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<div class="section" id="complete-basis-set">
<span id="sec-cbs"></span><span id="index-0"></span><h1>Complete Basis Set<a class="headerlink" href="#complete-basis-set" title="Permalink to this headline">¶</a></h1>
<div class="toctree-wrapper compound">
</div>
<p><em>Code author: Lori A. Burns</em></p>
<p><em>Section author: Lori A. Burns</em></p>
<dl class="function">
<dt id="wrappers.complete_basis_set">
<code class="descname">complete_basis_set</code><span class="sig-paren">(</span><em>name</em><span class="optional">[</span>, <em>scf_basis</em>, <em>scf_scheme</em>, <em>corl_wfn</em>, <em>corl_basis</em>, <em>corl_scheme</em>, <em>delta_wfn</em>, <em>delta_wfn_lesser</em>, <em>delta_basis</em>, <em>delta_scheme</em>, <em>delta2_wfn</em>, <em>delta2_wfn_lesser</em>, <em>delta2_basis</em>, <em>delta2_scheme</em>, <em>delta3_wfn</em>, <em>delta3_wfn_lesser</em>, <em>delta3_basis</em>, <em>delta3_scheme</em>, <em>delta4_wfn</em>, <em>delta4_wfn_lesser</em>, <em>delta4_basis</em>, <em>delta4_scheme</em>, <em>delta5_wfn</em>, <em>delta5_wfn_lesser</em>, <em>delta5_basis</em>, <em>delta5_scheme</em><span class="optional">]</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/wrappers.html#complete_basis_set"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#wrappers.complete_basis_set" title="Permalink to this definition">¶</a></dt>
<dd><p>Function to define a multistage energy method from combinations of
basis set extrapolations and delta corrections and condense the
components into a minimum number of calculations.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Aliases:</th><td class="field-body">cbs()</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">(<em>float</em>) – Total electronic energy in Hartrees</td>
</tr>
<tr class="field-odd field"><th class="field-name">PSI variables:</th><td class="field-body"></td>
</tr>
</tbody>
</table>
<table class="hlist"><tr><td><ul class="simple">
<li><a class="reference internal" href="glossary_psivariables.html#psivar-CBSTOTALENERGY"><code class="xref std std-psivar docutils literal"><span class="pre">CBS</span> <span class="pre">TOTAL</span> <span class="pre">ENERGY</span></code></a></li>
<li><a class="reference internal" href="glossary_psivariables.html#psivar-CBSREFERENCEENERGY"><code class="xref std std-psivar docutils literal"><span class="pre">CBS</span> <span class="pre">REFERENCE</span> <span class="pre">ENERGY</span></code></a></li>
<li><a class="reference internal" href="glossary_psivariables.html#psivar-CBSCORRELATIONENERGY"><code class="xref std std-psivar docutils literal"><span class="pre">CBS</span> <span class="pre">CORRELATION</span> <span class="pre">ENERGY</span></code></a></li>
<li><a class="reference internal" href="glossary_psivariables.html#psivar-CURRENTENERGY"><code class="xref std std-psivar docutils literal"><span class="pre">CURRENT</span> <span class="pre">ENERGY</span></code></a></li>
<li><a class="reference internal" href="glossary_psivariables.html#psivar-CURRENTREFERENCEENERGY"><code class="xref std std-psivar docutils literal"><span class="pre">CURRENT</span> <span class="pre">REFERENCE</span> <span class="pre">ENERGY</span></code></a></li>
<li><a class="reference internal" href="glossary_psivariables.html#psivar-CURRENTCORRELATIONENERGY"><code class="xref std std-psivar docutils literal"><span class="pre">CURRENT</span> <span class="pre">CORRELATION</span> <span class="pre">ENERGY</span></code></a></li>
</ul>
</td></tr></table>
<div class="admonition caution">
<p class="first admonition-title">Caution</p>
<p>Some features are not yet implemented. Buy a developer a coffee.</p>
<ul class="last simple">
<li>No way to tell function to boost fitting basis size for all calculations.</li>
<li>No way to extrapolate def2 family basis sets</li>
<li>Need to add more extrapolation schemes</li>
</ul>
</div>
<p>As represented in the equation below, a CBS energy method is defined in several
sequential stages (scf, corl, delta, delta2, delta3, delta4, delta5) covering treatment
of the reference total energy, the correlation energy, a delta correction to the
correlation energy, and a second delta correction, etc.. Each is activated by its
stage_wfn keyword and is only allowed if all preceding stages are active.</p>
<div class="math" id="eq-cbs">
<span id="index-1"></span><p><img src="_images/math/dc7ee176476c1c8c6385cb631ef6f6b64aae76e0.png" alt="E_{total}^{\text{CBS}} = \mathcal{F}_{\textbf{scf\_scheme}} \left(E_{total,\; \text{SCF}}^{\textbf{scf\_basis}}\right) \; + \mathcal{F}_{\textbf{corl\_scheme}} \left(E_{corl,\; \textbf{corl\_wfn}}^{\textbf{corl\_basis}}\right) \; + \delta_{\textbf{delta\_wfn\_lesser}}^{\textbf{delta\_wfn}} \; + \delta_{\textbf{delta2\_wfn\_lesser}}^{\textbf{delta2\_wfn}} \; + \delta_{\textbf{delta3\_wfn\_lesser}}^{\textbf{delta3\_wfn}} \; + \delta_{\textbf{delta4\_wfn\_lesser}}^{\textbf{delta4\_wfn}} \; + \delta_{\textbf{delta5\_wfn\_lesser}}^{\textbf{delta5\_wfn}}"/></p>
</div><p>Here, <img class="math" src="_images/math/3c228c67510f108dd0f92d4397f191d7ce8f3efb.png" alt="\mathcal{F}" style="vertical-align: 0px"/> is an energy or energy extrapolation scheme, and the following also hold.</p>
<div class="math">
<p><img src="_images/math/6b2ca9dfbf16ba4eda063af2348a3adf84c0dd3d.png" alt="\delta_{\textbf{delta\_wfn\_lesser}}^{\textbf{delta\_wfn}} \; = \mathcal{F}_{\textbf{delta\_scheme}} \left(E_{corl,\; \textbf{delta\_wfn}}^{\textbf{delta\_basis}}\right) - \mathcal{F}_{\textbf{delta\_scheme}} \left(E_{corl,\; \textbf{delta\_wfn\_lesser}}^{\textbf{delta\_basis}}\right)"/></p>
</div><div class="math">
<p><img src="_images/math/3837e23ed5ce3bd999509b93f4867fb46ce7aa29.png" alt="\delta_{\textbf{delta2\_wfn\_lesser}}^{\textbf{delta2\_wfn}} \; = \mathcal{F}_{\textbf{delta2\_scheme}} \left(E_{corl,\; \textbf{delta2\_wfn}}^{\textbf{delta2\_basis}}\right) - \mathcal{F}_{\textbf{delta2\_scheme}} \left(E_{corl,\; \textbf{delta2\_wfn\_lesser}}^{\textbf{delta2\_basis}}\right)"/></p>
</div><div class="math">
<p><img src="_images/math/c5440087c569bae9bdc5949ca32ba2398f4768be.png" alt="\delta_{\textbf{delta3\_wfn\_lesser}}^{\textbf{delta3\_wfn}} \; = \mathcal{F}_{\textbf{delta3\_scheme}} \left(E_{corl,\; \textbf{delta3\_wfn}}^{\textbf{delta3\_basis}}\right) - \mathcal{F}_{\textbf{delta3\_scheme}} \left(E_{corl,\; \textbf{delta3\_wfn\_lesser}}^{\textbf{delta3\_basis}}\right)"/></p>
</div><div class="math">
<p><img src="_images/math/2423fe70b570255cf9cee22cbdc07216beab2ade.png" alt="\delta_{\textbf{delta4\_wfn\_lesser}}^{\textbf{delta4\_wfn}} \; = \mathcal{F}_{\textbf{delta4\_scheme}} \left(E_{corl,\; \textbf{delta4\_wfn}}^{\textbf{delta4\_basis}}\right) - \mathcal{F}_{\textbf{delta4\_scheme}} \left(E_{corl,\; \textbf{delta4\_wfn\_lesser}}^{\textbf{delta4\_basis}}\right)"/></p>
</div><div class="math">
<p><img src="_images/math/a6f4954a2fb25afcea4b5145dc509e88ea01d38d.png" alt="\delta_{\textbf{delta5\_wfn\_lesser}}^{\textbf{delta5\_wfn}} \; = \mathcal{F}_{\textbf{delta5\_scheme}} \left(E_{corl,\; \textbf{delta5\_wfn}}^{\textbf{delta5\_basis}}\right) - \mathcal{F}_{\textbf{delta5\_scheme}} \left(E_{corl,\; \textbf{delta5\_wfn\_lesser}}^{\textbf{delta5\_basis}}\right)"/></p>
</div><p>A translation of this ungainly equation to example [5] below is as
follows. In words, this is a double- and triple-zeta 2-point
Helgaker-extrapolated CCSD(T) coupled-cluster correlation correction
appended to a triple- and quadruple-zeta 2-point
Helgaker-extrapolated MP2 correlation energy appended to a SCF/aug-cc-pVQZ
reference energy.</p>
<div class="math">
<p><img src="_images/math/c1de2370061ad81a169fe0782c7c805cc6ae5b33.png" alt="E_{total}^{\text{CBS}} = \mathcal{F}_{\text{highest\_1}} \left(E_{total,\; \text{SCF}}^{\text{aug-cc-pVQZ}}\right) \; + \mathcal{F}_{\text{corl\_xtpl\_helgaker\_2}} \left(E_{corl,\; \text{MP2}}^{\text{aug-cc-pV[TQ]Z}}\right) \; + \delta_{\text{MP2}}^{\text{CCSD(T)}}"/></p>
</div><div class="math">
<p><img src="_images/math/adcf3c13919161c842f2e7ee0166527f2347b899.png" alt="\delta_{\text{MP2}}^{\text{CCSD(T)}} \; = \mathcal{F}_{\text{corl\_xtpl\_helgaker\_2}} \left(E_{corl,\; \text{CCSD(T)}}^{\text{aug-cc-pV[DT]Z}}\right) - \mathcal{F}_{\text{corl\_xtpl\_helgaker\_2}} \left(E_{corl,\; \text{MP2}}^{\text{aug-cc-pV[DT]Z}}\right)"/></p>
</div><ul>
<li><dl class="first docutils">
<dt>Energy Methods</dt>
<dd><p class="first">The presence of a stage_wfn keyword is the indicator to incorporate
(and check for stage_basis and stage_scheme keywords) and compute
that stage in defining the CBS energy.</p>
<p>The cbs() function requires, at a minimum, <code class="docutils literal"><span class="pre">name='scf'</span></code> and <code class="docutils literal"><span class="pre">scf_basis</span></code>
keywords to be specified for reference-step only jobs and <code class="docutils literal"><span class="pre">name</span></code> and
<code class="docutils literal"><span class="pre">corl_basis</span></code> keywords for correlated jobs.</p>
<p>The following energy methods have been set up for cbs().</p>
<table class="hlist"><tr><td><ul class="simple">
<li>scf</li>
<li>mp2</li>
<li>mp2.5</li>
<li>mp3</li>
<li>mp4(sdq)</li>
<li>mp4</li>
<li>mp<em>n</em></li>
<li>omp2</li>
</ul>
</td><td><ul class="simple">
<li>omp2.5</li>
<li>omp3</li>
<li>ocepa</li>
<li>cepa0</li>
<li>cepa(0)</li>
<li>cepa(1)</li>
<li>cepa(3)</li>
</ul>
</td><td><ul class="simple">
<li>acpf</li>
<li>aqcc</li>
<li>qcisd</li>
<li>cc2</li>
<li>ccsd</li>
<li>fno-df-ccsd</li>
<li>bccd</li>
</ul>
</td><td><ul class="simple">
<li>cc3</li>
<li>qcisd(t)</li>
<li>ccsd(t)</li>
<li>fno-df-ccsd(t)</li>
<li>bccd(t)</li>
<li>cisd</li>
<li>cisdt</li>
</ul>
</td><td><ul class="simple">
<li>cisdtq</li>
<li>ci<em>n</em></li>
<li>fci</li>
<li>mrccsd</li>
<li>mrccsd(t)</li>
<li>mrccsdt</li>
<li>mrccsdt(q)</li>
</ul>
</td></tr></table>
</dd>
</dl>
</li>
</ul>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>name</strong> (<em>string</em>) – <p><code class="docutils literal"><span class="pre">'scf'</span></code> || <code class="docutils literal"><span class="pre">'ccsd'</span></code> || etc.</p>
<p>First argument, usually unlabeled. Indicates the computational method
for the correlation energy, unless only reference step to be performed,
in which case should be <code class="docutils literal"><span class="pre">'scf'</span></code>. Overruled if stage_wfn keywords supplied.</p>
</td>
</tr>
</tbody>
</table>
<p>:type scf_wfn:string
:param scf_wfn: <img class="math" src="_images/math/fcb47d177e58f83257e03078e39b830ee90caec8.png" alt="\Rightarrow" style="vertical-align: -1px"/> <code class="docutils literal"><span class="pre">'scf'</span></code> <img class="math" src="_images/math/589f0defd3f7d56ed5fb2872215af7ebba9db67a.png" alt="\Leftarrow" style="vertical-align: -1px"/> || <code class="docutils literal"><span class="pre">'c4-scf'</span></code> || etc.</p>
<blockquote>
<div>Indicates the energy method for which the reference energy is to be
obtained. Generally unnecessary, as ‘scf’ is <em>the</em> scf in <span class="sc">Psi4</span> but
can be used to direct lone scf components to run in <span class="sc">Psi4</span> or Cfour
in a mixed-program composite method.</div></blockquote>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple">
<li><strong>corl_wfn</strong> (<em>string</em>) – <p><code class="docutils literal"><span class="pre">'mp2'</span></code> || <code class="docutils literal"><span class="pre">'ccsd(t)'</span></code> || etc.</p>
<p>Indicates the energy method for which the correlation energy is to be
obtained. Can also be specified with <code class="docutils literal"><span class="pre">name</span></code> or as the unlabeled
first argument to the function.</p>
</li>
<li><strong>delta_wfn</strong> (<em>string</em>) – <p><code class="docutils literal"><span class="pre">'ccsd'</span></code> || <code class="docutils literal"><span class="pre">'ccsd(t)'</span></code> || etc.</p>
<p>Indicates the (superior) energy method for which a delta correction
to the correlation energy is to be obtained.</p>
</li>
<li><strong>delta_wfn_lesser</strong> (<em>string</em>) – <p><img class="math" src="_images/math/fcb47d177e58f83257e03078e39b830ee90caec8.png" alt="\Rightarrow" style="vertical-align: -1px"/> <code class="docutils literal"><span class="pre">corl_wfn</span></code> <img class="math" src="_images/math/589f0defd3f7d56ed5fb2872215af7ebba9db67a.png" alt="\Leftarrow" style="vertical-align: -1px"/> || <code class="docutils literal"><span class="pre">'mp2'</span></code> || etc.</p>
<p>Indicates the inferior energy method for which a delta correction
to the correlation energy is to be obtained.</p>
</li>
<li><strong>delta2_wfn</strong> (<em>string</em>) – <p><code class="docutils literal"><span class="pre">'ccsd'</span></code> || <code class="docutils literal"><span class="pre">'ccsd(t)'</span></code> || etc.</p>
<p>Indicates the (superior) energy method for which a second delta correction
to the correlation energy is to be obtained.</p>
</li>
<li><strong>delta2_wfn_lesser</strong> (<em>string</em>) – <p><img class="math" src="_images/math/fcb47d177e58f83257e03078e39b830ee90caec8.png" alt="\Rightarrow" style="vertical-align: -1px"/> <code class="docutils literal"><span class="pre">delta_wfn</span></code> <img class="math" src="_images/math/589f0defd3f7d56ed5fb2872215af7ebba9db67a.png" alt="\Leftarrow" style="vertical-align: -1px"/> || <code class="docutils literal"><span class="pre">'ccsd(t)'</span></code> || etc.</p>
<p>Indicates the inferior energy method for which a second delta correction
to the correlation energy is to be obtained.</p>
</li>
<li><strong>delta3_wfn</strong> (<em>string</em>) – <p><code class="docutils literal"><span class="pre">'ccsd'</span></code> || <code class="docutils literal"><span class="pre">'ccsd(t)'</span></code> || etc.</p>
<p>Indicates the (superior) energy method for which a third delta correction
to the correlation energy is to be obtained.</p>
</li>
<li><strong>delta3_wfn_lesser</strong> (<em>string</em>) – <p><img class="math" src="_images/math/fcb47d177e58f83257e03078e39b830ee90caec8.png" alt="\Rightarrow" style="vertical-align: -1px"/> <code class="docutils literal"><span class="pre">delta2_wfn</span></code> <img class="math" src="_images/math/589f0defd3f7d56ed5fb2872215af7ebba9db67a.png" alt="\Leftarrow" style="vertical-align: -1px"/> || <code class="docutils literal"><span class="pre">'ccsd(t)'</span></code> || etc.</p>
<p>Indicates the inferior energy method for which a third delta correction
to the correlation energy is to be obtained.</p>
</li>
<li><strong>delta4_wfn</strong> (<em>string</em>) – <p><code class="docutils literal"><span class="pre">'ccsd'</span></code> || <code class="docutils literal"><span class="pre">'ccsd(t)'</span></code> || etc.</p>
<p>Indicates the (superior) energy method for which a fourth delta correction
to the correlation energy is to be obtained.</p>
</li>
<li><strong>delta4_wfn_lesser</strong> (<em>string</em>) – <p><img class="math" src="_images/math/fcb47d177e58f83257e03078e39b830ee90caec8.png" alt="\Rightarrow" style="vertical-align: -1px"/> <code class="docutils literal"><span class="pre">delta3_wfn</span></code> <img class="math" src="_images/math/589f0defd3f7d56ed5fb2872215af7ebba9db67a.png" alt="\Leftarrow" style="vertical-align: -1px"/> || <code class="docutils literal"><span class="pre">'ccsd(t)'</span></code> || etc.</p>
<p>Indicates the inferior energy method for which a fourth delta correction
to the correlation energy is to be obtained.</p>
</li>
<li><strong>delta5_wfn</strong> (<em>string</em>) – <p><code class="docutils literal"><span class="pre">'ccsd'</span></code> || <code class="docutils literal"><span class="pre">'ccsd(t)'</span></code> || etc.</p>
<p>Indicates the (superior) energy method for which a fifth delta correction
to the correlation energy is to be obtained.</p>
</li>
<li><strong>delta5_wfn_lesser</strong> (<em>string</em>) – <p><img class="math" src="_images/math/fcb47d177e58f83257e03078e39b830ee90caec8.png" alt="\Rightarrow" style="vertical-align: -1px"/> <code class="docutils literal"><span class="pre">delta4_wfn</span></code> <img class="math" src="_images/math/589f0defd3f7d56ed5fb2872215af7ebba9db67a.png" alt="\Leftarrow" style="vertical-align: -1px"/> || <code class="docutils literal"><span class="pre">'ccsd(t)'</span></code> || etc.</p>
<p>Indicates the inferior energy method for which a fifth delta correction
to the correlation energy is to be obtained.</p>
</li>
</ul>
</td>
</tr>
</tbody>
</table>
<ul>
<li><dl class="first docutils">
<dt>Basis Sets</dt>
<dd><p class="first last">Currently, the basis set set through <code class="docutils literal"><span class="pre">set</span></code> commands have no influence
on a cbs calculation.</p>
</dd>
</dl>
</li>
</ul>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple">
<li><strong>scf_basis</strong> (<a class="reference internal" href="basissets_byelement.html#apdx-basiselement"><span>basis string</span></a>) – <p><img class="math" src="_images/math/fcb47d177e58f83257e03078e39b830ee90caec8.png" alt="\Rightarrow" style="vertical-align: -1px"/> <code class="docutils literal"><span class="pre">corl_basis</span></code> <img class="math" src="_images/math/589f0defd3f7d56ed5fb2872215af7ebba9db67a.png" alt="\Leftarrow" style="vertical-align: -1px"/> || <code class="docutils literal"><span class="pre">'cc-pV[TQ]Z'</span></code> || <code class="docutils literal"><span class="pre">'jun-cc-pv[tq5]z'</span></code> || <code class="docutils literal"><span class="pre">'6-31G*'</span></code> || etc.</p>
<p>Indicates the sequence of basis sets employed for the reference energy.
If any correlation method is specified, <code class="docutils literal"><span class="pre">scf_basis</span></code> can default
to <code class="docutils literal"><span class="pre">corl_basis</span></code>.</p>
</li>
<li><strong>corl_basis</strong> (<a class="reference internal" href="basissets_byelement.html#apdx-basiselement"><span>basis string</span></a>) – <p><code class="docutils literal"><span class="pre">'cc-pV[TQ]Z'</span></code> || <code class="docutils literal"><span class="pre">'jun-cc-pv[tq5]z'</span></code> || <code class="docutils literal"><span class="pre">'6-31G*'</span></code> || etc.</p>
<p>Indicates the sequence of basis sets employed for the correlation energy.</p>
</li>
<li><strong>delta_basis</strong> (<a class="reference internal" href="basissets_byelement.html#apdx-basiselement"><span>basis string</span></a>) – <p><code class="docutils literal"><span class="pre">'cc-pV[TQ]Z'</span></code> || <code class="docutils literal"><span class="pre">'jun-cc-pv[tq5]z'</span></code> || <code class="docutils literal"><span class="pre">'6-31G*'</span></code> || etc.</p>
<p>Indicates the sequence of basis sets employed for the delta correction
to the correlation energy.</p>
</li>
<li><strong>delta2_basis</strong> (<a class="reference internal" href="basissets_byelement.html#apdx-basiselement"><span>basis string</span></a>) – <p><code class="docutils literal"><span class="pre">'cc-pV[TQ]Z'</span></code> || <code class="docutils literal"><span class="pre">'jun-cc-pv[tq5]z'</span></code> || <code class="docutils literal"><span class="pre">'6-31G*'</span></code> || etc.</p>
<p>Indicates the sequence of basis sets employed for the second delta correction
to the correlation energy.</p>
</li>
<li><strong>delta3_basis</strong> (<a class="reference internal" href="basissets_byelement.html#apdx-basiselement"><span>basis string</span></a>) – <p><code class="docutils literal"><span class="pre">'cc-pV[TQ]Z'</span></code> || <code class="docutils literal"><span class="pre">'jun-cc-pv[tq5]z'</span></code> || <code class="docutils literal"><span class="pre">'6-31G*'</span></code> || etc.</p>
<p>Indicates the sequence of basis sets employed for the third delta correction
to the correlation energy.</p>
</li>
<li><strong>delta4_basis</strong> (<a class="reference internal" href="basissets_byelement.html#apdx-basiselement"><span>basis string</span></a>) – <p><code class="docutils literal"><span class="pre">'cc-pV[TQ]Z'</span></code> || <code class="docutils literal"><span class="pre">'jun-cc-pv[tq5]z'</span></code> || <code class="docutils literal"><span class="pre">'6-31G*'</span></code> || etc.</p>
<p>Indicates the sequence of basis sets employed for the fourth delta correction
to the correlation energy.</p>
</li>
<li><strong>delta5_basis</strong> (<a class="reference internal" href="basissets_byelement.html#apdx-basiselement"><span>basis string</span></a>) – <p><code class="docutils literal"><span class="pre">'cc-pV[TQ]Z'</span></code> || <code class="docutils literal"><span class="pre">'jun-cc-pv[tq5]z'</span></code> || <code class="docutils literal"><span class="pre">'6-31G*'</span></code> || etc.</p>
<p>Indicates the sequence of basis sets employed for the fifth delta correction
to the correlation energy.</p>
</li>
</ul>
</td>
</tr>
</tbody>
</table>
<ul>
<li><dl class="first docutils">
<dt>Schemes</dt>
<dd><p class="first last">Transformations of the energy through basis set extrapolation for each
stage of the CBS definition. A complaint is generated if number of basis
sets in stage_basis does not exactly satisfy requirements of stage_scheme.
An exception is the default, <code class="docutils literal"><span class="pre">'highest_1'</span></code>, which uses the best basis
set available. See <a class="reference internal" href="#extrapolation-schemes">Extrapolation Schemes</a> for all available schemes.</p>
</dd>
</dl>
</li>
</ul>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first simple">
<li><strong>scf_scheme</strong> (<em>function</em>) – <p><img class="math" src="_images/math/fcb47d177e58f83257e03078e39b830ee90caec8.png" alt="\Rightarrow" style="vertical-align: -1px"/> <code class="docutils literal"><span class="pre">highest_1</span></code> <img class="math" src="_images/math/589f0defd3f7d56ed5fb2872215af7ebba9db67a.png" alt="\Leftarrow" style="vertical-align: -1px"/> || <code class="docutils literal"><span class="pre">scf_xtpl_helgaker_3</span></code> || etc.</p>
<p>Indicates the basis set extrapolation scheme to be applied to the reference energy.
Defaults to <a class="reference internal" href="#wrappers.scf_xtpl_helgaker_3" title="wrappers.scf_xtpl_helgaker_3"><code class="xref py py-func docutils literal"><span class="pre">scf_xtpl_helgaker_3()</span></code></a> if three valid basis sets
present in <code class="docutils literal"><span class="pre">scf_basis</span></code>, <a class="reference internal" href="#wrappers.scf_xtpl_helgaker_2" title="wrappers.scf_xtpl_helgaker_2"><code class="xref py py-func docutils literal"><span class="pre">scf_xtpl_helgaker_2()</span></code></a> if two valid basis
sets present in <code class="docutils literal"><span class="pre">scf_basis</span></code>, and <a class="reference internal" href="#wrappers.highest_1" title="wrappers.highest_1"><code class="xref py py-func docutils literal"><span class="pre">highest_1()</span></code></a> otherwise.</p>
</li>
<li><strong>corl_scheme</strong> (<em>function</em>) – <p><img class="math" src="_images/math/fcb47d177e58f83257e03078e39b830ee90caec8.png" alt="\Rightarrow" style="vertical-align: -1px"/> <code class="docutils literal"><span class="pre">highest_1</span></code> <img class="math" src="_images/math/589f0defd3f7d56ed5fb2872215af7ebba9db67a.png" alt="\Leftarrow" style="vertical-align: -1px"/> || <code class="docutils literal"><span class="pre">corl_xtpl_helgaker_2</span></code> || etc.</p>
<p>Indicates the basis set extrapolation scheme to be applied to the correlation energy.
Defaults to <a class="reference internal" href="#wrappers.corl_xtpl_helgaker_2" title="wrappers.corl_xtpl_helgaker_2"><code class="xref py py-func docutils literal"><span class="pre">corl_xtpl_helgaker_2()</span></code></a> if two valid basis sets
present in <code class="docutils literal"><span class="pre">corl_basis</span></code> and <a class="reference internal" href="#wrappers.highest_1" title="wrappers.highest_1"><code class="xref py py-func docutils literal"><span class="pre">highest_1()</span></code></a> otherwise.</p>
</li>
<li><strong>delta_scheme</strong> (<em>function</em>) – <p><img class="math" src="_images/math/fcb47d177e58f83257e03078e39b830ee90caec8.png" alt="\Rightarrow" style="vertical-align: -1px"/> <code class="docutils literal"><span class="pre">highest_1</span></code> <img class="math" src="_images/math/589f0defd3f7d56ed5fb2872215af7ebba9db67a.png" alt="\Leftarrow" style="vertical-align: -1px"/> || <code class="docutils literal"><span class="pre">corl_xtpl_helgaker_2</span></code> || etc.</p>
<p>Indicates the basis set extrapolation scheme to be applied to the delta correction
to the correlation energy.
Defaults to <a class="reference internal" href="#wrappers.corl_xtpl_helgaker_2" title="wrappers.corl_xtpl_helgaker_2"><code class="xref py py-func docutils literal"><span class="pre">corl_xtpl_helgaker_2()</span></code></a> if two valid basis sets
present in <code class="docutils literal"><span class="pre">delta_basis</span></code> and <a class="reference internal" href="#wrappers.highest_1" title="wrappers.highest_1"><code class="xref py py-func docutils literal"><span class="pre">highest_1()</span></code></a> otherwise.</p>
</li>
<li><strong>delta2_scheme</strong> (<em>function</em>) – <p><img class="math" src="_images/math/fcb47d177e58f83257e03078e39b830ee90caec8.png" alt="\Rightarrow" style="vertical-align: -1px"/> <code class="docutils literal"><span class="pre">highest_1</span></code> <img class="math" src="_images/math/589f0defd3f7d56ed5fb2872215af7ebba9db67a.png" alt="\Leftarrow" style="vertical-align: -1px"/> || <code class="docutils literal"><span class="pre">corl_xtpl_helgaker_2</span></code> || etc.</p>
<p>Indicates the basis set extrapolation scheme to be applied to the second delta correction
to the correlation energy.
Defaults to <a class="reference internal" href="#wrappers.corl_xtpl_helgaker_2" title="wrappers.corl_xtpl_helgaker_2"><code class="xref py py-func docutils literal"><span class="pre">corl_xtpl_helgaker_2()</span></code></a> if two valid basis sets
present in <code class="docutils literal"><span class="pre">delta2_basis</span></code> and <a class="reference internal" href="#wrappers.highest_1" title="wrappers.highest_1"><code class="xref py py-func docutils literal"><span class="pre">highest_1()</span></code></a> otherwise.</p>
</li>
<li><strong>delta3_scheme</strong> (<em>function</em>) – <p><img class="math" src="_images/math/fcb47d177e58f83257e03078e39b830ee90caec8.png" alt="\Rightarrow" style="vertical-align: -1px"/> <code class="docutils literal"><span class="pre">highest_1</span></code> <img class="math" src="_images/math/589f0defd3f7d56ed5fb2872215af7ebba9db67a.png" alt="\Leftarrow" style="vertical-align: -1px"/> || <code class="docutils literal"><span class="pre">corl_xtpl_helgaker_2</span></code> || etc.</p>
<p>Indicates the basis set extrapolation scheme to be applied to the third delta correction
to the correlation energy.
Defaults to <a class="reference internal" href="#wrappers.corl_xtpl_helgaker_2" title="wrappers.corl_xtpl_helgaker_2"><code class="xref py py-func docutils literal"><span class="pre">corl_xtpl_helgaker_2()</span></code></a> if two valid basis sets
present in <code class="docutils literal"><span class="pre">delta3_basis</span></code> and <a class="reference internal" href="#wrappers.highest_1" title="wrappers.highest_1"><code class="xref py py-func docutils literal"><span class="pre">highest_1()</span></code></a> otherwise.</p>
</li>
<li><strong>delta4_scheme</strong> (<em>function</em>) – <p><img class="math" src="_images/math/fcb47d177e58f83257e03078e39b830ee90caec8.png" alt="\Rightarrow" style="vertical-align: -1px"/> <code class="docutils literal"><span class="pre">highest_1</span></code> <img class="math" src="_images/math/589f0defd3f7d56ed5fb2872215af7ebba9db67a.png" alt="\Leftarrow" style="vertical-align: -1px"/> || <code class="docutils literal"><span class="pre">corl_xtpl_helgaker_2</span></code> || etc.</p>
<p>Indicates the basis set extrapolation scheme to be applied to the fourth delta correction
to the correlation energy.
Defaults to <a class="reference internal" href="#wrappers.corl_xtpl_helgaker_2" title="wrappers.corl_xtpl_helgaker_2"><code class="xref py py-func docutils literal"><span class="pre">corl_xtpl_helgaker_2()</span></code></a> if two valid basis sets
present in <code class="docutils literal"><span class="pre">delta4_basis</span></code> and <a class="reference internal" href="#wrappers.highest_1" title="wrappers.highest_1"><code class="xref py py-func docutils literal"><span class="pre">highest_1()</span></code></a> otherwise.</p>
</li>
<li><strong>delta5_scheme</strong> (<em>function</em>) – <p><img class="math" src="_images/math/fcb47d177e58f83257e03078e39b830ee90caec8.png" alt="\Rightarrow" style="vertical-align: -1px"/> <code class="docutils literal"><span class="pre">highest_1</span></code> <img class="math" src="_images/math/589f0defd3f7d56ed5fb2872215af7ebba9db67a.png" alt="\Leftarrow" style="vertical-align: -1px"/> || <code class="docutils literal"><span class="pre">corl_xtpl_helgaker_2</span></code> || etc.</p>
<p>Indicates the basis set extrapolation scheme to be applied to the fifth delta correction
to the correlation energy.
Defaults to <a class="reference internal" href="#wrappers.corl_xtpl_helgaker_2" title="wrappers.corl_xtpl_helgaker_2"><code class="xref py py-func docutils literal"><span class="pre">corl_xtpl_helgaker_2()</span></code></a> if two valid basis sets
present in <code class="docutils literal"><span class="pre">delta5_basis</span></code> and <a class="reference internal" href="#wrappers.highest_1" title="wrappers.highest_1"><code class="xref py py-func docutils literal"><span class="pre">highest_1()</span></code></a> otherwise.</p>
</li>
<li><strong>molecule</strong> (<a class="reference internal" href="notes_py.html#op-py-molecule"><span>molecule</span></a>) – <p><code class="docutils literal"><span class="pre">h2o</span></code> || etc.</p>
<p>The target molecule, if not the last molecule defined.</p>
</li>
</ul>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Examples:</th><td class="field-body"></td>
</tr>
</tbody>
</table>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="c"># [1] replicates with cbs() the simple model chemistry scf/cc-pVDZ: set basis cc-pVDZ energy('scf')</span>
<span class="gp">>>> </span><span class="n">cbs</span><span class="p">(</span><span class="s">'scf'</span><span class="p">,</span> <span class="n">scf_basis</span><span class="o">=</span><span class="s">'cc-pVDZ'</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="c"># [2] replicates with cbs() the simple model chemistry mp2/jun-cc-pVDZ: set basis jun-cc-pVDZ energy('mp2')</span>
<span class="gp">>>> </span><span class="n">cbs</span><span class="p">(</span><span class="s">'mp2'</span><span class="p">,</span> <span class="n">corl_basis</span><span class="o">=</span><span class="s">'jun-cc-pVDZ'</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="c"># [3] DTQ-zeta extrapolated scf reference energy</span>
<span class="gp">>>> </span><span class="n">cbs</span><span class="p">(</span><span class="s">'scf'</span><span class="p">,</span> <span class="n">scf_basis</span><span class="o">=</span><span class="s">'cc-pV[DTQ]Z'</span><span class="p">,</span> <span class="n">scf_scheme</span><span class="o">=</span><span class="n">scf_xtpl_helgaker_3</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="c"># [4] DT-zeta extrapolated mp2 correlation energy atop a T-zeta reference</span>
<span class="gp">>>> </span><span class="n">cbs</span><span class="p">(</span><span class="s">'mp2'</span><span class="p">,</span> <span class="n">corl_basis</span><span class="o">=</span><span class="s">'cc-pv[dt]z'</span><span class="p">,</span> <span class="n">corl_scheme</span><span class="o">=</span><span class="n">corl_xtpl_helgaker_2</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="c"># [5] a DT-zeta extrapolated coupled-cluster correction atop a TQ-zeta extrapolated mp2 correlation energy atop a Q-zeta reference</span>
<span class="gp">>>> </span><span class="n">cbs</span><span class="p">(</span><span class="s">'mp2'</span><span class="p">,</span> <span class="n">corl_basis</span><span class="o">=</span><span class="s">'aug-cc-pv[tq]z'</span><span class="p">,</span> <span class="n">corl_scheme</span><span class="o">=</span><span class="n">corl_xtpl_helgaker_2</span><span class="p">,</span> <span class="n">delta_wfn</span><span class="o">=</span><span class="s">'ccsd(t)'</span><span class="p">,</span> <span class="n">delta_basis</span><span class="o">=</span><span class="s">'aug-cc-pv[dt]z'</span><span class="p">,</span> <span class="n">delta_scheme</span><span class="o">=</span><span class="n">corl_xtpl_helgaker_2</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="c"># [6] a D-zeta ccsd(t) correction atop a DT-zeta extrapolated ccsd cluster correction atop a TQ-zeta extrapolated mp2 correlation energy atop a Q-zeta reference</span>
<span class="gp">>>> </span><span class="n">cbs</span><span class="p">(</span><span class="s">'mp2'</span><span class="p">,</span> <span class="n">corl_basis</span><span class="o">=</span><span class="s">'aug-cc-pv[tq]z'</span><span class="p">,</span> <span class="n">corl_scheme</span><span class="o">=</span><span class="n">corl_xtpl_helgaker_2</span><span class="p">,</span> <span class="n">delta_wfn</span><span class="o">=</span><span class="s">'ccsd'</span><span class="p">,</span> <span class="n">delta_basis</span><span class="o">=</span><span class="s">'aug-cc-pv[dt]z'</span><span class="p">,</span> <span class="n">delta_scheme</span><span class="o">=</span><span class="n">corl_xtpl_helgaker_2</span><span class="p">,</span> <span class="n">delta2_wfn</span><span class="o">=</span><span class="s">'ccsd(t)'</span><span class="p">,</span> <span class="n">delta2_wfn_lesser</span><span class="o">=</span><span class="s">'ccsd'</span><span class="p">,</span> <span class="n">delta2_basis</span><span class="o">=</span><span class="s">'aug-cc-pvdz'</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="c"># [7] cbs() coupled with database()</span>
<span class="gp">>>> </span><span class="n">database</span><span class="p">(</span><span class="s">'mp2'</span><span class="p">,</span> <span class="s">'BASIC'</span><span class="p">,</span> <span class="n">subset</span><span class="o">=</span><span class="p">[</span><span class="s">'h2o'</span><span class="p">,</span><span class="s">'nh3'</span><span class="p">],</span> <span class="n">symm</span><span class="o">=</span><span class="s">'on'</span><span class="p">,</span> <span class="n">func</span><span class="o">=</span><span class="n">cbs</span><span class="p">,</span> <span class="n">corl_basis</span><span class="o">=</span><span class="s">'cc-pV[tq]z'</span><span class="p">,</span> <span class="n">corl_scheme</span><span class="o">=</span><span class="n">corl_xtpl_helgaker_2</span><span class="p">,</span> <span class="n">delta_wfn</span><span class="o">=</span><span class="s">'ccsd(t)'</span><span class="p">,</span> <span class="n">delta_basis</span><span class="o">=</span><span class="s">'sto-3g'</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="c"># [8] cbs() coupled with optimize()</span>
<span class="gp">>>> </span><span class="n">optimize</span><span class="p">(</span><span class="s">'mp2'</span><span class="p">,</span> <span class="n">corl_basis</span><span class="o">=</span><span class="s">'cc-pV[DT]Z'</span><span class="p">,</span> <span class="n">corl_scheme</span><span class="o">=</span><span class="n">corl_xtpl_helgaker_2</span><span class="p">,</span> <span class="n">func</span><span class="o">=</span><span class="n">cbs</span><span class="p">)</span>
</pre></div>
</div>
</dd></dl>
<div class="section" id="output">
<span id="index-2"></span><h2>Output<a class="headerlink" href="#output" title="Permalink to this headline">¶</a></h2>
<p>At the beginning of a cbs() job is printed a listing of the individual
energy calculations which will be performed. The output snippet below is
from the example job [2] above. It shows first each model chemistry needed
to compute the aggregate model chemistry requested through cbs(). Then,
since, for example, an <code class="docutils literal"><span class="pre">energy('ccsd(t)')</span></code> yields CCSD(T), CCSD, MP2,
and SCF energy values, the wrapper condenses this task list into the second
list of minimum number of calculations which will actually be run.</p>
<div class="highlight-python"><div class="highlight"><pre>Naive listing of computations required.
scf / aug-cc-pvqz for SCF TOTAL ENERGY
mp2 / aug-cc-pvtz for MP2 CORRELATION ENERGY
mp2 / aug-cc-pvqz for MP2 CORRELATION ENERGY
ccsd(t) / aug-cc-pvdz for CCSD(T) CORRELATION ENERGY
ccsd(t) / aug-cc-pvtz for CCSD(T) CORRELATION ENERGY
mp2 / aug-cc-pvdz for MP2 CORRELATION ENERGY
mp2 / aug-cc-pvtz for MP2 CORRELATION ENERGY
Enlightened listing of computations required.
mp2 / aug-cc-pvqz for MP2 CORRELATION ENERGY
ccsd(t) / aug-cc-pvdz for CCSD(T) CORRELATION ENERGY
ccsd(t) / aug-cc-pvtz for CCSD(T) CORRELATION ENERGY
</pre></div>
</div>
<p>At the end of a cbs() job is printed a summary section like the one below. First,
in the components section, are listed the results for each model chemistry available, whether
required for the cbs job (*) or not. Next, in the stages section, are listed the results for
each extrapolation. The energies of this section must be dotted with the weightings in column Wt
to get the total cbs energy. Finally, in the CBS section, are listed the results for each stage
of the cbs procedure. The stage energies of this section sum outright to the total cbs energy.</p>
<div class="highlight-python"><div class="highlight"><pre>==> Components <==
----------------------------------------------------------------------------------
Method / Basis Rqd Energy [H] Variable
----------------------------------------------------------------------------------
scf / aug-cc-pvqz * -1.11916375 SCF TOTAL ENERGY
mp2 / aug-cc-pvqz * -0.03407997 MP2 CORRELATION ENERGY
scf / aug-cc-pvdz -1.11662884 SCF TOTAL ENERGY
mp2 / aug-cc-pvdz * -0.02881480 MP2 CORRELATION ENERGY
ccsd(t) / aug-cc-pvdz * -0.03893812 CCSD(T) CORRELATION ENERGY
ccsd / aug-cc-pvdz -0.03893812 CCSD CORRELATION ENERGY
scf / aug-cc-pvtz -1.11881134 SCF TOTAL ENERGY
mp2 / aug-cc-pvtz * -0.03288936 MP2 CORRELATION ENERGY
ccsd(t) / aug-cc-pvtz * -0.04201004 CCSD(T) CORRELATION ENERGY
ccsd / aug-cc-pvtz -0.04201004 CCSD CORRELATION ENERGY
----------------------------------------------------------------------------------
==> Stages <==
----------------------------------------------------------------------------------
Stage Method / Basis Wt Energy [H] Scheme
----------------------------------------------------------------------------------
scf scf / aug-cc-pvqz 1 -1.11916375 highest_1
corl mp2 / aug-cc-pv[tq]z 1 -0.03494879 corl_xtpl_helgaker_2
delta ccsd(t) / aug-cc-pv[dt]z 1 -0.04330347 corl_xtpl_helgaker_2
delta mp2 / aug-cc-pv[dt]z -1 -0.03460497 corl_xtpl_helgaker_2
----------------------------------------------------------------------------------
==> CBS <==
----------------------------------------------------------------------------------
Stage Method / Basis Energy [H] Scheme
----------------------------------------------------------------------------------
scf scf / aug-cc-pvqz -1.11916375 highest_1
corl mp2 / aug-cc-pv[tq]z -0.03494879 corl_xtpl_helgaker_2
delta ccsd(t) - mp2 / aug-cc-pv[dt]z -0.00869851 corl_xtpl_helgaker_2
total CBS -1.16281105
----------------------------------------------------------------------------------
</pre></div>
</div>
</div>
<div class="section" id="extrapolation-schemes">
<span id="index-3"></span><h2>Extrapolation Schemes<a class="headerlink" href="#extrapolation-schemes" title="Permalink to this headline">¶</a></h2>
<dl class="function">
<dt id="wrappers.highest_1">
<code class="descname">highest_1</code><span class="sig-paren">(</span><em>**largs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/wrappers.html#highest_1"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#wrappers.highest_1" title="Permalink to this definition">¶</a></dt>
<dd><p>Scheme for total or correlation energies with a single basis or the highest
zeta-level among an array of bases. Used by <a class="reference internal" href="#wrappers.complete_basis_set" title="wrappers.complete_basis_set"><code class="xref py py-func docutils literal"><span class="pre">complete_basis_set()</span></code></a>.</p>
<div class="math">
<p><img src="_images/math/0196f0e24142a1f5fe3924272e46ba75aa1b82f1.png" alt="E_{total}^X = E_{total}^X"/></p>
</div></dd></dl>
<dl class="function">
<dt id="wrappers.scf_xtpl_helgaker_2">
<code class="descname">scf_xtpl_helgaker_2</code><span class="sig-paren">(</span><em>**largs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/wrappers.html#scf_xtpl_helgaker_2"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#wrappers.scf_xtpl_helgaker_2" title="Permalink to this definition">¶</a></dt>
<dd><p>Extrapolation scheme for reference energies with two adjacent zeta-level bases.
Used by <a class="reference internal" href="#wrappers.complete_basis_set" title="wrappers.complete_basis_set"><code class="xref py py-func docutils literal"><span class="pre">complete_basis_set()</span></code></a>.</p>
<div class="math">
<p><img src="_images/math/321c13cdef886fdc32b1df677fdb9cc8e8e45e2c.png" alt="E_{total}^X = E_{total}^{\infty} + \beta e^{-\alpha X}, \alpha = 1.63"/></p>
</div></dd></dl>
<dl class="function">
<dt id="wrappers.scf_xtpl_helgaker_3">
<code class="descname">scf_xtpl_helgaker_3</code><span class="sig-paren">(</span><em>**largs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/wrappers.html#scf_xtpl_helgaker_3"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#wrappers.scf_xtpl_helgaker_3" title="Permalink to this definition">¶</a></dt>
<dd><p>Extrapolation scheme for reference energies with three adjacent zeta-level bases.
Used by <a class="reference internal" href="#wrappers.complete_basis_set" title="wrappers.complete_basis_set"><code class="xref py py-func docutils literal"><span class="pre">complete_basis_set()</span></code></a>.</p>
<div class="math">
<p><img src="_images/math/e31997feb01590b3983724df034a8ce37169ba86.png" alt="E_{total}^X = E_{total}^{\infty} + \beta e^{-\alpha X}"/></p>
</div></dd></dl>
<dl class="function">
<dt id="wrappers.corl_xtpl_helgaker_2">
<code class="descname">corl_xtpl_helgaker_2</code><span class="sig-paren">(</span><em>**largs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/wrappers.html#corl_xtpl_helgaker_2"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#wrappers.corl_xtpl_helgaker_2" title="Permalink to this definition">¶</a></dt>
<dd><p>Extrapolation scheme for correlation energies with two adjacent zeta-level bases.
Used by <a class="reference internal" href="#wrappers.complete_basis_set" title="wrappers.complete_basis_set"><code class="xref py py-func docutils literal"><span class="pre">complete_basis_set()</span></code></a>.</p>
<div class="math">
<p><img src="_images/math/35dae3e0883c9efd6879b278786ec978acdc1a42.png" alt="E_{corl}^X = E_{corl}^{\infty} + \beta X^{-3}"/></p>
</div></dd></dl>
</div>
<div class="section" id="aliases">
<h2>Aliases<a class="headerlink" href="#aliases" title="Permalink to this headline">¶</a></h2>
<p>When a particular composite method or its functional form is going to be
reused often, it is convenient to define an alias to it. A convenient
place for such Python code to reside is in <a class="reference external" href="https://github.com/psi4/psi4public/blob/master/lib/python/aliases.py">psi4/lib/python/aliases.py</a>
(source location) or <code class="docutils literal"><span class="pre">psi4/share/psi/python/aliases.py</span></code> (installed
location). No recompilation is necessary after defining an alias. Some
existing examples are below.</p>
<dl class="function">
<dt id="aliases.sherrill_gold_standard">
<code class="descname">sherrill_gold_standard</code><span class="sig-paren">(</span><em>name='mp2'</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/aliases.html#sherrill_gold_standard"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#aliases.sherrill_gold_standard" title="Permalink to this definition">¶</a></dt>
<dd><p>Function to call the quantum chemical method known as ‘Gold Standard’
in the Sherrill group. Uses <a class="reference internal" href="#wrappers.complete_basis_set" title="wrappers.complete_basis_set"><code class="xref py py-func docutils literal"><span class="pre">complete_basis_set()</span></code></a> to evaluate
the following expression. Two-point extrapolation of the correlation energy
performed according to <a class="reference internal" href="#wrappers.corl_xtpl_helgaker_2" title="wrappers.corl_xtpl_helgaker_2"><code class="xref py py-func docutils literal"><span class="pre">corl_xtpl_helgaker_2()</span></code></a>.</p>
<div class="math">
<p><img src="_images/math/215ec68ef5c69fd5f44fe2723ed4035409bbc8bf.png" alt="E_{total}^{\text{Au\_std}} = E_{total,\; \text{SCF}}^{\text{aug-cc-pVQZ}} \; + E_{corl,\; \text{MP2}}^{\text{aug-cc-pV[TQ]Z}} \; + \delta_{\text{MP2}}^{\text{CCSD(T)}}\big\vert_{\text{aug-cc-pVTZ}}"/></p>
</div><div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="c"># [1] single-point energy by this composite method</span>
<span class="gp">>>> </span><span class="n">energy</span><span class="p">(</span><span class="s">'sherrill_gold_standard'</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="c"># [2] finite-difference geometry optimization</span>
<span class="gp">>>> </span><span class="n">optimize</span><span class="p">(</span><span class="s">'sherrill_gold_standard'</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="c"># [3] finite-difference geometry optimization, overwriting some pre-defined sherrill_gold_standard options</span>
<span class="gp">>>> </span><span class="n">optimize</span><span class="p">(</span><span class="s">'sherrill_gold_standard'</span><span class="p">,</span> <span class="n">corl_basis</span><span class="o">=</span><span class="s">'cc-pV[DT]Z'</span><span class="p">,</span> <span class="n">delta_basis</span><span class="o">=</span><span class="s">'3-21g'</span><span class="p">)</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="aliases.allen_focal_point">
<code class="descname">allen_focal_point</code><span class="sig-paren">(</span><em>name='mp2'</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/aliases.html#allen_focal_point"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#aliases.allen_focal_point" title="Permalink to this definition">¶</a></dt>
<dd><p>Function to call Wes Allen-style Focal
Point Analysis. JCP 127 014306. Uses
<a class="reference internal" href="#wrappers.complete_basis_set" title="wrappers.complete_basis_set"><code class="xref py py-func docutils literal"><span class="pre">complete_basis_set()</span></code></a> to evaluate the following
expression. SCF employs a three-point extrapolation according
to <a class="reference internal" href="#wrappers.scf_xtpl_helgaker_3" title="wrappers.scf_xtpl_helgaker_3"><code class="xref py py-func docutils literal"><span class="pre">scf_xtpl_helgaker_3()</span></code></a>. MP2, CCSD, and
CCSD(T) employ two-point extrapolation performed according to
<a class="reference internal" href="#wrappers.corl_xtpl_helgaker_2" title="wrappers.corl_xtpl_helgaker_2"><code class="xref py py-func docutils literal"><span class="pre">corl_xtpl_helgaker_2()</span></code></a>. CCSDT and CCSDT(Q)
are plain deltas. This wrapper requires <a class="reference internal" href="mrcc.html#sec-mrcc"><span>Kallay’s MRCC code</span></a>.</p>
<div class="math">
<p><img src="_images/math/589e4c7aa61c6f1701d505f5f75ed93ebaef6026.png" alt="E_{total}^{\text{FPA}} = E_{total,\; \text{SCF}}^{\text{cc-pV[Q56]Z}} \; + E_{corl,\; \text{MP2}}^{\text{cc-pV[56]Z}} \; + \delta_{\text{MP2}}^{\text{CCSD}}\big\vert_{\text{cc-pV[56]Z}} \; + \delta_{\text{CCSD}}^{\text{CCSD(T)}}\big\vert_{\text{cc-pV[56]Z}} \; + \delta_{\text{CCSD(T)}}^{\text{CCSDT}}\big\vert_{\text{cc-pVTZ}} \; + \delta_{\text{CCSDT}}^{\text{CCSDT(Q)}}\big\vert_{\text{cc-pVDZ}}"/></p>
</div><div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="c"># [1] single-point energy by this composite method</span>
<span class="gp">>>> </span><span class="n">energy</span><span class="p">(</span><span class="s">'allen_focal_point'</span><span class="p">)</span>
</pre></div>
</div>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="c"># [2] finite-difference geometry optimization embarrasingly parallel</span>
<span class="gp">>>> </span><span class="n">optimize</span><span class="p">(</span><span class="s">'allen_focal_point'</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s">'sow'</span><span class="p">)</span>
</pre></div>
</div>
</dd></dl>
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<h3><a href="index.html">Table Of Contents</a></h3>
<ul>
<li><a class="reference internal" href="#">Complete Basis Set</a><ul>
<li><a class="reference internal" href="#output">Output</a></li>
<li><a class="reference internal" href="#extrapolation-schemes">Extrapolation Schemes</a></li>
<li><a class="reference internal" href="#aliases">Aliases</a></li>
</ul>
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