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18 changes: 2 additions & 16 deletions _sources/docs/tutorials/correlation.ipynb
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"# Static versus dynamic correlation correlation\n",
"\n",
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},
"source": [
"# Core-hole localization\n",
"A special aspect of X-ray spectroscopy calculations which involve an explicit core-hole, e.g. X-ray photoelectron spectroscopy (XPS) or X-ray emission spectroscopy (XES), is the delocalization-induced relaxation error (DIRE). DIRE affects symmetric molecules where care must be taken to localize the core-hole, especially when HF or DFT theory levels are used. Below follows an illustration of DIRE in the case of the ethylene molecule. We will calculate the ionization energy of the C 1s core orbitals. The ionization energy is calculated as:\n",
"A special aspect of X-ray spectroscopy calculations which involve an explicit core-hole, e.g. X-ray photoelectron spectroscopy (XPS) or X-ray emission spectroscopy (XES), is the delocalization-induced relaxation error (DIRE) {cite}`dire2022`. DIRE affects symmetric molecules where care must be taken to localize the core-hole, especially when HF or DFT theory levels are used. Below follows an illustration of DIRE in the case of the ethylene molecule. We will calculate the ionization energy of the C 1s core orbitals. The ionization energy is calculated as:\n",
"\n",
"$$\n",
"\\textrm{IE} = E_\\textrm{FCH} - E_\\textrm{GS}\n",
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"tags": []
},
"source": [
"Now that we have calculated the ionization energies for both the localized and delocalized CH, let us plot the results. The dotted line marks the measured ionization energy."
"Now that we have calculated the ionization energies for both the localized and delocalized CH, let us plot the results. The dotted line marks the measured ionization energy {cite}`xpsethylene2011`."
]
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{
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"source": [
"# Analysis\n",
"\n",
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"# Exercises\n",
"\n",
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"# Special aspects\n",
"\n",
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Expand Down Expand Up @@ -655,7 +655,7 @@ <h1>X-ray spectroscopies</h1>

<section class="tex2jax_ignore mathjax_ignore" id="x-ray-spectroscopies">
<span id="sec-x-ray"></span><h1>X-ray spectroscopies<a class="headerlink" href="#x-ray-spectroscopies" title="Link to this heading">#</a></h1>
<p>Tuning the photon energy to the X-ray regime, processes involving the transition of core electrons can be probed, providing measurements which are very sensitive to elements and local environment <span id="id1">[<a class="reference internal" href="../refs.html#id9" title="U. Bergmann, V. K. Yachandra, and J. Yano. X-Ray Free Electron Lasers: Applications in Materials, Chemistry, and Biology. The Royal Society of Chemistry, 2017. ISBN 978-1-84973-100-3. URL: https://doi.org/10.1039/9781782624097.">BYY17</a>, <a class="reference internal" href="../refs.html#id80" title="P. Norman and A. Dreuw. Simulating x-ray spectroscopies and calculating core-excited states of molecules. Chem. Rev., 118:7208-7248, 2018. URL: https://doi.org/10.1021/acs.chemrev.8b00156.">ND18</a>, <a class="reference internal" href="../refs.html#id118" title="J. A. van Bokhoven and C. Laberti. X-Ray Absorption and X-Ray Emission Spectroscopy: Theory and Applications. John Wiley &amp; Sons, 2016. ISBN 9781118844236. URL: https://doi.org/10.1002/9781118844243.">vBL16</a>]</span>. Here we will discuss the modeling of four such spectroscopies:</p>
<p>Tuning the photon energy to the X-ray regime, processes involving the transition of core electrons can be probed, providing measurements which are very sensitive to elements and local environment <span id="id1">[<a class="reference internal" href="../refs.html#id9" title="U. Bergmann, V. K. Yachandra, and J. Yano. X-Ray Free Electron Lasers: Applications in Materials, Chemistry, and Biology. The Royal Society of Chemistry, 2017. ISBN 978-1-84973-100-3. URL: https://doi.org/10.1039/9781782624097.">BYY17</a>, <a class="reference internal" href="../refs.html#id82" title="P. Norman and A. Dreuw. Simulating x-ray spectroscopies and calculating core-excited states of molecules. Chem. Rev., 118:7208-7248, 2018. URL: https://doi.org/10.1021/acs.chemrev.8b00156.">ND18</a>, <a class="reference internal" href="../refs.html#id120" title="J. A. van Bokhoven and C. Laberti. X-Ray Absorption and X-Ray Emission Spectroscopy: Theory and Applications. John Wiley &amp; Sons, 2016. ISBN 9781118844236. URL: https://doi.org/10.1002/9781118844243.">vBL16</a>]</span>. Here we will discuss the modeling of four such spectroscopies:</p>
<figure class="align-default" id="xray-processes">
<img alt="../../_images/processes.svg" src="../../_images/processes.svg" />
<figcaption>
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Expand Down Expand Up @@ -3742,7 +3742,7 @@ <h3>Spin-orbit coupling<a class="headerlink" href="#spin-orbit-coupling" title="
<section id="spurious-valence-mixing-in-xas">
<span id="sec-xray-cons-spur-val"></span><h2>Spurious valence mixing in XAS<a class="headerlink" href="#spurious-valence-mixing-in-xas" title="Link to this heading">#</a></h2>
<p>Within a damped response theory framework or when performing explicit real-time propagation, a CVS-like scheme which separates core-transitions from the valence-continuum is usually not performed. If such calculations are run with an atom-centered basis set (as most are), this can then lead to spurious mixing with valence-excited states. What happens is that resonances in the valence-continuum occur close to core-excitations, leading to unphysical mixing which affects excitation energies and (more significantly) intensities. These issues occur both for methods featuring only single-excited configurations (<em>e.g.</em> TDDFT) and higher-excited configurations (<em>e.g.</em> ADC) and need to be avoided.</p>
<p>These issues have been observed for, <em>e.g.</em>, <span class="math notranslate nohighlight">\(L_{2,3}\)</span>-edge of silicon <span id="id1">[<a class="reference internal" href="../refs.html#id31" title="T. Fransson, D. Burdakova, and P. Norman. K- and L-edge X-ray absorption spectrum calculations of closed-shell carbon, silicon, germanium, and sulfur compounds using damped four-component density functional response theory. Phys. Chem. Chem. Phys., 18:13591-13603, 2016. URL: https://doi.org/10.1039/C6CP00561F.">FBN16</a>, <a class="reference internal" href="../refs.html#id56" title="M. Kadek, L. Konecny, B. Gao, M. Repisky, and K. Ruud. X-ray absorption resonances near L2,3-edges from real-time propagation of the Dirac–Kohn–Sham density matrix. Phys. Chem. Chem. Phys., 17:22566-22570, 2015. URL: https://doi.org/10.1039/C5CP03712C.">KKG+15</a>]</span>, and are usually more common at lower energies. They can be identified by studying the amplitudes and the <span class="math notranslate nohighlight">\(t^2\)</span> values for post-HF methods, and can be avoided by chosing appropriate basis sets, freezing certain virtual orbitals, or by re-introducing the CVS approximation (or some other flavour) within the CPP/RT framework. The latter approach is recommended at least for CPP-ADC, as converging the response vectors has otherwise been seen to be difficult <span id="id2">[<a class="reference internal" href="../refs.html#id93" title="D. R. Rehn, Z. Rinkevicius, M. Herbst, M. Li, X. Scheurer, M. Brand, A. L. Dempwolff, I. E. Brumboiu, T. Fransson, A. Dreuw, and P. Norman. Gator: a Python-driven program for spectroscopy simulations using correlated wave functions. WIREs Comput. Mol. Sci., 2021. URL: https://doi.org/10.1002/wcms.1528.">RRH+21</a>]</span>.</p>
<p>These issues have been observed for, <em>e.g.</em>, <span class="math notranslate nohighlight">\(L_{2,3}\)</span>-edge of silicon <span id="id1">[<a class="reference internal" href="../refs.html#id33" title="T. Fransson, D. Burdakova, and P. Norman. K- and L-edge X-ray absorption spectrum calculations of closed-shell carbon, silicon, germanium, and sulfur compounds using damped four-component density functional response theory. Phys. Chem. Chem. Phys., 18:13591-13603, 2016. URL: https://doi.org/10.1039/C6CP00561F.">FBN16</a>, <a class="reference internal" href="../refs.html#id58" title="M. Kadek, L. Konecny, B. Gao, M. Repisky, and K. Ruud. X-ray absorption resonances near L2,3-edges from real-time propagation of the Dirac–Kohn–Sham density matrix. Phys. Chem. Chem. Phys., 17:22566-22570, 2015. URL: https://doi.org/10.1039/C5CP03712C.">KKG+15</a>]</span>, and are usually more common at lower energies. They can be identified by studying the amplitudes and the <span class="math notranslate nohighlight">\(t^2\)</span> values for post-HF methods, and can be avoided by chosing appropriate basis sets, freezing certain virtual orbitals, or by re-introducing the CVS approximation (or some other flavour) within the CPP/RT framework. The latter approach is recommended at least for CPP-ADC, as converging the response vectors has otherwise been seen to be difficult <span id="id2">[<a class="reference internal" href="../refs.html#id95" title="D. R. Rehn, Z. Rinkevicius, M. Herbst, M. Li, X. Scheurer, M. Brand, A. L. Dempwolff, I. E. Brumboiu, T. Fransson, A. Dreuw, and P. Norman. Gator: a Python-driven program for spectroscopy simulations using correlated wave functions. WIREs Comput. Mol. Sci., 2021. URL: https://doi.org/10.1002/wcms.1528.">RRH+21</a>]</span>.</p>
</section>
</section>

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