/usr/share/doc/psi4/html/psimrcc.html is in psi4-data 1:0.3-5.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 | <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<title>PSIMRCC Implementation of Mk-MRCC Theory — Psi4 [] Docs</title>
<link rel="stylesheet" href="_static/psi4.css" type="text/css" />
<link rel="stylesheet" href="_static/pygments.css" type="text/css" />
<link rel="stylesheet" href="./" type="text/css" />
<script type="text/javascript">
var DOCUMENTATION_OPTIONS = {
URL_ROOT: './',
VERSION: '',
COLLAPSE_INDEX: false,
FILE_SUFFIX: '.html',
HAS_SOURCE: true
};
</script>
<script type="text/javascript" src="_static/jquery.js"></script>
<script type="text/javascript" src="_static/underscore.js"></script>
<script type="text/javascript" src="_static/doctools.js"></script>
<script type="text/javascript" src="_static/jquery.cookie.js"></script>
<script type="text/javascript" src="_static/toggle_sections.js"></script>
<script type="text/javascript" src="_static/toggle_sidebar.js"></script>
<script type="text/javascript" src="_static/toggle_codeprompt.js"></script>
<link rel="shortcut icon" href="_static/favicon-psi4.ico"/>
<link rel="top" title="Psi4 [] Docs" href="index.html" />
<link rel="up" title="Theoretical Methods: SCF to FCI" href="methods.html" />
<link rel="next" title="CI: Configuration Interaction" href="detci.html" />
<link rel="prev" title="OCC: Orbital-Optimized Coupled-Cluster and Møller–Plesset Perturbation Theories" href="occ.html" />
</head>
<body role="document">
<div class="relbar-top">
<div class="related" role="navigation" aria-label="related navigation">
<h3>Navigation</h3>
<ul>
<li class="right" style="margin-right: 10px">
<a href="genindex.html" title="General Index"
accesskey="I">index</a></li>
<li class="right" >
<a href="py-modindex.html" title="Python Module Index"
>modules</a> </li>
<li class="right" >
<a href="contents.html" title="Table Of Contents"
accesskey="C">toc</a> </li>
<li class="right" >
<a href="detci.html" title="CI: Configuration Interaction"
accesskey="N">next</a> </li>
<li class="right" >
<a href="occ.html" title="OCC: Orbital-Optimized Coupled-Cluster and Møller–Plesset Perturbation Theories"
accesskey="P">previous</a> </li>
<li><a href="index.html">Psi4 []</a> » </li>
<li class="nav-item nav-item-1"><a href="methods.html" accesskey="U">Theoretical Methods: SCF to FCI</a> »</li>
</ul>
</div>
</div>
<div class="document">
<div class="documentwrapper">
<div class="bodywrapper">
<div class="body" role="main">
<a class="reference internal image-reference" href="_images/psi4banner.png"><img alt="Psi4 Project Logo" src="_images/psi4banner.png" style="width: 100%;" /></a>
<div class="section" id="psimrcc-implementation-of-mk-mrcc-theory">
<span id="sec-psimrcc"></span><span id="index-0"></span><h1>PSIMRCC Implementation of Mk-MRCC Theory<a class="headerlink" href="#psimrcc-implementation-of-mk-mrcc-theory" title="Permalink to this headline">¶</a></h1>
<p><em>Code author: Francesco A. Evangelista and Andrew C. Simmonett</em></p>
<p><em>Section author: Alexander E. Vaughn</em></p>
<p><em>Module:</em> <a class="reference internal" href="autodir_options_c/module__psimrcc.html#apdx-psimrcc"><span>Keywords</span></a>, <a class="reference internal" href="autodir_psivariables/module__psimrcc.html#apdx-psimrcc-psivar"><span>PSI Variables</span></a>, <a class="reference external" href="https://github.com/psi4/psi4public/blob/master/src/bin/psimrcc">PSIMRCC</a></p>
<p>State-specific Multireference coupled cluster theories provide highly
accurate energies and properties of electronic states that require
a multiconfigurational zeroth-order wavefunction. The PSIMRCC
module contained in <span class="sc">Psi4</span> implements the state-specific
multireference coupled-cluster approach of Mukherjee and co-workers
(Mk-MRCC). This method is implemented and shown to be a powerful tool in
<a class="reference internal" href="bibliography.html#evangelista-2006-154113" id="id1">[Evangelista:2006:154113]</a> and <a class="reference internal" href="bibliography.html#evangelista-2008-124104" id="id2">[Evangelista:2008:124104]</a>. Mk-MRCC is
based on the Jeziorski-Monkhorst ansatz <a class="reference internal" href="bibliography.html#jeziorski-1981-1668" id="id3">[Jeziorski:1981:1668]</a> for the
wavefunction, <img class="math" src="_images/math/fcb42b580fc37b67d357c1314f2be5e2057d0917.png" alt="\Psi" style="vertical-align: -1px"/></p>
<div class="math">
<p><img src="_images/math/a82c54ce94410385c4be321103914de7ac9cdc8e.png" alt="\left| \Psi \right \rangle = \sum_\mu^d e^{\hat{T}^\mu} \left| \Phi_\mu \right\rangle c_\mu \, \text{,}"/></p>
</div><p>where <img class="math" src="_images/math/43683e2e610738c15b14d6f0c665681767395149.png" alt="\Phi_\mu" style="vertical-align: -6px"/> are the reference determinants,
<img class="math" src="_images/math/dfd83367e1aca7f386eb1f7abbea59136e72658f.png" alt="\hat{T}^\mu" style="vertical-align: 0px"/> are reference-specific excitation operators, and
<img class="math" src="_images/math/360349f624c2dbf07b7acd0c00ced7ccc5f80f0c.png" alt="c_\mu" style="vertical-align: -6px"/> are expansion coefficients obtained through diagonalization
of the Mk-MRCC effective Hamiltonian matrix that allows the various
reference determinants to interact. As an example of how this works
the Mk-MRCCSD excitation operators for each reference is contracted
two-body terms</p>
<div class="math">
<p><img src="_images/math/4f01c8ed99ec695c92c838417ebf4ea099051e5e.png" alt="\hat{T}^\mu = \hat{T}^\mu_1 + \hat{T}^\mu_2"/></p>
</div><p>where</p>
<div class="math">
<p><img src="_images/math/2e61a3f74b59661783dafcee2394a4f671346b80.png" alt="\hat{T}^\mu_1 = \sum_i^{\textrm{occ}(\mu)} \sum_a^{\textrm{vir}(\mu)} t_i^a (\mu) \hat{a}^\dagger_a \hat{a}_i"/></p>
</div><p>and</p>
<div class="math">
<p><img src="_images/math/073afd07c7a47ce514626de75aff29f3fec8e032.png" alt="\hat{T}^\mu_2 =\frac{1}{4} \sum_i^{\textrm{occ}(\mu)} \sum_a^{\textrm{vir}(\mu)} t_{ij}^{ab} (\mu) \hat{a}^\dagger_b \hat{a}_j \hat{a}^\dagger_a \hat{a}_i"/></p>
</div><p>The Mk-MRCC energy is a chosen eigenvalue of the effective Hamiltonian,
<img class="math" src="_images/math/5713e86d2699be483c164ef9d1cbab2202e4a8c1.png" alt="\textrm{H}^{eff}_{\mu \nu}" style="vertical-align: -8px"/></p>
<div class="math">
<p><img src="_images/math/fd3da65b60718149b984c1e8886395fdc32be691.png" alt="\sum_\nu \textrm{H}^{eff}_{\mu \nu} c_\nu =E c_\nu"/></p>
</div><p>where</p>
<div class="math">
<p><img src="_images/math/03b824bec1b710e919caed2dc6bbb648ab66b699.png" alt="\textrm{H}^{eff}_{\mu \nu} = \left \langle \Phi_\mu \right | \hat{H}e^{\hat{T}^\nu} \left | \Phi_\nu \right \rangle \, \textrm{.}"/></p>
</div><p><span class="sc">Psi4</span> currently implements Mk-MRCC with singles and doubles
[Mk-MRCCSD] and Mk-MRCCSD with perturbative triples [Mk-MRCCSD(T)]
as formulated in <a class="reference internal" href="bibliography.html#evangelista-2010-074107" id="id4">[Evangelista:2010:074107]</a>. A companion perturbation
method (Mk-MRPT2) has been developed based on the Mukherjee formalisim
as shown in <a class="reference internal" href="bibliography.html#evangelista-2009-4728" id="id5">[Evangelista:2009:4728]</a>.</p>
<p>The current version of the code is limited to reference active spaces
in which all determinants are connected to each other by no more than two
excitations. In practice, this usually means that the active space can have
at most two particles, or at most two holes. Examples would include
CAS(2,2), CAS(2,8), CAS(4,3), etc., where CAS(n,m) refers to a
complete-active-space configuration interaction (CAS-CI) reference with n
electrons in m orbitals. If the user specifies active spaces that do not fit
these limitations, then the code will still run, but some relevant
determinants will be missing, and the answer obtained will be an approximation
to the true Mk-MRCC procedure.</p>
<p>The PSIMRCC code itself does not perform orbital optimization. Hence, the
references used might be considered CAS-CI references, but not CASSCF
references (CASSCF implies that the orbitals have been optimized specifically
to minimize the energy of the CAS-CI reference). However, if one wishes to
use two-configuration self-consistent-field (TCSCF) orbitals, those can
be obtained using the multi-configuration self-consistent-field (MCSCF)
component of PSIMRCC (specifying <a class="reference internal" href="autodoc_glossary_options_c.html#term-reference-mcscf"><span class="xref std std-term">REFERENCE</span></a> to be <code class="docutils literal"><span class="pre">twocon</span></code>).
This is suitable for describing diradicals. Otherwise, one may use RHF or
ROHF orbitals as input to PSIMRCC. Due to a current limitation in the code,
one must obtain orbitals using PSIMRCC’s MCSCF module regardless of what
orbital type is chosen, <code class="docutils literal"><span class="pre">twocon</span></code>, <code class="docutils literal"><span class="pre">rhf</span></code>, or <code class="docutils literal"><span class="pre">rohf</span></code>. An example of the
MCSCF input is given below.</p>
<p>PSIMRCC is most commonly used for low-spin cases (singlets or open-shell
singlets). It is capable of performing computations on higher spin states
(e.g., triplets), but in general, not all the required matrix elements have
been coded for high-spin cases, meaning that results will correspond to an
approximate Mk-MRCC computation for high-spin cases.</p>
<div class="section" id="a-simple-example">
<h2>A Simple Example<a class="headerlink" href="#a-simple-example" title="Permalink to this headline">¶</a></h2>
<p>The <a class="reference internal" href="autodoc_glossary_options_c.html#term-corr-wfn-psimrcc"><span class="xref std std-term">CORR_WFN</span></a> allows you to select one of three methods
Mk-MRPT2 [<code class="docutils literal"><span class="pre">PT2</span></code>], Mk-MRCCSD [<code class="docutils literal"><span class="pre">CCSD</span></code>], or Mk-MRCCSD(T) [<code class="docutils literal"><span class="pre">CCSD_T</span></code>].
The <a class="reference internal" href="autodoc_glossary_options_c.html#term-corr-multp-psimrcc"><span class="xref std std-term">CORR_MULTP</span></a> option allows you to select the Slater
determinants with a particular <img class="math" src="_images/math/19bd28226d5c470d30f7497311211ab6221ac711.png" alt="M_s" style="vertical-align: -3px"/> value. The <a class="reference internal" href="autodoc_glossary_options_c.html#term-wfn-sym-psimrcc"><span class="xref std std-term">WFN_SYM</span></a>
keyword is neccesary if you do not want to compute the energy of the
totally-symmetric state. The <a class="reference internal" href="autodoc_glossary_options_c.html#term-follow-root-psimrcc"><span class="xref std std-term">FOLLOW_ROOT</span></a> option may be used
to follow different roots of the effective Hamiltonian. A value of 1
instructs PSIMRCC to follow the solution with the lowest energy given
a certain set of determinants.</p>
<div class="highlight-python"><div class="highlight"><pre>molecule o2 {
0 3
O
O 1 2.265122720724
units au
}
set {
basis cc-pvtz
}
set mcscf {
reference rohf
docc [3,0,0,0,0,2,1,1] # Doubly occupied MOs
socc [0,0,1,1,0,0,0,0] # Singly occupied MOs
}
set psimrcc {
corr_wfn ccsd # Do Mk-MRCCSD
frozen_docc [1,0,0,0,0,1,0,0] # Frozen MOs
restricted_docc [2,0,0,0,0,1,1,1] # Doubly occupied MOs
active [0,0,1,1,0,0,0,0] # Active MOs
frozen_uocc [0,0,0,0,0,0,0,0] # Frozen virtual MOs
corr_multp 1 # Select the Ms = 0 component
follow_root 1
wfn_sym B1g # Select the B1g state
}
energy('psimrcc')
</pre></div>
</div>
<p>Note that the oxygen molecule has 16 electrons (including core), while
the <code class="docutils literal"><span class="pre">docc</span></code> array contains only 7 doubly-occupied orbitals (or 14
electrons). Hence, two more electrons are available to place into
the active space (given by <code class="docutils literal"><span class="pre">active</span></code>), which consists of 2 orbitals.
Thus there are two active electrons in two orbitals. In this particular
example, we are using standard ROHF orbitals for the Mk-MRCCSD procedure,
rather than TCSCF orbitals. Nevertheless, with the present code,
these orbitals must be provided through the MCSCF module, as specified in the
<code class="docutils literal"><span class="pre">set</span> <span class="pre">mcscf</span></code> section above.</p>
</div>
<div class="section" id="orbital-ordering-and-selection-of-the-model-space">
<h2>Orbital ordering and selection of the model space<a class="headerlink" href="#orbital-ordering-and-selection-of-the-model-space" title="Permalink to this headline">¶</a></h2>
<p>The reference determinants <img class="math" src="_images/math/43683e2e610738c15b14d6f0c665681767395149.png" alt="\Phi_\mu" style="vertical-align: -6px"/> are specified in PSIMRCC
via occupational numbers. PSIMRCC requires that four arrays be specified
for this purpose.</p>
<ul class="simple">
<li>Frozen doubly occupied orbitals (<a href="#id6"><span class="problematic" id="id7">|psimrcc__frozen_docc|</span></a>) are doubly
occupied in each reference determinant and are not correlated in the
MRCC procedure.</li>
<li>Doubly occupied orbitals (<a href="#id8"><span class="problematic" id="id9">|psimrcc__restricted_docc|</span></a>) are doubly
occupied in each reference determinant and are correlated in the MRCC
procedure.</li>
<li>Active orbitals (<a href="#id10"><span class="problematic" id="id11">|psimrcc__active|</span></a>) are partially occupied in each
reference determinant.</li>
<li>Frozen virtual orbitals (<a href="#id12"><span class="problematic" id="id13">|psimrcc__frozen_uocc|</span></a>) are unoccupied in
all reference determinants and are excluded from the correlated wave
function.</li>
</ul>
<p>The model space is selected by considering all possible occupations
of the electrons among the orbitals in the active space that result
in determinants with the correct symmetry (<a class="reference internal" href="autodoc_glossary_options_c.html#term-wfn-sym-psimrcc"><span class="xref std std-term">WFN_SYM</span></a>)
and the correct <img class="math" src="_images/math/8569bb797b14308b6402e0b19a2b4b6dcc9a6dd1.png" alt="\textrm{M}_s" style="vertical-align: -3px"/> value specified by the keyword
<a class="reference internal" href="autodoc_glossary_options_c.html#term-corr-multp-psimrcc"><span class="xref std std-term">CORR_MULTP</span></a>. Note that this does not consider the multiplicity
of the wavefunction. Thus, in order to obtain the wavefunction
with a set of <img class="math" src="_images/math/7d6c6236038bcb70ae2b99a0b36375ae77bc23db.png" alt="\textrm{M}_s = 0" style="vertical-align: -3px"/> reference determinants for
an open-shell system you should request a <a class="reference internal" href="autodoc_glossary_options_c.html#term-corr-multp-psimrcc"><span class="xref std std-term">CORR_MULTP</span></a> of
1 within the PSIMRCC module, and select the root of the effective
Hamiltonian that corresponds to the state of interest. In addition,
the <a class="reference internal" href="autodoc_glossary_options_c.html#term-wfn-sym-psimrcc"><span class="xref std std-term">WFN_SYM</span></a> keyword needs to be specified otherwise the
wavefunction belonging to the all-symmetric irrep will be selected. In
addition, it should be noted that for an open-shell singlet based
on two <img class="math" src="_images/math/7d6c6236038bcb70ae2b99a0b36375ae77bc23db.png" alt="\textrm{M}_s = 0" style="vertical-align: -3px"/> determinants the eigenvector is
[<img class="math" src="_images/math/8a26f31852cf4ec5ba2aebbb139e62d716c3b109.png" alt="\frac{1}{\sqrt{2}}\text{,}\frac{1}{\sqrt{2}}" style="vertical-align: -10px"/>], which corresponds
to a wavefunction of the following form:</p>
<div class="math">
<p><img src="_images/math/1fc3d725aeacb1f72eb0341f50017bdc9aee0a9b.png" alt="\frac{1}{\sqrt{2}} \left( \chi_1 \alpha (1) \chi_2 \beta (2) + \chi_2 \alpha(1) \chi_1 \beta (2) \right)"/></p>
</div><p>See Appendix <a class="reference internal" href="autodir_options_c/module__psimrcc.html#apdx-psimrcc"><span>PSIMRCC</span></a> for a complete list of PSIMRCC options.</p>
<style type="text/css"><!--
.green {color: red;}
.sc {font-variant: small-caps;}
--></style></div>
</div>
</div>
</div>
</div>
<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
<div class="sphinxsidebarwrapper">
<h3><a href="index.html">Table Of Contents</a></h3>
<ul>
<li><a class="reference internal" href="#">PSIMRCC Implementation of Mk-MRCC Theory</a><ul>
<li><a class="reference internal" href="#a-simple-example">A Simple Example</a></li>
<li><a class="reference internal" href="#orbital-ordering-and-selection-of-the-model-space">Orbital ordering and selection of the model space</a></li>
</ul>
</li>
</ul>
<h4>Previous topic</h4>
<p class="topless"><a href="occ.html"
title="previous chapter">OCC: Orbital-Optimized Coupled-Cluster and Møller–Plesset Perturbation Theories</a></p>
<h4>Next topic</h4>
<p class="topless"><a href="detci.html"
title="next chapter">CI: Configuration Interaction</a></p>
<div role="note" aria-label="source link">
<h3>This Page</h3>
<ul class="this-page-menu">
<li><a href="_sources/psimrcc.txt"
rel="nofollow">Show Source</a></li>
</ul>
</div>
<div id="searchbox" style="display: none" role="search">
<h3>Quick search</h3>
<form class="search" action="search.html" method="get">
<input type="text" name="q" />
<input type="submit" value="Go" />
<input type="hidden" name="check_keywords" value="yes" />
<input type="hidden" name="area" value="default" />
</form>
<p class="searchtip" style="font-size: 90%">
Enter search terms or a module, class or function name.
</p>
</div>
<script type="text/javascript">$('#searchbox').show(0);</script>
</div>
</div>
<div class="clearer"></div>
</div>
<div class="relbar-bottom">
<div class="related" role="navigation" aria-label="related navigation">
<h3>Navigation</h3>
<ul>
<li class="right" style="margin-right: 10px">
<a href="genindex.html" title="General Index"
>index</a></li>
<li class="right" >
<a href="py-modindex.html" title="Python Module Index"
>modules</a> </li>
<li class="right" >
<a href="contents.html" title="Table Of Contents"
>toc</a> </li>
<li class="right" >
<a href="detci.html" title="CI: Configuration Interaction"
>next</a> </li>
<li class="right" >
<a href="occ.html" title="OCC: Orbital-Optimized Coupled-Cluster and Møller–Plesset Perturbation Theories"
>previous</a> </li>
<li><a href="index.html">Psi4 []</a> » </li>
<li class="nav-item nav-item-1"><a href="methods.html" >Theoretical Methods: SCF to FCI</a> »</li>
</ul>
</div>
</div>
<div class="footer" role="contentinfo">
© Copyright 2015, The Psi4 Project.
Last updated on Tuesday, 12 January 2016 03:10PM.
Created using <a href="http://sphinx-doc.org/">Sphinx</a> 1.3.3.
</div>
<!-- cloud_sptheme 1.3 -->
</body>
</html>
|