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<body>
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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">Molecular 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="#org6b771fc">1. Context</a>
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<ul>
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<li><a href="#org5d974c0">1.1. Data structure</a></li>
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<li><a href="#orgdeab8e8">1.2. Access functions</a></li>
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<li><a href="#org14e57b5">1.3. Initialization functions</a></li>
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</ul>
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</li>
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<li><a href="#orgd3eff00">2. Computation</a>
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<ul>
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<li><a href="#org05d35a7">2.1. Computation of MOs</a>
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<ul>
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<li><a href="#org0cf55a7">2.1.1. Get</a></li>
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<li><a href="#orgf867ffe">2.1.2. Provide</a></li>
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<li><a href="#orgda0b11b">2.1.3. Compute</a></li>
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<li><a href="#org266cf4d">2.1.4. 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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</ul>
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</div>
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</div>
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<div id="outline-container-org6b771fc" class="outline-2">
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<h2 id="org6b771fc"><span class="section-number-2">1</span> Context</h2>
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<div class="outline-text-2" id="text-1">
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<p>
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The following arrays are stored in the context:
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</p>
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<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<colgroup>
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<col class="org-left" />
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<col class="org-left" />
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</colgroup>
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<tbody>
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<tr>
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<td class="org-left"><code>type</code></td>
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<td class="org-left"> </td>
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<td class="org-left">Gaussian (<code>'G'</code>) or Slater (<code>'S'</code>)</td>
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</tr>
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<tr>
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<td class="org-left"><code>mo_num</code></td>
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<td class="org-left"> </td>
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<td class="org-left">Number of MOs</td>
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</tr>
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<tr>
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<td class="org-left"><code>coefficient</code></td>
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<td class="org-left"><code>[mo_num, ao_num]</code></td>
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<td class="org-left">Orbital coefficients</td>
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</tr>
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</tbody>
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</table>
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<p>
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Computed data:
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</p>
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<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<colgroup>
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<col class="org-left" />
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</colgroup>
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<tbody>
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<tr>
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<td class="org-left"><code>mo_vgl</code></td>
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<td class="org-left"><code>[5][walk_num][elec_num][mo_num]</code></td>
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<td class="org-left">Value, gradients, Laplacian of the MOs at electron positions</td>
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</tr>
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<tr>
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<td class="org-left"><code>mo_vgl_date</code></td>
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<td class="org-left"><code>uint64_t</code></td>
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<td class="org-left">Late modification date of Value, gradients, Laplacian of the MOs at electron positions</td>
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</tr>
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</tbody>
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</table>
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</div>
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<div id="outline-container-org5d974c0" class="outline-3">
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<h3 id="org5d974c0"><span class="section-number-3">1.1</span> Data structure</h3>
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<div class="outline-text-3" id="text-1-1">
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<div class="org-src-container">
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<pre class="src src-c"><span style="color: #a020f0;">typedef</span> <span style="color: #a020f0;">struct</span> <span style="color: #228b22;">qmckl_mo_basis_struct</span> {
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<span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">mo_num</span>;
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<span style="color: #228b22;">double</span> * <span style="color: #a0522d;">coefficient</span>;
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<span style="color: #228b22;">double</span> * <span style="color: #a0522d;">mo_vgl</span>;
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<span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">mo_vgl_date</span>;
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<span style="color: #228b22;">int32_t</span> <span style="color: #a0522d;">uninitialized</span>;
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<span style="color: #228b22;">bool</span> <span style="color: #a0522d;">provided</span>;
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<span style="color: #228b22;">char</span> <span style="color: #a0522d;">type</span>;
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} <span style="color: #228b22;">qmckl_mo_basis_struct</span>;
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</pre>
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</div>
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<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>
|
|
</div>
|
|
|
|
<div id="outline-container-orgdeab8e8" class="outline-3">
|
|
<h3 id="orgdeab8e8"><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_mo_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-org14e57b5" class="outline-3">
|
|
<h3 id="org14e57b5"><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_mo_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_mo_basis_mo_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;">mo_num</span>);
|
|
<span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_set_mo_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>);
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
When the basis set is completely entered, other data structures are
|
|
computed to accelerate the calculations.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd3eff00" class="outline-2">
|
|
<h2 id="orgd3eff00"><span class="section-number-2">2</span> Computation</h2>
|
|
<div class="outline-text-2" id="text-2">
|
|
</div>
|
|
<div id="outline-container-org05d35a7" class="outline-3">
|
|
<h3 id="org05d35a7"><span class="section-number-3">2.1</span> Computation of MOs</h3>
|
|
<div class="outline-text-3" id="text-2-1">
|
|
</div>
|
|
<div id="outline-container-org0cf55a7" class="outline-4">
|
|
<h4 id="org0cf55a7"><span class="section-number-4">2.1.1</span> Get</h4>
|
|
<div class="outline-text-4" id="text-2-1-1">
|
|
<div class="org-src-container">
|
|
<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_get_mo_basis_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;">mo_vgl</span>);
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgf867ffe" class="outline-4">
|
|
<h4 id="orgf867ffe"><span class="section-number-4">2.1.2</span> Provide</h4>
|
|
</div>
|
|
|
|
<div id="outline-container-orgda0b11b" class="outline-4">
|
|
<h4 id="orgda0b11b"><span class="section-number-4">2.1.3</span> Compute</h4>
|
|
<div class="outline-text-4" id="text-2-1-3">
|
|
<table id="org74692e0" 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>mo_num</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">Number of MOs</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>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>coef_normalized[mo_num][ao_num]</code></td>
|
|
<td class="org-left">in</td>
|
|
<td class="org-left">AO to MO transformation matrix</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">in</td>
|
|
<td class="org-left">Value, gradients and Laplacian of the AOs</td>
|
|
</tr>
|
|
|
|
<tr>
|
|
<td class="org-left"><code>double</code></td>
|
|
<td class="org-left"><code>mo_vgl[5][walk_num][elec_num][mo_num]</code></td>
|
|
<td class="org-left">out</td>
|
|
<td class="org-left">Value, gradients and Laplacian of the MOs</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_mo_basis_gaussian_vgl_f(context, </span><span style="color: #a020f0;">&</span>
|
|
ao_num, mo_num, elec_num, walk_num, <span style="color: #a020f0;">&</span>
|
|
coef_normalized, ao_vgl, mo_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, mo_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;">double precision</span> , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> ao_vgl(ao_num,elec_num,walk_num,5)</span>
|
|
<span style="color: #228b22;">double precision</span> , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> coef_normalized(ao_num,mo_num)</span>
|
|
<span style="color: #228b22;">double precision</span> , <span style="color: #a020f0;">intent</span>(out) ::<span style="color: #a0522d;"> mo_vgl(mo_num,elec_num,walk_num,5)</span>
|
|
<span style="color: #228b22;">logical</span>*8 ::<span style="color: #a0522d;"> TransA, TransB</span>
|
|
<span style="color: #228b22;">double precision</span> ::<span style="color: #a0522d;"> alpha, beta</span>
|
|
<span style="color: #228b22;">integer</span> ::<span style="color: #a0522d;"> info_qmckl_dgemm_value</span>
|
|
<span style="color: #228b22;">integer</span> ::<span style="color: #a0522d;"> info_qmckl_dgemm_Gx </span>
|
|
<span style="color: #228b22;">integer</span> ::<span style="color: #a0522d;"> info_qmckl_dgemm_Gy </span>
|
|
<span style="color: #228b22;">integer</span> ::<span style="color: #a0522d;"> info_qmckl_dgemm_Gz </span>
|
|
<span style="color: #228b22;">integer</span> ::<span style="color: #a0522d;"> info_qmckl_dgemm_lap </span>
|
|
<span style="color: #228b22;">integer</span>*8 ::<span style="color: #a0522d;"> M, N, K, LDA, LDB, LDC, i,j</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>
|
|
TransA = <span style="color: #a020f0;">.False.</span>
|
|
TransB = <span style="color: #a020f0;">.False.</span>
|
|
alpha = 1.0d0
|
|
beta = 0.0d0
|
|
|
|
info = QMCKL_SUCCESS
|
|
info_qmckl_dgemm_value = QMCKL_SUCCESS
|
|
info_qmckl_dgemm_Gx = QMCKL_SUCCESS
|
|
info_qmckl_dgemm_Gy = QMCKL_SUCCESS
|
|
info_qmckl_dgemm_Gz = QMCKL_SUCCESS
|
|
info_qmckl_dgemm_lap = 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)
|
|
M = 1_8
|
|
N = mo_num * 1_8
|
|
K = ao_num * 1_8
|
|
LDA = M
|
|
LDB = K
|
|
LDC = M
|
|
|
|
<span style="color: #a020f0;">do</span> iwalk = 1, walk_num
|
|
<span style="color: #a020f0;">do</span> ielec = 1, elec_num
|
|
! <span style="color: #b22222;">Value</span>
|
|
info_qmckl_dgemm_value = qmckl_dgemm(context,TransA, TransB, M, N, K, alpha, <span style="color: #a020f0;">&</span>
|
|
ao_vgl(:, ielec, iwalk, 1), LDA, <span style="color: #a020f0;">&</span>
|
|
coef_normalized(1:ao_num,1:mo_num),<span style="color: #a020f0;">size</span>(coef_normalized,1) * 1_8, <span style="color: #a020f0;">&</span>
|
|
beta, <span style="color: #a020f0;">&</span>
|
|
mo_vgl(:,ielec,iwalk,1),LDC)
|
|
! <span style="color: #b22222;">Grad_x</span>
|
|
info_qmckl_dgemm_Gx = qmckl_dgemm(context,TransA, TransB, M, N, K, alpha, <span style="color: #a020f0;">&</span>
|
|
ao_vgl(:, ielec, iwalk, 2), LDA, <span style="color: #a020f0;">&</span>
|
|
coef_normalized(1:ao_num,1:mo_num),<span style="color: #a020f0;">size</span>(coef_normalized,1) * 1_8, <span style="color: #a020f0;">&</span>
|
|
beta, <span style="color: #a020f0;">&</span>
|
|
mo_vgl(:,ielec,iwalk,2),LDC)
|
|
! <span style="color: #b22222;">Grad_y</span>
|
|
info_qmckl_dgemm_Gy = qmckl_dgemm(context,TransA, TransB, M, N, K, alpha, <span style="color: #a020f0;">&</span>
|
|
ao_vgl(:, ielec, iwalk, 3), LDA, <span style="color: #a020f0;">&</span>
|
|
coef_normalized(1:ao_num,1:mo_num),<span style="color: #a020f0;">size</span>(coef_normalized,1) * 1_8, <span style="color: #a020f0;">&</span>
|
|
beta, <span style="color: #a020f0;">&</span>
|
|
mo_vgl(:,ielec,iwalk,3),LDC)
|
|
! <span style="color: #b22222;">Grad_z</span>
|
|
info_qmckl_dgemm_Gz = qmckl_dgemm(context,TransA, TransB, M, N, K, alpha, <span style="color: #a020f0;">&</span>
|
|
ao_vgl(:, ielec, iwalk, 4), LDA, <span style="color: #a020f0;">&</span>
|
|
coef_normalized(1:ao_num,1:mo_num),<span style="color: #a020f0;">size</span>(coef_normalized,1) * 1_8, <span style="color: #a020f0;">&</span>
|
|
beta, <span style="color: #a020f0;">&</span>
|
|
mo_vgl(:,ielec,iwalk,4),LDC)
|
|
! <span style="color: #b22222;">Lapl_z</span>
|
|
info_qmckl_dgemm_lap = qmckl_dgemm(context, TransA, TransB, M, N, K, alpha, <span style="color: #a020f0;">&</span>
|
|
ao_vgl(:, ielec, iwalk, 5), LDA, <span style="color: #a020f0;">&</span>
|
|
coef_normalized(1:ao_num,1:mo_num),<span style="color: #a020f0;">size</span>(coef_normalized,1) * 1_8, <span style="color: #a020f0;">&</span>
|
|
beta, <span style="color: #a020f0;">&</span>
|
|
mo_vgl(:,ielec,iwalk,5),LDC)
|
|
<span style="color: #a020f0;">end do</span>
|
|
<span style="color: #a020f0;">end do</span>
|
|
|
|
<span style="color: #a020f0;">if</span>(info_qmckl_dgemm_value <span style="color: #a020f0;">.eq.</span> QMCKL_SUCCESS <span style="color: #a020f0;">.and.</span> <span style="color: #a020f0;">&</span>
|
|
info_qmckl_dgemm_Gx <span style="color: #a020f0;">.eq.</span> QMCKL_SUCCESS <span style="color: #a020f0;">.and.</span> <span style="color: #a020f0;">&</span>
|
|
info_qmckl_dgemm_Gy <span style="color: #a020f0;">.eq.</span> QMCKL_SUCCESS <span style="color: #a020f0;">.and.</span> <span style="color: #a020f0;">&</span>
|
|
info_qmckl_dgemm_Gz <span style="color: #a020f0;">.eq.</span> QMCKL_SUCCESS <span style="color: #a020f0;">.and.</span> <span style="color: #a020f0;">&</span>
|
|
info_qmckl_dgemm_lap <span style="color: #a020f0;">.eq.</span> QMCKL_SUCCESS ) <span style="color: #a020f0;">then</span>
|
|
info = QMCKL_SUCCESS
|
|
<span style="color: #a020f0;">else</span>
|
|
info = QMCKL_FAILURE
|
|
<span style="color: #a020f0;">end if</span>
|
|
|
|
<span style="color: #a020f0;">end function</span> <span style="color: #0000ff;">qmckl_compute_mo_basis_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_mo_basis_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;">ao_num</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">mo_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;">walk_num</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">coef_normalized</span>,
|
|
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span>* <span style="color: #a0522d;">ao_vgl</span>,
|
|
<span style="color: #228b22;">double</span>* <span style="color: #a020f0;">const</span> <span style="color: #a0522d;">mo_vgl</span> );
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
|
|
<div id="outline-container-org266cf4d" class="outline-4">
|
|
<h4 id="org266cf4d"><span class="section-number-4">2.1.4</span> Test</h4>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div id="postamble" class="status">
|
|
<p class="author">Author: TREX CoE</p>
|
|
<p class="date">Created: 2021-10-06 Wed 21:45</p>
|
|
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
|
</div>
|
|
</body>
|
|
</html>
|