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<a accesskey="h" href=""> UP </a>
|
<a accesskey="H" href="index.html"> HOME </a>
</div><div id="content">
<h1 class="title">Code examples</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#orgb1f3341">1. Python</a>
<ul>
<li><a href="#org855fe5c">1.1. Check numerically that MOs are orthonormal</a></li>
</ul>
</li>
<li><a href="#orgc6a20ae">2. Fortran</a>
<ul>
<li><a href="#org21e91c4">2.1. Checking errors</a></li>
<li><a href="#orga9cd00c">2.2. Computing an atomic orbital on a grid</a></li>
</ul>
</li>
</ul>
</div>
</div>
<div id="outline-container-orgb1f3341" class="outline-2">
<h2 id="orgb1f3341"><span class="section-number-2">1</span> Python</h2>
<div class="outline-text-2" id="text-1">
</div>
<div id="outline-container-org855fe5c" class="outline-3">
<h3 id="org855fe5c"><span class="section-number-3">1.1</span> Check numerically that MOs are orthonormal</h3>
<div class="outline-text-3" id="text-1-1">
<p>
In this example, we will compute numerically the overlap
between the molecular orbitals:
</p>
<p>
\[
S_{ij} = \int \phi_i(\mathbf{r}) \phi_j(\mathbf{r})
\text{d}\mathbf{r} \sim \sum_{k=1}^{N} \phi_i(\mathbf{r}_k)
\phi_j(\mathbf{r}_k) \delta \mathbf{r}
\]
\[
S_{ij} = \langle \phi_i | \phi_j \rangle
\sim \sum_{k=1}^{N} \langle \phi_i | \mathbf{r}_k \rangle
\langle \mathbf{r}_k | \phi_j \rangle
\]
</p>
<div class="org-src-container">
<pre class="src src-python"><span style="color: #a020f0;">import</span> numpy <span style="color: #a020f0;">as</span> np
<span style="color: #a020f0;">import</span> qmckl
</pre>
</div>
<p>
First, we create a context for the QMCkl calculation, and load the
wave function stored in <code>h2o_5z.h5</code> inside it. It is a Hartree-Fock
determinant for the water molecule in the cc-pV5Z basis set.
</p>
<div class="org-src-container">
<pre class="src src-python"><span style="color: #a0522d;">trexio_filename</span> = <span style="color: #8b2252;">"..//share/qmckl/test_data/h2o_5z.h5"</span>
<span style="color: #a0522d;">context</span> = qmckl.context_create()
qmckl.trexio_read(context, trexio_filename)
</pre>
</div>
<p>
We now define the grid points \(\mathbf{r}_k\) as a regular grid around the
molecule.
</p>
<p>
We fetch the nuclear coordinates from the context,
</p>
<div class="org-src-container">
<pre class="src src-python"><span style="color: #a0522d;">nucl_num</span> = qmckl.get_nucleus_num(context)
<span style="color: #a0522d;">nucl_charge</span> = qmckl.get_nucleus_charge(context, nucl_num)
<span style="color: #a0522d;">nucl_coord</span> = qmckl.get_nucleus_coord(context, <span style="color: #8b2252;">'N'</span>, nucl_num*3)
<span style="color: #a0522d;">nucl_coord</span> = np.reshape(nucl_coord, (3, nucl_num))
<span style="color: #a020f0;">for</span> i <span style="color: #a020f0;">in</span> <span style="color: #483d8b;">range</span>(nucl_num):
<span style="color: #a020f0;">print</span>(<span style="color: #8b2252;">"%d %+f %+f %+f"</span>%(<span style="color: #483d8b;">int</span>(nucl_charge[i]),
nucl_coord[i,0],
nucl_coord[i,1],
nucl_coord[i,2]) )
</pre>
</div>
<pre class="example">
8 +0.000000 +0.000000 +0.000000
1 -1.430429 +0.000000 -1.107157
1 +1.430429 +0.000000 -1.107157
</pre>
<p>
and compute the coordinates of the grid points:
</p>
<div class="org-src-container">
<pre class="src src-python"><span style="color: #a0522d;">nx</span> = ( 120, 120, 120 )
<span style="color: #a0522d;">shift</span> = np.array([5.,5.,5.])
<span style="color: #a0522d;">point_num</span> = nx[0] * nx[1] * nx[2]
<span style="color: #a0522d;">rmin</span> = np.array( <span style="color: #483d8b;">list</span>([ np.<span style="color: #483d8b;">min</span>(nucl_coord[:,a]) <span style="color: #a020f0;">for</span> a <span style="color: #a020f0;">in</span> <span style="color: #483d8b;">range</span>(3) ]) )
<span style="color: #a0522d;">rmax</span> = np.array( <span style="color: #483d8b;">list</span>([ np.<span style="color: #483d8b;">max</span>(nucl_coord[:,a]) <span style="color: #a020f0;">for</span> a <span style="color: #a020f0;">in</span> <span style="color: #483d8b;">range</span>(3) ]) )
<span style="color: #a0522d;">linspace</span> = [ <span style="color: #008b8b;">None</span> <span style="color: #a020f0;">for</span> i <span style="color: #a020f0;">in</span> <span style="color: #483d8b;">range</span>(3) ]
<span style="color: #a0522d;">step</span> = [ <span style="color: #008b8b;">None</span> <span style="color: #a020f0;">for</span> i <span style="color: #a020f0;">in</span> <span style="color: #483d8b;">range</span>(3) ]
<span style="color: #a020f0;">for</span> a <span style="color: #a020f0;">in</span> <span style="color: #483d8b;">range</span>(3):
linspace[a], <span style="color: #a0522d;">step</span>[a] = np.linspace(rmin[a]-shift[a],
rmax[a]+shift[a],
num=nx[a],
retstep=<span style="color: #008b8b;">True</span>)
<span style="color: #a0522d;">dr</span> = step[0] * step[1] * step[2]
</pre>
</div>
<p>
Now the grid is ready, we can create the list of grid points
\(\mathbf{r}_k\) on which the MOs \(\phi_i\) will be evaluated, and
transfer them to the QMCkl context:
</p>
<div class="org-src-container">
<pre class="src src-python"><span style="color: #a0522d;">point</span> = []
<span style="color: #a020f0;">for</span> x <span style="color: #a020f0;">in</span> linspace[0]:
<span style="color: #a020f0;">for</span> y <span style="color: #a020f0;">in</span> linspace[1]:
<span style="color: #a020f0;">for</span> z <span style="color: #a020f0;">in</span> linspace[2]:
<span style="color: #a0522d;">point</span> += [ [x, y, z] ]
<span style="color: #a0522d;">point</span> = np.array(point)
<span style="color: #a0522d;">point_num</span> = <span style="color: #483d8b;">len</span>(point)
qmckl.set_point(context, <span style="color: #8b2252;">'N'</span>, point_num, np.reshape(point, (point_num*3)))
</pre>
</div>
<p>
Then, we evaluate all the MOs at the grid points (and time the execution),
and thus obtain the matrix \(M_{ki} = \langle \mathbf{r}_k | \phi_i \rangle =
\phi_i(\mathbf{r}_k)\).
</p>
<div class="org-src-container">
<pre class="src src-python"><span style="color: #a020f0;">import</span> time
<span style="color: #a0522d;">mo_num</span> = qmckl.get_mo_basis_mo_num(context)
<span style="color: #a0522d;">before</span> = time.time()
<span style="color: #a0522d;">mo_value</span> = qmckl.get_mo_basis_mo_value(context, point_num*mo_num)
<span style="color: #a0522d;">after</span> = time.time()
<span style="color: #a0522d;">mo_value</span> = np.reshape( mo_value, (point_num, mo_num) )
<span style="color: #a020f0;">print</span>(<span style="color: #8b2252;">"Number of MOs: "</span>, mo_num)
<span style="color: #a020f0;">print</span>(<span style="color: #8b2252;">"Number of grid points: "</span>, point_num)
<span style="color: #a020f0;">print</span>(<span style="color: #8b2252;">"Execution time : "</span>, (after - before), <span style="color: #8b2252;">"seconds"</span>)
</pre>
</div>
<pre class="example">
Number of MOs: 201
Number of grid points: 1728000
Execution time : 3.511528968811035 seconds
</pre>
<p>
and finally we compute the overlap between all the MOs as
\(M^\dagger M\).
</p>
<div class="org-src-container">
<pre class="src src-python"><span style="color: #a0522d;">overlap</span> = mo_value.T @ mo_value * dr
<span style="color: #a020f0;">print</span> (overlap)
</pre>
</div>
<pre class="example">
[[ 9.88693941e-01 2.34719693e-03 -1.50518232e-08 ... 3.12084178e-09
-5.81064929e-10 3.70130091e-02]
[ 2.34719693e-03 9.99509628e-01 3.18930040e-09 ... -2.46888958e-10
-1.06064273e-09 -7.65567973e-03]
[-1.50518232e-08 3.18930040e-09 9.99995073e-01 ... -5.84882580e-06
-1.21598117e-06 4.59036468e-08]
...
[ 3.12084178e-09 -2.46888958e-10 -5.84882580e-06 ... 1.00019107e+00
-2.03342837e-04 -1.36954855e-08]
[-5.81064929e-10 -1.06064273e-09 -1.21598117e-06 ... -2.03342837e-04
9.99262427e-01 1.18264754e-09]
[ 3.70130091e-02 -7.65567973e-03 4.59036468e-08 ... -1.36954855e-08
1.18264754e-09 8.97215950e-01]]
</pre>
</div>
</div>
</div>
<div id="outline-container-orgc6a20ae" class="outline-2">
<h2 id="orgc6a20ae"><span class="section-number-2">2</span> Fortran</h2>
<div class="outline-text-2" id="text-2">
</div>
<div id="outline-container-org21e91c4" class="outline-3">
<h3 id="org21e91c4"><span class="section-number-3">2.1</span> Checking errors</h3>
<div class="outline-text-3" id="text-2-1">
<p>
All QMCkl functions return an error code. A convenient way to handle
errors is to write an error-checking function that displays the
error in text format and exits the program.
</p>
<div class="org-src-container">
<pre class="src src-f90" id="org6b4d369"><span style="color: #a020f0;">subroutine</span> <span style="color: #0000ff;">qmckl_check_error</span>(rc, message)
<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_exit_code), <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> rc</span>
<span style="color: #228b22;">character</span>(len=*) , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> message</span>
<span style="color: #228b22;">character</span>(len=128) ::<span style="color: #a0522d;"> str_buffer</span>
<span style="color: #a020f0;">if</span> (rc /= QMCKL_SUCCESS) <span style="color: #a020f0;">then</span>
<span style="color: #a020f0;">print</span> *, message
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">qmckl_string_of_error</span>(rc, str_buffer)
<span style="color: #a020f0;">print</span> *, str_buffer
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">exit</span>(rc)
<span style="color: #a020f0;">end if</span>
<span style="color: #a020f0;">end subroutine</span> <span style="color: #0000ff;">qmckl_check_error</span>
</pre>
</div>
</div>
</div>
<div id="outline-container-orga9cd00c" class="outline-3">
<h3 id="orga9cd00c"><span class="section-number-3">2.2</span> Computing an atomic orbital on a grid</h3>
<div class="outline-text-3" id="text-2-2">
<p>
The following program, in Fortran, computes the values of an atomic
orbital on a regular 3-dimensional grid. The 100<sup>3</sup> grid points are
automatically defined, such that the molecule fits in a box with 5
atomic units in the borders.
</p>
<p>
This program uses the <code>qmckl_check_error</code> function defined above.
</p>
<p>
To use this program, run
</p>
<div class="org-src-container">
<pre class="src src-bash">$ ao_grid &lt;trexio_file&gt; &lt;AO_id&gt; &lt;point_num&gt;
</pre>
</div>
<div class="org-src-container">
<pre class="src src-f90"><span style="color: #a020f0;">subroutine</span> <span style="color: #0000ff;">qmckl_check_error</span>(rc, message)
<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_exit_code), <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> rc</span>
<span style="color: #228b22;">character</span>(len=*) , <span style="color: #a020f0;">intent</span>(in) ::<span style="color: #a0522d;"> message</span>
<span style="color: #228b22;">character</span>(len=128) ::<span style="color: #a0522d;"> str_buffer</span>
<span style="color: #a020f0;">if</span> (rc /= QMCKL_SUCCESS) <span style="color: #a020f0;">then</span>
<span style="color: #a020f0;">print</span> *, message
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">qmckl_string_of_error</span>(rc, str_buffer)
<span style="color: #a020f0;">print</span> *, str_buffer
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">exit</span>(rc)
<span style="color: #a020f0;">end if</span>
<span style="color: #a020f0;">end subroutine</span> <span style="color: #0000ff;">qmckl_check_error</span>
<span style="color: #a020f0;">program</span> <span style="color: #0000ff;">ao_grid</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>(qmckl_context) ::<span style="color: #a0522d;"> qmckl_ctx </span>! <span style="color: #b22222;">QMCkl context</span>
<span style="color: #228b22;">integer</span>(qmckl_exit_code) ::<span style="color: #a0522d;"> rc </span>! <span style="color: #b22222;">Exit code of QMCkl functions</span>
<span style="color: #228b22;">character</span>(len=128) ::<span style="color: #a0522d;"> trexio_filename</span>
<span style="color: #228b22;">character</span>(len=128) ::<span style="color: #a0522d;"> str_buffer</span>
<span style="color: #228b22;">integer</span> ::<span style="color: #a0522d;"> ao_id</span>
<span style="color: #228b22;">integer</span> ::<span style="color: #a0522d;"> point_num_x</span>
<span style="color: #228b22;">integer</span>(<span style="color: #008b8b;">c_int64_t</span>) ::<span style="color: #a0522d;"> nucl_num</span>
<span style="color: #228b22;">double precision</span>, <span style="color: #a020f0;">allocatable</span> ::<span style="color: #a0522d;"> nucl_coord(:,:)</span>
<span style="color: #228b22;">integer</span>(<span style="color: #008b8b;">c_int64_t</span>) ::<span style="color: #a0522d;"> point_num</span>
<span style="color: #228b22;">integer</span>(<span style="color: #008b8b;">c_int64_t</span>) ::<span style="color: #a0522d;"> ao_num</span>
<span style="color: #228b22;">integer</span>(<span style="color: #008b8b;">c_int64_t</span>) ::<span style="color: #a0522d;"> ipoint, i, j, k</span>
<span style="color: #228b22;">double precision</span> ::<span style="color: #a0522d;"> x, y, z, dr(3)</span>
<span style="color: #228b22;">double precision</span> ::<span style="color: #a0522d;"> rmin(3), rmax(3)</span>
<span style="color: #228b22;">double precision</span>, <span style="color: #a020f0;">allocatable</span> ::<span style="color: #a0522d;"> points(:,:)</span>
<span style="color: #228b22;">double precision</span>, <span style="color: #a020f0;">allocatable</span> ::<span style="color: #a0522d;"> ao_vgl(:,:,:)</span>
</pre>
</div>
<p>
Start by fetching the command-line arguments:
</p>
<div class="org-src-container">
<pre class="src src-f90"><span style="color: #a020f0;">if</span> (iargc() /= 3) <span style="color: #a020f0;">then</span>
<span style="color: #a020f0;">print</span> *, <span style="color: #8b2252;">'Syntax: ao_grid &lt;trexio_file&gt; &lt;AO_id&gt; &lt;point_num&gt;'</span>
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">exit</span>(-1)
<span style="color: #a020f0;">end if</span>
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">getarg</span>(1, trexio_filename)
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">getarg</span>(2, str_buffer)
<span style="color: #a020f0;">read</span>(str_buffer, *) ao_id
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">getarg</span>(3, str_buffer)
<span style="color: #a020f0;">read</span>(str_buffer, *) point_num_x
<span style="color: #a020f0;">if</span> (point_num_x &lt; 0 <span style="color: #a020f0;">.or.</span> point_num_x &gt; 300) <span style="color: #a020f0;">then</span>
<span style="color: #a020f0;">print</span> *, <span style="color: #8b2252;">'Error: 0 &lt; point_num &lt; 300'</span>
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">exit</span>(-1)
<span style="color: #a020f0;">end if</span>
</pre>
</div>
<p>
Create the QMCkl context and initialize it with the wave function
present in the TREXIO file:
</p>
<div class="org-src-container">
<pre class="src src-f90">qmckl_ctx = qmckl_context_create()
rc = qmckl_trexio_read(qmckl_ctx, trexio_filename, 1_8*<span style="color: #a020f0;">len</span>(<span style="color: #a020f0;">trim</span>(trexio_filename)))
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">qmckl_check_error</span>(rc, <span style="color: #8b2252;">'Read TREXIO'</span>)
</pre>
</div>
<p>
We need to check that <code>ao_id</code> is in the range, so we get the total
number of AOs from QMCkl:
</p>
<div class="org-src-container">
<pre class="src src-f90">rc = qmckl_get_ao_basis_ao_num(qmckl_ctx, ao_num)
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">qmckl_check_error</span>(rc, <span style="color: #8b2252;">'Getting ao_num'</span>)
<span style="color: #a020f0;">if</span> (ao_id &lt; 0 <span style="color: #a020f0;">.or.</span> ao_id &gt; ao_num) <span style="color: #a020f0;">then</span>
<span style="color: #a020f0;">print</span> *, <span style="color: #8b2252;">'Error: 0 &lt; ao_id &lt; '</span>, ao_num
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">exit</span>(-1)
<span style="color: #a020f0;">end if</span>
</pre>
</div>
<p>
Now we will compute the limits of the box in which the molecule fits.
For that, we first need to ask QMCkl the coordinates of nuclei.
</p>
<div class="org-src-container">
<pre class="src src-f90">rc = qmckl_get_nucleus_num(qmckl_ctx, nucl_num)
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">qmckl_check_error</span>(rc, <span style="color: #8b2252;">'Get nucleus num'</span>)
<span style="color: #a020f0;">allocate</span>( nucl_coord(3, nucl_num) )
rc = qmckl_get_nucleus_coord(qmckl_ctx, <span style="color: #8b2252;">'N'</span>, nucl_coord, 3_8*nucl_num)
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">qmckl_check_error</span>(rc, <span style="color: #8b2252;">'Get nucleus coord'</span>)
</pre>
</div>
<p>
We now compute the coordinates of opposite points of the box, and
the distance between points along the 3 directions:
</p>
<div class="org-src-container">
<pre class="src src-f90">rmin(1) = <span style="color: #a020f0;">minval</span>( nucl_coord(1,:) ) - 5.d0
rmin(2) = <span style="color: #a020f0;">minval</span>( nucl_coord(2,:) ) - 5.d0
rmin(3) = <span style="color: #a020f0;">minval</span>( nucl_coord(3,:) ) - 5.d0
rmax(1) = <span style="color: #a020f0;">maxval</span>( nucl_coord(1,:) ) + 5.d0
rmax(2) = <span style="color: #a020f0;">maxval</span>( nucl_coord(2,:) ) + 5.d0
rmax(3) = <span style="color: #a020f0;">maxval</span>( nucl_coord(3,:) ) + 5.d0
dr(1:3) = (rmax(1:3) - rmin(1:3)) / <span style="color: #a020f0;">dble</span>(point_num_x-1)
</pre>
</div>
<p>
We now produce the list of point coordinates where the AO will be
evaluated:
</p>
<div class="org-src-container">
<pre class="src src-f90">point_num = point_num_x**3
<span style="color: #a020f0;">allocate</span>( points(point_num, 3) )
ipoint=0
z = rmin(3)
<span style="color: #a020f0;">do</span> k=1,point_num_x
y = rmin(2)
<span style="color: #a020f0;">do</span> j=1,point_num_x
x = rmin(1)
<span style="color: #a020f0;">do</span> i=1,point_num_x
ipoint = ipoint+1
points(ipoint,1) = x
points(ipoint,2) = y
points(ipoint,3) = z
x = x + dr(1)
<span style="color: #a020f0;">end do</span>
y = y + dr(2)
<span style="color: #a020f0;">end do</span>
z = z + dr(3)
<span style="color: #a020f0;">end do</span>
</pre>
</div>
<p>
We give the points to QMCkl:
</p>
<div class="org-src-container">
<pre class="src src-f90">rc = qmckl_set_point(qmckl_ctx, <span style="color: #8b2252;">'T'</span>, point_num, points, <span style="color: #a020f0;">size</span>(points)*1_8 )
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">qmckl_check_error</span>(rc, <span style="color: #8b2252;">'Setting points'</span>)
</pre>
</div>
<p>
We allocate the space required to retrieve the values, gradients and
Laplacian of all AOs, and ask to retrieve the values of the
AOs computed at the point positions.
</p>
<div class="org-src-container">
<pre class="src src-f90"><span style="color: #a020f0;">allocate</span>( ao_vgl(ao_num, 5, point_num) )
rc = qmckl_get_ao_basis_ao_vgl(qmckl_ctx, ao_vgl, ao_num*5_8*point_num)
<span style="color: #a020f0;">call</span> <span style="color: #0000ff;">qmckl_check_error</span>(rc, <span style="color: #8b2252;">'Setting points'</span>)
</pre>
</div>
<p>
We finally print the value and Laplacian of the AO:
</p>
<div class="org-src-container">
<pre class="src src-f90"><span style="color: #a020f0;">do</span> ipoint=1, point_num
<span style="color: #a020f0;">print</span> <span style="color: #8b2252;">'(3(F10.6,X),2(E20.10,X))'</span>, points(ipoint, 1:3), ao_vgl(ao_id,1,ipoint), ao_vgl(ao_id,5,ipoint)
<span style="color: #a020f0;">end do</span>
</pre>
</div>
<div class="org-src-container">
<pre class="src src-f90"> <span style="color: #a020f0;">deallocate</span>( nucl_coord, points, ao_vgl )
<span style="color: #a020f0;">end program</span> <span style="color: #0000ff;">ao_grid</span>
</pre>
</div>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: TREX CoE</p>
<p class="date">Created: 2022-06-29 Wed 11:33</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
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