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<body>
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<div id="org-div-home-and-up">
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<a accesskey="h" href=""> UP </a>
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<a accesskey="H" href="index.html"> HOME </a>
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</div><div id="content">
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<h1 class="title">Atomic Orbitals</h1>
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<div id="table-of-contents">
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<ul>
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<li><a href="#orgf9a2516">1. Context</a>
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<ul>
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<li><a href="#orgd70bc4a">1.1. Data structure</a></li>
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<li><a href="#orgfc136a4">1.2. Access functions</a></li>
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<li><a href="#orgacef441">1.3. Initialization functions</a></li>
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<li><a href="#orge2bab03">1.4. Fortran interfaces</a></li>
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</ul>
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</li>
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<li><a href="#org71b5a68">2. Radial part</a>
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<ul>
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<li><a href="#org4bbd485">2.1. <span class="todo TODO">TODO</span> Helper functions to accelerate calculations</a></li>
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<li><a href="#orgcad1bdf">2.2. General functions for Gaussian basis functions</a></li>
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<li><a href="#org8d107bb">2.3. <span class="todo TODO">TODO</span> General functions for Slater basis functions</a></li>
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<li><a href="#orgd023d83">2.4. <span class="todo TODO">TODO</span> General functions for Radial functions on a grid</a></li>
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<li><a href="#org1cf016f">2.5. Computation of primitives</a>
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<ul>
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<li><a href="#orgb2927a3">2.5.1. Get</a></li>
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<li><a href="#orgfbd0669">2.5.2. Provide</a></li>
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<li><a href="#org4906bd2">2.5.3. Compute</a></li>
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<li><a href="#org84159a0">2.5.4. Test</a></li>
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<li><a href="#org12eff54">2.5.5. Ideas for improvement</a></li>
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</ul>
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</li>
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<li><a href="#org8077c4a">2.6. Computation of shells</a>
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<ul>
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<li><a href="#org1f9aaad">2.6.1. Get</a></li>
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<li><a href="#org581d78a">2.6.2. Provide</a></li>
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<li><a href="#org7d7f83d">2.6.3. Compute</a></li>
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<li><a href="#org68532f4">2.6.4. Test</a></li>
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</ul>
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</li>
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</ul>
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</li>
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<li><a href="#org8acae7d">3. Polynomial part</a>
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<ul>
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<li><a href="#org2a53367">3.1. General functions for Powers of \(x-X_i\)</a>
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<ul>
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<li><a href="#orgefaeb6d">3.1.1. Requirements</a></li>
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<li><a href="#org205467f">3.1.2. C Header</a></li>
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<li><a href="#org3b977b5">3.1.3. Source</a></li>
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<li><a href="#orgb9f14b4">3.1.4. C interface</a></li>
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<li><a href="#org028ecc8">3.1.5. Fortran interface</a></li>
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<li><a href="#orgf9f1ffa">3.1.6. Test</a></li>
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</ul>
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</li>
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<li><a href="#orgba21cce">3.2. General functions for Value, Gradient and Laplacian of a polynomial</a>
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<ul>
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<li><a href="#org37e025e">3.2.1. Requirements</a></li>
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<li><a href="#orgd9f14b3">3.2.2. C Header</a></li>
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<li><a href="#orgc190714">3.2.3. Source</a></li>
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<li><a href="#org01b83e2">3.2.4. C interface</a></li>
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<li><a href="#org6ac38d8">3.2.5. Fortran interface</a></li>
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<li><a href="#org4843f1f">3.2.6. Test</a></li>
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</ul>
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</li>
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</ul>
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</li>
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<li><a href="#orgfe5f70a">4. Combining radial and polynomial parts</a>
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<li>
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<ul>
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<li><a href="#orgb177076">4.0.1. Get</a></li>
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<li><a href="#orga04f341">4.0.2. Provide</a></li>
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<li><a href="#orga7af53f">4.0.3. Compute</a></li>
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<li><a href="#orgffbbf89">4.0.4. Test</a></li>
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</li>
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</ul>
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</li>
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|
|
</div>
|
|
|
|
<div id="outline-container-orgf9a2516" class="outline-2">
|
|
<h2 id="orgf9a2516"><span class="section-number-2">1</span> Context</h2>
|
|
<div class="outline-text-2" id="text-1">
|
|
<p>
|
|
The following arrays are stored in the context:
|
|
</p>
|
|
|
|
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
|
|
|
|
<colgroup>
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
</colgroup>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-left"><code>type</code></td>
|
|
<td class="org-left"> </td>
|
|
<td class="org-left">Gaussian (<code>'G'</code>) or Slater (<code>'S'</code>)</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>shell_num</code></td>
|
|
<td class="org-left"> </td>
|
|
<td class="org-left">Number of shells</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>prim_num</code></td>
|
|
<td class="org-left"> </td>
|
|
<td class="org-left">Total number of primitives</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>nucleus_index</code></td>
|
|
<td class="org-left"><code>[nucl_num]</code></td>
|
|
<td class="org-left">Index of the first shell of each nucleus</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>nucleus_shell_num</code></td>
|
|
<td class="org-left"><code>[nucl_num]</code></td>
|
|
<td class="org-left">Number of shells per nucleus</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>shell_ang_mom</code></td>
|
|
<td class="org-left"><code>[shell_num]</code></td>
|
|
<td class="org-left">Angular momentum of each shell</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>shell_prim_num</code></td>
|
|
<td class="org-left"><code>[shell_num]</code></td>
|
|
<td class="org-left">Number of primitives in each shell</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>shell_prim_index</code></td>
|
|
<td class="org-left"><code>[shell_num]</code></td>
|
|
<td class="org-left">Address of the first primitive of each shell in the <code>EXPONENT</code> array</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>shell_factor</code></td>
|
|
<td class="org-left"><code>[shell_num]</code></td>
|
|
<td class="org-left">Normalization factor for each shell</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>exponent</code></td>
|
|
<td class="org-left"><code>[prim_num]</code></td>
|
|
<td class="org-left">Array of exponents</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>coefficient</code></td>
|
|
<td class="org-left"><code>[prim_num]</code></td>
|
|
<td class="org-left">Array of coefficients</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>prim_factor</code></td>
|
|
<td class="org-left"><code>[prim_num]</code></td>
|
|
<td class="org-left">Normalization factors of the primtives</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>ao_num</code></td>
|
|
<td class="org-left"> </td>
|
|
<td class="org-left">Number of AOs</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>ao_cartesian</code></td>
|
|
<td class="org-left"> </td>
|
|
<td class="org-left">If true, use polynomials. Otherwise, use spherical harmonics</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>ao_factor</code></td>
|
|
<td class="org-left"><code>[ao_num]</code></td>
|
|
<td class="org-left">Normalization factor of the AO</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>ao_shell</code></td>
|
|
<td class="org-left"><code>[ao_num]</code></td>
|
|
<td class="org-left">For each AO, specify to which shell it belongs</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
|
|
<p>
|
|
Computed data:
|
|
</p>
|
|
|
|
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
|
|
|
|
<colgroup>
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
</colgroup>
|
|
<thead>
|
|
<tr>
|
|
<th scope="col" class="org-left"><code>coefficient_normalized</code></th>
|
|
<th scope="col" class="org-left"><code>[prim_num]</code></th>
|
|
<th scope="col" class="org-left">Normalized primitive coefficients</th>
|
|
</tr>
|
|
|
|
<tr>
|
|
<th scope="col" class="org-left"><code>nucleus_prim_index</code></th>
|
|
<th scope="col" class="org-left"><code>[nucl_num]</code></th>
|
|
<th scope="col" class="org-left">Index of the first primitive for each nucleus</th>
|
|
</tr>
|
|
|
|
<tr>
|
|
<th scope="col" class="org-left"><code>nucleus_max_ang_mom</code></th>
|
|
<th scope="col" class="org-left"><code>[nucl_num]</code></th>
|
|
<th scope="col" class="org-left">Maximum angular momentum for each nucleus</th>
|
|
</tr>
|
|
|
|
<tr>
|
|
<th scope="col" class="org-left"><code>nucleus_range</code></th>
|
|
<th scope="col" class="org-left"><code>[nucl_num]</code></th>
|
|
<th scope="col" class="org-left">Distance beyond which all the AOs are zero</th>
|
|
</tr>
|
|
</thead>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-left"><code>primitive_vgl</code></td>
|
|
<td class="org-left"><code>[5][walk_num][elec_num][prim_num]</code></td>
|
|
<td class="org-left">Value, gradients, Laplacian of the primitives at electron positions</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>primitive_vgl_date</code></td>
|
|
<td class="org-left"><code>uint64_t</code></td>
|
|
<td class="org-left">Late modification date of Value, gradients, Laplacian of the primitives at electron positions</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>shell_vgl</code></td>
|
|
<td class="org-left"><code>[5][walk_num][elec_num][shell_num]</code></td>
|
|
<td class="org-left">Value, gradients, Laplacian of the primitives at electron positions</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>shell_vgl_date</code></td>
|
|
<td class="org-left"><code>uint64_t</code></td>
|
|
<td class="org-left">Late modification date of Value, gradients, Laplacian of the AOs at electron positions</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>ao_vgl</code></td>
|
|
<td class="org-left"><code>[5][walk_num][elec_num][ao_num]</code></td>
|
|
<td class="org-left">Value, gradients, Laplacian of the primitives at electron positions</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>ao_vgl_date</code></td>
|
|
<td class="org-left"><code>uint64_t</code></td>
|
|
<td class="org-left">Late modification date of Value, gradients, Laplacian of the AOs at electron positions</td>
|
|
</tr>
|
|
</tbody>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-left"><code>nucl_shell_index</code></td>
|
|
<td class="org-left"><code>[nucl_num]</code></td>
|
|
<td class="org-left">Index of the first shell for each nucleus</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>exponent_sorted</code></td>
|
|
<td class="org-left"><code>[prim_num]</code></td>
|
|
<td class="org-left">Array of exponents for sorted primitives</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>coeff_norm_sorted</code></td>
|
|
<td class="org-left"><code>[prim_num]</code></td>
|
|
<td class="org-left">Array of normalized coefficients for sorted primitives</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>prim_factor_sorted</code></td>
|
|
<td class="org-left"><code>[prim_num]</code></td>
|
|
<td class="org-left">Normalization factors of the sorted primtives</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
|
|
<p>
|
|
For H<sub>2</sub> with the following basis set,
|
|
</p>
|
|
|
|
<pre class="example">
|
|
HYDROGEN
|
|
S 5
|
|
1 3.387000E+01 6.068000E-03
|
|
2 5.095000E+00 4.530800E-02
|
|
3 1.159000E+00 2.028220E-01
|
|
4 3.258000E-01 5.039030E-01
|
|
5 1.027000E-01 3.834210E-01
|
|
S 1
|
|
1 3.258000E-01 1.000000E+00
|
|
S 1
|
|
1 1.027000E-01 1.000000E+00
|
|
P 1
|
|
1 1.407000E+00 1.000000E+00
|
|
P 1
|
|
1 3.880000E-01 1.000000E+00
|
|
D 1
|
|
1 1.057000E+00 1.0000000
|
|
</pre>
|
|
|
|
<p>
|
|
we have:
|
|
</p>
|
|
|
|
<pre class="example">
|
|
type = 'G'
|
|
shell_num = 12
|
|
prim_num = 20
|
|
ao_num = 38
|
|
nucleus_index = [0 , 6]
|
|
shell_ang_mom = [0, 0, 0, 1, 1, 2, 0, 0, 0, 1, 1, 2]
|
|
shell_factor = [ 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.]
|
|
shell_prim_num = [5, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1]
|
|
shell_prim_index = [0 , 5 , 6 , 7 , 8 , 9 , 10, 15, 16, 17, 18, 19]
|
|
exponent = [ 33.87, 5.095, 1.159, 0.3258, 0.1027, 0.3258, 0.1027, 1.407,
|
|
0.388, 1.057, 33.87, 5.095, 1.159, 0.3258, 0.1027, 0.3258, 0.1027, 1.407,
|
|
0.388, 1.057]
|
|
coefficient = [ 0.006068, 0.045308, 0.202822, 0.503903, 0.383421, 1.0, 1.0,
|
|
1.0, 1.0, 1.0, 0.006068, 0.045308, 0.202822, 0.503903, 0.383421, 1.0, 1.0,
|
|
1.0, 1.0, 1.0]
|
|
prim_factor = [ 1.0006253235944540e+01, 2.4169531573445120e+00, 7.9610924849766440e-01
|
|
3.0734305383061117e-01, 1.2929684417481876e-01, 3.0734305383061117e-01,
|
|
1.2929684417481876e-01, 2.1842769845268308e+00, 4.3649547399719840e-01,
|
|
1.8135965626177861e+00, 1.0006253235944540e+01, 2.4169531573445120e+00,
|
|
7.9610924849766440e-01, 3.0734305383061117e-01, 1.2929684417481876e-01,
|
|
3.0734305383061117e-01, 1.2929684417481876e-01, 2.1842769845268308e+00,
|
|
4.3649547399719840e-01, 1.8135965626177861e+00 ]
|
|
</pre>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd70bc4a" class="outline-3">
|
|
<h3 id="orgd70bc4a"><span class="section-number-3">1.1</span> Data structure</h3>
|
|
<div class="outline-text-3" id="text-1-1">
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #a020f0;">typedef</span> <span style="color: #a020f0;">struct</span> <span style="color: #228b22;">qmckl_ao_basis_struct</span> {
|
|
<span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">shell_num</span>;
|
|
<span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">prim_num</span>;
|
|
<span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">ao_num</span>;
|
|
<span style="color: #228b22;">int64_t</span> * <span style="color: #a0522d;">nucleus_index</span>;
|
|
<span style="color: #228b22;">int64_t</span> * <span style="color: #a0522d;">nucleus_shell_num</span>;
|
|
<span style="color: #228b22;">int32_t</span> * <span style="color: #a0522d;">shell_ang_mom</span>;
|
|
<span style="color: #228b22;">int64_t</span> * <span style="color: #a0522d;">shell_prim_num</span>;
|
|
<span style="color: #228b22;">int64_t</span> * <span style="color: #a0522d;">shell_prim_index</span>;
|
|
<span style="color: #228b22;">double</span> * <span style="color: #a0522d;">shell_factor</span>;
|
|
<span style="color: #228b22;">double</span> * <span style="color: #a0522d;">exponent</span>;
|
|
<span style="color: #228b22;">double</span> * <span style="color: #a0522d;">coefficient</span>;
|
|
<span style="color: #228b22;">double</span> * <span style="color: #a0522d;">prim_factor</span>;
|
|
<span style="color: #228b22;">double</span> * <span style="color: #a0522d;">ao_factor</span>;
|
|
|
|
<span style="color: #228b22;">int64_t</span> * <span style="color: #a0522d;">nucleus_prim_index</span>;
|
|
<span style="color: #228b22;">double</span> * <span style="color: #a0522d;">coefficient_normalized</span>;
|
|
<span style="color: #228b22;">int32_t</span> * <span style="color: #a0522d;">nucleus_max_ang_mom</span>;
|
|
<span style="color: #228b22;">double</span> * <span style="color: #a0522d;">nucleus_range</span>;
|
|
<span style="color: #228b22;">double</span> * <span style="color: #a0522d;">primitive_vgl</span>;
|
|
<span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">primitive_vgl_date</span>;
|
|
<span style="color: #228b22;">double</span> * <span style="color: #a0522d;">shell_vgl</span>;
|
|
<span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">shell_vgl_date</span>;
|
|
<span style="color: #228b22;">double</span> * <span style="color: #a0522d;">ao_vgl</span>;
|
|
<span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">ao_vgl_date</span>;
|
|
|
|
<span style="color: #228b22;">int32_t</span> <span style="color: #a0522d;">uninitialized</span>;
|
|
<span style="color: #228b22;">bool</span> <span style="color: #a0522d;">provided</span>;
|
|
<span style="color: #228b22;">bool</span> <span style="color: #a0522d;">ao_cartesian</span>;
|
|
<span style="color: #228b22;">char</span> <span style="color: #a0522d;">type</span>;
|
|
} <span style="color: #228b22;">qmckl_ao_basis_struct</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
The <code>uninitialized</code> integer contains one bit set to one for each
|
|
initialization function which has not been called. It becomes equal
|
|
to zero after all initialization functions have been called. The
|
|
struct is then initialized and <code>provided == true</code>.
|
|
Some values are initialized by default, and are not concerned by
|
|
this mechanism.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_init_ao_basis</span>(<span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_init_ao_basis</span>(<span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>) {
|
|
|
|
<span style="color: #a020f0;">if</span> (qmckl_context_check(context) == QMCKL_NULL_CONTEXT) {
|
|
<span style="color: #a020f0;">return</span> <span style="color: #008b8b;">false</span>;
|
|
}
|
|
|
|
<span style="color: #228b22;">qmckl_context_struct</span>* <span style="color: #a020f0;">const</span> <span style="color: #a0522d;">ctx</span> = (<span style="color: #228b22;">qmckl_context_struct</span>* <span style="color: #a020f0;">const</span>) context;
|
|
assert (ctx != <span style="color: #008b8b;">NULL</span>);
|
|
|
|
ctx->ao_basis.uninitialized = (1 << 14) - 1;
|
|
|
|
/* <span style="color: #b22222;">Default values </span>*/
|
|
ctx->ao_basis.ao_cartesian = <span style="color: #008b8b;">true</span>;
|
|
|
|
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
|
|
}
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgfc136a4" class="outline-3">
|
|
<h3 id="orgfc136a4"><span class="section-number-3">1.2</span> Access functions</h3>
|
|
<div class="outline-text-3" id="text-1-2">
|
|
<p>
|
|
When all the data for the AOs have been provided, the following
|
|
function returns <code>true</code>.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">bool</span> <span style="color: #0000ff;">qmckl_ao_basis_provided</span> (<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgacef441" class="outline-3">
|
|
<h3 id="orgacef441"><span class="section-number-3">1.3</span> Initialization functions</h3>
|
|
<div class="outline-text-3" id="text-1-3">
|
|
<p>
|
|
To set the basis set, all the following functions need to be
|
|
called.
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_set_ao_basis_type</span> (<span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>, <span style="color: #a020f0;">const</span> <span style="color: #228b22;">char</span> <span style="color: #a0522d;">t</span>);
|
|
<span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_set_ao_basis_shell_num</span> (<span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>, <span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">shell_num</span>);
|
|
<span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_set_ao_basis_prim_num</span> (<span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>, <span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">prim_num</span>);
|
|
<span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_set_ao_basis_ao_num</span> (<span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>, <span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">ao_num</span>);
|
|
<span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_set_ao_basis_nucleus_index</span> (<span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>, <span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> * <span style="color: #a0522d;">nucleus_index</span>);
|
|
<span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_set_ao_basis_nucleus_shell_num</span>(<span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>, <span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> * <span style="color: #a0522d;">nucleus_shell_num</span>);
|
|
<span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_set_ao_basis_shell_ang_mom</span> (<span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>, <span style="color: #a020f0;">const</span> <span style="color: #228b22;">int32_t</span> * <span style="color: #a0522d;">shell_ang_mom</span>);
|
|
<span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_set_ao_basis_shell_prim_num</span> (<span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>, <span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> * <span style="color: #a0522d;">shell_prim_num</span>);
|
|
<span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_set_ao_basis_shell_prim_index</span> (<span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>, <span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> * <span style="color: #a0522d;">shell_prim_index</span>);
|
|
<span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_set_ao_basis_shell_factor</span> (<span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>, <span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> * <span style="color: #a0522d;">shell_factor</span>);
|
|
<span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_set_ao_basis_exponent</span> (<span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>, <span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> * <span style="color: #a0522d;">exponent</span>);
|
|
<span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_set_ao_basis_coefficient</span> (<span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>, <span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> * <span style="color: #a0522d;">coefficient</span>);
|
|
<span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_set_ao_basis_prim_factor</span> (<span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>, <span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> * <span style="color: #a0522d;">prim_factor</span>);
|
|
<span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_set_ao_basis_ao_factor</span> (<span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>, <span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> * <span style="color: #a0522d;">ao_factor</span>);
|
|
<span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_set_ao_basis_cartesian</span> (<span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>, <span style="color: #a020f0;">const</span> <span style="color: #228b22;">bool</span> <span style="color: #a0522d;">cartesian</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
When the basis set is completely entered, other data structures are
|
|
computed to accelerate the calculations. The primitives within each
|
|
contraction are sorted in ascending order of their exponents, such
|
|
that as soon as a primitive is zero all the following functions
|
|
vanish. Also, it is possible to compute a nuclear radius beyond which
|
|
all the primitives are zero up to the numerical accuracy defined in
|
|
the context.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orge2bab03" class="outline-3">
|
|
<h3 id="orge2bab03"><span class="section-number-3">1.4</span> Fortran interfaces</h3>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org71b5a68" class="outline-2">
|
|
<h2 id="org71b5a68"><span class="section-number-2">2</span> Radial part</h2>
|
|
<div class="outline-text-2" id="text-2">
|
|
</div>
|
|
<div id="outline-container-org4bbd485" class="outline-3">
|
|
<h3 id="org4bbd485"><span class="section-number-3">2.1</span> <span class="todo TODO">TODO</span> Helper functions to accelerate calculations</h3>
|
|
</div>
|
|
<div id="outline-container-orgcad1bdf" class="outline-3">
|
|
<h3 id="orgcad1bdf"><span class="section-number-3">2.2</span> General functions for Gaussian basis functions</h3>
|
|
<div class="outline-text-3" id="text-2-2">
|
|
<p>
|
|
<code>qmckl_ao_gaussian_vgl</code> computes the values, gradients and
|
|
Laplacians at a given point of <code>n</code> Gaussian functions centered at
|
|
the same point:
|
|
</p>
|
|
|
|
<p>
|
|
\[ v_i = \exp(-a_i |X-R|^2) \]
|
|
\[ \nabla_x v_i = -2 a_i (X_x - R_x) v_i \]
|
|
\[ \nabla_y v_i = -2 a_i (X_y - R_y) v_i \]
|
|
\[ \nabla_z v_i = -2 a_i (X_z - R_z) v_i \]
|
|
\[ \Delta v_i = a_i (4 |X-R|^2 a_i - 6) v_i \]
|
|
</p>
|
|
|
|
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
|
|
|
|
<colgroup>
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
</colgroup>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-left"><code>context</code></td>
|
|
<td class="org-left">input</td>
|
|
<td class="org-left">Global state</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>X(3)</code></td>
|
|
<td class="org-left">input</td>
|
|
<td class="org-left">Array containing the coordinates of the points</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>R(3)</code></td>
|
|
<td class="org-left">input</td>
|
|
<td class="org-left">Array containing the x,y,z coordinates of the center</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>n</code></td>
|
|
<td class="org-left">input</td>
|
|
<td class="org-left">Number of computed Gaussians</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>A(n)</code></td>
|
|
<td class="org-left">input</td>
|
|
<td class="org-left">Exponents of the Gaussians</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>VGL(ldv,5)</code></td>
|
|
<td class="org-left">output</td>
|
|
<td class="org-left">Value, gradients and Laplacian of the Gaussians</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>ldv</code></td>
|
|
<td class="org-left">input</td>
|
|
<td class="org-left">Leading dimension of array <code>VGL</code></td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
|
|
<p>
|
|
Requirements
|
|
</p>
|
|
|
|
<ul class="org-ul">
|
|
<li><code>context</code> is not 0</li>
|
|
<li><code>n</code> > 0</li>
|
|
<li><code>ldv</code> >= 5</li>
|
|
<li><code>A(i)</code> > 0 for all <code>i</code></li>
|
|
<li><code>X</code> is allocated with at least \(3 \times 8\) bytes</li>
|
|
<li><code>R</code> is allocated with at least \(3 \times 8\) bytes</li>
|
|
<li><code>A</code> is allocated with at least \(n \times 8\) bytes</li>
|
|
<li><code>VGL</code> is allocated with at least \(n \times 5 \times 8\) bytes</li>
|
|
</ul>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span>
|
|
<span style="color: #0000ff;">qmckl_ao_gaussian_vgl</span>(<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> *<span style="color: #a0522d;">X</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> *<span style="color: #a0522d;">R</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> *<span style="color: #a0522d;">n</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> *<span style="color: #a0522d;">A</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> *<span style="color: #a0522d;">VGL</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">ldv</span>);
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90"><span style="color: #228b22;">integer </span><span style="color: #a020f0;">function</span><span style="color: #a0522d;"> </span><span style="color: #0000ff;">qmckl_ao_gaussian_vgl_f</span><span style="color: #000000; background-color: #ffffff;">(context, X, R, n, A, VGL, ldv) result(info)</span>
|
|
<span style="color: #a020f0;">use</span> <span style="color: #0000ff;">qmckl</span>
|
|
<span style="color: #a020f0;">implicit</span> <span style="color: #228b22;">none</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> context</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> X(3), R(3)</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> n</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> A(n)</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">intent</span>(out) ::<span style="color: #a0522d;"> VGL(ldv,5)</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> ldv</span>
|
|
|
|
<span style="color: #228b22;">integer</span>*8 ::<span style="color: #a0522d;"> i,j</span>
|
|
<span style="color: #228b22;">real</span>*8 ::<span style="color: #a0522d;"> Y(3), r2, t, u, v</span>
|
|
|
|
info = QMCKL_SUCCESS
|
|
|
|
<span style="color: #a020f0;">if</span> (context == QMCKL_NULL_CONTEXT) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_CONTEXT
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
<span style="color: #a020f0;">if</span> (n <= 0) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_4
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
<span style="color: #a020f0;">if</span> (ldv < n) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_7
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
|
|
<span style="color: #a020f0;">do</span> i=1,3
|
|
Y(i) = X(i) - R(i)
|
|
<span style="color: #a020f0;">end do</span>
|
|
r2 = Y(1)*Y(1) + Y(2)*Y(2) + Y(3)*Y(3)
|
|
|
|
<span style="color: #a020f0;">do</span> i=1,n
|
|
VGL(i,1) = dexp(-A(i) * r2)
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
<span style="color: #a020f0;">do</span> i=1,n
|
|
VGL(i,5) = A(i) * VGL(i,1)
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
t = -2.d0 * ( X(1) - R(1) )
|
|
u = -2.d0 * ( X(2) - R(2) )
|
|
v = -2.d0 * ( X(3) - R(3) )
|
|
|
|
<span style="color: #a020f0;">do</span> i=1,n
|
|
VGL(i,2) = t * VGL(i,5)
|
|
VGL(i,3) = u * VGL(i,5)
|
|
VGL(i,4) = v * VGL(i,5)
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
t = 4.d0 * r2
|
|
<span style="color: #a020f0;">do</span> i=1,n
|
|
VGL(i,5) = (t * A(i) - 6.d0) * VGL(i,5)
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
<span style="color: #a020f0;">end function</span> <span style="color: #0000ff;">qmckl_ao_gaussian_vgl_f</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90"><span style="color: #228b22;">integer</span>(<span style="color: #008b8b;">c_int32_t</span>) <span style="color: #a020f0;">function</span> <span style="color: #0000ff;">test_qmckl_ao_gaussian_vgl</span>(context) <span style="color: #a020f0;">bind</span>(C)
|
|
<span style="color: #a020f0;">use</span> <span style="color: #0000ff;">qmckl</span>
|
|
<span style="color: #a020f0;">implicit</span> <span style="color: #228b22;">none</span>
|
|
|
|
<span style="color: #228b22;">integer</span>(<span style="color: #008b8b;">c_int64_t</span>), <span style="color: #a020f0;">intent</span>(in), <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> context</span>
|
|
|
|
<span style="color: #228b22;">integer</span>*8 ::<span style="color: #a0522d;"> n, ldv, j, i</span>
|
|
<span style="color: #228b22;">double precision</span> ::<span style="color: #a0522d;"> X(3), R(3), Y(3), r2</span>
|
|
<span style="color: #228b22;">double precision</span>, <span style="color: #a020f0;">allocatable</span> ::<span style="color: #a0522d;"> VGL(:,:), A(:)</span>
|
|
<span style="color: #228b22;">double precision</span> ::<span style="color: #a0522d;"> epsilon</span>
|
|
|
|
epsilon = qmckl_get_numprec_epsilon(context)
|
|
|
|
X = (/ 1.1 , 2.2 , 3.3 /)
|
|
R = (/ 0.1 , 1.2 , -2.3 /)
|
|
Y(:) = X(:) - R(:)
|
|
r2 = Y(1)**2 + Y(2)**2 + Y(3)**2
|
|
|
|
n = 10;
|
|
ldv = 100;
|
|
|
|
<span style="color: #a020f0;">allocate</span> (A(n), VGL(ldv,5))
|
|
<span style="color: #a020f0;">do</span> i=1,n
|
|
A(i) = 0.0013 * <span style="color: #a020f0;">dble</span>(<span style="color: #a020f0;">ishft</span>(1,i))
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
|
|
test_qmckl_ao_gaussian_vgl = <span style="color: #a020f0;">&</span>
|
|
qmckl_ao_gaussian_vgl(context, X, R, n, A, VGL, ldv)
|
|
<span style="color: #a020f0;">if</span> (test_qmckl_ao_gaussian_vgl /= 0) <span style="color: #a020f0;">return</span>
|
|
|
|
test_qmckl_ao_gaussian_vgl = -1
|
|
|
|
<span style="color: #a020f0;">do</span> i=1,n
|
|
test_qmckl_ao_gaussian_vgl = -11
|
|
<span style="color: #a020f0;">if</span> (dabs(1.d0 - VGL(i,1) / (<span style="color: #a020f0;">&</span>
|
|
dexp(-A(i) * r2) <span style="color: #a020f0;">&</span>
|
|
)) > epsilon ) <span style="color: #a020f0;">return</span>
|
|
|
|
test_qmckl_ao_gaussian_vgl = -12
|
|
<span style="color: #a020f0;">if</span> (dabs(1.d0 - VGL(i,2) / (<span style="color: #a020f0;">&</span>
|
|
-2.d0 * A(i) * Y(1) * dexp(-A(i) * r2) <span style="color: #a020f0;">&</span>
|
|
)) > epsilon ) <span style="color: #a020f0;">return</span>
|
|
|
|
test_qmckl_ao_gaussian_vgl = -13
|
|
<span style="color: #a020f0;">if</span> (dabs(1.d0 - VGL(i,3) / (<span style="color: #a020f0;">&</span>
|
|
-2.d0 * A(i) * Y(2) * dexp(-A(i) * r2) <span style="color: #a020f0;">&</span>
|
|
)) > epsilon ) <span style="color: #a020f0;">return</span>
|
|
|
|
test_qmckl_ao_gaussian_vgl = -14
|
|
<span style="color: #a020f0;">if</span> (dabs(1.d0 - VGL(i,4) / (<span style="color: #a020f0;">&</span>
|
|
-2.d0 * A(i) * Y(3) * dexp(-A(i) * r2) <span style="color: #a020f0;">&</span>
|
|
)) > epsilon ) <span style="color: #a020f0;">return</span>
|
|
|
|
test_qmckl_ao_gaussian_vgl = -15
|
|
<span style="color: #a020f0;">if</span> (dabs(1.d0 - VGL(i,5) / (<span style="color: #a020f0;">&</span>
|
|
A(i) * (4.d0*r2*A(i) - 6.d0) * dexp(-A(i) * r2) <span style="color: #a020f0;">&</span>
|
|
)) > epsilon ) <span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
test_qmckl_ao_gaussian_vgl = 0
|
|
|
|
<span style="color: #a020f0;">deallocate</span>(VGL)
|
|
<span style="color: #a020f0;">end function</span> <span style="color: #0000ff;">test_qmckl_ao_gaussian_vgl</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org8d107bb" class="outline-3">
|
|
<h3 id="org8d107bb"><span class="section-number-3">2.3</span> <span class="todo TODO">TODO</span> General functions for Slater basis functions</h3>
|
|
</div>
|
|
<div id="outline-container-orgd023d83" class="outline-3">
|
|
<h3 id="orgd023d83"><span class="section-number-3">2.4</span> <span class="todo TODO">TODO</span> General functions for Radial functions on a grid</h3>
|
|
</div>
|
|
<div id="outline-container-org1cf016f" class="outline-3">
|
|
<h3 id="org1cf016f"><span class="section-number-3">2.5</span> Computation of primitives</h3>
|
|
<div class="outline-text-3" id="text-2-5">
|
|
</div>
|
|
<div id="outline-container-orgb2927a3" class="outline-4">
|
|
<h4 id="orgb2927a3"><span class="section-number-4">2.5.1</span> Get</h4>
|
|
<div class="outline-text-4" id="text-2-5-1">
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_get_ao_basis_primitive_vgl</span>(<span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>, <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">const</span> <span style="color: #a0522d;">primitive_vgl</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgfbd0669" class="outline-4">
|
|
<h4 id="orgfbd0669"><span class="section-number-4">2.5.2</span> Provide</h4>
|
|
</div>
|
|
|
|
<div id="outline-container-org4906bd2" class="outline-4">
|
|
<h4 id="org4906bd2"><span class="section-number-4">2.5.3</span> Compute</h4>
|
|
<div class="outline-text-4" id="text-2-5-3">
|
|
<table id="org0872fde" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
|
|
|
|
<colgroup>
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
</colgroup>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-left">qmckl<sub>context</sub></td>
|
|
<td class="org-left">context</td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Global state</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">int64<sub>t</sub></td>
|
|
<td class="org-left">prim<sub>num</sub></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Number of primitives</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">int64<sub>t</sub></td>
|
|
<td class="org-left">elec<sub>num</sub></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Number of electrons</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">int64<sub>t</sub></td>
|
|
<td class="org-left">nucl<sub>num</sub></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Number of nuclei</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">int64<sub>t</sub></td>
|
|
<td class="org-left">walk<sub>num</sub></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Number of walkers</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">int64<sub>t</sub></td>
|
|
<td class="org-left">nucleus<sub>prim</sub><sub>index</sub>[nucl<sub>num</sub>]</td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Index of the 1st primitive of each nucleus</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">double</td>
|
|
<td class="org-left">elec<sub>coord</sub>[walk<sub>num</sub>][3][elec<sub>num</sub>]</td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Electron coordinates</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">double</td>
|
|
<td class="org-left">nucl<sub>coord</sub>[3][elec<sub>num</sub>]</td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Nuclear coordinates</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">double</td>
|
|
<td class="org-left">expo[prim<sub>num</sub>]</td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Exponents of the primitives</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">double</td>
|
|
<td class="org-left">primitive<sub>vgl</sub>[5][walk<sub>num</sub>][elec<sub>num</sub>][prim<sub>num</sub>]</td>
|
|
<td class="org-left">out</td>
|
|
<td class="org-left">Value, gradients and Laplacian of the primitives</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90"><span style="color: #228b22;">integer</span><span style="color: #a0522d;"> function qmckl_compute_ao_basis_primitive_gaussian_vgl_f(context, </span><span style="color: #a020f0;">&</span>
|
|
prim_num, elec_num, nucl_num, walk_num, <span style="color: #a020f0;">&</span>
|
|
nucleus_prim_index, elec_coord, nucl_coord, expo, primitive_vgl) <span style="color: #a020f0;">&</span>
|
|
<span style="color: #a020f0;">result</span>(info)
|
|
<span style="color: #a020f0;">use</span> <span style="color: #0000ff;">qmckl</span>
|
|
<span style="color: #a020f0;">implicit</span> <span style="color: #228b22;">none</span>
|
|
<span style="color: #228b22;">integer</span>(qmckl_context), <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> context</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> prim_num</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> nucl_num</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> elec_num</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> walk_num</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> nucleus_prim_index(nucl_num+1)</span>
|
|
<span style="color: #228b22;">double precision</span> , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> elec_coord(elec_num,3,walk_num)</span>
|
|
<span style="color: #228b22;">double precision</span> , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> nucl_coord(nucl_num,3)</span>
|
|
<span style="color: #228b22;">double precision</span> , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> expo(prim_num)</span>
|
|
<span style="color: #228b22;">double precision</span> , <span style="color: #a020f0;">intent</span>(out) ::<span style="color: #a0522d;"> primitive_vgl(prim_num,elec_num,walk_num,5)</span>
|
|
|
|
<span style="color: #228b22;">integer</span>*8 ::<span style="color: #a0522d;"> inucl, iprim, iwalk, ielec</span>
|
|
<span style="color: #228b22;">double precision</span> ::<span style="color: #a0522d;"> x, y, z, two_a, ar2, r2, v, cutoff</span>
|
|
|
|
info = QMCKL_SUCCESS
|
|
|
|
! <span style="color: #b22222;">Don't compute exponentials when the result will be almost zero.</span>
|
|
cutoff = -dlog(1.d-15)
|
|
|
|
<span style="color: #a020f0;">do</span> inucl=1,nucl_num
|
|
! <span style="color: #b22222;">C is zero-based, so shift bounds by one</span>
|
|
<span style="color: #a020f0;">do</span> iprim = nucleus_prim_index(inucl)+1, nucleus_prim_index(inucl+1)
|
|
<span style="color: #a020f0;">do</span> iwalk = 1, walk_num
|
|
<span style="color: #a020f0;">do</span> ielec = 1, elec_num
|
|
x = elec_coord(ielec,1,iwalk) - nucl_coord(inucl,1)
|
|
y = elec_coord(ielec,2,iwalk) - nucl_coord(inucl,2)
|
|
z = elec_coord(ielec,3,iwalk) - nucl_coord(inucl,3)
|
|
|
|
r2 = x*x + y*y + z*z
|
|
ar2 = expo(iprim)*r2
|
|
<span style="color: #a020f0;">if</span> (ar2 > cutoff) <span style="color: #a020f0;">cycle</span>
|
|
|
|
v = dexp(-ar2)
|
|
two_a = -2.d0 * expo(iprim) * v
|
|
|
|
primitive_vgl(iprim, ielec, iwalk, 1) = v
|
|
primitive_vgl(iprim, ielec, iwalk, 2) = two_a * x
|
|
primitive_vgl(iprim, ielec, iwalk, 3) = two_a * y
|
|
primitive_vgl(iprim, ielec, iwalk, 4) = two_a * z
|
|
primitive_vgl(iprim, ielec, iwalk, 5) = two_a * (3.d0 - 2.d0*ar2)
|
|
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
<span style="color: #a020f0;">end function</span> <span style="color: #0000ff;">qmckl_compute_ao_basis_primitive_gaussian_vgl_f</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org84159a0" class="outline-4">
|
|
<h4 id="org84159a0"><span class="section-number-4">2.5.4</span> Test</h4>
|
|
</div>
|
|
|
|
<div id="outline-container-org12eff54" class="outline-4">
|
|
<h4 id="org12eff54"><span class="section-number-4">2.5.5</span> Ideas for improvement</h4>
|
|
<div class="outline-text-4" id="text-2-5-5">
|
|
<div class="org-src-container">
|
|
<pre class="src src-c">// <span style="color: #b22222;">m : walkers</span>
|
|
// <span style="color: #b22222;">j : electrons</span>
|
|
// <span style="color: #b22222;">l : primitives</span>
|
|
|
|
k=0;
|
|
<span style="color: #a020f0;">for</span> (m=0 ; m<walk_num ; ++m) {
|
|
<span style="color: #a020f0;">for</span> (j=0 ; j<elec_num ; ++j) {
|
|
<span style="color: #a020f0;">for</span> (i=0 ; i<nucl_num ; ++i) {
|
|
|
|
r2 = nucl_elec_dist[i][j];
|
|
|
|
<span style="color: #a020f0;">if</span> (r2 < nucl_radius2[i]) {
|
|
|
|
<span style="color: #a020f0;">for</span> (l=0 ; l<prim_num ; ++l) {
|
|
tmp[k].i = i;
|
|
tmp[k].j = j;
|
|
tmp[k].m = m;
|
|
tmp[k].ar2 = -expo[l] *r2;
|
|
++k;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// <span style="color: #b22222;">sort(tmp) in increasing ar2;</span>
|
|
// <span style="color: #b22222;">Identify first ar2 above numerical accuracy threshold</span>
|
|
// <span style="color: #b22222;">Compute vectorized exponentials on significant values</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org8077c4a" class="outline-3">
|
|
<h3 id="org8077c4a"><span class="section-number-3">2.6</span> Computation of shells</h3>
|
|
<div class="outline-text-3" id="text-2-6">
|
|
</div>
|
|
<div id="outline-container-org1f9aaad" class="outline-4">
|
|
<h4 id="org1f9aaad"><span class="section-number-4">2.6.1</span> Get</h4>
|
|
<div class="outline-text-4" id="text-2-6-1">
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_get_ao_basis_shell_vgl</span>(<span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>, <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">const</span> <span style="color: #a0522d;">shell_vgl</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org581d78a" class="outline-4">
|
|
<h4 id="org581d78a"><span class="section-number-4">2.6.2</span> Provide</h4>
|
|
</div>
|
|
|
|
<div id="outline-container-org7d7f83d" class="outline-4">
|
|
<h4 id="org7d7f83d"><span class="section-number-4">2.6.3</span> Compute</h4>
|
|
<div class="outline-text-4" id="text-2-6-3">
|
|
<table id="org9d35127" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
|
|
|
|
<colgroup>
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
</colgroup>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-left"><code>qmckl_context</code></td>
|
|
<td class="org-left"><code>context</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Global state</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
<td class="org-left"><code>prim_num</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Number of primitives</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
<td class="org-left"><code>shell_num</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Number of shells</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
<td class="org-left"><code>elec_num</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Number of electrons</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
<td class="org-left"><code>nucl_num</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Number of nuclei</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
<td class="org-left"><code>walk_num</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Number of walkers</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
<td class="org-left"><code>nucleus_shell_num[nucl_num]</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Number of shells for each nucleus</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
<td class="org-left"><code>nucleus_index[nucl_num]</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Index of the 1st shell of each nucleus</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
<td class="org-left"><code>shell_prim_index[shell_num]</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Index of the 1st primitive of each shell</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
<td class="org-left"><code>shell_prim_num[shell_num]</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Number of primitives per shell</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>double</code></td>
|
|
<td class="org-left"><code>elec_coord[walk_num][3][elec_num]</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Electron coordinates</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>double</code></td>
|
|
<td class="org-left"><code>nucl_coord[3][elec_num]</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Nuclear coordinates</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>double</code></td>
|
|
<td class="org-left"><code>expo[prim_num]</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Exponents of the primitives</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>double</code></td>
|
|
<td class="org-left"><code>coef_normalized[prim_num]</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Coefficients of the primitives</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>double</code></td>
|
|
<td class="org-left"><code>shell_vgl[5][walk_num][elec_num][shell_num]</code></td>
|
|
<td class="org-left">out</td>
|
|
<td class="org-left">Value, gradients and Laplacian of the shells</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90"><span style="color: #228b22;">integer</span><span style="color: #a0522d;"> function qmckl_compute_ao_basis_shell_gaussian_vgl_f(context, </span><span style="color: #a020f0;">&</span>
|
|
prim_num, shell_num, elec_num, nucl_num, walk_num, <span style="color: #a020f0;">&</span>
|
|
nucleus_shell_num, nucleus_index, shell_prim_index, shell_prim_num, <span style="color: #a020f0;">&</span>
|
|
elec_coord, nucl_coord, expo, coef_normalized, shell_vgl) <span style="color: #a020f0;">&</span>
|
|
<span style="color: #a020f0;">result</span>(info)
|
|
<span style="color: #a020f0;">use</span> <span style="color: #0000ff;">qmckl</span>
|
|
<span style="color: #a020f0;">implicit</span> <span style="color: #228b22;">none</span>
|
|
<span style="color: #228b22;">integer</span>(qmckl_context), <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> context</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> prim_num</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> shell_num</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> nucl_num</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> elec_num</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> walk_num</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> nucleus_shell_num(nucl_num)</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> nucleus_index(nucl_num)</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> shell_prim_index(shell_num)</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> shell_prim_num(shell_num)</span>
|
|
<span style="color: #228b22;">double precision</span> , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> elec_coord(elec_num,3,walk_num)</span>
|
|
<span style="color: #228b22;">double precision</span> , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> nucl_coord(nucl_num,3)</span>
|
|
<span style="color: #228b22;">double precision</span> , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> expo(prim_num)</span>
|
|
<span style="color: #228b22;">double precision</span> , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> coef_normalized(prim_num)</span>
|
|
<span style="color: #228b22;">double precision</span> , <span style="color: #a020f0;">intent</span>(out) ::<span style="color: #a0522d;"> shell_vgl(shell_num,elec_num,walk_num,5)</span>
|
|
|
|
<span style="color: #228b22;">integer</span>*8 ::<span style="color: #a0522d;"> inucl, iprim, iwalk, ielec, ishell</span>
|
|
<span style="color: #228b22;">double precision</span> ::<span style="color: #a0522d;"> x, y, z, two_a, ar2, r2, v, cutoff</span>
|
|
|
|
info = QMCKL_SUCCESS
|
|
|
|
! <span style="color: #b22222;">Don't compute exponentials when the result will be almost zero.</span>
|
|
! <span style="color: #b22222;">TODO : Use numerical precision here</span>
|
|
cutoff = -dlog(1.d-15)
|
|
|
|
<span style="color: #a020f0;">do</span> inucl=1,nucl_num
|
|
|
|
<span style="color: #a020f0;">do</span> iwalk = 1, walk_num
|
|
<span style="color: #a020f0;">do</span> ielec = 1, elec_num
|
|
|
|
x = elec_coord(ielec,1,iwalk) - nucl_coord(inucl,1)
|
|
y = elec_coord(ielec,2,iwalk) - nucl_coord(inucl,2)
|
|
z = elec_coord(ielec,3,iwalk) - nucl_coord(inucl,3)
|
|
|
|
r2 = x*x + y*y + z*z
|
|
|
|
<span style="color: #a020f0;">do</span> ishell=nucleus_index(inucl)+1, nucleus_index(inucl)+nucleus_shell_num(inucl)
|
|
! <span style="color: #b22222;">C is zero-based, so shift bounds by one</span>
|
|
|
|
shell_vgl(ishell, ielec, iwalk, 1) = 0.d0
|
|
shell_vgl(ishell, ielec, iwalk, 2) = 0.d0
|
|
shell_vgl(ishell, ielec, iwalk, 3) = 0.d0
|
|
shell_vgl(ishell, ielec, iwalk, 4) = 0.d0
|
|
shell_vgl(ishell, ielec, iwalk, 5) = 0.d0
|
|
|
|
<span style="color: #a020f0;">do</span> iprim = shell_prim_index(ishell)+1, shell_prim_index(ishell)+shell_prim_num(ishell)
|
|
|
|
ar2 = expo(iprim)*r2
|
|
<span style="color: #a020f0;">if</span> (ar2 > cutoff) <span style="color: #a020f0;">then</span>
|
|
<span style="color: #a020f0;">cycle</span>
|
|
<span style="color: #a020f0;">end if</span>
|
|
|
|
v = coef_normalized(iprim) * dexp(-ar2)
|
|
two_a = -2.d0 * expo(iprim) * v
|
|
|
|
shell_vgl(ishell, ielec, iwalk, 1) = <span style="color: #a020f0;">&</span>
|
|
shell_vgl(ishell, ielec, iwalk, 1) + v
|
|
|
|
shell_vgl(ishell, ielec, iwalk, 2) = <span style="color: #a020f0;">&</span>
|
|
shell_vgl(ishell, ielec, iwalk, 2) + two_a * x
|
|
|
|
shell_vgl(ishell, ielec, iwalk, 3) = <span style="color: #a020f0;">&</span>
|
|
shell_vgl(ishell, ielec, iwalk, 3) + two_a * y
|
|
|
|
shell_vgl(ishell, ielec, iwalk, 4) = <span style="color: #a020f0;">&</span>
|
|
shell_vgl(ishell, ielec, iwalk, 4) + two_a * z
|
|
|
|
shell_vgl(ishell, ielec, iwalk, 5) = <span style="color: #a020f0;">&</span>
|
|
shell_vgl(ishell, ielec, iwalk, 5) + two_a * (3.d0 - 2.d0*ar2)
|
|
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
<span style="color: #a020f0;">end function</span> <span style="color: #0000ff;">qmckl_compute_ao_basis_shell_gaussian_vgl_f</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_compute_ao_basis_shell_gaussian_vgl</span> (
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">prim_num</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">shell_num</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">elec_num</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">nucl_num</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">walk_num</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span>* <span style="color: #a0522d;">nucleus_shell_num</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span>* <span style="color: #a0522d;">nucleus_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span>* <span style="color: #a0522d;">shell_prim_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span>* <span style="color: #a0522d;">shell_prim_num</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">elec_coord</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">nucl_coord</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">expo</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">coef_normalized</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">const</span> <span style="color: #a0522d;">shell_vgl</span> );
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org68532f4" class="outline-4">
|
|
<h4 id="org68532f4"><span class="section-number-4">2.6.4</span> Test</h4>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org8acae7d" class="outline-2">
|
|
<h2 id="org8acae7d"><span class="section-number-2">3</span> Polynomial part</h2>
|
|
<div class="outline-text-2" id="text-3">
|
|
<p>
|
|
Going from the atomic basis set to AOs implies a systematic
|
|
construction of all the angular functions of each shell. We
|
|
consider two cases for the angular functions: the real-valued
|
|
spherical harmonics, and the polynomials in Cartesian coordinates.
|
|
In the case of spherical harmonics, the AOs are ordered in
|
|
increasing magnetic quantum number (\(-l \le m \le l\)), and in the
|
|
case of polynomials we choose the canonical ordering, i.e
|
|
</p>
|
|
|
|
\begin{eqnarray}
|
|
p & : & p_x, p_y, p_z \nonumber \\
|
|
d & : & d_{xx}, d_{xy}, d_{xz}, d_{yy}, d_{yz}, d_{zz} \nonumber \\
|
|
f & : & f_{xxx}, f_{xxy}, f_{xxz}, f_{xyy}, f_{xyz}, f_{xzz}, f_{yyy}, f_{yyz}, f_{yzz}, f_{zzz} \nonumber \\
|
|
{\rm etc.} \nonumber
|
|
\end{eqnarray}
|
|
</div>
|
|
|
|
<div id="outline-container-org2a53367" class="outline-3">
|
|
<h3 id="org2a53367"><span class="section-number-3">3.1</span> General functions for Powers of \(x-X_i\)</h3>
|
|
<div class="outline-text-3" id="text-3-1">
|
|
<p>
|
|
The <code>qmckl_ao_power</code> function computes all the powers of the <code>n</code>
|
|
input data up to the given maximum value given in input for each of
|
|
the \(n\) points:
|
|
</p>
|
|
|
|
<p>
|
|
\[ P_{ik} = X_i^k \]
|
|
</p>
|
|
|
|
<table id="org8cb3ad1" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
|
|
|
|
<colgroup>
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
</colgroup>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-left">qmckl<sub>context</sub></td>
|
|
<td class="org-left">context</td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Global state</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">int64<sub>t</sub></td>
|
|
<td class="org-left">n</td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Number of values</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">double</td>
|
|
<td class="org-left">X[n]</td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Array containing the input values</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">int32<sub>t</sub></td>
|
|
<td class="org-left">LMAX[n]</td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Array containing the maximum power for each value</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">double</td>
|
|
<td class="org-left">P[n][ldp]</td>
|
|
<td class="org-left">out</td>
|
|
<td class="org-left">Array containing all the powers of <code>X</code></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">int64<sub>t</sub></td>
|
|
<td class="org-left">ldp</td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Leading dimension of array <code>P</code></td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
</div>
|
|
|
|
<div id="outline-container-orgefaeb6d" class="outline-4">
|
|
<h4 id="orgefaeb6d"><span class="section-number-4">3.1.1</span> Requirements</h4>
|
|
<div class="outline-text-4" id="text-3-1-1">
|
|
<ul class="org-ul">
|
|
<li><code>context</code> is not <code>QMCKL_NULL_CONTEXT</code></li>
|
|
<li><code>n</code> > 0</li>
|
|
<li><code>X</code> is allocated with at least \(n \times 8\) bytes</li>
|
|
<li><code>LMAX</code> is allocated with at least \(n \times 4\) bytes</li>
|
|
<li><code>P</code> is allocated with at least \(n \times \max_i \text{LMAX}_i \times 8\) bytes</li>
|
|
<li><code>LDP</code> >= \(\max_i\) <code>LMAX[i]</code></li>
|
|
</ul>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org205467f" class="outline-4">
|
|
<h4 id="org205467f"><span class="section-number-4">3.1.2</span> C Header</h4>
|
|
<div class="outline-text-4" id="text-3-1-2">
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_ao_power</span> (
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">n</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">X</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int32_t</span>* <span style="color: #a0522d;">LMAX</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">const</span> <span style="color: #a0522d;">P</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">ldp</span> );
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org3b977b5" class="outline-4">
|
|
<h4 id="org3b977b5"><span class="section-number-4">3.1.3</span> Source</h4>
|
|
<div class="outline-text-4" id="text-3-1-3">
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90"><span style="color: #228b22;">integer </span><span style="color: #a020f0;">function</span><span style="color: #a0522d;"> </span><span style="color: #0000ff;">qmckl_ao_power_f</span><span style="color: #000000; background-color: #ffffff;">(context, n, X, LMAX, P, ldp) result(info)</span>
|
|
<span style="color: #a020f0;">use</span> <span style="color: #0000ff;">qmckl</span>
|
|
<span style="color: #a020f0;">implicit</span> <span style="color: #228b22;">none</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> context</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> n</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> X(n)</span>
|
|
<span style="color: #228b22;">integer</span> , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> LMAX(n)</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">intent</span>(out) ::<span style="color: #a0522d;"> P(ldp,n)</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> ldp</span>
|
|
|
|
<span style="color: #228b22;">integer</span>*8 ::<span style="color: #a0522d;"> i,k</span>
|
|
|
|
info = QMCKL_SUCCESS
|
|
|
|
<span style="color: #a020f0;">if</span> (context == QMCKL_NULL_CONTEXT) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_CONTEXT
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
<span style="color: #a020f0;">if</span> (n <= ldp) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_2
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
k = <span style="color: #a020f0;">MAXVAL</span>(LMAX)
|
|
<span style="color: #a020f0;">if</span> (LDP < k) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_6
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
<span style="color: #a020f0;">if</span> (k <= 0) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_4
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
<span style="color: #a020f0;">do</span> i=1,n
|
|
P(1,i) = X(i)
|
|
<span style="color: #a020f0;">do</span> k=2,LMAX(i)
|
|
P(k,i) = P(k-1,i) * X(i)
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
<span style="color: #a020f0;">end function</span> <span style="color: #0000ff;">qmckl_ao_power_f</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgb9f14b4" class="outline-4">
|
|
<h4 id="orgb9f14b4"><span class="section-number-4">3.1.4</span> C interface</h4>
|
|
</div>
|
|
<div id="outline-container-org028ecc8" class="outline-4">
|
|
<h4 id="org028ecc8"><span class="section-number-4">3.1.5</span> Fortran interface</h4>
|
|
</div>
|
|
|
|
<div id="outline-container-orgf9f1ffa" class="outline-4">
|
|
<h4 id="orgf9f1ffa"><span class="section-number-4">3.1.6</span> Test</h4>
|
|
<div class="outline-text-4" id="text-3-1-6">
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90"><span style="color: #228b22;">integer</span>(<span style="color: #008b8b;">c_int32_t</span>) <span style="color: #a020f0;">function</span> <span style="color: #0000ff;">test_qmckl_ao_power</span>(context) <span style="color: #a020f0;">bind</span>(C)
|
|
<span style="color: #a020f0;">use</span> <span style="color: #0000ff;">qmckl</span>
|
|
<span style="color: #a020f0;">implicit</span> <span style="color: #228b22;">none</span>
|
|
|
|
<span style="color: #228b22;">integer</span>(qmckl_context), <span style="color: #a020f0;">intent</span>(in), <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> context</span>
|
|
|
|
<span style="color: #228b22;">integer</span>*8 ::<span style="color: #a0522d;"> n, LDP</span>
|
|
<span style="color: #228b22;">integer</span>, <span style="color: #a020f0;">allocatable</span> ::<span style="color: #a0522d;"> LMAX(:)</span>
|
|
<span style="color: #228b22;">double precision</span>, <span style="color: #a020f0;">allocatable</span> ::<span style="color: #a0522d;"> X(:), P(:,:)</span>
|
|
<span style="color: #228b22;">integer</span>*8 ::<span style="color: #a0522d;"> i,j</span>
|
|
<span style="color: #228b22;">double precision</span> ::<span style="color: #a0522d;"> epsilon</span>
|
|
|
|
epsilon = qmckl_get_numprec_epsilon(context)
|
|
|
|
n = 100;
|
|
LDP = 10;
|
|
|
|
<span style="color: #a020f0;">allocate</span>(X(n), P(LDP,n), LMAX(n))
|
|
|
|
<span style="color: #a020f0;">do</span> j=1,n
|
|
X(j) = -5.d0 + 0.1d0 * <span style="color: #a020f0;">dble</span>(j)
|
|
LMAX(j) = 1 + <span style="color: #a020f0;">int</span>(<span style="color: #a020f0;">mod</span>(j, 5),4)
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
test_qmckl_ao_power = qmckl_ao_power(context, n, X, LMAX, P, LDP)
|
|
<span style="color: #a020f0;">if</span> (test_qmckl_ao_power /= QMCKL_SUCCESS) <span style="color: #a020f0;">return</span>
|
|
|
|
test_qmckl_ao_power = QMCKL_FAILURE
|
|
|
|
<span style="color: #a020f0;">do</span> j=1,n
|
|
<span style="color: #a020f0;">do</span> i=1,LMAX(j)
|
|
<span style="color: #a020f0;">if</span> ( X(j)**i == 0.d0 ) <span style="color: #a020f0;">then</span>
|
|
<span style="color: #a020f0;">if</span> ( P(i,j) /= 0.d0) <span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">else</span>
|
|
<span style="color: #a020f0;">if</span> ( dabs(1.d0 - P(i,j) / (X(j)**i)) > epsilon ) <span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">end if</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
test_qmckl_ao_power = QMCKL_SUCCESS
|
|
<span style="color: #a020f0;">deallocate</span>(X,P,LMAX)
|
|
<span style="color: #a020f0;">end function</span> <span style="color: #0000ff;">test_qmckl_ao_power</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgba21cce" class="outline-3">
|
|
<h3 id="orgba21cce"><span class="section-number-3">3.2</span> General functions for Value, Gradient and Laplacian of a polynomial</h3>
|
|
<div class="outline-text-3" id="text-3-2">
|
|
<p>
|
|
A polynomial is centered on a nucleus \(\mathbf{R}_i\)
|
|
</p>
|
|
|
|
<p>
|
|
\[
|
|
P_l(\mathbf{r},\mathbf{R}_i) = (x-X_i)^a (y-Y_i)^b (z-Z_i)^c
|
|
\]
|
|
</p>
|
|
|
|
<p>
|
|
The gradients with respect to electron coordinates are
|
|
</p>
|
|
|
|
\begin{eqnarray*}
|
|
\frac{\partial }{\partial x} P_l\left(\mathbf{r},\mathbf{R}_i \right) &
|
|
= & a (x-X_i)^{a-1} (y-Y_i)^b (z-Z_i)^c \\
|
|
\frac{\partial }{\partial y} P_l\left(\mathbf{r},\mathbf{R}_i \right) &
|
|
= & b (x-X_i)^a (y-Y_i)^{b-1} (z-Z_i)^c \\
|
|
\frac{\partial }{\partial z} P_l\left(\mathbf{r},\mathbf{R}_i \right) &
|
|
= & c (x-X_i)^a (y-Y_i)^b (z-Z_i)^{c-1} \\
|
|
\end{eqnarray*}
|
|
|
|
<p>
|
|
and the Laplacian is
|
|
</p>
|
|
|
|
\begin{eqnarray*}
|
|
\left( \frac{\partial }{\partial x^2} +
|
|
\frac{\partial }{\partial y^2} +
|
|
\frac{\partial }{\partial z^2} \right) P_l
|
|
\left(\mathbf{r},\mathbf{R}_i \right) & = &
|
|
a(a-1) (x-X_i)^{a-2} (y-Y_i)^b (z-Z_i)^c + \\
|
|
&& b(b-1) (x-X_i)^a (y-Y_i)^{b-1} (z-Z_i)^c + \\
|
|
&& c(c-1) (x-X_i)^a (y-Y_i)^b (z-Z_i)^{c-1}.
|
|
\end{eqnarray*}
|
|
|
|
<p>
|
|
<code>qmckl_ao_polynomial_vgl</code> computes the values, gradients and
|
|
Laplacians at a given point in space, of all polynomials with an
|
|
angular momentum up to <code>lmax</code>.
|
|
</p>
|
|
|
|
<table id="org9050b2b" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
|
|
|
|
<colgroup>
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
</colgroup>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-left">qmckl<sub>context</sub></td>
|
|
<td class="org-left">context</td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Global state</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">double</td>
|
|
<td class="org-left">X[3]</td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Array containing the coordinates of the points</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">double</td>
|
|
<td class="org-left">R[3]</td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Array containing the x,y,z coordinates of the center</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">int32<sub>t</sub></td>
|
|
<td class="org-left">lmax</td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Maximum angular momentum</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">int64<sub>t</sub></td>
|
|
<td class="org-left">n</td>
|
|
<td class="org-left">inout</td>
|
|
<td class="org-left">Number of computed polynomials</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">int32<sub>t</sub></td>
|
|
<td class="org-left">L[n][ldl]</td>
|
|
<td class="org-left">out</td>
|
|
<td class="org-left">Contains a,b,c for all <code>n</code> results</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">int64<sub>t</sub></td>
|
|
<td class="org-left">ldl</td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Leading dimension of <code>L</code></td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">double</td>
|
|
<td class="org-left">VGL[n][ldv]</td>
|
|
<td class="org-left">out</td>
|
|
<td class="org-left">Value, gradients and Laplacian of the polynomials</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left">int64<sub>t</sub></td>
|
|
<td class="org-left">ldv</td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Leading dimension of array <code>VGL</code></td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
</div>
|
|
|
|
<div id="outline-container-org37e025e" class="outline-4">
|
|
<h4 id="org37e025e"><span class="section-number-4">3.2.1</span> Requirements</h4>
|
|
<div class="outline-text-4" id="text-3-2-1">
|
|
<ul class="org-ul">
|
|
<li><code>context</code> is not <code>QMCKL_NULL_CONTEXT</code></li>
|
|
<li><code>n</code> > 0</li>
|
|
<li><code>lmax</code> >= 0</li>
|
|
<li><code>ldl</code> >= 3</li>
|
|
<li><code>ldv</code> >= 5</li>
|
|
<li><code>X</code> is allocated with at least \(3 \times 8\) bytes</li>
|
|
<li><code>R</code> is allocated with at least \(3 \times 8\) bytes</li>
|
|
<li><code>n</code> >= <code>(lmax+1)(lmax+2)(lmax+3)/6</code></li>
|
|
<li><code>L</code> is allocated with at least \(3 \times n \times 4\) bytes</li>
|
|
<li><code>VGL</code> is allocated with at least \(5 \times n \times 8\) bytes</li>
|
|
<li>On output, <code>n</code> should be equal to <code>(lmax+1)(lmax+2)(lmax+3)/6</code></li>
|
|
<li>On output, the powers are given in the following order (l=a+b+c):
|
|
<ul class="org-ul">
|
|
<li>Increasing values of <code>l</code></li>
|
|
<li>Within a given value of <code>l</code>, alphabetical order of the
|
|
string made by a*"x" + b*"y" + c*"z" (in Python notation).
|
|
For example, with a=0, b=2 and c=1 the string is "yyz"</li>
|
|
</ul></li>
|
|
</ul>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd9f14b3" class="outline-4">
|
|
<h4 id="orgd9f14b3"><span class="section-number-4">3.2.2</span> C Header</h4>
|
|
<div class="outline-text-4" id="text-3-2-2">
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_compute_ao_vgl</span> (
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">X</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">R</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int32_t</span> <span style="color: #a0522d;">lmax</span>,
|
|
<span style="color: #228b22;">int64_t</span>* <span style="color: #a0522d;">n</span>,
|
|
<span style="color: #228b22;">int32_t</span>* <span style="color: #a020f0;">const</span> <span style="color: #a0522d;">L</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">ldl</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">const</span> <span style="color: #a0522d;">VGL</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">ldv</span> );
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgc190714" class="outline-4">
|
|
<h4 id="orgc190714"><span class="section-number-4">3.2.3</span> Source</h4>
|
|
<div class="outline-text-4" id="text-3-2-3">
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90"><span style="color: #228b22;">integer </span><span style="color: #a020f0;">function</span><span style="color: #a0522d;"> </span><span style="color: #0000ff;">qmckl_ao_polynomial_vgl_f</span><span style="color: #000000; background-color: #ffffff;">(context, X, R, lmax, n, L, ldl, VGL, ldv) result(info)</span>
|
|
<span style="color: #a020f0;">use</span> <span style="color: #0000ff;">qmckl</span>
|
|
<span style="color: #a020f0;">implicit</span> <span style="color: #228b22;">none</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> context</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> X(3), R(3)</span>
|
|
<span style="color: #228b22;">integer</span> , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> lmax</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(out) ::<span style="color: #a0522d;"> n</span>
|
|
<span style="color: #228b22;">integer</span> , <span style="color: #a020f0;">intent</span>(out) ::<span style="color: #a0522d;"> L(ldl,(lmax+1)*(lmax+2)*(lmax+3)/6)</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> ldl</span>
|
|
<span style="color: #228b22;">real</span>*8 , <span style="color: #a020f0;">intent</span>(out) ::<span style="color: #a0522d;"> VGL(ldv,(lmax+1)*(lmax+2)*(lmax+3)/6)</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> ldv</span>
|
|
|
|
<span style="color: #228b22;">integer</span>*8 ::<span style="color: #a0522d;"> i,j</span>
|
|
<span style="color: #228b22;">integer</span> ::<span style="color: #a0522d;"> a,b,c,d</span>
|
|
<span style="color: #228b22;">real</span>*8 ::<span style="color: #a0522d;"> Y(3)</span>
|
|
<span style="color: #228b22;">integer</span> ::<span style="color: #a0522d;"> lmax_array(3)</span>
|
|
<span style="color: #228b22;">real</span>*8 ::<span style="color: #a0522d;"> pows(-2:lmax,3)</span>
|
|
<span style="color: #228b22;">double precision</span> ::<span style="color: #a0522d;"> xy, yz, xz</span>
|
|
<span style="color: #228b22;">double precision</span> ::<span style="color: #a0522d;"> da, db, dc, dd</span>
|
|
|
|
info = 0
|
|
|
|
<span style="color: #a020f0;">if</span> (context == QMCKL_NULL_CONTEXT) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_CONTEXT
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
<span style="color: #a020f0;">if</span> (lmax < 0) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_4
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
<span style="color: #a020f0;">if</span> (ldl < 3) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_7
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
<span style="color: #a020f0;">if</span> (ldv < 5) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_INVALID_ARG_9
|
|
<span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
|
|
<span style="color: #a020f0;">do</span> i=1,3
|
|
Y(i) = X(i) - R(i)
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
lmax_array(1:3) = lmax
|
|
<span style="color: #a020f0;">if</span> (lmax == 0) <span style="color: #a020f0;">then</span>
|
|
VGL(1,1) = 1.d0
|
|
vgL(2:5,1) = 0.d0
|
|
l(1:3,1) = 0
|
|
n=1
|
|
<span style="color: #a020f0;">else if</span> (lmax > 0) <span style="color: #a020f0;">then</span>
|
|
pows(-2:0,1:3) = 1.d0
|
|
<span style="color: #a020f0;">do</span> i=1,lmax
|
|
pows(i,1) = pows(i-1,1) * Y(1)
|
|
pows(i,2) = pows(i-1,2) * Y(2)
|
|
pows(i,3) = pows(i-1,3) * Y(3)
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
VGL(1:5,1:4) = 0.d0
|
|
l (1:3,1:4) = 0
|
|
|
|
VGL(1 ,1 ) = 1.d0
|
|
vgl(1:5,2:4) = 0.d0
|
|
|
|
l (1,2) = 1
|
|
vgl(1,2) = pows(1,1)
|
|
vgL(2,2) = 1.d0
|
|
|
|
l (2,3) = 1
|
|
vgl(1,3) = pows(1,2)
|
|
vgL(3,3) = 1.d0
|
|
|
|
l (3,4) = 1
|
|
vgl(1,4) = pows(1,3)
|
|
vgL(4,4) = 1.d0
|
|
|
|
n=4
|
|
<span style="color: #a020f0;">endif</span>
|
|
|
|
! <span style="color: #b22222;">l>=2</span>
|
|
dd = 2.d0
|
|
<span style="color: #a020f0;">do</span> d=2,lmax
|
|
da = dd
|
|
<span style="color: #a020f0;">do</span> a=d,0,-1
|
|
db = dd-da
|
|
<span style="color: #a020f0;">do</span> b=d-a,0,-1
|
|
c = d - a - b
|
|
dc = dd - da - db
|
|
n = n+1
|
|
|
|
l(1,n) = a
|
|
l(2,n) = b
|
|
l(3,n) = c
|
|
|
|
xy = pows(a,1) * pows(b,2)
|
|
yz = pows(b,2) * pows(c,3)
|
|
xz = pows(a,1) * pows(c,3)
|
|
|
|
vgl(1,n) = xy * pows(c,3)
|
|
|
|
xy = dc * xy
|
|
xz = db * xz
|
|
yz = da * yz
|
|
|
|
vgl(2,n) = pows(a-1,1) * yz
|
|
vgl(3,n) = pows(b-1,2) * xz
|
|
vgl(4,n) = pows(c-1,3) * xy
|
|
|
|
vgl(5,n) = <span style="color: #a020f0;">&</span>
|
|
(da-1.d0) * pows(a-2,1) * yz + <span style="color: #a020f0;">&</span>
|
|
(db-1.d0) * pows(b-2,2) * xz + <span style="color: #a020f0;">&</span>
|
|
(dc-1.d0) * pows(c-2,3) * xy
|
|
|
|
db = db - 1.d0
|
|
<span style="color: #a020f0;">end do</span>
|
|
da = da - 1.d0
|
|
<span style="color: #a020f0;">end do</span>
|
|
dd = dd + 1.d0
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
info = QMCKL_SUCCESS
|
|
|
|
<span style="color: #a020f0;">end function</span> <span style="color: #0000ff;">qmckl_ao_polynomial_vgl_f</span>
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org01b83e2" class="outline-4">
|
|
<h4 id="org01b83e2"><span class="section-number-4">3.2.4</span> C interface</h4>
|
|
</div>
|
|
|
|
<div id="outline-container-org6ac38d8" class="outline-4">
|
|
<h4 id="org6ac38d8"><span class="section-number-4">3.2.5</span> Fortran interface</h4>
|
|
</div>
|
|
|
|
<div id="outline-container-org4843f1f" class="outline-4">
|
|
<h4 id="org4843f1f"><span class="section-number-4">3.2.6</span> Test</h4>
|
|
<div class="outline-text-4" id="text-3-2-6">
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90"><span style="color: #228b22;">integer</span>(<span style="color: #008b8b;">c_int32_t</span>) <span style="color: #a020f0;">function</span> <span style="color: #0000ff;">test_qmckl_ao_polynomial_vgl</span>(context) <span style="color: #a020f0;">bind</span>(C)
|
|
<span style="color: #a020f0;">use</span> <span style="color: #0000ff;">qmckl</span>
|
|
<span style="color: #a020f0;">implicit</span> <span style="color: #228b22;">none</span>
|
|
|
|
<span style="color: #228b22;">integer</span>(<span style="color: #008b8b;">c_int64_t</span>), <span style="color: #a020f0;">intent</span>(in), <span style="color: #a020f0;">value</span> ::<span style="color: #a0522d;"> context</span>
|
|
|
|
<span style="color: #228b22;">integer</span> ::<span style="color: #a0522d;"> lmax, d, i</span>
|
|
<span style="color: #228b22;">integer</span>, <span style="color: #a020f0;">allocatable</span> ::<span style="color: #a0522d;"> L(:,:)</span>
|
|
<span style="color: #228b22;">integer</span>*8 ::<span style="color: #a0522d;"> n, ldl, ldv, j</span>
|
|
<span style="color: #228b22;">double precision</span> ::<span style="color: #a0522d;"> X(3), R(3), Y(3)</span>
|
|
<span style="color: #228b22;">double precision</span>, <span style="color: #a020f0;">allocatable</span> ::<span style="color: #a0522d;"> VGL(:,:)</span>
|
|
<span style="color: #228b22;">double precision</span> ::<span style="color: #a0522d;"> w</span>
|
|
<span style="color: #228b22;">double precision</span> ::<span style="color: #a0522d;"> epsilon</span>
|
|
|
|
epsilon = qmckl_get_numprec_epsilon(context)
|
|
|
|
X = (/ 1.1 , 2.2 , 3.3 /)
|
|
R = (/ 0.1 , 1.2 , -2.3 /)
|
|
Y(:) = X(:) - R(:)
|
|
|
|
lmax = 4;
|
|
ldl = 3;
|
|
ldv = 100;
|
|
|
|
d = (lmax+1)*(lmax+2)*(lmax+3)/6
|
|
|
|
<span style="color: #a020f0;">allocate</span> (L(ldl,d), VGL(ldv,d))
|
|
|
|
test_qmckl_ao_polynomial_vgl = <span style="color: #a020f0;">&</span>
|
|
qmckl_ao_polynomial_vgl(context, X, R, lmax, n, L, ldl, VGL, ldv)
|
|
|
|
<span style="color: #a020f0;">if</span> (test_qmckl_ao_polynomial_vgl /= QMCKL_SUCCESS) <span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">if</span> (n /= d) <span style="color: #a020f0;">return</span>
|
|
|
|
<span style="color: #a020f0;">do</span> j=1,n
|
|
test_qmckl_ao_polynomial_vgl = QMCKL_FAILURE
|
|
<span style="color: #a020f0;">do</span> i=1,3
|
|
<span style="color: #a020f0;">if</span> (L(i,j) < 0) <span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
test_qmckl_ao_polynomial_vgl = QMCKL_FAILURE
|
|
<span style="color: #a020f0;">if</span> (dabs(1.d0 - VGL(1,j) / (<span style="color: #a020f0;">&</span>
|
|
Y(1)**L(1,j) * Y(2)**L(2,j) * Y(3)**L(3,j) <span style="color: #a020f0;">&</span>
|
|
)) > epsilon ) <span style="color: #a020f0;">return</span>
|
|
|
|
test_qmckl_ao_polynomial_vgl = QMCKL_FAILURE
|
|
<span style="color: #a020f0;">if</span> (L(1,j) < 1) <span style="color: #a020f0;">then</span>
|
|
<span style="color: #a020f0;">if</span> (VGL(2,j) /= 0.d0) <span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">else</span>
|
|
<span style="color: #a020f0;">if</span> (dabs(1.d0 - VGL(2,j) / (<span style="color: #a020f0;">&</span>
|
|
L(1,j) * Y(1)**(L(1,j)-1) * Y(2)**L(2,j) * Y(3)**L(3,j) <span style="color: #a020f0;">&</span>
|
|
)) > epsilon ) <span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">end if</span>
|
|
|
|
test_qmckl_ao_polynomial_vgl = QMCKL_FAILURE
|
|
<span style="color: #a020f0;">if</span> (L(2,j) < 1) <span style="color: #a020f0;">then</span>
|
|
<span style="color: #a020f0;">if</span> (VGL(3,j) /= 0.d0) <span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">else</span>
|
|
<span style="color: #a020f0;">if</span> (dabs(1.d0 - VGL(3,j) / (<span style="color: #a020f0;">&</span>
|
|
L(2,j) * Y(1)**L(1,j) * Y(2)**(L(2,j)-1) * Y(3)**L(3,j) <span style="color: #a020f0;">&</span>
|
|
)) > epsilon ) <span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">end if</span>
|
|
|
|
test_qmckl_ao_polynomial_vgl = QMCKL_FAILURE
|
|
<span style="color: #a020f0;">if</span> (L(3,j) < 1) <span style="color: #a020f0;">then</span>
|
|
<span style="color: #a020f0;">if</span> (VGL(4,j) /= 0.d0) <span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">else</span>
|
|
<span style="color: #a020f0;">if</span> (dabs(1.d0 - VGL(4,j) / (<span style="color: #a020f0;">&</span>
|
|
L(3,j) * Y(1)**L(1,j) * Y(2)**L(2,j) * Y(3)**(L(3,j)-1) <span style="color: #a020f0;">&</span>
|
|
)) > epsilon ) <span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">end if</span>
|
|
|
|
test_qmckl_ao_polynomial_vgl = QMCKL_FAILURE
|
|
w = 0.d0
|
|
<span style="color: #a020f0;">if</span> (L(1,j) > 1) <span style="color: #a020f0;">then</span>
|
|
w = w + L(1,j) * (L(1,j)-1) * Y(1)**(L(1,j)-2) * Y(2)**L(2,j) * Y(3)**L(3,j)
|
|
<span style="color: #a020f0;">end if</span>
|
|
<span style="color: #a020f0;">if</span> (L(2,j) > 1) <span style="color: #a020f0;">then</span>
|
|
w = w + L(2,j) * (L(2,j)-1) * Y(1)**L(1,j) * Y(2)**(L(2,j)-2) * Y(3)**L(3,j)
|
|
<span style="color: #a020f0;">end if</span>
|
|
<span style="color: #a020f0;">if</span> (L(3,j) > 1) <span style="color: #a020f0;">then</span>
|
|
w = w + L(3,j) * (L(3,j)-1) * Y(1)**L(1,j) * Y(2)**L(2,j) * Y(3)**(L(3,j)-2)
|
|
<span style="color: #a020f0;">end if</span>
|
|
<span style="color: #a020f0;">if</span> (dabs(1.d0 - VGL(5,j) / w) > epsilon ) <span style="color: #a020f0;">return</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
test_qmckl_ao_polynomial_vgl = QMCKL_SUCCESS
|
|
|
|
<span style="color: #a020f0;">deallocate</span>(L,VGL)
|
|
<span style="color: #a020f0;">end function</span> <span style="color: #0000ff;">test_qmckl_ao_polynomial_vgl</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">int</span> <span style="color: #0000ff;">test_qmckl_ao_polynomial_vgl</span>(<span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>);
|
|
assert(0 == test_qmckl_ao_polynomial_vgl(context));
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgfe5f70a" class="outline-2">
|
|
<h2 id="orgfe5f70a"><span class="section-number-2">4</span> Combining radial and polynomial parts</h2>
|
|
<div class="outline-text-2" id="text-4">
|
|
</div>
|
|
<div id="outline-container-orgb177076" class="outline-4">
|
|
<h4 id="orgb177076"><span class="section-number-4">4.0.1</span> Get</h4>
|
|
<div class="outline-text-4" id="text-4-0-1">
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_get_ao_vgl</span>(<span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>, <span style="color: #228b22;">double</span>* <span style="color: #a020f0;">const</span> <span style="color: #a0522d;">ao_vgl</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orga04f341" class="outline-4">
|
|
<h4 id="orga04f341"><span class="section-number-4">4.0.2</span> Provide</h4>
|
|
</div>
|
|
|
|
<div id="outline-container-orga7af53f" class="outline-4">
|
|
<h4 id="orga7af53f"><span class="section-number-4">4.0.3</span> Compute</h4>
|
|
<div class="outline-text-4" id="text-4-0-3">
|
|
<table id="orgc0f0ca3" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
|
|
|
|
<colgroup>
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
|
|
<col class="org-left" />
|
|
</colgroup>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-left"><code>qmckl_context</code></td>
|
|
<td class="org-left"><code>context</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Global state</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
<td class="org-left"><code>ao_num</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Number of AOs</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
<td class="org-left"><code>shell_num</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Number of shells</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
<td class="org-left"><code>elec_num</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Number of electrons</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
<td class="org-left"><code>nucl_num</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Number of nuclei</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
<td class="org-left"><code>walk_num</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Number of walkers</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>double</code></td>
|
|
<td class="org-left"><code>elec_coord[walk_num][3][elec_num]</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Electron coordinates</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>double</code></td>
|
|
<td class="org-left"><code>nucl_coord[3][nucl_num]</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Nuclear coordinates</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
<td class="org-left"><code>nucleus_index[nucl_num]</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Index of the 1st shell of each nucleus</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>int64_t</code></td>
|
|
<td class="org-left"><code>nucleus_shell_num[nucl_num]</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Number of shells per nucleus</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>double</code></td>
|
|
<td class="org-left"><code>nucleus_range[nucl_num]</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Range beyond which all is zero</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>int32_t</code></td>
|
|
<td class="org-left"><code>nucleus_max_ang_mom[nucl_num]</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Maximum angular momentum per nucleus</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>int32_t</code></td>
|
|
<td class="org-left"><code>shell_ang_mom[shell_num]</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Angular momentum of each shell</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>double</code></td>
|
|
<td class="org-left"><code>ao_factor[ao_num]</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Normalization factor of the AOs</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>double</code></td>
|
|
<td class="org-left"><code>shell_vgl[5][walk_num][elec_num][shell_num]</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Value, gradients and Laplacian of the shells</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>double</code></td>
|
|
<td class="org-left"><code>ao_vgl[5][walk_num][elec_num][ao_num]</code></td>
|
|
<td class="org-left">out</td>
|
|
<td class="org-left">Value, gradients and Laplacian of the AOs</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-f90"><span style="color: #228b22;">integer</span><span style="color: #a0522d;"> function qmckl_compute_ao_vgl_f(context, </span><span style="color: #a020f0;">&</span>
|
|
ao_num, shell_num, elec_num, nucl_num, walk_num, <span style="color: #a020f0;">&</span>
|
|
elec_coord, nucl_coord, nucleus_index, nucleus_shell_num, <span style="color: #a020f0;">&</span>
|
|
nucleus_range, nucleus_max_ang_mom, shell_ang_mom, <span style="color: #a020f0;">&</span>
|
|
ao_factor, shell_vgl, ao_vgl) <span style="color: #a020f0;">&</span>
|
|
<span style="color: #a020f0;">result</span>(info)
|
|
<span style="color: #a020f0;">use</span> <span style="color: #0000ff;">qmckl</span>
|
|
<span style="color: #a020f0;">implicit</span> <span style="color: #228b22;">none</span>
|
|
<span style="color: #228b22;">integer</span>(qmckl_context), <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> context</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> ao_num</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> shell_num</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> elec_num</span>
|
|
<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> nucl_num</span>
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<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> walk_num</span>
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<span style="color: #228b22;">double precision</span> , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> elec_coord(elec_num,3,walk_num)</span>
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<span style="color: #228b22;">double precision</span> , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> nucl_coord(nucl_num,3)</span>
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<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> nucleus_index(nucl_num)</span>
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<span style="color: #228b22;">integer</span>*8 , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> nucleus_shell_num(nucl_num)</span>
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<span style="color: #228b22;">double precision</span> , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> nucleus_range(nucl_num)</span>
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<span style="color: #228b22;">integer</span> , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> nucleus_max_ang_mom(nucl_num)</span>
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<span style="color: #228b22;">integer</span> , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> shell_ang_mom(shell_num)</span>
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<span style="color: #228b22;">double precision</span> , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> ao_factor(ao_num)</span>
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<span style="color: #228b22;">double precision</span> , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> shell_vgl(shell_num,elec_num,walk_num,5)</span>
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<span style="color: #228b22;">double precision</span> , <span style="color: #a020f0;">intent</span>(out) ::<span style="color: #a0522d;"> ao_vgl(ao_num,elec_num,walk_num,5)</span>
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<span style="color: #228b22;">double precision</span> ::<span style="color: #a0522d;"> e_coord(3), n_coord(3)</span>
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<span style="color: #228b22;">integer</span>*8 ::<span style="color: #a0522d;"> n_poly</span>
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<span style="color: #228b22;">integer</span> ::<span style="color: #a0522d;"> l, il, k</span>
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<span style="color: #228b22;">integer</span>*8 ::<span style="color: #a0522d;"> ielec, inucl, ishell, iwalk</span>
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<span style="color: #228b22;">integer</span> ::<span style="color: #a0522d;"> lstart(0:20)</span>
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<span style="color: #228b22;">double precision</span> ::<span style="color: #a0522d;"> x, y, z, r2</span>
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<span style="color: #228b22;">double precision</span> ::<span style="color: #a0522d;"> cutoff</span>
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<span style="color: #228b22;">integer</span>, <span style="color: #a020f0;">external</span> ::<span style="color: #a0522d;"> qmckl_ao_polynomial_vgl_f</span>
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<span style="color: #228b22;">double precision</span>, <span style="color: #a020f0;">allocatable</span> ::<span style="color: #a0522d;"> poly_vgl(:,:)</span>
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<span style="color: #228b22;">integer</span> , <span style="color: #a020f0;">allocatable</span> ::<span style="color: #a0522d;"> powers(:,:)</span>
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<span style="color: #a020f0;">allocate</span>(poly_vgl(5,ao_num), powers(3,ao_num))
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! <span style="color: #b22222;">Pre-computed data</span>
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<span style="color: #a020f0;">do</span> l=0,20
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lstart(l) = l*(l+1)*(l+2)/6 +1
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<span style="color: #a020f0;">end do</span>
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info = QMCKL_SUCCESS
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! <span style="color: #b22222;">Don't compute polynomials when the radial part is zero.</span>
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! <span style="color: #b22222;">TODO : Use numerical precision here</span>
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cutoff = -dlog(1.d-15)
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|
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<span style="color: #a020f0;">do</span> iwalk = 1,walk_num
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<span style="color: #a020f0;">do</span> ielec = 1, elec_num
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e_coord(1) = elec_coord(ielec,1,iwalk)
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e_coord(2) = elec_coord(ielec,2,iwalk)
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e_coord(3) = elec_coord(ielec,3,iwalk)
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|
k=1
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<span style="color: #a020f0;">do</span> inucl=1,nucl_num
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n_coord(1) = nucl_coord(inucl,1)
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n_coord(2) = nucl_coord(inucl,2)
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n_coord(3) = nucl_coord(inucl,3)
|
|
|
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! <span style="color: #b22222;">Test if the electron is in the range of the nucleus</span>
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|
x = e_coord(1) - n_coord(1)
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y = e_coord(2) - n_coord(2)
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z = e_coord(3) - n_coord(3)
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|
|
r2 = x*x + z*z + z*z
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|
|
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<span style="color: #a020f0;">if</span> (r2 > cutoff*nucleus_range(inucl)) <span style="color: #a020f0;">then</span>
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<span style="color: #a020f0;">cycle</span>
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|
<span style="color: #a020f0;">end if</span>
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|
|
|
! <span style="color: #b22222;">Compute polynomials</span>
|
|
info = qmckl_ao_polynomial_vgl_f(context, e_coord, n_coord, <span style="color: #a020f0;">&</span>
|
|
nucleus_max_ang_mom(inucl), n_poly, powers, 3_8, <span style="color: #a020f0;">&</span>
|
|
poly_vgl, 5_8)
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|
|
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! <span style="color: #b22222;">Loop over shells</span>
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<span style="color: #a020f0;">do</span> ishell = nucleus_index(inucl)+1, nucleus_index(inucl)+nucleus_shell_num(inucl)
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l = shell_ang_mom(ishell)
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|
<span style="color: #a020f0;">do</span> il = lstart(l), lstart(l+1)-1
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|
! <span style="color: #b22222;">Value</span>
|
|
ao_vgl(k,ielec,iwalk,1) = <span style="color: #a020f0;">&</span>
|
|
poly_vgl(1,il) * shell_vgl(ishell,ielec,iwalk,1) * ao_factor(k)
|
|
|
|
! <span style="color: #b22222;">Grad_x</span>
|
|
ao_vgl(k,ielec,iwalk,2) = ( <span style="color: #a020f0;">&</span>
|
|
poly_vgl(2,il) * shell_vgl(ishell,ielec,iwalk,1) + <span style="color: #a020f0;">&</span>
|
|
poly_vgl(1,il) * shell_vgl(ishell,ielec,iwalk,2) <span style="color: #a020f0;">&</span>
|
|
) * ao_factor(k)
|
|
|
|
! <span style="color: #b22222;">Grad_y</span>
|
|
ao_vgl(k,ielec,iwalk,3) = ( <span style="color: #a020f0;">&</span>
|
|
poly_vgl(3,il) * shell_vgl(ishell,ielec,iwalk,1) + <span style="color: #a020f0;">&</span>
|
|
poly_vgl(1,il) * shell_vgl(ishell,ielec,iwalk,3) <span style="color: #a020f0;">&</span>
|
|
) * ao_factor(k)
|
|
|
|
! <span style="color: #b22222;">Grad_z</span>
|
|
ao_vgl(k,ielec,iwalk,4) = ( <span style="color: #a020f0;">&</span>
|
|
poly_vgl(4,il) * shell_vgl(ishell,ielec,iwalk,1) + <span style="color: #a020f0;">&</span>
|
|
poly_vgl(1,il) * shell_vgl(ishell,ielec,iwalk,4) <span style="color: #a020f0;">&</span>
|
|
) * ao_factor(k)
|
|
|
|
! <span style="color: #b22222;">Lapl_z</span>
|
|
ao_vgl(k,ielec,iwalk,5) = ( <span style="color: #a020f0;">&</span>
|
|
poly_vgl(5,il) * shell_vgl(ishell,ielec,iwalk,1) + <span style="color: #a020f0;">&</span>
|
|
poly_vgl(1,il) * shell_vgl(ishell,ielec,iwalk,5) + <span style="color: #a020f0;">&</span>
|
|
2.d0 * ( <span style="color: #a020f0;">&</span>
|
|
poly_vgl(2,il) * shell_vgl(ishell,ielec,iwalk,2) + <span style="color: #a020f0;">&</span>
|
|
poly_vgl(3,il) * shell_vgl(ishell,ielec,iwalk,3) + <span style="color: #a020f0;">&</span>
|
|
poly_vgl(4,il) * shell_vgl(ishell,ielec,iwalk,4) ) <span style="color: #a020f0;">&</span>
|
|
) * ao_factor(k)
|
|
|
|
k = k+1
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
<span style="color: #a020f0;">deallocate</span>(poly_vgl, powers)
|
|
<span style="color: #a020f0;">end function</span> <span style="color: #0000ff;">qmckl_compute_ao_vgl_f</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_compute_ao_vgl</span> (
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">qmckl_context</span> <span style="color: #a0522d;">context</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">ao_num</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">shell_num</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">elec_num</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">nucl_num</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">walk_num</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">elec_coord</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">nucl_coord</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span>* <span style="color: #a0522d;">nucleus_index</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span>* <span style="color: #a0522d;">nucleus_shell_num</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">nucleus_range</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int32_t</span>* <span style="color: #a0522d;">nucleus_max_ang_mom</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int32_t</span>* <span style="color: #a0522d;">shell_ang_mom</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">ao_factor</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">shell_vgl</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">const</span> <span style="color: #a0522d;">ao_vgl</span> );
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgffbbf89" class="outline-4">
|
|
<h4 id="orgffbbf89"><span class="section-number-4">4.0.4</span> Test</h4>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div id="postamble" class="status">
|
|
<p class="author">Author: TREX CoE</p>
|
|
<p class="date">Created: 2021-07-13 Tue 07:55</p>
|
|
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
|
</div>
|
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</body>
|
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</html>
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