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<div id="org-div-home-and-up">
<a accesskey="h" href=""> UP </a>
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<a accesskey="H" href="index.html"> HOME </a>
</div><div id="content">
<h1 class="title">Molecular Orbitals</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org477d06b">1. Context</a>
<ul>
<li><a href="#orgd3e5d78">1.1. Data structure</a></li>
<li><a href="#org79512bf">1.2. Access functions</a></li>
<li><a href="#orgf736025">1.3. Initialization functions</a></li>
</ul>
</li>
<li><a href="#org0b1019e">2. Computation</a>
<ul>
<li><a href="#org3a17dd3">2.1. Computation of MOs</a>
<ul>
<li><a href="#org27bd7af">2.1.1. Get</a></li>
<li><a href="#org95ea42c">2.1.2. Provide</a></li>
<li><a href="#orgadab0b6">2.1.3. Compute</a></li>
<li><a href="#org3633f3d">2.1.4. Test</a></li>
</ul>
</li>
</ul>
</li>
</ul>
</div>
</div>
<div id="outline-container-org477d06b" class="outline-2">
<h2 id="org477d06b"><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>mo_num</code></td>
<td class="org-left">&#xa0;</td>
<td class="org-left">Number of MOs</td>
</tr>
<tr>
<td class="org-left"><code>coefficient</code></td>
<td class="org-left"><code>[mo_num][ao_num]</code></td>
<td class="org-left">Orbital coefficients</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>
<tbody>
<tr>
<td class="org-left"><code>mo_vgl</code></td>
<td class="org-left"><code>[5][elec_num][mo_num]</code></td>
<td class="org-left">Value, gradients, Laplacian of the MOs at electron positions</td>
</tr>
<tr>
<td class="org-left"><code>mo_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 MOs at electron positions</td>
</tr>
</tbody>
</table>
</div>
<div id="outline-container-orgd3e5d78" class="outline-3">
<h3 id="orgd3e5d78"><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_mo_basis_struct</span> {
<span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">mo_num</span>;
<span style="color: #228b22;">double</span> * <span style="color: #a0522d;">coefficient</span>;
<span style="color: #228b22;">double</span> * <span style="color: #a0522d;">mo_vgl</span>;
<span style="color: #228b22;">int64_t</span> <span style="color: #a0522d;">mo_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;">qmckl_mo_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_mo_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_mo_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-&gt;mo_basis.uninitialized = (1 &lt;&lt; 2) - 1;
<span style="color: #a020f0;">return</span> QMCKL_SUCCESS;
}
</pre>
</div>
</div>
</div>
<div id="outline-container-org79512bf" class="outline-3">
<h3 id="org79512bf"><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-orgf736025" class="outline-3">
<h3 id="orgf736025"><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_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-org0b1019e" class="outline-2">
<h2 id="org0b1019e"><span class="section-number-2">2</span> Computation</h2>
<div class="outline-text-2" id="text-2">
</div>
<div id="outline-container-org3a17dd3" class="outline-3">
<h3 id="org3a17dd3"><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-org27bd7af" class="outline-4">
<h4 id="org27bd7af"><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-org95ea42c" class="outline-4">
<h4 id="org95ea42c"><span class="section-number-4">2.1.2</span> Provide</h4>
</div>
<div id="outline-container-orgadab0b6" class="outline-4">
<h4 id="orgadab0b6"><span class="section-number-4">2.1.3</span> Compute</h4>
<div class="outline-text-4" id="text-2-1-3">
<table id="org5be9ec8" 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>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][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][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_vgl_f(context, </span><span style="color: #a020f0;">&amp;</span>
ao_num, mo_num, elec_num, <span style="color: #a020f0;">&amp;</span>
coef_normalized, ao_vgl, mo_vgl) <span style="color: #a020f0;">&amp;</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;">double precision</span> , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> ao_vgl(ao_num,elec_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,5)</span>
<span style="color: #228b22;">character</span> ::<span style="color: #a0522d;"> TransA, TransB</span>
<span style="color: #228b22;">double precision</span>,<span style="color: #a020f0;">dimension</span>(:,:),<span style="color: #a020f0;">allocatable</span> ::<span style="color: #a0522d;"> mo_vgl_big</span>
<span style="color: #228b22;">double precision</span>,<span style="color: #a020f0;">dimension</span>(:,:),<span style="color: #a020f0;">allocatable</span> ::<span style="color: #a0522d;"> ao_vgl_big</span>
!<span style="color: #b22222;">double precision,dimension(:,:),allocatable :: coef_trans</span>
!<span style="color: #b22222;">double precision,dimension(:),allocatable :: coef_all</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>*8 ::<span style="color: #a0522d;"> M, N, K, LDA, LDB, LDC, i,j, idx</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>
<span style="color: #a020f0;">allocate</span>(mo_vgl_big(mo_num,elec_num*5))
<span style="color: #a020f0;">allocate</span>(ao_vgl_big(ao_num,elec_num*5))
!<span style="color: #b22222;">allocate(coef_all(mo_num*ao_num))</span>
!<span style="color: #b22222;">allocate(coef_trans(mo_num,ao_num))</span>
TransA = <span style="color: #8b2252;">'T'</span>
TransB = <span style="color: #8b2252;">'N'</span>
alpha = 1.0d0
beta = 0.0d0
info = QMCKL_SUCCESS
info_qmckl_dgemm_value = 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 = mo_num
N = elec_num*5
K = ao_num * 1_8
LDA = <span style="color: #a020f0;">size</span>(coef_normalized,1)
idx = 0
!<span style="color: #b22222;">do j = 1,ao_num</span>
!<span style="color: #b22222;">do i = 1,mo_num</span>
! <span style="color: #b22222;">idx = idx + 1</span>
! <span style="color: #b22222;">coef_all(idx) = coef_normalized(i,j)</span>
!<span style="color: #b22222;">end do</span>
!<span style="color: #b22222;">end do</span>
!<span style="color: #b22222;">idx = 0</span>
!<span style="color: #b22222;">do j = 1,mo_num</span>
!<span style="color: #b22222;">do i = 1,ao_num</span>
! <span style="color: #b22222;">idx = idx + 1</span>
! <span style="color: #b22222;">coef_trans(j,i) = coef_all(idx)</span>
!<span style="color: #b22222;">end do</span>
!<span style="color: #b22222;">end do</span>
ao_vgl_big = <span style="color: #a020f0;">reshape</span>(ao_vgl(:, :, :),(/ao_num, elec_num*5_8/))
LDB = <span style="color: #a020f0;">size</span>(ao_vgl_big,1)
LDC = <span style="color: #a020f0;">size</span>(mo_vgl_big,1)
info = qmckl_dgemm(context,TransA, TransB, M, N, K, alpha, <span style="color: #a020f0;">&amp;</span>
coef_normalized,<span style="color: #a020f0;">size</span>(coef_normalized,1)*1_8, <span style="color: #a020f0;">&amp;</span>
ao_vgl_big, <span style="color: #a020f0;">size</span>(ao_vgl_big,1)*1_8, <span style="color: #a020f0;">&amp;</span>
beta, <span style="color: #a020f0;">&amp;</span>
mo_vgl_big,LDC)
mo_vgl = <span style="color: #a020f0;">reshape</span>(mo_vgl_big,(/mo_num,elec_num,5_8/))
<span style="color: #a020f0;">deallocate</span>(mo_vgl_big)
<span style="color: #a020f0;">deallocate</span>(ao_vgl_big)
<span style="color: #a020f0;">end function</span> <span style="color: #0000ff;">qmckl_compute_mo_basis_vgl_f</span>
</pre>
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<pre class="src src-c"><span style="color: #228b22;">qmckl_exit_code</span> <span style="color: #0000ff;">qmckl_compute_mo_basis_vgl</span> (
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">context</span> <span style="color: #a0522d;">qmckl_context</span>,
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">ao_num</span> <span style="color: #a0522d;">int64_t</span>,
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">mo_num</span> <span style="color: #a0522d;">int64_t</span>,
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">elec_num</span> <span style="color: #a0522d;">int64_t</span>,
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">coef_normalized</span>* <span style="color: #228b22;">double</span>,
<span style="color: #a020f0;">const</span> <span style="color: #228b22;">ao_vgl</span>* <span style="color: #228b22;">double</span>,
<span style="color: #228b22;">mo_vgl</span>* <span style="color: #a020f0;">const</span> <span style="color: #228b22;">double</span> );
</pre>
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<h4 id="org3633f3d"><span class="section-number-4">2.1.4</span> Test</h4>
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<div id="postamble" class="status">
<p class="author">Author: TREX CoE</p>
<p class="date">Created: 2022-01-21 Fri 07:53</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
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