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<div class="section" id="evaluation-of-one-electron-properties">
<span id="sec-oeprop"></span><span id="index-0"></span><h1>Evaluation of One-Electron Properties<a class="headerlink" href="#evaluation-of-one-electron-properties" title="Permalink to this headline">¶</a></h1>
<p><em>Code author: Robert M. Parrish and Andrew C. Simmonett</em></p>
<p><em>Section author: Andrew C. Simmonett</em></p>
<p><span class="sc">Psi4</span> is capable of computing a number of one-electron properties
summarized in the table below.</p>
<table border="1" class="docutils" id="id1">
<caption><span class="caption-text">Current one-electron property capabilities of <span class="sc">Psi4</span></span><a class="headerlink" href="#id1" title="Permalink to this table">¶</a></caption>
<colgroup>
<col width="25%" />
<col width="16%" />
<col width="58%" />
</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head">Feature</th>
<th class="head">Keyword</th>
<th class="head">Notes</th>
</tr>
</thead>
<tbody valign="top">
<tr class="row-even"><td>Electric dipole moment</td>
<td>DIPOLE</td>
<td> </td>
</tr>
<tr class="row-odd"><td>Electric quadrupole moment</td>
<td>QUADRUPOLE</td>
<td>Raw (traced) moments and traceless multipoles</td>
</tr>
<tr class="row-even"><td>All moments up order N</td>
<td>MULTIPOLE(N)</td>
<td>Only raw (traced) moments. Sets global variables e.g. “DIPOLE X”, “32-POLE XYYZZ”</td>
</tr>
<tr class="row-odd"><td>Transition dipole moment</td>
<td>TRANSITION_DIPOLE</td>
<td> </td>
</tr>
<tr class="row-even"><td>Transition quadrupole moment</td>
<td>TRANSITION_QUADRUPOLE</td>
<td> </td>
</tr>
<tr class="row-odd"><td>Electrostatic potential, at nuclei</td>
<td>ESP_AT_NUCLEI</td>
<td>Sets global variables “ESP AT CENTER n”, n = 1 to natoms</td>
</tr>
<tr class="row-even"><td>Electrostatic potential, on grid</td>
<td>GRID_ESP</td>
<td>Generates V at each point in grid_esp.dat. See <a class="reference internal" href="#sec-oeprop-grid"><span>Properties evaluated on a grid</span></a></td>
</tr>
<tr class="row-odd"><td>Electric field, on grid</td>
<td>GRID_FIELD</td>
<td>Generates {Ex,Ey,Ez} at each point grid_field.dat. See <a class="reference internal" href="#sec-oeprop-grid"><span>Properties evaluated on a grid</span></a></td>
</tr>
<tr class="row-even"><td>Molecular orbital extents</td>
<td>MO_EXTENTS</td>
<td> </td>
</tr>
<tr class="row-odd"><td>Mulliken atomic charges</td>
<td>MULLIKEN_CHARGES</td>
<td> </td>
</tr>
<tr class="row-even"><td>Löwdin atomic charges</td>
<td>LOWDIN_CHARGES</td>
<td> </td>
</tr>
<tr class="row-odd"><td>Wiberg bond indices</td>
<td>WIBERG_LOWDIN_INDICES</td>
<td>Uses (Löwdin) symmetrically orthogonalized orbitals</td>
</tr>
<tr class="row-even"><td>Mayer bond indices</td>
<td>MAYER_INDICES</td>
<td> </td>
</tr>
<tr class="row-odd"><td>Natural orbital occupations</td>
<td>NO_OCCUPATIONS</td>
<td> </td>
</tr>
</tbody>
</table>
<p>There are two ways the computation of one-electron properties can be requested.
Firstly, the properties can be evaluated from the last
computed one-particle density, using the following syntax:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="n">oeprop</span><span class="p">(</span><span class="s">"MO_EXTENTS"</span><span class="p">,</span> <span class="s">"MULTIPOLE(4)"</span><span class="p">,</span> <span class="n">title</span> <span class="o">=</span> <span class="s">"hello!"</span><span class="p">)</span>
</pre></div>
</div>
<p>Note that it is the user’s responsibility to ensure that the relaxed density
matrix is computed using the method of interest, which may require setting
additional keywords (see the method’s manual section for details). The named
argument, <em>title</em>, is completely optional and is prepended to any
globals variables set during the computation. The unnamed arguments are the
properties to be computed. These can appear in any order, and multiple
properties may be requested, as in the example above. Note that, due to Python
syntax restrictions, the title argument must appear after the list of
properties to compute. The available properties are shown in the table above.</p>
<p>The syntax above works well for computing properties using the SCF
wavefunction, however, may be difficult (or impossible) to use for some of the
correlated levels of theory. Alternatively, one-electron properties can be
computed using the built-in property() function, e.g.:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="nb">property</span><span class="p">(</span><span class="s">'ccsd'</span><span class="p">,</span> <span class="n">properties</span><span class="o">=</span><span class="p">[</span><span class="s">'dipole'</span><span class="p">])</span>
</pre></div>
</div>
<p>The <a class="reference internal" href="prop.html#driver.property" title="driver.property"><code class="xref py py-func docutils literal"><span class="pre">property()</span></code></a> function provides limited functionality, but is a lot easier to
use for correlated methods. For capabilities of <a class="reference internal" href="prop.html#driver.property" title="driver.property"><code class="xref py py-func docutils literal"><span class="pre">property()</span></code></a> see the
corresponding section of the manual.</p>
<div class="section" id="basic-keywords">
<h2>Basic Keywords<a class="headerlink" href="#basic-keywords" title="Permalink to this headline">¶</a></h2>
<p>Multipole moments may be computed at any origin, which is controlled by the
global <a class="reference internal" href="autodoc_glossary_options_c.html#term-properties-origin-globals"><span class="xref std std-term">PROPERTIES_ORIGIN</span></a> keyword. The keyword takes an array with
the following possible values:</p>
<table border="1" class="docutils" id="id2">
<caption><span class="caption-text">Allowed origin specifications</span><a class="headerlink" href="#id2" title="Permalink to this table">¶</a></caption>
<colgroup>
<col width="28%" />
<col width="72%" />
</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head">Keyword</th>
<th class="head">Interpretation</th>
</tr>
</thead>
<tbody valign="top">
<tr class="row-even"><td>[x, y, z]</td>
<td>Origin is at the coordinates, in the same units as the geometry specification</td>
</tr>
<tr class="row-odd"><td>[“COM”]</td>
<td>Origin is at the center of mass</td>
</tr>
<tr class="row-even"><td>[“NUCLEAR_CHARGE”]</td>
<td>Origin is at the center of nuclear charge</td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="properties-evaluated-on-a-grid">
<span id="sec-oeprop-grid"></span><h2>Properties evaluated on a grid<a class="headerlink" href="#properties-evaluated-on-a-grid" title="Permalink to this headline">¶</a></h2>
<p>Certain properties may be evaluated a user-specified grid points. The grid
points are completely arbitrary and are specified by providing a file called
grid.dat containing the x,y,z values for each point in order:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="n">x1</span><span class="p">,</span> <span class="n">y1</span><span class="p">,</span> <span class="n">z1</span>
<span class="n">x2</span><span class="p">,</span> <span class="n">y2</span><span class="p">,</span> <span class="n">z2</span>
<span class="o">..........</span>
<span class="n">xn</span><span class="p">,</span> <span class="n">yn</span><span class="p">,</span> <span class="n">zn</span>
</pre></div>
</div>
<p>The grid.dat file is completely free form; any number of spaces and/or newlines
between entries is permitted. The units of the coordinates in grid.dat are the
same as those used to specify the molecule’s geometry, and the output
quantities are always in atomic units. The requested properties will be
written out in the same order as the grid point specification in grid.dat; see
the above table for the format and file name of the output.</p>
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<li><a class="reference internal" href="#">Evaluation of One-Electron Properties</a><ul>
<li><a class="reference internal" href="#basic-keywords">Basic Keywords</a></li>
<li><a class="reference internal" href="#properties-evaluated-on-a-grid">Properties evaluated on a grid</a></li>
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