>
|
|
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
\[
|
|
|
|
|
\hat{V}_A^{\text{l}}(r) = -\frac{Z_A^{\text{eff}}}{r} +
|
|
|
|
|
\frac{Z_A^{\text{eff}}}{r}\, \exp\left( -\alpha_A\, r^2\right) +
|
|
|
|
|
Z_{\text{eff}}\, \alpha_A\, r\, \exp\left( -\beta_A\, r^2\right) +
|
|
|
|
|
\gamma_A \exp\left( -\delta_A\, r^2\right),
|
|
|
|
|
\]
|
|
|
|
|
</p>
|
|
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
and the component obtained after localizing the non-local operator is
|
|
|
|
|
</p>
|
|
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
\[
|
|
|
|
|
\hat{V}_A^{\text{nl}}(r) =
|
|
|
|
|
\zeta_A\, \exp\left( -\eta_A\, r^2\right) |0\rangle \langle 0| +
|
|
|
|
|
\mu_A \, \exp\left( -\nu_A \, r^2\right) |1\rangle \langle 1|
|
|
|
|
|
\]
|
|
|
|
|
</p>
|
|
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
where \(r=|\mathbf{r-R}_A|\) is the distance to the nucleus on which the
|
|
|
|
|
potential is centered, \(Z_A^{\text{eff}}\) is the effective charge
|
|
|
|
|
due to the removed electrons, \(|0\rangle \langle 0|\)
|
|
|
|
|
and \(|1\rangle \langle 1|\) are projections over zero and one principal angular
|
|
|
|
|
momenta, respectively (generalization to higher angular momenta is
|
|
|
|
|
straightforward), and all the parameters labeled by Greek
|
|
|
|
|
letters are parameters.
|
|
|
|
|
</p>
|
|
|
|
|
|
|
|
|
|
<ul class="org-ul">
|
|
|
|
|
<li>\(\hat{V}_\text{ecp,l} = \sum_A \hat{V}_A^{\text{l}}\) : local component</li>
|
|
|
|
|
<li>\(\hat{V}_\text{ecp,nl} = \sum_A \hat{V}_A^{\text{nl}}\) : non-local component</li>
|
|
|
|
|
</ul>
|
|
|
|
|
|
2021-06-22 22:32:47 +02:00
|
|
|
<table id="org0701dfb" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
2021-06-18 12:05:06 +02:00
|
|
|
|
|
|
|
|
|
|
|
|
|
<colgroup>
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
</colgroup>
|
|
|
|
|
<tbody>
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>lmax_plus_1</code></td>
|
|
|
|
|
<td class="org-left"><code>int</code></td>
|
|
|
|
|
<td class="org-left"><code>(nucleus.num)</code></td>
|
|
|
|
|
<td class="org-left">\(l_{\max} + 1\)</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>z_core</code></td>
|
|
|
|
|
<td class="org-left"><code>float</code></td>
|
|
|
|
|
<td class="org-left"><code>(nucleus.num)</code></td>
|
|
|
|
|
<td class="org-left">Charges to remove</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>local_n</code></td>
|
|
|
|
|
<td class="org-left"><code>int</code></td>
|
|
|
|
|
<td class="org-left"><code>(nucleus.num)</code></td>
|
|
|
|
|
<td class="org-left">Number of local function</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>local_num_n_max</code></td>
|
|
|
|
|
<td class="org-left"><code>int</code></td>
|
|
|
|
|
<td class="org-left"> </td>
|
|
|
|
|
<td class="org-left">Maximum value of <code>local_n</code></td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>local_exponent</code></td>
|
|
|
|
|
<td class="org-left"><code>float</code></td>
|
|
|
|
|
<td class="org-left"><code>(ecp.local_num_n_max, nucleus.num)</code></td>
|
|
|
|
|
<td class="org-left"> </td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>local_coef</code></td>
|
|
|
|
|
<td class="org-left"><code>float</code></td>
|
|
|
|
|
<td class="org-left"><code>(ecp.local_num_n_max, nucleus.num)</code></td>
|
|
|
|
|
<td class="org-left"> </td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>local_power</code></td>
|
|
|
|
|
<td class="org-left"><code>int</code></td>
|
|
|
|
|
<td class="org-left"><code>(ecp.local_num_n_max, nucleus.num)</code></td>
|
|
|
|
|
<td class="org-left"> </td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>non_local_n</code></td>
|
|
|
|
|
<td class="org-left"><code>int</code></td>
|
|
|
|
|
<td class="org-left"><code>(nucleus.num)</code></td>
|
|
|
|
|
<td class="org-left"> </td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>non_local_num_n_max</code></td>
|
|
|
|
|
<td class="org-left"><code>int</code></td>
|
|
|
|
|
<td class="org-left"> </td>
|
|
|
|
|
<td class="org-left"> </td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>non_local_exponent</code></td>
|
|
|
|
|
<td class="org-left"><code>float</code></td>
|
|
|
|
|
<td class="org-left"><code>(ecp.non_local_num_n_max, nucleus.num)</code></td>
|
|
|
|
|
<td class="org-left"> </td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>non_local_coef</code></td>
|
|
|
|
|
<td class="org-left"><code>float</code></td>
|
|
|
|
|
<td class="org-left"><code>(ecp.non_local_num_n_max, nucleus.num)</code></td>
|
|
|
|
|
<td class="org-left"> </td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>non_local_power</code></td>
|
|
|
|
|
<td class="org-left"><code>int</code></td>
|
|
|
|
|
<td class="org-left"><code>(ecp.non_local_num_n_max, nucleus.num)</code></td>
|
|
|
|
|
<td class="org-left"> </td>
|
|
|
|
|
</tr>
|
|
|
|
|
</tbody>
|
|
|
|
|
</table>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
|
2021-06-22 22:32:47 +02:00
|
|
|
<div id="outline-container-org86016e6" class="outline-2">
|
|
|
|
|
<h2 id="org86016e6"><span class="section-number-2">5</span> Basis set</h2>
|
2021-06-18 12:05:06 +02:00
|
|
|
<div class="outline-text-2" id="text-5">
|
|
|
|
|
<p>
|
|
|
|
|
We consider here basis functions centered on nuclei. Hence, we enable
|
|
|
|
|
the possibility to define <i>dummy atoms</i> to place basis functions in
|
|
|
|
|
random positions.
|
|
|
|
|
</p>
|
|
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
The atomic basis set is defined as a list of shells. Each shell \(s\) is
|
|
|
|
|
centered on a center \(A\), possesses a given angular momentum \(l\) and a
|
|
|
|
|
radial function \(R_s\). The radial function is a linear combination of
|
|
|
|
|
\(N_{\text{prim}}\) <i>primitive</i> functions that can be of type
|
|
|
|
|
Slater (\(p=1\)) or Gaussian (\(p=2\)),
|
|
|
|
|
parameterized by exponents \(\gamma_{ks}\) and coefficients \(a_{ks}\):
|
|
|
|
|
\[
|
|
|
|
|
R_s(\mathbf{r}) = \mathcal{N}_s \vert\mathbf{r}-\mathbf{R}_A\vert^{n_s}
|
|
|
|
|
\sum_{k=1}^{N_{\text{prim}}} a_{ks}\, f_{ks}(\gamma_{ks},p)\,
|
|
|
|
|
\exp \left( - \gamma_{ks}
|
|
|
|
|
\vert \mathbf{r}-\mathbf{R}_A \vert ^p \right).
|
|
|
|
|
\]
|
|
|
|
|
</p>
|
|
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
In the case of Gaussian functions, \(n_s\) is always zero.
|
|
|
|
|
</p>
|
|
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
Different codes normalize functions at different levels. Computing
|
|
|
|
|
normalization factors requires the ability to compute overlap
|
|
|
|
|
integrals, so the normalization factors should be written in the
|
|
|
|
|
file to ensure that the file is self-contained and does not need the
|
|
|
|
|
client program to have the ability to compute such integrals.
|
|
|
|
|
</p>
|
|
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
Some codes assume that the contraction coefficients are for a linear
|
|
|
|
|
combination of <i>normalized</i> primitives. This implies that a normalization
|
|
|
|
|
constant for the primitive \(ks\) needs to be computed and stored. If
|
|
|
|
|
this normalization factor is not required, \(f_{ks}=1\).
|
|
|
|
|
</p>
|
|
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
Some codes assume that the basis function are normalized. This
|
|
|
|
|
implies the computation of an extra normalization factor, \(\mathcal{N}_s\).
|
|
|
|
|
If the the basis function is not considered normalized, \(\mathcal{N}_s=1\).
|
|
|
|
|
</p>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
All the basis set parameters are stored in one-dimensional arrays:
|
|
|
|
|
</p>
|
|
|
|
|
|
2021-06-22 22:32:47 +02:00
|
|
|
<table id="org5968aad" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
2021-06-18 12:05:06 +02:00
|
|
|
|
|
|
|
|
|
|
|
|
|
<colgroup>
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
</colgroup>
|
|
|
|
|
<tbody>
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>type</code></td>
|
|
|
|
|
<td class="org-left"><code>str</code></td>
|
|
|
|
|
<td class="org-left"> </td>
|
|
|
|
|
<td class="org-left">Type of basis set: "Gaussian" or "Slater"</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>num</code></td>
|
|
|
|
|
<td class="org-left"><code>int</code></td>
|
|
|
|
|
<td class="org-left"> </td>
|
|
|
|
|
<td class="org-left">Total Number of shells</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>prim_num</code></td>
|
|
|
|
|
<td class="org-left"><code>int</code></td>
|
|
|
|
|
<td class="org-left"> </td>
|
|
|
|
|
<td class="org-left">Total number of primitives</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>nucleus_index</code></td>
|
|
|
|
|
<td class="org-left"><code>index</code></td>
|
|
|
|
|
<td class="org-left"><code>(nucleus.num)</code></td>
|
|
|
|
|
<td class="org-left">Index of the first shell of each nucleus (\(A\))</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>nucleus_shell_num</code></td>
|
|
|
|
|
<td class="org-left"><code>int</code></td>
|
|
|
|
|
<td class="org-left"><code>(nucleus.num)</code></td>
|
|
|
|
|
<td class="org-left">Number of shells for each nucleus</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>shell_ang_mom</code></td>
|
|
|
|
|
<td class="org-left"><code>int</code></td>
|
|
|
|
|
<td class="org-left"><code>(basis.num)</code></td>
|
|
|
|
|
<td class="org-left">Angular momentum <code>0:S, 1:P, 2:D, ...</code></td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>shell_prim_num</code></td>
|
|
|
|
|
<td class="org-left"><code>int</code></td>
|
|
|
|
|
<td class="org-left"><code>(basis.num)</code></td>
|
|
|
|
|
<td class="org-left">Number of primitives in the shell (\(N_{\text{prim}}\))</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>shell_factor</code></td>
|
|
|
|
|
<td class="org-left"><code>float</code></td>
|
|
|
|
|
<td class="org-left"><code>(basis.num)</code></td>
|
|
|
|
|
<td class="org-left">Normalization factor of the shell (\(\mathcal{N}_s\))</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>shell_prim_index</code></td>
|
|
|
|
|
<td class="org-left"><code>index</code></td>
|
|
|
|
|
<td class="org-left"><code>(basis.num)</code></td>
|
|
|
|
|
<td class="org-left">Index of the first primitive in the complete list</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>exponent</code></td>
|
|
|
|
|
<td class="org-left"><code>float</code></td>
|
|
|
|
|
<td class="org-left"><code>(basis.prim_num)</code></td>
|
2021-06-18 12:32:12 +02:00
|
|
|
<td class="org-left">Exponents of the primitives (\(\gamma_{ks}\))</td>
|
2021-06-18 12:05:06 +02:00
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>coefficient</code></td>
|
|
|
|
|
<td class="org-left"><code>float</code></td>
|
|
|
|
|
<td class="org-left"><code>(basis.prim_num)</code></td>
|
|
|
|
|
<td class="org-left">Coefficients of the primitives (\(a_{ks}\))</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>prim_factor</code></td>
|
|
|
|
|
<td class="org-left"><code>float</code></td>
|
|
|
|
|
<td class="org-left"><code>(basis.prim_num)</code></td>
|
|
|
|
|
<td class="org-left">Normalization coefficients for the primitives (\(f_{ks}\))</td>
|
|
|
|
|
</tr>
|
|
|
|
|
</tbody>
|
|
|
|
|
</table>
|
|
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
For example, consider H<sub>2</sub> with the following basis set (in GAMESS
|
|
|
|
|
format), where both the AOs and primitives are considered normalized:
|
|
|
|
|
</p>
|
|
|
|
|
|
|
|
|
|
<pre class="example">
|
|
|
|
|
HYDROGEN
|
|
|
|
|
S 5
|
|
|
|
|
1 3.387000E+01 6.068000E-03
|
|
|
|
|
2 5.095000E+00 4.530800E-02
|
|
|
|
|
3 1.159000E+00 2.028220E-01
|
|
|
|
|
4 3.258000E-01 5.039030E-01
|
|
|
|
|
5 1.027000E-01 3.834210E-01
|
|
|
|
|
S 1
|
|
|
|
|
1 3.258000E-01 1.000000E+00
|
|
|
|
|
S 1
|
|
|
|
|
1 1.027000E-01 1.000000E+00
|
|
|
|
|
P 1
|
|
|
|
|
1 1.407000E+00 1.000000E+00
|
|
|
|
|
P 1
|
|
|
|
|
1 3.880000E-01 1.000000E+00
|
|
|
|
|
D 1
|
|
|
|
|
1 1.057000E+00 1.0000000
|
|
|
|
|
</pre>
|
|
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
we have:
|
|
|
|
|
</p>
|
|
|
|
|
|
|
|
|
|
<pre class="example">
|
|
|
|
|
type = "Gaussian"
|
|
|
|
|
num = 12
|
|
|
|
|
prim_num = 20
|
|
|
|
|
|
|
|
|
|
nucleus_index = [0 , 6]
|
|
|
|
|
shell_ang_mom = [0 , 0 , 0 , 1 , 1 , 2 , 0 , 0 , 0 , 1 , 1 , 2 ]
|
|
|
|
|
shell_prim_num = [5 , 1 , 1 , 1 , 1 , 1 , 5 , 1 , 1 , 1 , 1 , 1 ]
|
|
|
|
|
shell_prim_index = [0 , 5 , 6 , 7 , 8 , 9 , 10, 15, 16, 17, 18, 19]
|
|
|
|
|
shell_factor = [1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.]
|
|
|
|
|
|
|
|
|
|
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]
|
|
|
|
|
|
|
|
|
|
prim_factor =
|
|
|
|
|
[ 1.0006253235944540e+01, 2.4169531573445120e+00, 7.9610924849766440e-01
|
|
|
|
|
3.0734305383061117e-01, 1.2929684417481876e-01, 3.0734305383061117e-01,
|
|
|
|
|
1.2929684417481876e-01, 2.1842769845268308e+00, 4.3649547399719840e-01,
|
|
|
|
|
1.8135965626177861e+00, 1.0006253235944540e+01, 2.4169531573445120e+00,
|
|
|
|
|
7.9610924849766440e-01, 3.0734305383061117e-01, 1.2929684417481876e-01,
|
|
|
|
|
3.0734305383061117e-01, 1.2929684417481876e-01, 2.1842769845268308e+00,
|
|
|
|
|
4.3649547399719840e-01, 1.8135965626177861e+00 ]
|
|
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
|
2021-06-22 22:32:47 +02:00
|
|
|
<div id="outline-container-org96b16b7" class="outline-2">
|
|
|
|
|
<h2 id="org96b16b7"><span class="section-number-2">6</span> Atomic orbitals</h2>
|
2021-06-18 12:05:06 +02:00
|
|
|
<div class="outline-text-2" id="text-6">
|
|
|
|
|
<p>
|
|
|
|
|
Going from the atomic basis set to AOs implies a systematic
|
|
|
|
|
construction of all the angular functions of each shell. We
|
|
|
|
|
consider two cases for the angular functions: the real-valued
|
|
|
|
|
spherical harmonics, and the polynomials in Cartesian coordinates.
|
|
|
|
|
In the case of spherical harmonics, the AOs are ordered in
|
|
|
|
|
increasing magnetic quantum number (\(-l \le m \le l\)), and in the case
|
|
|
|
|
of polynomials we impose the canonical ordering of the
|
|
|
|
|
Libint2 library, i.e
|
|
|
|
|
</p>
|
|
|
|
|
|
|
|
|
|
\begin{eqnarray}
|
|
|
|
|
p & : & p_x, p_y, p_z \nonumber \\
|
|
|
|
|
d & : & d_{xx}, d_{xy}, d_{xz}, d_{yy}, d_{yz}, d_{zz} \nonumber \\
|
|
|
|
|
f & : & f_{xxx}, f_{xxy}, f_{xxz}, f_{xyy}, f_{xyz}, f_{xzz}, f_{yyy}, f_{yyz}, f_{yzz}, …f_{zzz} \nonumber \\
|
|
|
|
|
{\rm etc.} \nonumber
|
|
|
|
|
\end{eqnarray}
|
|
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
AOs are defined as
|
|
|
|
|
</p>
|
|
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
\[
|
|
|
|
|
\chi_i (\mathbf{r}) = \mathcal{N}_i\, P_{\eta(i)}(\mathbf{r})\, R_{\theta(i)} (\mathbf{r})
|
|
|
|
|
\]
|
|
|
|
|
</p>
|
|
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
where \(i\) is the atomic orbital index,
|
|
|
|
|
\(P\) encodes for either the
|
|
|
|
|
polynomials or the spherical harmonics, \(\theta(i)\) returns the
|
|
|
|
|
shell on which the AO is expanded, and \(\eta(i)\) denotes which
|
|
|
|
|
angular function is chosen.
|
|
|
|
|
\(\mathcal{N}_i\) is a normalization factor that enables the
|
|
|
|
|
possibility to have different normalization coefficients within a
|
|
|
|
|
shell, as in the GAMESS convention where
|
|
|
|
|
\(\mathcal{N}_{x^2} \ne \mathcal{N}_{xy}\) because
|
|
|
|
|
\[ \left[ \iiint \left(x-X_A \right)^2 R_{\theta(i)}
|
|
|
|
|
(\mathbf{r}) dx\, dy\, dz \right]^{-1/2} \ne
|
|
|
|
|
\left[ \iiint \left( x-X_A \right) \left( y-Y_A \right) R_{\theta(i)}
|
|
|
|
|
(\mathbf{r}) dx\, dy\, dz \right]^{-1/2}. \]
|
|
|
|
|
</p>
|
|
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
In such a case, one should set the normalization of the shell (in
|
2021-06-22 22:32:47 +02:00
|
|
|
the <a href="#org86016e6">Basis set</a> section) to \(\mathcal{N}_{z^2}\), which is the
|
2021-06-18 12:05:06 +02:00
|
|
|
normalization factor of the atomic orbitals in spherical coordinates.
|
|
|
|
|
The normalization factor of the \(xy\) function which should be
|
|
|
|
|
introduced here should be \(\frac{\mathcal{N}_{xy}}{\mathcal{N}_{z^2}}\).
|
|
|
|
|
</p>
|
|
|
|
|
|
2021-06-22 22:32:47 +02:00
|
|
|
<table id="orgba83541" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
2021-06-18 12:05:06 +02:00
|
|
|
|
|
|
|
|
|
|
|
|
|
<colgroup>
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
</colgroup>
|
|
|
|
|
<tbody>
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>cartesian</code></td>
|
|
|
|
|
<td class="org-left"><code>int</code></td>
|
|
|
|
|
<td class="org-left"> </td>
|
|
|
|
|
<td class="org-left"><code>1</code>: true, <code>0</code>: false</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>num</code></td>
|
|
|
|
|
<td class="org-left"><code>int</code></td>
|
|
|
|
|
<td class="org-left"> </td>
|
|
|
|
|
<td class="org-left">Total number of atomic orbitals</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>shell</code></td>
|
|
|
|
|
<td class="org-left"><code>index</code></td>
|
|
|
|
|
<td class="org-left"><code>(ao.num)</code></td>
|
|
|
|
|
<td class="org-left">basis set shell for each AO</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>normalization</code></td>
|
|
|
|
|
<td class="org-left"><code>float</code></td>
|
|
|
|
|
<td class="org-left"><code>(ao.num)</code></td>
|
|
|
|
|
<td class="org-left">Normalization factors</td>
|
|
|
|
|
</tr>
|
|
|
|
|
</tbody>
|
|
|
|
|
</table>
|
|
|
|
|
</div>
|
|
|
|
|
|
2021-06-22 22:32:47 +02:00
|
|
|
<div id="outline-container-orge8be744" class="outline-3">
|
|
|
|
|
<h3 id="ao_one_e"><a id="orge8be744"></a><span class="section-number-3">6.1</span> One-electron integrals</h3>
|
2021-06-18 12:05:06 +02:00
|
|
|
<div class="outline-text-3" id="text-ao_one_e">
|
|
|
|
|
<ul class="org-ul">
|
|
|
|
|
<li>\[ \hat{V}_{\text{ne}} = \sum_{A=1}^{N_\text{nucl}}
|
|
|
|
|
\sum_{i=1}^{N_\text{elec}} \frac{-Z_A }{\vert \mathbf{R}_A -
|
|
|
|
|
\mathbf{r}_i \vert} \] : electron-nucleus attractive potential,</li>
|
|
|
|
|
<li>\[ \hat{T}_{\text{e}} =
|
|
|
|
|
\sum_{i=1}^{N_\text{elec}} -\frac{1}{2}\hat{\Delta}_i \] : electronic kinetic energy</li>
|
|
|
|
|
<li>\(\hat{h} = \hat{T}_\text{e} + \hat{V}_\text{ne} +
|
|
|
|
|
\hat{V}_\text{ecp,l} + \hat{V}_\text{ecp,nl}\) : core electronic Hamiltonian</li>
|
|
|
|
|
</ul>
|
|
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
The one-electron integrals for a one-electron operator \(\hat{O}\) are
|
|
|
|
|
\[ \langle p \vert \hat{O} \vert q \rangle \], returned as a matrix
|
|
|
|
|
over atomic orbitals.
|
|
|
|
|
</p>
|
|
|
|
|
|
2021-06-22 22:32:47 +02:00
|
|
|
<table id="org8a5916c" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
2021-06-18 12:05:06 +02:00
|
|
|
|
|
|
|
|
|
|
|
|
|
<colgroup>
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
</colgroup>
|
|
|
|
|
<tbody>
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>overlap</code></td>
|
|
|
|
|
<td class="org-left"><code>float</code></td>
|
|
|
|
|
<td class="org-left"><code>(ao.num, ao.num)</code></td>
|
|
|
|
|
<td class="org-left">\(\langle p \vert q \rangle\)</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>kinetic</code></td>
|
|
|
|
|
<td class="org-left"><code>float</code></td>
|
|
|
|
|
<td class="org-left"><code>(ao.num, ao.num)</code></td>
|
|
|
|
|
<td class="org-left">\(\langle p \vert \hat{T}_e \vert q \rangle\)</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>potential_n_e</code></td>
|
|
|
|
|
<td class="org-left"><code>float</code></td>
|
|
|
|
|
<td class="org-left"><code>(ao.num, ao.num)</code></td>
|
|
|
|
|
<td class="org-left">\(\langle p \vert \hat{V}_{\text{ne}} \vert q \rangle\)</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>ecp_local</code></td>
|
|
|
|
|
<td class="org-left"><code>float</code></td>
|
|
|
|
|
<td class="org-left"><code>(ao.num, ao.num)</code></td>
|
2021-06-18 12:32:12 +02:00
|
|
|
<td class="org-left">\(\langle p \vert \hat{V}_{\text{ecp,l}} \vert q \rangle\)</td>
|
2021-06-18 12:05:06 +02:00
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>ecp_non_local</code></td>
|
|
|
|
|
<td class="org-left"><code>float</code></td>
|
|
|
|
|
<td class="org-left"><code>(ao.num, ao.num)</code></td>
|
2021-06-18 12:32:12 +02:00
|
|
|
<td class="org-left">\(\langle p \vert \hat{V}_{\text{ecp,nl}} \vert q \rangle\)</td>
|
2021-06-18 12:05:06 +02:00
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>core_hamiltonian</code></td>
|
|
|
|
|
<td class="org-left"><code>float</code></td>
|
|
|
|
|
<td class="org-left"><code>(ao.num, ao.num)</code></td>
|
|
|
|
|
<td class="org-left">\(\langle p \vert \hat{h} \vert q \rangle\)</td>
|
|
|
|
|
</tr>
|
|
|
|
|
</tbody>
|
|
|
|
|
</table>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
|
2021-06-22 22:32:47 +02:00
|
|
|
<div id="outline-container-org1337252" class="outline-3">
|
|
|
|
|
<h3 id="ao_two_e"><a id="org1337252"></a><span class="section-number-3">6.2</span> Two-electron integrals</h3>
|
2021-06-18 12:05:06 +02:00
|
|
|
<div class="outline-text-3" id="text-ao_two_e">
|
|
|
|
|
<p>
|
|
|
|
|
The two-electron integrals for a two-electron operator \(\hat{O}\) are
|
|
|
|
|
\[ \langle p q \vert \hat{O} \vert r s \rangle \] in physicists
|
|
|
|
|
notation or \[ ( pr \vert \hat{O} \vert qs ) \] in chemists
|
|
|
|
|
notation, where \(p,q,r,s\) are indices over atomic orbitals.
|
|
|
|
|
</p>
|
|
|
|
|
|
|
|
|
|
<p>
|
|
|
|
|
Functions are provided to get the indices in physicists or chemists
|
|
|
|
|
notation.
|
|
|
|
|
</p>
|
|
|
|
|
|
|
|
|
|
<ul class="org-ul">
|
|
|
|
|
<li>\[ \hat{W}_{\text{ee}} = \sum_{i=2}^{N_\text{elec}} \sum_{j=1}^{i-1} \frac{1}{\vert \mathbf{r}_i - \mathbf{r}_j \vert} \] : electron-electron repulsive potential operator.</li>
|
|
|
|
|
<li>\[ \hat{W}^{lr}_{\text{ee}} = \sum_{i=2}^{N_\text{elec}}
|
|
|
|
|
\sum_{j=1}^{i-1} \frac{\text{erf}(\vert \mathbf{r}_i -
|
|
|
|
|
\mathbf{r}_j \vert)}{\vert \mathbf{r}_i - \mathbf{r}_j \vert} \] : electron-electron long range potential</li>
|
|
|
|
|
</ul>
|
|
|
|
|
|
2021-06-22 22:32:47 +02:00
|
|
|
<table id="org9db7635" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
2021-06-18 12:05:06 +02:00
|
|
|
|
|
|
|
|
|
|
|
|
|
<colgroup>
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
</colgroup>
|
|
|
|
|
<tbody>
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>eri</code></td>
|
|
|
|
|
<td class="org-left"><code>float sparse</code></td>
|
|
|
|
|
<td class="org-left"><code>(ao.num, ao.num, ao.num, ao.num)</code></td>
|
|
|
|
|
<td class="org-left">Electron repulsion integrals</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>eri_lr</code></td>
|
|
|
|
|
<td class="org-left"><code>float sparse</code></td>
|
|
|
|
|
<td class="org-left"><code>(ao.num, ao.num, ao.num, ao.num)</code></td>
|
|
|
|
|
<td class="org-left">Long-range Electron repulsion integrals</td>
|
|
|
|
|
</tr>
|
|
|
|
|
</tbody>
|
|
|
|
|
</table>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
|
2021-06-22 22:32:47 +02:00
|
|
|
<div id="outline-container-org2f3ed38" class="outline-2">
|
|
|
|
|
<h2 id="org2f3ed38"><span class="section-number-2">7</span> Molecular orbitals</h2>
|
2021-06-18 12:05:06 +02:00
|
|
|
<div class="outline-text-2" id="text-7">
|
2021-06-22 22:32:47 +02:00
|
|
|
<table id="org2e94a16" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
2021-06-18 12:05:06 +02:00
|
|
|
|
|
|
|
|
|
|
|
|
|
<colgroup>
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
</colgroup>
|
|
|
|
|
<tbody>
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>type</code></td>
|
|
|
|
|
<td class="org-left"><code>str</code></td>
|
|
|
|
|
<td class="org-left"> </td>
|
|
|
|
|
<td class="org-left">String identify the set of MOs</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>num</code></td>
|
|
|
|
|
<td class="org-left"><code>int</code></td>
|
|
|
|
|
<td class="org-left"> </td>
|
|
|
|
|
<td class="org-left">Number of MOs</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>coefficient</code></td>
|
|
|
|
|
<td class="org-left"><code>float</code></td>
|
|
|
|
|
<td class="org-left"><code>(ao.num, mo.num)</code></td>
|
|
|
|
|
<td class="org-left">MO coefficients</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>class</code></td>
|
|
|
|
|
<td class="org-left"><code>str</code></td>
|
|
|
|
|
<td class="org-left"><code>(mo.num)</code></td>
|
|
|
|
|
<td class="org-left">Core, Inactive, Active, Virtual, Deleted</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>symmetry</code></td>
|
|
|
|
|
<td class="org-left"><code>str</code></td>
|
|
|
|
|
<td class="org-left"><code>(mo.num)</code></td>
|
|
|
|
|
<td class="org-left">Symmetry in the point group</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>occupation</code></td>
|
|
|
|
|
<td class="org-left"><code>float</code></td>
|
|
|
|
|
<td class="org-left"><code>(mo.num)</code></td>
|
|
|
|
|
<td class="org-left">Occupation number</td>
|
|
|
|
|
</tr>
|
|
|
|
|
</tbody>
|
|
|
|
|
</table>
|
|
|
|
|
</div>
|
|
|
|
|
|
2021-06-22 22:32:47 +02:00
|
|
|
<div id="outline-container-org72bc6af" class="outline-3">
|
|
|
|
|
<h3 id="org72bc6af"><span class="section-number-3">7.1</span> One-electron integrals</h3>
|
2021-06-18 12:05:06 +02:00
|
|
|
<div class="outline-text-3" id="text-7-1">
|
|
|
|
|
<p>
|
|
|
|
|
The operators as the same as those defined in the
|
|
|
|
|
<a href="#ao_one_e">AO one-electron integrals section</a>. Here, the integrals are given in
|
|
|
|
|
the basis of molecular orbitals.
|
|
|
|
|
</p>
|
|
|
|
|
|
2021-06-22 22:32:47 +02:00
|
|
|
<table id="org7bc73bb" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
2021-06-18 12:05:06 +02:00
|
|
|
|
|
|
|
|
|
|
|
|
|
<colgroup>
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
</colgroup>
|
|
|
|
|
<tbody>
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>overlap</code></td>
|
|
|
|
|
<td class="org-left"><code>float</code></td>
|
|
|
|
|
<td class="org-left"><code>(mo.num, mo.num)</code></td>
|
|
|
|
|
<td class="org-left">\(\langle i \vert j \rangle\)</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>kinetic</code></td>
|
|
|
|
|
<td class="org-left"><code>float</code></td>
|
|
|
|
|
<td class="org-left"><code>(mo.num, mo.num)</code></td>
|
|
|
|
|
<td class="org-left">\(\langle i \vert \hat{T}_e \vert j \rangle\)</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>potential_n_e</code></td>
|
|
|
|
|
<td class="org-left"><code>float</code></td>
|
|
|
|
|
<td class="org-left"><code>(mo.num, mo.num)</code></td>
|
|
|
|
|
<td class="org-left">\(\langle i \vert \hat{V}_{\text{ne}} \vert j \rangle\)</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>ecp_local</code></td>
|
|
|
|
|
<td class="org-left"><code>float</code></td>
|
|
|
|
|
<td class="org-left"><code>(mo.num, mo.num)</code></td>
|
2021-06-18 12:32:12 +02:00
|
|
|
<td class="org-left">\(\langle i \vert \hat{V}_{\text{ecp,l}} \vert j \rangle\)</td>
|
2021-06-18 12:05:06 +02:00
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>ecp_non_local</code></td>
|
|
|
|
|
<td class="org-left"><code>float</code></td>
|
|
|
|
|
<td class="org-left"><code>(mo.num, mo.num)</code></td>
|
2021-06-18 12:32:12 +02:00
|
|
|
<td class="org-left">\(\langle i \vert \hat{V}_{\text{ecp,nl}} \vert j \rangle\)</td>
|
2021-06-18 12:05:06 +02:00
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>core_hamiltonian</code></td>
|
|
|
|
|
<td class="org-left"><code>float</code></td>
|
|
|
|
|
<td class="org-left"><code>(mo.num, mo.num)</code></td>
|
|
|
|
|
<td class="org-left">\(\langle i \vert \hat{h} \vert j \rangle\)</td>
|
|
|
|
|
</tr>
|
|
|
|
|
</tbody>
|
|
|
|
|
</table>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
|
2021-06-22 22:32:47 +02:00
|
|
|
<div id="outline-container-orgd1fde5a" class="outline-3">
|
|
|
|
|
<h3 id="orgd1fde5a"><span class="section-number-3">7.2</span> Two-electron integrals</h3>
|
2021-06-18 12:05:06 +02:00
|
|
|
<div class="outline-text-3" id="text-7-2">
|
|
|
|
|
<p>
|
|
|
|
|
The operators as the same as those defined in the
|
|
|
|
|
<a href="#ao_one_e">AO one-electron integrals section</a>. Here, the integrals are given in
|
|
|
|
|
the basis of molecular orbitals.
|
|
|
|
|
</p>
|
|
|
|
|
|
2021-06-22 22:32:47 +02:00
|
|
|
<table id="org35a9ecf" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
2021-06-18 12:05:06 +02:00
|
|
|
|
|
|
|
|
|
|
|
|
|
<colgroup>
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
</colgroup>
|
|
|
|
|
<tbody>
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>eri</code></td>
|
|
|
|
|
<td class="org-left"><code>float sparse</code></td>
|
|
|
|
|
<td class="org-left"><code>(mo.num, mo.num, mo.num, mo.num)</code></td>
|
|
|
|
|
<td class="org-left">Electron repulsion integrals</td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>eri_lr</code></td>
|
|
|
|
|
<td class="org-left"><code>float sparse</code></td>
|
|
|
|
|
<td class="org-left"><code>(mo.num, mo.num, mo.num, mo.num)</code></td>
|
|
|
|
|
<td class="org-left">Long-range Electron repulsion integrals</td>
|
|
|
|
|
</tr>
|
|
|
|
|
</tbody>
|
|
|
|
|
</table>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
|
2021-06-22 22:32:47 +02:00
|
|
|
<div id="outline-container-org22ac68f" class="outline-2">
|
|
|
|
|
<h2 id="org22ac68f"><span class="section-number-2">8</span> <span class="todo TODO">TODO</span> Slater determinants</h2>
|
2021-06-18 12:05:06 +02:00
|
|
|
</div>
|
2021-06-22 22:32:47 +02:00
|
|
|
<div id="outline-container-org177ee41" class="outline-2">
|
|
|
|
|
<h2 id="org177ee41"><span class="section-number-2">9</span> <span class="todo TODO">TODO</span> Reduced density matrices</h2>
|
2021-06-18 12:05:06 +02:00
|
|
|
<div class="outline-text-2" id="text-9">
|
2021-06-22 22:32:47 +02:00
|
|
|
<table id="orgdbd98ae" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
2021-06-18 12:05:06 +02:00
|
|
|
|
|
|
|
|
|
|
|
|
|
<colgroup>
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
|
|
|
|
|
<col class="org-left" />
|
|
|
|
|
</colgroup>
|
|
|
|
|
<tbody>
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>one_e</code></td>
|
|
|
|
|
<td class="org-left"><code>float</code></td>
|
|
|
|
|
<td class="org-left"><code>(mo.num, mo.num)</code></td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>one_e_up</code></td>
|
|
|
|
|
<td class="org-left"><code>float</code></td>
|
|
|
|
|
<td class="org-left"><code>(mo.num, mo.num)</code></td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>one_e_dn</code></td>
|
|
|
|
|
<td class="org-left"><code>float</code></td>
|
|
|
|
|
<td class="org-left"><code>(mo.num, mo.num)</code></td>
|
|
|
|
|
</tr>
|
|
|
|
|
|
|
|
|
|
<tr>
|
|
|
|
|
<td class="org-left"><code>two_e</code></td>
|
|
|
|
|
<td class="org-left"><code>float sparse</code></td>
|
|
|
|
|
<td class="org-left"><code>(mo.num, mo.num, mo.num, mo.num)</code></td>
|
|
|
|
|
</tr>
|
|
|
|
|
</tbody>
|
|
|
|
|
</table>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
|
2021-06-22 22:32:47 +02:00
|
|
|
<div id="outline-container-orgbbdb680" class="outline-2">
|
|
|
|
|
<h2 id="orgbbdb680"><span class="section-number-2">10</span> Appendix</h2>
|
2021-06-18 12:05:06 +02:00
|
|
|
<div class="outline-text-2" id="text-10">
|
|
|
|
|
</div>
|
2021-06-22 22:32:47 +02:00
|
|
|
<div id="outline-container-orgca98b95" class="outline-3">
|
|
|
|
|
<h3 id="orgca98b95"><span class="section-number-3">10.1</span> Python script from table to json</h3>
|
2021-06-18 12:05:06 +02:00
|
|
|
<div class="outline-text-3" id="text-10-1">
|
|
|
|
|
<div class="org-src-container">
|
2021-06-22 22:32:47 +02:00
|
|
|
<pre class="src src-python" id="org059451c"><span style="color: #a020f0;">print</span>(<span style="color: #8b2252;">"""#+begin_src python :tangle trex.json"""</span>)
|
2021-06-18 12:05:06 +02:00
|
|
|
<span style="color: #a020f0;">print</span>(<span style="color: #8b2252;">""" "%s": {"""</span>%(title))
|
|
|
|
|
<span style="color: #a0522d;">indent</span> = <span style="color: #8b2252;">" "</span>
|
|
|
|
|
<span style="color: #a0522d;">f1</span> = 0 ; <span style="color: #a0522d;">f2</span> = 0 ; <span style="color: #a0522d;">f3</span> = 0
|
|
|
|
|
<span style="color: #a020f0;">for</span> line <span style="color: #a020f0;">in</span> data:
|
|
|
|
|
<span style="color: #a0522d;">line</span> = [ x.replace(<span style="color: #8b2252;">"~"</span>,<span style="color: #8b2252;">""</span>) <span style="color: #a020f0;">for</span> x <span style="color: #a020f0;">in</span> line ]
|
|
|
|
|
<span style="color: #a0522d;">name</span> = <span style="color: #8b2252;">'"'</span>+line[0]+<span style="color: #8b2252;">'"'</span>
|
|
|
|
|
<span style="color: #a0522d;">typ</span> = <span style="color: #8b2252;">'"'</span>+line[1]+<span style="color: #8b2252;">'"'</span>
|
|
|
|
|
<span style="color: #a0522d;">dims</span> = line[2]
|
|
|
|
|
<span style="color: #a020f0;">if</span> <span style="color: #8b2252;">'('</span> <span style="color: #a020f0;">in</span> dims:
|
|
|
|
|
<span style="color: #a0522d;">dims</span> = dims.strip()[1:-1]
|
|
|
|
|
<span style="color: #a0522d;">dims</span> = [ <span style="color: #8b2252;">'"'</span>+x.strip()+<span style="color: #8b2252;">'"'</span> <span style="color: #a020f0;">for</span> x <span style="color: #a020f0;">in</span> dims.split(<span style="color: #8b2252;">','</span>) ]
|
|
|
|
|
<span style="color: #a0522d;">dims</span> = <span style="color: #8b2252;">"[ "</span> + <span style="color: #8b2252;">", "</span>.join(dims) + <span style="color: #8b2252;">" ]"</span>
|
|
|
|
|
<span style="color: #a020f0;">else</span>:
|
|
|
|
|
<span style="color: #a0522d;">dims</span> = <span style="color: #8b2252;">"[ ]"</span>
|
|
|
|
|
<span style="color: #a0522d;">f1</span> = <span style="color: #483d8b;">max</span>(f1, <span style="color: #483d8b;">len</span>(name))
|
|
|
|
|
<span style="color: #a0522d;">f2</span> = <span style="color: #483d8b;">max</span>(f2, <span style="color: #483d8b;">len</span>(typ))
|
|
|
|
|
<span style="color: #a0522d;">f3</span> = <span style="color: #483d8b;">max</span>(f3, <span style="color: #483d8b;">len</span>(dims))
|
|
|
|
|
|
|
|
|
|
<span style="color: #a0522d;">fmt</span> = <span style="color: #8b2252;">"%%s%%%ds : [ %%%ds, %%%ds ]"</span> % (f1, f2, f3)
|
|
|
|
|
<span style="color: #a020f0;">for</span> line <span style="color: #a020f0;">in</span> data:
|
|
|
|
|
<span style="color: #a0522d;">line</span> = [ x.replace(<span style="color: #8b2252;">"~"</span>,<span style="color: #8b2252;">""</span>) <span style="color: #a020f0;">for</span> x <span style="color: #a020f0;">in</span> line ]
|
|
|
|
|
<span style="color: #a0522d;">name</span> = <span style="color: #8b2252;">'"'</span>+line[0]+<span style="color: #8b2252;">'"'</span>
|
|
|
|
|
<span style="color: #a0522d;">typ</span> = <span style="color: #8b2252;">'"'</span>+line[1]+<span style="color: #8b2252;">'"'</span>
|
|
|
|
|
<span style="color: #a0522d;">dims</span> = line[2]
|
|
|
|
|
<span style="color: #a020f0;">if</span> <span style="color: #8b2252;">'('</span> <span style="color: #a020f0;">in</span> dims:
|
|
|
|
|
<span style="color: #a0522d;">dims</span> = dims.strip()[1:-1]
|
|
|
|
|
<span style="color: #a0522d;">dims</span> = [ <span style="color: #8b2252;">'"'</span>+x.strip()+<span style="color: #8b2252;">'"'</span> <span style="color: #a020f0;">for</span> x <span style="color: #a020f0;">in</span> dims.split(<span style="color: #8b2252;">','</span>) ]
|
|
|
|
|
dims.reverse()
|
|
|
|
|
<span style="color: #a0522d;">dims</span> = <span style="color: #8b2252;">"[ "</span> + <span style="color: #8b2252;">", "</span>.join(dims) + <span style="color: #8b2252;">" ]"</span>
|
|
|
|
|
<span style="color: #a020f0;">else</span>:
|
|
|
|
|
<span style="color: #a020f0;">if</span> dims.strip() != <span style="color: #8b2252;">""</span>:
|
|
|
|
|
<span style="color: #a0522d;">dims</span> = <span style="color: #8b2252;">"ERROR"</span>
|
|
|
|
|
<span style="color: #a020f0;">else</span>:
|
|
|
|
|
<span style="color: #a0522d;">dims</span> = <span style="color: #8b2252;">"[]"</span>
|
|
|
|
|
<span style="color: #483d8b;">buffer</span> = fmt % (indent, name, typ.ljust(f2), dims.ljust(f3))
|
|
|
|
|
<span style="color: #a0522d;">indent</span> = <span style="color: #8b2252;">" , "</span>
|
|
|
|
|
<span style="color: #a020f0;">print</span>(<span style="color: #483d8b;">buffer</span>)
|
|
|
|
|
|
|
|
|
|
<span style="color: #a020f0;">if</span> last == 0:
|
|
|
|
|
<span style="color: #a020f0;">print</span>(<span style="color: #8b2252;">" } ,"</span>)
|
|
|
|
|
<span style="color: #a020f0;">else</span>:
|
|
|
|
|
<span style="color: #a020f0;">print</span>(<span style="color: #8b2252;">" }"</span>)
|
|
|
|
|
<span style="color: #a020f0;">print</span>(<span style="color: #8b2252;">"""#+end_src"""</span>)
|
|
|
|
|
|
|
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<div class="org-src-container">
|
|
|
|
|
<pre class="src src-python">}
|
|
|
|
|
</pre>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
</div>
|
|
|
|
|
<div id="postamble" class="status">
|
2021-06-18 12:11:36 +02:00
|
|
|
<p class="author">Author: TREX-CoE</p>
|
2021-06-22 22:32:47 +02:00
|
|
|
<p class="date">Created: 2021-06-22 Tue 20:32</p>
|
2021-06-18 12:05:06 +02:00
|
|
|
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
|
|
|
|
</div>
|
|
|
|
|
</body>
|
|
|
|
|
</html>
|
