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<h1>Activity 9: Comparing simulation and experiment with R-factors</h1>
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<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-unusual-tilt-of-co-molecule-on-fe-001">The unusual tilt of CO molecule on Fe(001)</a></li>
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<section class="tex2jax_ignore mathjax_ignore" id="activity-9-comparing-simulation-and-experiment-with-r-factors">
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<span id="rfactor"></span><h1>Activity 9: Comparing simulation and experiment with R-factors<a class="headerlink" href="#activity-9-comparing-simulation-and-experiment-with-r-factors" title="Link to this heading">#</a></h1>
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<p>In order to extract precise crystallographic information from electronic spectroscopy, we need to compare MsSpec calculations with experimental results and adjust the modelling parameters to simulate the experiment as accurately as possible.</p>
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<p><em>R-factors</em> (reliability factors) are commonly used for this task. In the following example, we will see how MsSpec can extract the adsorption geometry of a molecule.</p>
|
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<section id="the-unusual-tilt-of-co-molecule-on-fe-001">
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<h2>The unusual tilt of CO molecule on Fe(001)<a class="headerlink" href="#the-unusual-tilt-of-co-molecule-on-fe-001" title="Link to this heading">#</a></h2>
|
||
<p>The carbon monoxide molecule can be adsorbed onto a Fe(001) surface in the hollow site. It was experimentally demonstrated that the CO molecule is tilted by 55<span class="math notranslate nohighlight">\(\pm\)</span>2° in <100> azimuthal directions. The molecule is bonded to the Fe surface by the carbon atom and the adsorption height was estimated to be <span class="math notranslate nohighlight">\(\sim\)</span> 0.6 Å.</p>
|
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<div class="admonition seealso" id="cofe-paper">
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||
<p class="admonition-title">See also</p>
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||
<p>based on this paper from R. S. Saiki <em>et al.</em>
|
||
<a class="reference external" href="https://doi.org/10.1103/PhysRevLett.63.283">Phys. Rev. Lett. <strong>63(3)</strong> p283-6 (1989)</a></p>
|
||
</div>
|
||
<p>We will try to reproduce the polar scan of the figure below of CO adsorbed in the hollow site of the Fe(001) surface with simple single scattering calculations with MsSpec and by using R-Factors to find the best adsorption geometry. We will use the simple cluster displayed on the left hand side of the figure.</p>
|
||
<figure class="align-default" id="cofe-fig1">
|
||
<a class="reference internal image-reference" href="../_images/COFe_fig1.jpg"><img alt="" class="align-center" src="../_images/COFe_fig1.jpg" style="width: 600px;" />
|
||
</a>
|
||
<figcaption>
|
||
<p><span class="caption-text">Small cluster used for SSC calculations (left) and (right) Normalized polar scan of the C(1s) at 1202 eV for [100] and [1-10] azimths.</span><a class="headerlink" href="#cofe-fig1" title="Link to this image">#</a></p>
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<i class="fa-solid fa-circle-question"></i> Quiz</label><div class="sd-tab-content docutils">
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<p>Download <a class="reference download internal" download="" href="../_downloads/179b010d01a3689041dba01413ac667b/COFe.py"><span class="xref download myst">this script</span></a> and write the body of the function <code class="docutils literal notranslate"><span class="pre">create_cluster</span></code>. The function should return a
|
||
small cluster of 5 Fe atoms with the CO molecule adsorbed like in figure <code class="xref std std-numref docutils literal notranslate"><span class="pre">Fig.</span> <span class="pre">%s</span></code> below. The function
|
||
will accept 4 keyword arguments to control the adsorption geometry.</p>
|
||
<figure class="align-default" id="cofe-fig2">
|
||
<a class="reference internal image-reference" href="../_images/COFe_fig2.jpg"><img alt="CO-Fe adsorption geometry" class="align-center" src="../_images/COFe_fig2.jpg" style="width: 600px;" />
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||
</a>
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||
<figcaption>
|
||
<p><span class="caption-text">Adsorption geometry of carbon monoxide on Fe(001).</span><a class="headerlink" href="#cofe-fig2" title="Link to this image">#</a></p>
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</figcaption>
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</figure>
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<div class="admonition note">
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<p class="admonition-title">Note</p>
|
||
<p>Remember to use the <a class="reference external" href="https://wiki.fysik.dtu.dk/ase/ase/build/build.html#ase.build.bulk"><code class="docutils literal notranslate"><span class="pre">ase.build.bulk</span></code></a>, the <a class="reference external" href="https://msspec.cnrs.fr/faq/hemispherical_cluster/hemispherical_cluster.html#hemispherical-cluster-faq"><code class="docutils literal notranslate"><span class="pre">msspec.utils.hemispherical_cluster</span></code></a> and the <a class="reference external" href="https://wiki.fysik.dtu.dk/ase/ase/build/surface.html#ase.build.add_adsorbate"><code class="docutils literal notranslate"><span class="pre">ase.build.add_adsorbate</span></code></a>
|
||
functions.</p>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p>Now that the <code class="docutils literal notranslate"><span class="pre">create_cluster</span></code> function is done, look at the rest of the script. The next function is called <code class="docutils literal notranslate"><span class="pre">compute_polar_scan</span></code> and will obviously be used to compute the <span class="math notranslate nohighlight">\(\theta\)</span>-scan of the C1s for a given cluster geometry.
|
||
Finally there is the <em>Main part</em> that is built in two sections:</p>
|
||
<ol class="arabic simple">
|
||
<li><p>A section containing nested <em>for loops</em></p></li>
|
||
<li><p>A final section for <em>R-Factor analysis</em></p></li>
|
||
</ol>
|
||
<div class="sd-tab-set docutils">
|
||
<input checked="checked" id="sd-tab-item-1" name="sd-tab-set-1" type="radio">
|
||
<label class="sd-tab-label" for="sd-tab-item-1">
|
||
<i class="fa-solid fa-circle-question"></i> Quiz</label><div class="sd-tab-content docutils">
|
||
<ol class="arabic simple">
|
||
<li><p>Complete the nested for loops in section 1) in order to compute polar scans for CO molecule tilted from 45° to 60° with a 1° step and aligned either along the [100] direction of Fe, 30° from this direction or along [110]. The adsorption height is 0.6 Å and the bond length is 1.157 Å.</p></li>
|
||
<li><p>What is the best <span class="math notranslate nohighlight">\((\theta, \phi)\)</span> according to the R-Factor analysis</p></li>
|
||
</ol>
|
||
</div>
|
||
</div>
|
||
<p>MsSpec uses 12 different R-Factors formula to compare the calculted curve to the experimental data. The set of parameters giving the best agreement according to the majority of those 12 R-factors is assumed to be the best solution. Here are the R-factors formula used in MsSpec</p>
|
||
<figure class="align-default" id="rfactors-formula">
|
||
<a class="reference internal image-reference" href="../_images/formula.jpg"><img alt="R-Factor result" class="align-center" src="../_images/formula.jpg" style="width: 800px;" />
|
||
</a>
|
||
<figcaption>
|
||
<p><span class="caption-text">The 12 R-Factors used in MsSpec. The Pendry’s R-Factor is n°11.</span><a class="headerlink" href="#rfactors-formula" title="Link to this image">#</a></p>
|
||
</figcaption>
|
||
</figure>
|
||
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|
||
<i class="fa-solid fa-circle-question"></i> Quiz</label><div class="sd-tab-content docutils">
|
||
<p>How many R-Factors do agree that <span class="math notranslate nohighlight">\((\theta,\phi)=(55,0)\)</span> gives the best agreement ?</p>
|
||
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|
||
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|
||
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|
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<i class="fa-solid fa-list"></i> Contents
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<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-unusual-tilt-of-co-molecule-on-fe-001">The unusual tilt of CO molecule on Fe(001)</a></li>
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By Sylvain Tricot
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