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<div class="section" id="sapt-symmetry-adapted-perturbation-theory">
<span id="sec-sapt"></span><span id="index-0"></span><h1>SAPT: Symmetry-Adapted Perturbation Theory<a class="headerlink" href="#sapt-symmetry-adapted-perturbation-theory" title="Permalink to this headline">¶</a></h1>
<p><em>Code author: Edward G. Hohenstein and Rob M. Parrish</em></p>
<p><em>Section author: Edward G. Hohenstein</em></p>
<p><em>Module:</em> <a class="reference internal" href="autodir_options_c/module__sapt.html#apdx-sapt"><span>Keywords</span></a>, <a class="reference internal" href="autodir_psivariables/module__sapt.html#apdx-sapt-psivar"><span>PSI Variables</span></a>, <a class="reference external" href="https://github.com/psi4/psi4public/blob/master/src/lib/libsapt_solver">LIBSAPT_SOLVER</a></p>
<div class="admonition warning">
<p class="first admonition-title">Warning</p>
<p class="last">In rare cases with systems having a high degree of symmetry,
<span class="sc">Psi4</span> gives (very obviously) wrong answers for SAPT computations
when the specification is in Z-matrix format. Use a Cartesian representation
to avoid this problem.</p>
</div>
<div class="admonition caution">
<p class="first admonition-title">Caution</p>
<p class="last">In early versions (notably <span class="sc">Psi4</span> alpha circa 2011
and before), frozen core was implemented incompletely and for
only selected terms. Comparisons with papers published using early
<span class="sc">Psi4</span> SAPT code may show discrepancies of 0.01-0.10 kcal/mol in
individual terms, particularly E_{exch}^{(11)} and E_{exch}^{(12)}.</p>
</div>
<p>Symmetry-adapted perturbation theory (SAPT) provides a means of directly
computing the noncovalent interaction between two molecules, that is, the
interaction energy is determined without computing the total energy of the
monomers or dimer. In addition, SAPT provides a decomposition of the
interaction energy into physically meaningful components: <em>i.e.,</em>
electrostatic, exchange, induction, and dispersion terms. In SAPT, the
Hamiltonian of the dimer is partitioned into contributions from each
monomer and the interaction.</p>
<div class="math">
<p><img src="_images/math/38925e9d7d4fbd7e9a78e27e46e20c6f4cf2cab3.png" alt="H=F_A+W_A+F_B+W_B+V"/></p>
</div><p>Here, the Hamiltonian is written as a sum of the usual monomer Fock
operators, <img class="math" src="_images/math/68b0fc4683e0c8842b3a6cc6920f022f1c0db3fa.png" alt="F" style="vertical-align: 0px"/>, the fluctuation potential of each monomer, <img class="math" src="_images/math/a74ef8173c38d8f5718fd92b309bece2c063c461.png" alt="W" style="vertical-align: 0px"/>, and the
interaction potential, <img class="math" src="_images/math/57b15dec6cc2aff6f74462a73e17ab6d2431e92a.png" alt="V" style="vertical-align: 0px"/>. The monomer Fock operators, <img class="math" src="_images/math/ccb92331da2c4cc40a70318c004eb910ab5e7a8e.png" alt="F_A+F_B" style="vertical-align: -3px"/>, are
treated as the zeroth-order Hamiltonian and the interaction energy is
evaluated through a perturbative expansion of <img class="math" src="_images/math/57b15dec6cc2aff6f74462a73e17ab6d2431e92a.png" alt="V" style="vertical-align: 0px"/>, <img class="math" src="_images/math/bcf03564897621cbb5181aa4978f7bb1a10ac3b9.png" alt="W_A" style="vertical-align: -3px"/>, and <img class="math" src="_images/math/7a540ce8239edccd2de0c988020db7de63f55879.png" alt="W_B" style="vertical-align: -3px"/>.
Through first-order in <img class="math" src="_images/math/57b15dec6cc2aff6f74462a73e17ab6d2431e92a.png" alt="V" style="vertical-align: 0px"/>, electrostatic and exchange interactions are
included; induction and dispersion first appear at second-order in <img class="math" src="_images/math/57b15dec6cc2aff6f74462a73e17ab6d2431e92a.png" alt="V" style="vertical-align: 0px"/>. For
a complete description of SAPT, the reader is referred to the excellent
review by Jeziorski, Moszynski, and Szalewicz <a class="reference internal" href="bibliography.html#jeziorski-1994-1887" id="id1">[Jeziorski:1994:1887]</a>.</p>
<p>Several truncations of the SAPT expansion are available in the SAPT
module of <span class="sc">Psi4</span>. The simplest truncation of SAPT is denoted SAPT0
and defined in Eq. <a href="#equation-SAPT0">(1)</a>.</p>
<div class="math" id="equation-SAPT0">
<p><span class="eqno">(1)</span><img src="_images/math/b1d67202dad6bba4bb931ceeef455be9a5f5ada6.png" alt="E_{SAPT0} = E_{elst}^{(10)} + E_{exch}^{(10)} + E_{ind,resp}^{(20)} +
E_{exch-ind,resp}^{(20)} + E_{disp}^{(20)} + E_{exch-disp}^{(20)}"/></p>
</div><p>In this notation, <img class="math" src="_images/math/d483265c965cc330597b72bdaddf1f052dc52e96.png" alt="E^{(vw)}" style="vertical-align: 0px"/> defines the order in <img class="math" src="_images/math/57b15dec6cc2aff6f74462a73e17ab6d2431e92a.png" alt="V" style="vertical-align: 0px"/> and in <img class="math" src="_images/math/0a5e2d40a4de60e75dba03f704f56a98e33e3695.png" alt="W_A+W_B" style="vertical-align: -3px"/>; the
subscript, <img class="math" src="_images/math/560b141fb1d93d5acc672f20eee4c8a2f6483e83.png" alt="resp" style="vertical-align: -4px"/>, indicates that orbital relaxation effects are included.</p>
<div class="math" id="equation-SAPT2">
<p><span class="eqno">(2)</span><img src="_images/math/a16b1833860bc3612fc1f28f17b2cdd0882068b4.png" alt="E_{SAPT2} = E_{SAPT0} + E_{elst,resp}^{(12)} + E_{exch}^{(11)} +
E_{exch}^{(12)} +\/ ^{t}\!E_{ind}^{(22)} +\/ ^{t}\!E_{exch-ind}^{(22)}"/></p>
</div><div class="math" id="equation-SAPT2p">
<p><span class="eqno">(3)</span><img src="_images/math/9016cc61d302a4334bea548e723eb30b0592746c.png" alt="E_{SAPT2+} = E_{SAPT2} + E_{disp}^{(21)} + E_{disp}^{(22)}"/></p>
</div><div class="math" id="equation-SAPT2pparen3">
<p><span class="eqno">(4)</span><img src="_images/math/4eca9f9f6767693e303771eb8f84ed04130e3745.png" alt="E_{SAPT2+(3)} = E_{SAPT2+} + E_{elst,resp}^{(13)} + E_{disp}^{(30)}"/></p>
</div><div class="math" id="equation-SAPT2p3">
<p><span class="eqno">(5)</span><img src="_images/math/c81b3e98c85338255683678a0971aaa8fc5c0365.png" alt="E_{SAPT2+3} = E_{SAPT2+(3)}
+ E_{exch-disp}^{(30)} + E_{ind-disp}^{(30)} + E_{exch-ind-disp}^{(30)}"/></p>
</div><p>A thorough analysis of the performance of these truncations of SAPT can be
found in a review by Hohenstein and Sherrill <a class="reference internal" href="bibliography.html#hohenstein-2012-wires" id="id2">[Hohenstein:2012:WIREs]</a>,
and a systematic study of the accuracy of these truncations (with and
without an improved CCD treatment of dispersion) usng different basis sets
is reported in <a class="reference internal" href="bibliography.html#parker-2014-094106" id="id3">[Parker:2014:094106]</a>.</p>
<p>The SAPT module relies entirely on the density-fitting approximation
of the two-electron integrals. The factorization of the SAPT energy
expressions, as implemented in <span class="sc">Psi4</span>, assumes the use of density-fitted
two-electron integrals, therefore, the SAPT module cannot be run with
exact integrals. In practice, we have found that the density-fitting
approximation introduces negligible errors into the SAPT energy
(often less than 0.01 kcal/mol for small dimers) and greatly
improves efficiency.</p>
<div class="section" id="a-first-example">
<h2>A First Example<a class="headerlink" href="#a-first-example" title="Permalink to this headline">¶</a></h2>
<p>The following is the simplest possible input that will perform all
available SAPT computations (normally, you would pick one of these methods).</p>
<div class="highlight-python"><div class="highlight"><pre>molecule water_dimer {
0 1
O -1.551007 -0.114520 0.000000
H -1.934259 0.762503 0.000000
H -0.599677 0.040712 0.000000
--
0 1
O 1.350625 0.111469 0.000000
H 1.680398 -0.373741 -0.758561
H 1.680398 -0.373741 0.758561
units angstrom
no_reorient
symmetry c1
}
set globals {
basis aug-cc-pvdz
}
energy('sapt0')
energy('sapt2')
energy('sapt2+')
energy('sapt2+(3)')
energy('sapt2+3')
</pre></div>
</div>
<p>The SAPT module uses the standard <span class="sc">Psi4</span> partitioning of the dimer
into monomers. SAPT does not use spatial symmetry and needs the geometry
of the system to remain fixed throughout monomer and dimer calculations.
These requirements are imposed whenever a SAPT calculation is requested
but can also be set explicitly with the <code class="docutils literal"><span class="pre">no_reorient</span></code> and <code class="docutils literal"><span class="pre">symmetry</span>
<span class="pre">c1</span></code> molecule keywords, as in the example above. A final note is that the
SAPT module is only capable of performing SAPT computations for
interactions between closed-shell singlets.</p>
<p>The example input shown above would not be used in practice.
To exploit the efficiency of the density-fitted SAPT implementation in
<span class="sc">Psi4</span>, the SCF computations should also be performed with density-fitted
(DF) integrals.</p>
<div class="highlight-python"><div class="highlight"><pre>set globals {
basis aug-cc-pvdz
df_basis_scf aug-cc-pvdz-jkfit
df_basis_sapt aug-cc-pvdz-ri
guess sad
scf_type df
}
set sapt {
print 1
}
</pre></div>
</div>
<p>These options will perform the SAPT computation with DF-HF and a
superposition-of-atomic-densities guess. This is the preferred method of
running the SAPT module.</p>
</div>
<div class="section" id="sapt0">
<span id="index-1"></span><h2>SAPT0<a class="headerlink" href="#sapt0" title="Permalink to this headline">¶</a></h2>
<p>Generally speaking, SAPT0 should be applied to large systems or large data
sets. The performance of SAPT0 relies entirely on error cancellation, which
seems to be optimal with a truncated aug-cc-pVDZ basis, namely,
jun-cc-pVDZ (which we have referred to in previous work as
aug-cc-pVDZ’). We do not recommend using SAPT0 with large basis sets
like aug-cc-pVTZ. A systematic study of the accuracy of SAPT0 and other SAPT
truncations, using different basis sets, is reported in
<a class="reference internal" href="bibliography.html#parker-2014-094106" id="id4">[Parker:2014:094106]</a>.
The SAPT module has been used to perform SAPT0 computations with over
200 atoms and 2800 basis functions; this code should be scalable to 4000
basis functions. Publications resulting from the use of the SAPT0 code
should cite the following publications: <a class="reference internal" href="bibliography.html#hohenstein-2010-184111" id="id5">[Hohenstein:2010:184111]</a> and
<a class="reference internal" href="bibliography.html#hohenstein-2011-174107" id="id6">[Hohenstein:2011:174107]</a>.</p>
<div class="section" id="basic-sapt0-keywords">
<h3>Basic SAPT0 Keywords<a class="headerlink" href="#basic-sapt0-keywords" title="Permalink to this headline">¶</a></h3>
<div class="section" id="sapt-level">
<h4><a class="reference internal" href="autodoc_glossary_options_c.html#term-sapt-level-sapt"><span class="xref std std-term">SAPT_LEVEL</span></a><a class="headerlink" href="#sapt-level" title="Permalink to this headline">¶</a></h4>
<blockquote>
<div><p>The level of theory for SAPT</p>
<ul class="simple">
<li><strong>Type</strong>: string</li>
<li><strong>Possible Values</strong>: SAPT0, SAPT2, SAPT2+, SAPT2+3</li>
<li><strong>Default</strong>: SAPT0</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="basis">
<h4><a class="reference internal" href="autodoc_glossary_options_c.html#term-basis-sapt"><span class="xref std std-term">BASIS</span></a><a class="headerlink" href="#basis" title="Permalink to this headline">¶</a></h4>
<blockquote>
<div><p>Primary basis set, describes the monomer molecular orbitals</p>
<ul class="simple">
<li><strong>Type</strong>: string</li>
<li><strong>Possible Values</strong>: <a class="reference internal" href="basissets_byelement.html#apdx-basiselement"><span>basis string</span></a></li>
<li><strong>Default</strong>: No Default</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="df-basis-sapt">
<h4><a class="reference internal" href="autodoc_glossary_options_c.html#term-df-basis-sapt-sapt"><span class="xref std std-term">DF_BASIS_SAPT</span></a><a class="headerlink" href="#df-basis-sapt" title="Permalink to this headline">¶</a></h4>
<blockquote>
<div><p>Auxiliary basis set for SAPT density fitting computations. <a class="reference internal" href="basissets_byfamily.html#apdx-basisfamily"><span>Defaults</span></a> to a RI basis.</p>
<ul class="simple">
<li><strong>Type</strong>: string</li>
<li><strong>Possible Values</strong>: <a class="reference internal" href="basissets_byelement.html#apdx-basiselement"><span>basis string</span></a></li>
<li><strong>Default</strong>: No Default</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="df-basis-elst">
<h4><a class="reference internal" href="autodoc_glossary_options_c.html#term-df-basis-elst-sapt"><span class="xref std std-term">DF_BASIS_ELST</span></a><a class="headerlink" href="#df-basis-elst" title="Permalink to this headline">¶</a></h4>
<blockquote>
<div><p>Auxiliary basis set for SAPT Elst10 and Exch10 density fitting computations, may be important if heavier elements are involved. Defaults to <a class="reference internal" href="autodoc_glossary_options_c.html#term-df-basis-sapt-sapt"><span class="xref std std-term">DF_BASIS_SAPT</span></a></p>
<ul class="simple">
<li><strong>Type</strong>: string</li>
<li><strong>Possible Values</strong>: <a class="reference internal" href="basissets_byelement.html#apdx-basiselement"><span>basis string</span></a></li>
<li><strong>Default</strong>: No Default</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="freeze-core">
<h4><a class="reference internal" href="autodoc_glossary_options_c.html#term-freeze-core-sapt"><span class="xref std std-term">FREEZE_CORE</span></a><a class="headerlink" href="#freeze-core" title="Permalink to this headline">¶</a></h4>
<blockquote>
<div><p>The scope of core orbitals to freeze in evaluation of SAPT <img class="math" src="_images/math/ec7f0604b9d141e2736481a4ac14960d9fe1bab3.png" alt="E_{disp}^{(20)}" style="vertical-align: -8px"/> and <img class="math" src="_images/math/e405ddfda48867f455cd9cf0e6277ff66bbf8802.png" alt="E_{exch-disp}^{(20)}" style="vertical-align: -8px"/> terms. Recommended true for all SAPT computations</p>
<ul class="simple">
<li><strong>Type</strong>: string</li>
<li><strong>Possible Values</strong>: FALSE, TRUE</li>
<li><strong>Default</strong>: FALSE</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="d-convergence">
<h4><a class="reference internal" href="autodoc_glossary_options_c.html#term-d-convergence-sapt"><span class="xref std std-term">D_CONVERGENCE</span></a><a class="headerlink" href="#d-convergence" title="Permalink to this headline">¶</a></h4>
<blockquote>
<div><p>Convergence criterion for residual of the CPHF coefficients in the SAPT <img class="math" src="_images/math/b377ecdee22f10915c68e0bdebc341f1b17d2e1e.png" alt="E_{ind,resp}^{(20)}" style="vertical-align: -8px"/> term.</p>
<ul class="simple">
<li><strong>Type</strong>: <a class="reference internal" href="notes_c.html#op-c-conv"><span>conv double</span></a></li>
<li><strong>Default</strong>: 1e-8</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="e-convergence">
<h4><a class="reference internal" href="autodoc_glossary_options_c.html#term-e-convergence-sapt"><span class="xref std std-term">E_CONVERGENCE</span></a><a class="headerlink" href="#e-convergence" title="Permalink to this headline">¶</a></h4>
<blockquote>
<div><p>Convergence criterion for energy (change) in the SAPT <img class="math" src="_images/math/b377ecdee22f10915c68e0bdebc341f1b17d2e1e.png" alt="E_{ind,resp}^{(20)}" style="vertical-align: -8px"/> term during solution of the CPHF equations.</p>
<ul class="simple">
<li><strong>Type</strong>: <a class="reference internal" href="notes_c.html#op-c-conv"><span>conv double</span></a></li>
<li><strong>Default</strong>: 1e-10</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="maxiter">
<h4><a class="reference internal" href="autodoc_glossary_options_c.html#term-maxiter-sapt"><span class="xref std std-term">MAXITER</span></a><a class="headerlink" href="#maxiter" title="Permalink to this headline">¶</a></h4>
<blockquote>
<div><p>Maxmum number of CPHF iterations</p>
<ul class="simple">
<li><strong>Type</strong>: integer</li>
<li><strong>Default</strong>: 50</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="print">
<h4><a class="reference internal" href="autodoc_glossary_options_c.html#term-print-sapt"><span class="xref std std-term">PRINT</span></a><a class="headerlink" href="#print" title="Permalink to this headline">¶</a></h4>
<blockquote>
<div><p>The amount of information to print to the output file for the sapt module. For 0, only the header and final results are printed. For 1, (recommended for large calculations) some intermediate quantities are also printed.</p>
<ul class="simple">
<li><strong>Type</strong>: integer</li>
<li><strong>Default</strong>: 1</li>
</ul>
</div></blockquote>
</div>
</div>
<div class="section" id="advanced-sapt0-keywords">
<h3>Advanced SAPT0 Keywords<a class="headerlink" href="#advanced-sapt0-keywords" title="Permalink to this headline">¶</a></h3>
<div class="section" id="aio-cphf">
<h4><a class="reference internal" href="autodoc_glossary_options_c.html#term-aio-cphf-sapt"><span class="xref std std-term">AIO_CPHF</span></a><a class="headerlink" href="#aio-cphf" title="Permalink to this headline">¶</a></h4>
<blockquote>
<div><p>Do use asynchronous disk I/O in the solution of the CPHF equations? Use may speed up the computation slightly at the cost of spawning an additional thread.</p>
<ul class="simple">
<li><strong>Type</strong>: <a class="reference internal" href="notes_c.html#op-c-boolean"><span>boolean</span></a></li>
<li><strong>Default</strong>: false</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="aio-df-ints">
<h4><a class="reference internal" href="autodoc_glossary_options_c.html#term-aio-df-ints-sapt"><span class="xref std std-term">AIO_DF_INTS</span></a><a class="headerlink" href="#aio-df-ints" title="Permalink to this headline">¶</a></h4>
<blockquote>
<div><p>Do use asynchronous disk I/O in the formation of the DF integrals? Use may speed up the computation slightly at the cost of spawning an additional thread.</p>
<ul class="simple">
<li><strong>Type</strong>: <a class="reference internal" href="notes_c.html#op-c-boolean"><span>boolean</span></a></li>
<li><strong>Default</strong>: false</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="no-response">
<h4><a class="reference internal" href="autodoc_glossary_options_c.html#term-no-response-sapt"><span class="xref std std-term">NO_RESPONSE</span></a><a class="headerlink" href="#no-response" title="Permalink to this headline">¶</a></h4>
<blockquote>
<div><p>Don’t solve the CPHF equations? Evaluate <img class="math" src="_images/math/924ba130d4bcbf91b50d0c3e64d2abdb53e8d00e.png" alt="E_{ind}^{(20)}" style="vertical-align: -5px"/> and <img class="math" src="_images/math/1162b24f84fb5db66e831b3648170d94da43baf9.png" alt="E_{exch-ind}^{(20)}" style="vertical-align: -5px"/> instead of their response-including coupterparts. Only turn on this option if the induction energy is not going to be used.</p>
<ul class="simple">
<li><strong>Type</strong>: <a class="reference internal" href="notes_c.html#op-c-boolean"><span>boolean</span></a></li>
<li><strong>Default</strong>: false</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="ints-tolerance">
<h4><a class="reference internal" href="autodoc_glossary_options_c.html#term-ints-tolerance-sapt"><span class="xref std std-term">INTS_TOLERANCE</span></a><a class="headerlink" href="#ints-tolerance" title="Permalink to this headline">¶</a></h4>
<blockquote>
<div><p>Minimum absolute value below which all three-index DF integrals and those contributing to four-index integrals are neglected. The default is conservative, but there isn’t much to be gained from loosening it, especially for higher-order SAPT.</p>
<ul class="simple">
<li><strong>Type</strong>: <a class="reference internal" href="notes_c.html#op-c-conv"><span>conv double</span></a></li>
<li><strong>Default</strong>: 1.0e-12</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="denominator-delta">
<h4><a class="reference internal" href="autodoc_glossary_options_c.html#term-denominator-delta-sapt"><span class="xref std std-term">DENOMINATOR_DELTA</span></a><a class="headerlink" href="#denominator-delta" title="Permalink to this headline">¶</a></h4>
<blockquote>
<div><p>Maximum error allowed (Max error norm in Delta tensor) in the approximate energy denominators employed for most of the <img class="math" src="_images/math/ec7f0604b9d141e2736481a4ac14960d9fe1bab3.png" alt="E_{disp}^{(20)}" style="vertical-align: -8px"/> and <img class="math" src="_images/math/e405ddfda48867f455cd9cf0e6277ff66bbf8802.png" alt="E_{exch-disp}^{(20)}" style="vertical-align: -8px"/> evaluation.</p>
<ul class="simple">
<li><strong>Type</strong>: double</li>
<li><strong>Default</strong>: 1.0e-6</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="denominator-algorithm">
<h4><a class="reference internal" href="autodoc_glossary_options_c.html#term-denominator-algorithm-sapt"><span class="xref std std-term">DENOMINATOR_ALGORITHM</span></a><a class="headerlink" href="#denominator-algorithm" title="Permalink to this headline">¶</a></h4>
<blockquote>
<div><p>Denominator algorithm for PT methods. Laplace transformations are slightly more efficient.</p>
<ul class="simple">
<li><strong>Type</strong>: string</li>
<li><strong>Possible Values</strong>: LAPLACE, CHOLESKY</li>
<li><strong>Default</strong>: LAPLACE</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="sapt-os-scale">
<h4><a class="reference internal" href="autodoc_glossary_options_c.html#term-sapt-os-scale-sapt"><span class="xref std std-term">SAPT_OS_SCALE</span></a><a class="headerlink" href="#sapt-os-scale" title="Permalink to this headline">¶</a></h4>
<blockquote>
<div><p>The scale factor used for opposite-spin pairs in SCS computations. SS/OS decomposition performed for <img class="math" src="_images/math/ec7f0604b9d141e2736481a4ac14960d9fe1bab3.png" alt="E_{disp}^{(20)}" style="vertical-align: -8px"/> and <img class="math" src="_images/math/e405ddfda48867f455cd9cf0e6277ff66bbf8802.png" alt="E_{exch-disp}^{(20)}" style="vertical-align: -8px"/> terms.</p>
<ul class="simple">
<li><strong>Type</strong>: double</li>
<li><strong>Default</strong>: 6.0/5.0</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="sapt-ss-scale">
<h4><a class="reference internal" href="autodoc_glossary_options_c.html#term-sapt-ss-scale-sapt"><span class="xref std std-term">SAPT_SS_SCALE</span></a><a class="headerlink" href="#sapt-ss-scale" title="Permalink to this headline">¶</a></h4>
<blockquote>
<div><p>The scale factor used for same-spin pairs in SCS computations. SS/OS decomposition performed for <img class="math" src="_images/math/ec7f0604b9d141e2736481a4ac14960d9fe1bab3.png" alt="E_{disp}^{(20)}" style="vertical-align: -8px"/> and <img class="math" src="_images/math/e405ddfda48867f455cd9cf0e6277ff66bbf8802.png" alt="E_{exch-disp}^{(20)}" style="vertical-align: -8px"/> terms.</p>
<ul class="simple">
<li><strong>Type</strong>: double</li>
<li><strong>Default</strong>: 1.0/3.0</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="debug">
<h4><a class="reference internal" href="autodoc_glossary_options_c.html#term-debug-globals"><span class="xref std std-term">DEBUG</span></a><a class="headerlink" href="#debug" title="Permalink to this headline">¶</a></h4>
<blockquote>
<div><p>The amount of information to print to the output file</p>
<ul class="simple">
<li><strong>Type</strong>: integer</li>
<li><strong>Default</strong>: 0</li>
</ul>
</div></blockquote>
</div>
</div>
</div>
<div class="section" id="higher-order-sapt">
<span id="index-2"></span><h2>Higher-Order SAPT<a class="headerlink" href="#higher-order-sapt" title="Permalink to this headline">¶</a></h2>
<p>For smaller systems (up to the size of a nucleic acid base pair), more
accurate interaction energies can be obtained through higher-order SAPT
computations. The SAPT module can perform density-fitted evaluations
of SAPT2, SAPT2+, SAPT2+(3), and SAPT2+3 energies. Publications resulting
from the use of the higher-order SAPT code should cite the following:
<a class="reference internal" href="bibliography.html#hohenstein-2010-014101" id="id7">[Hohenstein:2010:014101]</a>.</p>
<p>For methods SAPT2+ and above, one can replace the many-body treatment of
dispersion by an improved method based on coupled-cluster doubles (CCD).
This approach tends to give good improvements when dispersion effects
are very large, as in the PCCP dimer (see <a class="reference internal" href="bibliography.html#hohenstein-2011-2842" id="id8">[Hohenstein:2011:2842]</a>).
As shown in <a class="reference internal" href="bibliography.html#parker-2014-094106" id="id9">[Parker:2014:094106]</a>, whether or not CCD dispersion offers
more accurate interaction energies tends to depend on the SAPT truncation
and basis set employed, due to cancellations of errors. Thanks to
natural orbital methods <a class="reference internal" href="bibliography.html#parrish-2013-174102" id="id10">[Parrish:2013:174102]</a>, the SAPT code in Psi
is able to include CCD dispersion with only a modest additional cost.
Computations employing CCD dispersion should cite <a class="reference internal" href="bibliography.html#parrish-2013-174102" id="id11">[Parrish:2013:174102]</a>.</p>
<p>A brief note on memory usage: the higher-order SAPT code assumes that
certain quantities can be held in core. This code requires sufficient
memory to hold <img class="math" src="_images/math/89535c3e7936927bd76e14d5e96cb44945a0abdd.png" alt="3o^2v^2+v^2N_{aux}" style="vertical-align: -3px"/> arrays in core. With this
requirement computations on the adenine-thymine complex can be performed
with an aug-cc-pVTZ basis in less than 64GB of memory.</p>
<p>Higher-order SAPT is treated separately from the higly optimized SAPT0
code, therefore, higher-order SAPT uses a separate set of keywords.
The following keywords are relevant for higher-order SAPT.</p>
<div class="section" id="basic-keywords-for-higher-order-sapt">
<h3>Basic Keywords for Higher-order SAPT<a class="headerlink" href="#basic-keywords-for-higher-order-sapt" title="Permalink to this headline">¶</a></h3>
<div class="section" id="id12">
<h4><a class="reference internal" href="autodoc_glossary_options_c.html#term-basis-sapt"><span class="xref std std-term">BASIS</span></a><a class="headerlink" href="#id12" title="Permalink to this headline">¶</a></h4>
<blockquote>
<div><p>Primary basis set, describes the monomer molecular orbitals</p>
<ul class="simple">
<li><strong>Type</strong>: string</li>
<li><strong>Possible Values</strong>: <a class="reference internal" href="basissets_byelement.html#apdx-basiselement"><span>basis string</span></a></li>
<li><strong>Default</strong>: No Default</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="id13">
<h4><a class="reference internal" href="autodoc_glossary_options_c.html#term-df-basis-sapt-sapt"><span class="xref std std-term">DF_BASIS_SAPT</span></a><a class="headerlink" href="#id13" title="Permalink to this headline">¶</a></h4>
<blockquote>
<div><p>Auxiliary basis set for SAPT density fitting computations. <a class="reference internal" href="basissets_byfamily.html#apdx-basisfamily"><span>Defaults</span></a> to a RI basis.</p>
<ul class="simple">
<li><strong>Type</strong>: string</li>
<li><strong>Possible Values</strong>: <a class="reference internal" href="basissets_byelement.html#apdx-basiselement"><span>basis string</span></a></li>
<li><strong>Default</strong>: No Default</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="id14">
<h4><a class="reference internal" href="autodoc_glossary_options_c.html#term-freeze-core-globals"><span class="xref std std-term">FREEZE_CORE</span></a><a class="headerlink" href="#id14" title="Permalink to this headline">¶</a></h4>
<blockquote>
<div><p>Specifies how many core orbitals to freeze in correlated computations. <code class="docutils literal"><span class="pre">TRUE</span></code> will default to freezing the standard default number of core orbitals. For PSI, the standard number of core orbitals is the number of orbitals in the nearest previous noble gas atom. More precise control over the number of frozen orbitals can be attained by using the keywords <a class="reference internal" href="autodoc_glossary_options_c.html#term-num-frozen-docc-globals"><span class="xref std std-term">NUM_FROZEN_DOCC</span></a> (gives the total number of orbitals to freeze, program picks the lowest-energy orbitals) or <a class="reference internal" href="autodoc_glossary_options_c.html#term-frozen-docc-globals"><span class="xref std std-term">FROZEN_DOCC</span></a> (gives the number of orbitals to freeze per irreducible representation)</p>
<ul class="simple">
<li><strong>Type</strong>: string</li>
<li><strong>Possible Values</strong>: FALSE, TRUE</li>
<li><strong>Default</strong>: FALSE</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="id15">
<h4><a class="reference internal" href="autodoc_glossary_options_c.html#term-print-sapt"><span class="xref std std-term">PRINT</span></a><a class="headerlink" href="#id15" title="Permalink to this headline">¶</a></h4>
<blockquote>
<div><p>The amount of information to print to the output file for the sapt module. For 0, only the header and final results are printed. For 1, (recommended for large calculations) some intermediate quantities are also printed.</p>
<ul class="simple">
<li><strong>Type</strong>: integer</li>
<li><strong>Default</strong>: 1</li>
</ul>
</div></blockquote>
</div>
</div>
<div class="section" id="advanced-keywords-for-higher-order-sapt">
<h3>Advanced Keywords for Higher-order SAPT<a class="headerlink" href="#advanced-keywords-for-higher-order-sapt" title="Permalink to this headline">¶</a></h3>
<div class="section" id="id16">
<h4><a class="reference internal" href="autodoc_glossary_options_c.html#term-ints-tolerance-sapt"><span class="xref std std-term">INTS_TOLERANCE</span></a><a class="headerlink" href="#id16" title="Permalink to this headline">¶</a></h4>
<blockquote>
<div><p>Minimum absolute value below which all three-index DF integrals and those contributing to four-index integrals are neglected. The default is conservative, but there isn’t much to be gained from loosening it, especially for higher-order SAPT.</p>
<ul class="simple">
<li><strong>Type</strong>: <a class="reference internal" href="notes_c.html#op-c-conv"><span>conv double</span></a></li>
<li><strong>Default</strong>: 1.0e-12</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="sapt-mem-check">
<h4><a class="reference internal" href="autodoc_glossary_options_c.html#term-sapt-mem-check-sapt"><span class="xref std std-term">SAPT_MEM_CHECK</span></a><a class="headerlink" href="#sapt-mem-check" title="Permalink to this headline">¶</a></h4>
<blockquote>
<div><p>Do force SAPT2 and higher to die if it thinks there isn’t enough memory? Turning this off is ill-advised.</p>
<ul class="simple">
<li><strong>Type</strong>: <a class="reference internal" href="notes_c.html#op-c-boolean"><span>boolean</span></a></li>
<li><strong>Default</strong>: true</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="id17">
<h4><a class="reference internal" href="autodoc_glossary_options_c.html#term-debug-globals"><span class="xref std std-term">DEBUG</span></a><a class="headerlink" href="#id17" title="Permalink to this headline">¶</a></h4>
<blockquote>
<div><p>The amount of information to print to the output file</p>
<ul class="simple">
<li><strong>Type</strong>: integer</li>
<li><strong>Default</strong>: 0</li>
</ul>
</div></blockquote>
</div>
</div>
</div>
<div class="section" id="mp2-natural-orbitals">
<h2>MP2 Natural Orbitals<a class="headerlink" href="#mp2-natural-orbitals" title="Permalink to this headline">¶</a></h2>
<p>One of the unique features of the SAPT module is its ability to use
MP2 natural orbitals (NOs) to speed up the evaluation of the triples
contribution to disperison. By transforming to the MP2 NO basis, we can
throw away virtual orbitals that are expected to contribute little to the
dispersion energy. Speedups in excess of <img class="math" src="_images/math/37f0c1132c18acf8b90015486a923dc8920922ff.png" alt="50 \times" style="vertical-align: 0px"/> are possible. In
practice, this approximation is very good and should always be applied.
Publications resulting from the use of MP2 NO-based approximations should
cite the following: <a class="reference internal" href="bibliography.html#hohenstein-2010-104107" id="id18">[Hohenstein:2010:104107]</a>.</p>
<div class="section" id="basic-keywords-controlling-mp2-no-approximations">
<h3>Basic Keywords Controlling MP2 NO Approximations<a class="headerlink" href="#basic-keywords-controlling-mp2-no-approximations" title="Permalink to this headline">¶</a></h3>
<div class="section" id="nat-orbs-t2">
<h4><a class="reference internal" href="autodoc_glossary_options_c.html#term-nat-orbs-t2-sapt"><span class="xref std std-term">NAT_ORBS_T2</span></a><a class="headerlink" href="#nat-orbs-t2" title="Permalink to this headline">¶</a></h4>
<blockquote>
<div><p>Do use MP2 natural orbital approximations for the <img class="math" src="_images/math/e3e07080ce723935daee3f3587fb1ad02043aed6.png" alt="v^4" style="vertical-align: 0px"/> block of two-electron integrals in the evaluation of second-order T2 amplitudes? Recommended true for all SAPT computations.</p>
<ul class="simple">
<li><strong>Type</strong>: <a class="reference internal" href="notes_c.html#op-c-boolean"><span>boolean</span></a></li>
<li><strong>Default</strong>: false</li>
</ul>
</div></blockquote>
</div>
<div class="section" id="occ-tolerance">
<h4><a class="reference internal" href="autodoc_glossary_options_c.html#term-occ-tolerance-sapt"><span class="xref std std-term">OCC_TOLERANCE</span></a><a class="headerlink" href="#occ-tolerance" title="Permalink to this headline">¶</a></h4>
<blockquote>
<div><p>Minimum occupation (eigenvalues of the MP2 OPDM) below which virtual natural orbitals are discarded for in each of the above three truncations</p>
<ul class="simple">
<li><strong>Type</strong>: <a class="reference internal" href="notes_c.html#op-c-conv"><span>conv double</span></a></li>
<li><strong>Default</strong>: 1.0e-6</li>
</ul>
</div></blockquote>
</div>
</div>
<div class="section" id="advanced-keywords-controlling-mp2-no-approximations">
<h3>Advanced Keywords Controlling MP2 NO Approximations<a class="headerlink" href="#advanced-keywords-controlling-mp2-no-approximations" title="Permalink to this headline">¶</a></h3>
</div>
</div>
<div class="section" id="charge-transfer-in-sapt">
<span id="sec-saptct"></span><span id="index-3"></span><h2>Charge-Transfer in SAPT<a class="headerlink" href="#charge-transfer-in-sapt" title="Permalink to this headline">¶</a></h2>
<p>It is possible to obtain the stabilization energy of a complex due to
charge-transfer effects from a SAPT computation. The charge-transfer energy
can be computed with the SAPT module as described by Stone
and Misquitta <a class="reference internal" href="bibliography.html#misquitta-2009-201" id="id19">[Misquitta:2009:201]</a>.</p>
<p>Charge-transfer energies can be obtained from the following calls to the
energy function.</p>
<div class="highlight-python"><div class="highlight"><pre><span class="n">energy</span><span class="p">(</span><span class="s">'sapt0-ct'</span><span class="p">)</span>
<span class="n">energy</span><span class="p">(</span><span class="s">'sapt2-ct'</span><span class="p">)</span>
<span class="n">energy</span><span class="p">(</span><span class="s">'sapt2+-ct'</span><span class="p">)</span>
<span class="n">energy</span><span class="p">(</span><span class="s">'sapt2+(3)-ct'</span><span class="p">)</span>
<span class="n">energy</span><span class="p">(</span><span class="s">'sapt2+3-ct'</span><span class="p">)</span>
</pre></div>
</div>
<p>A SAPT charge-transfer analysis will perform 5 HF computations: the dimer
in the dimer basis, monomer A in the dimer basis, monomer B in the dimer
basis, monomer A in the monomer A basis, and monomer B in the monomer B
basis. Next, it performs two SAPT computations, one in the dimer basis and
one in the monomer basis. Finally, it will print a summary of the
charge-transfer results:</p>
<div class="highlight-python"><div class="highlight"><pre> SAPT Charge Transfer Analysis
-----------------------------------------------------------------------------
SAPT Induction (Dimer Basis) -2.0970 mH -1.3159 kcal mol^-1
SAPT Induction (Monomer Basis) -1.1396 mH -0.7151 kcal mol^-1
SAPT Charge Transfer -0.9574 mH -0.6008 kcal mol^-1
</pre></div>
</div>
<p>These results are for the water dimer geometry shown above computed with
SAPT0/aug-cc-pVDZ.</p>
</div>
<div class="section" id="monomer-centered-basis-computations">
<span id="index-4"></span><h2>Monomer-Centered Basis Computations<a class="headerlink" href="#monomer-centered-basis-computations" title="Permalink to this headline">¶</a></h2>
<p>The charge-transfer analysis above is carried out by taking the
difference between SAPT induction as calculated in the dimer-centered
basis (i.e., each monomer sees the basis functions on both monomers)
vs. the monomer-centered basis (i.e., each monomer utilizes only its
own basis set). It is also possible to run a SAPT computation at any
level using only the monomer-centered basis. To do this, simply add
<code class="docutils literal"><span class="pre">sapt_basis='monomer'</span></code> to the energy function, such as</p>
<div class="highlight-python"><div class="highlight"><pre><span class="n">energy</span><span class="p">(</span><span class="s">'sapt2'</span><span class="p">,</span><span class="n">sapt_basis</span><span class="o">=</span><span class="s">'monomer'</span><span class="p">)</span>
</pre></div>
</div>
<p>This procedure leads to faster compuations, but it converges more slowly
towards the complete basis set limit than the default procedure, which uses
the dimer-centered basis set. Hence, monomer-centered basis SAPT
computations are not recommended.</p>
</div>
<div class="section" id="interpreting-sapt-results">
<h2>Interpreting SAPT Results<a class="headerlink" href="#interpreting-sapt-results" title="Permalink to this headline">¶</a></h2>
<p>We will examine the results of a SAPT2+3/aug-cc-pVDZ computation on the
water dimer. This computation can be performed with the following
input:</p>
<div class="highlight-python"><div class="highlight"><pre>molecule water_dimer {
0 1
O -1.551007 -0.114520 0.000000
H -1.934259 0.762503 0.000000
H -0.599677 0.040712 0.000000
--
0 1
O 1.350625 0.111469 0.000000
H 1.680398 -0.373741 -0.758561
H 1.680398 -0.373741 0.758561
units angstrom
}
set globals {
basis aug-cc-pvdz
guess sad
scf_type df
}
set sapt {
print 1
nat_orbs_t2 true
freeze_core true
}
energy('sapt2+3')
</pre></div>
</div>
<p>To reiterate some of the options mentioned above: the
<a class="reference internal" href="autodoc_glossary_options_c.html#term-nat-orbs-t2-sapt"><span class="xref std std-term">NAT_ORBS_T2</span></a> option will compute MP2 natural orbitals and use
them in the evaluation of the triples correction to dispersion, and the
<a class="reference internal" href="autodoc_glossary_options_c.html#term-freeze-core-sapt"><span class="xref std std-term">FREEZE_CORE</span></a> option will freeze the core throughout the SAPT
computation. This SAPT2+3/aug-cc-pVDZ computation produces the following
results:</p>
<div class="highlight-python"><div class="highlight"><pre> SAPT Results
--------------------------------------------------------------------------
Electrostatics -13.06429805 mH -8.19797114 kcal mol^-1
Elst10,r -13.37543274 mH -8.39321111 kcal mol^-1
Elst12,r 0.04490253 mH 0.02817676 kcal mol^-1
Elst13,r 0.26623216 mH 0.16706321 kcal mol^-1
Exchange 13.41793548 mH 8.41988199 kcal mol^-1
Exch10 11.21823471 mH 7.03954885 kcal mol^-1
Exch10(S^2) 11.13803867 mH 6.98922508 kcal mol^-1
Exch11(S^2) 0.04558910 mH 0.02860760 kcal mol^-1
Exch12(S^2) 2.15411167 mH 1.35172554 kcal mol^-1
Induction -3.91333155 mH -2.45565272 kcal mol^-1
Ind20,r -4.57531220 mH -2.87105187 kcal mol^-1
Ind30,r -4.91715479 mH -3.08556135 kcal mol^-1
Ind22 -0.83761074 mH -0.52560870 kcal mol^-1
Exch-Ind20,r 2.47828867 mH 1.55514969 kcal mol^-1
Exch-Ind30,r 4.33916816 mH 2.72286924 kcal mol^-1
Exch-Ind22 0.45370482 mH 0.28470409 kcal mol^-1
delta HF,r (2) -1.43240211 mH -0.89884593 kcal mol^-1
delta HF,r (3) -0.85441547 mH -0.53615383 kcal mol^-1
Dispersion -3.62061213 mH -2.27196851 kcal mol^-1
Disp20 -3.54292109 mH -2.22321664 kcal mol^-1
Disp30 0.05959981 mH 0.03739945 kcal mol^-1
Disp21 0.11216179 mH 0.07038259 kcal mol^-1
Disp22 (SDQ) -0.17924270 mH -0.11247650 kcal mol^-1
Disp22 (T) -0.47692549 mH -0.29927528 kcal mol^-1
Est. Disp22 (T) -0.54385253 mH -0.34127263 kcal mol^-1
Exch-Disp20 0.64545652 mH 0.40503010 kcal mol^-1
Exch-Disp30 -0.01823411 mH -0.01144207 kcal mol^-1
Ind-Disp30 -0.91816995 mH -0.57616037 kcal mol^-1
Exch-Ind-Disp30 0.76459013 mH 0.47978757 kcal mol^-1
Total HF -5.68662366 mH -3.56841037 kcal mol^-1
Total SAPT0 -8.58408823 mH -5.38659691 kcal mol^-1
Total SAPT2 -6.72339084 mH -4.21899163 kcal mol^-1
Total SAPT2+ -7.26739725 mH -4.56036082 kcal mol^-1
Total SAPT2+(3) -6.94156528 mH -4.35589816 kcal mol^-1
Total SAPT2+3 -7.11337921 mH -4.46371303 kcal mol^-1
</pre></div>
</div>
<p>At the bottom of this output are the total SAPT energies (defined above),
they are composed of subsets of the individual terms printed above. The
individual terms are grouped according to the component of the interaction
to which they contribute. The total component energies (<em>i.e.,</em>
electrostatics, exchange, induction, and dispersion) represent what we
regard as the best estimate available at a given level of SAPT computed
from a subset of the terms of that grouping. The groupings shown above are
not unique and are certainly not rigorously defined. We regard the groupings
used in <span class="sc">Psi4</span> as a “chemist’s grouping” as opposed to a more
mathematically based grouping, which would group all exchange terms
(<em>i.e.</em> <img class="math" src="_images/math/ca068542bd70d981c9ab4d98525ea9157e893046.png" alt="E_{exch-ind,resp}^{(20)}" style="vertical-align: -8px"/>, <img class="math" src="_images/math/e405ddfda48867f455cd9cf0e6277ff66bbf8802.png" alt="E_{exch-disp}^{(20)}" style="vertical-align: -8px"/>, <em>etc.</em> in
the exchange component. A final note is that both <code class="docutils literal"><span class="pre">Disp22(T)</span></code>
and <code class="docutils literal"><span class="pre">Est.Disp22(T)</span></code> results appear if MP2 natural orbitals are
used to evaluate the triples correction to dispersion. The <code class="docutils literal"><span class="pre">Disp22(T)</span></code>
result is the triples correction as computed in the truncated NO basis;
<code class="docutils literal"><span class="pre">Est.Disp22(T)</span></code> is a scaled result that attempts to recover
the effect of the truncated virtual space. The <code class="docutils literal"><span class="pre">Est.Disp22(T)</span></code>
value used in the SAPT energy and dispersion component (see <a class="reference internal" href="bibliography.html#hohenstein-2010-104107" id="id20">[Hohenstein:2010:104107]</a>
for details).</p>
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<h3><a href="index.html">Table Of Contents</a></h3>
<ul>
<li><a class="reference internal" href="#">SAPT: Symmetry-Adapted Perturbation Theory</a><ul>
<li><a class="reference internal" href="#a-first-example">A First Example</a></li>
<li><a class="reference internal" href="#sapt0">SAPT0</a><ul>
<li><a class="reference internal" href="#basic-sapt0-keywords">Basic SAPT0 Keywords</a><ul>
<li><a class="reference internal" href="#sapt-level"><code class="docutils literal"><span class="pre">SAPT_LEVEL</span></code></a></li>
<li><a class="reference internal" href="#basis"><code class="docutils literal"><span class="pre">BASIS</span></code></a></li>
<li><a class="reference internal" href="#df-basis-sapt"><code class="docutils literal"><span class="pre">DF_BASIS_SAPT</span></code></a></li>
<li><a class="reference internal" href="#df-basis-elst"><code class="docutils literal"><span class="pre">DF_BASIS_ELST</span></code></a></li>
<li><a class="reference internal" href="#freeze-core"><code class="docutils literal"><span class="pre">FREEZE_CORE</span></code></a></li>
<li><a class="reference internal" href="#d-convergence"><code class="docutils literal"><span class="pre">D_CONVERGENCE</span></code></a></li>
<li><a class="reference internal" href="#e-convergence"><code class="docutils literal"><span class="pre">E_CONVERGENCE</span></code></a></li>
<li><a class="reference internal" href="#maxiter"><code class="docutils literal"><span class="pre">MAXITER</span></code></a></li>
<li><a class="reference internal" href="#print"><code class="docutils literal"><span class="pre">PRINT</span></code></a></li>
</ul>
</li>
<li><a class="reference internal" href="#advanced-sapt0-keywords">Advanced SAPT0 Keywords</a><ul>
<li><a class="reference internal" href="#aio-cphf"><code class="docutils literal"><span class="pre">AIO_CPHF</span></code></a></li>
<li><a class="reference internal" href="#aio-df-ints"><code class="docutils literal"><span class="pre">AIO_DF_INTS</span></code></a></li>
<li><a class="reference internal" href="#no-response"><code class="docutils literal"><span class="pre">NO_RESPONSE</span></code></a></li>
<li><a class="reference internal" href="#ints-tolerance"><code class="docutils literal"><span class="pre">INTS_TOLERANCE</span></code></a></li>
<li><a class="reference internal" href="#denominator-delta"><code class="docutils literal"><span class="pre">DENOMINATOR_DELTA</span></code></a></li>
<li><a class="reference internal" href="#denominator-algorithm"><code class="docutils literal"><span class="pre">DENOMINATOR_ALGORITHM</span></code></a></li>
<li><a class="reference internal" href="#sapt-os-scale"><code class="docutils literal"><span class="pre">SAPT_OS_SCALE</span></code></a></li>
<li><a class="reference internal" href="#sapt-ss-scale"><code class="docutils literal"><span class="pre">SAPT_SS_SCALE</span></code></a></li>
<li><a class="reference internal" href="#debug"><code class="docutils literal"><span class="pre">DEBUG</span></code></a></li>
</ul>
</li>
</ul>
</li>
<li><a class="reference internal" href="#higher-order-sapt">Higher-Order SAPT</a><ul>
<li><a class="reference internal" href="#basic-keywords-for-higher-order-sapt">Basic Keywords for Higher-order SAPT</a><ul>
<li><a class="reference internal" href="#id12"><code class="docutils literal"><span class="pre">BASIS</span></code></a></li>
<li><a class="reference internal" href="#id13"><code class="docutils literal"><span class="pre">DF_BASIS_SAPT</span></code></a></li>
<li><a class="reference internal" href="#id14"><code class="docutils literal"><span class="pre">FREEZE_CORE</span></code></a></li>
<li><a class="reference internal" href="#id15"><code class="docutils literal"><span class="pre">PRINT</span></code></a></li>
</ul>
</li>
<li><a class="reference internal" href="#advanced-keywords-for-higher-order-sapt">Advanced Keywords for Higher-order SAPT</a><ul>
<li><a class="reference internal" href="#id16"><code class="docutils literal"><span class="pre">INTS_TOLERANCE</span></code></a></li>
<li><a class="reference internal" href="#sapt-mem-check"><code class="docutils literal"><span class="pre">SAPT_MEM_CHECK</span></code></a></li>
<li><a class="reference internal" href="#id17"><code class="docutils literal"><span class="pre">DEBUG</span></code></a></li>
</ul>
</li>
</ul>
</li>
<li><a class="reference internal" href="#mp2-natural-orbitals">MP2 Natural Orbitals</a><ul>
<li><a class="reference internal" href="#basic-keywords-controlling-mp2-no-approximations">Basic Keywords Controlling MP2 NO Approximations</a><ul>
<li><a class="reference internal" href="#nat-orbs-t2"><code class="docutils literal"><span class="pre">NAT_ORBS_T2</span></code></a></li>
<li><a class="reference internal" href="#occ-tolerance"><code class="docutils literal"><span class="pre">OCC_TOLERANCE</span></code></a></li>
</ul>
</li>
<li><a class="reference internal" href="#advanced-keywords-controlling-mp2-no-approximations">Advanced Keywords Controlling MP2 NO Approximations</a></li>
</ul>
</li>
<li><a class="reference internal" href="#charge-transfer-in-sapt">Charge-Transfer in SAPT</a></li>
<li><a class="reference internal" href="#monomer-centered-basis-computations">Monomer-Centered Basis Computations</a></li>
<li><a class="reference internal" href="#interpreting-sapt-results">Interpreting SAPT Results</a></li>
</ul>
</li>
</ul>
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