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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"> <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head> <head>
<!-- 2021-02-03 Wed 16:26 --> <!-- 2021-02-03 Wed 16:59 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" /> <meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Quantum Monte Carlo</title> <title>Quantum Monte Carlo</title>
@ -329,76 +329,75 @@ for the JavaScript code in this tag.
<h2>Table of Contents</h2> <h2>Table of Contents</h2>
<div id="text-table-of-contents"> <div id="text-table-of-contents">
<ul> <ul>
<li><a href="#org813b90b">1. Introduction</a> <li><a href="#org3c1efae">1. Introduction</a>
<ul> <ul>
<li><a href="#org6dfa1bc">1.1. Energy and local energy</a></li> <li><a href="#org85a0a0b">1.1. Energy and local energy</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgf59e340">2. Numerical evaluation of the energy of the hydrogen atom</a> <li><a href="#org6f77d3f">2. Numerical evaluation of the energy of the hydrogen atom</a>
<ul> <ul>
<li><a href="#orgd9bbb38">2.1. Local energy</a> <li><a href="#org9e28ed2">2.1. Local energy</a>
<ul> <ul>
<li><a href="#org19971eb">2.1.1. Exercise 1</a></li> <li><a href="#orgf6097b0">2.1.1. Exercise 1</a></li>
<li><a href="#orgc86d08a">2.1.2. Exercise 2</a></li> <li><a href="#org23dae5b">2.1.2. Exercise 2</a></li>
<li><a href="#orgf2b1ece">2.1.3. Exercise 3</a></li> <li><a href="#orgfa0dd30">2.1.3. Exercise 3</a></li>
<li><a href="#org30c5c6a">2.1.4. Exercise 4</a></li> <li><a href="#orgf9422b3">2.1.4. Exercise 4</a></li>
<li><a href="#org5ba9684">2.1.5. Exercise 5</a></li> <li><a href="#org9a98a25">2.1.5. Exercise 5</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org78ac743">2.2. Plot of the local energy along the \(x\) axis</a> <li><a href="#org4dc200a">2.2. Plot of the local energy along the \(x\) axis</a>
<ul> <ul>
<li><a href="#org674310c">2.2.1. Exercise</a></li> <li><a href="#org57af737">2.2.1. Exercise</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org79e713c">2.3. Numerical estimation of the energy</a> <li><a href="#orgf856ad9">2.3. Numerical estimation of the energy</a>
<ul> <ul>
<li><a href="#orgb32b9f2">2.3.1. Exercise</a></li> <li><a href="#org5b336d3">2.3.1. Exercise</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgcd32e90">2.4. Variance of the local energy</a> <li><a href="#orgcf8dd2d">2.4. Variance of the local energy</a>
<ul> <ul>
<li><a href="#org56c6c46">2.4.1. Exercise (optional)</a></li> <li><a href="#org1932bf3">2.4.1. Exercise (optional)</a></li>
<li><a href="#orge76103e">2.4.2. Exercise</a></li> <li><a href="#org7e92320">2.4.2. Exercise</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
</li> </li>
<li><a href="#orgd2b410e">3. Variational Monte Carlo</a> <li><a href="#org344d166">3. Variational Monte Carlo</a>
<ul> <ul>
<li><a href="#org7e2d1ab">3.1. Computation of the statistical error</a> <li><a href="#org7557f27">3.1. Computation of the statistical error</a>
<ul> <ul>
<li><a href="#org202952d">3.1.1. Exercise</a></li> <li><a href="#org2e5da03">3.1.1. Exercise</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org8009dba">3.2. Uniform sampling in the box</a> <li><a href="#org6d5f40f">3.2. Uniform sampling in the box</a>
<ul> <ul>
<li><a href="#org2827619">3.2.1. Exercise</a></li> <li><a href="#org29364d9">3.2.1. Exercise</a></li>
</ul> </ul>
</li> </li>
<li><a href="#org0de0313">3.3. Metropolis sampling with \(\Psi^2\)</a> <li><a href="#orgd8b523a">3.3. Metropolis sampling with \(\Psi^2\)</a>
<ul> <ul>
<li><a href="#orgdf21cbc">3.3.1. Optimal step size</a></li> <li><a href="#org3f8f8a0">3.3.1. Optimal step size</a></li>
<li><a href="#org7e22285">3.3.2. Exercise</a></li> <li><a href="#org0bb36e4">3.3.2. Exercise</a></li>
</ul> </ul>
</li> </li>
<li><a href="#orgcfba2cf">3.4. Generalized Metropolis algorithm</a> <li><a href="#orgd2b8682">3.4. Generalized Metropolis algorithm</a>
<ul> <ul>
<li><a href="#org32d2aaa">3.4.1. Gaussian random number generator</a></li> <li><a href="#orgd0861e4">3.4.1. Gaussian random number generator</a></li>
<li><a href="#org0f3c095">3.4.2. Exercise 1</a></li> <li><a href="#org0cf72a5">3.4.2. Exercise 1</a></li>
<li><a href="#org2493e9d">3.4.3. Exercise 2</a></li> <li><a href="#orgb298efc">3.4.3. Exercise 2</a></li>
</ul> </ul>
</li> </li>
</ul> </ul>
</li> </li>
<li><a href="#org15f595a">4. Project</a></li> <li><a href="#orgd5eecd6">4. Project</a></li>
<li><a href="#orge21458a">5. <span class="todo TODO">TODO</span> Last things to do</a></li> <li><a href="#orgdf684f7">5. Acknowledgments</a></li>
<li><a href="#org56dd2e2">6. Schedule</a></li>
</ul> </ul>
</div> </div>
</div> </div>
<div id="outline-container-org813b90b" class="outline-2"> <div id="outline-container-org3c1efae" class="outline-2">
<h2 id="org813b90b"><span class="section-number-2">1</span> Introduction</h2> <h2 id="org3c1efae"><span class="section-number-2">1</span> Introduction</h2>
<div class="outline-text-2" id="text-1"> <div class="outline-text-2" id="text-1">
<p> <p>
This website contains the QMC tutorial of the 2021 LTTC winter school This website contains the QMC tutorial of the 2021 LTTC winter school
@ -438,8 +437,8 @@ coordinates, etc).
</p> </p>
</div> </div>
<div id="outline-container-org6dfa1bc" class="outline-3"> <div id="outline-container-org85a0a0b" class="outline-3">
<h3 id="org6dfa1bc"><span class="section-number-3">1.1</span> Energy and local energy</h3> <h3 id="org85a0a0b"><span class="section-number-3">1.1</span> Energy and local energy</h3>
<div class="outline-text-3" id="text-1-1"> <div class="outline-text-3" id="text-1-1">
<p> <p>
For a given system with Hamiltonian \(\hat{H}\) and wave function \(\Psi\), we define the local energy as For a given system with Hamiltonian \(\hat{H}\) and wave function \(\Psi\), we define the local energy as
@ -522,8 +521,8 @@ energy computed over these configurations:
</div> </div>
</div> </div>
<div id="outline-container-orgf59e340" class="outline-2"> <div id="outline-container-org6f77d3f" class="outline-2">
<h2 id="orgf59e340"><span class="section-number-2">2</span> Numerical evaluation of the energy of the hydrogen atom</h2> <h2 id="org6f77d3f"><span class="section-number-2">2</span> Numerical evaluation of the energy of the hydrogen atom</h2>
<div class="outline-text-2" id="text-2"> <div class="outline-text-2" id="text-2">
<p> <p>
In this section, we consider the hydrogen atom with the following In this section, we consider the hydrogen atom with the following
@ -552,8 +551,8 @@ To do that, we will compute the local energy and check whether it is constant.
</p> </p>
</div> </div>
<div id="outline-container-orgd9bbb38" class="outline-3"> <div id="outline-container-org9e28ed2" class="outline-3">
<h3 id="orgd9bbb38"><span class="section-number-3">2.1</span> Local energy</h3> <h3 id="org9e28ed2"><span class="section-number-3">2.1</span> Local energy</h3>
<div class="outline-text-3" id="text-2-1"> <div class="outline-text-3" id="text-2-1">
<p> <p>
You will now program all quantities needed to compute the local energy of the H atom for the given wave function. You will now program all quantities needed to compute the local energy of the H atom for the given wave function.
@ -580,8 +579,8 @@ to catch the error.
</div> </div>
</div> </div>
<div id="outline-container-org19971eb" class="outline-4"> <div id="outline-container-orgf6097b0" class="outline-4">
<h4 id="org19971eb"><span class="section-number-4">2.1.1</span> Exercise 1</h4> <h4 id="orgf6097b0"><span class="section-number-4">2.1.1</span> Exercise 1</h4>
<div class="outline-text-4" id="text-2-1-1"> <div class="outline-text-4" id="text-2-1-1">
<div class="exercise"> <div class="exercise">
<p> <p>
@ -627,8 +626,8 @@ and returns the potential.
</div> </div>
</div> </div>
<div id="outline-container-orgc86d08a" class="outline-4"> <div id="outline-container-org23dae5b" class="outline-4">
<h4 id="orgc86d08a"><span class="section-number-4">2.1.2</span> Exercise 2</h4> <h4 id="org23dae5b"><span class="section-number-4">2.1.2</span> Exercise 2</h4>
<div class="outline-text-4" id="text-2-1-2"> <div class="outline-text-4" id="text-2-1-2">
<div class="exercise"> <div class="exercise">
<p> <p>
@ -664,8 +663,8 @@ input arguments, and returns a scalar.
</div> </div>
</div> </div>
<div id="outline-container-orgf2b1ece" class="outline-4"> <div id="outline-container-orgfa0dd30" class="outline-4">
<h4 id="orgf2b1ece"><span class="section-number-4">2.1.3</span> Exercise 3</h4> <h4 id="orgfa0dd30"><span class="section-number-4">2.1.3</span> Exercise 3</h4>
<div class="outline-text-4" id="text-2-1-3"> <div class="outline-text-4" id="text-2-1-3">
<div class="exercise"> <div class="exercise">
<p> <p>
@ -747,8 +746,8 @@ Therefore, the local kinetic energy is
</div> </div>
</div> </div>
<div id="outline-container-org30c5c6a" class="outline-4"> <div id="outline-container-orgf9422b3" class="outline-4">
<h4 id="org30c5c6a"><span class="section-number-4">2.1.4</span> Exercise 4</h4> <h4 id="orgf9422b3"><span class="section-number-4">2.1.4</span> Exercise 4</h4>
<div class="outline-text-4" id="text-2-1-4"> <div class="outline-text-4" id="text-2-1-4">
<div class="exercise"> <div class="exercise">
<p> <p>
@ -808,8 +807,8 @@ are calling is yours.
</div> </div>
</div> </div>
<div id="outline-container-org5ba9684" class="outline-4"> <div id="outline-container-org9a98a25" class="outline-4">
<h4 id="org5ba9684"><span class="section-number-4">2.1.5</span> Exercise 5</h4> <h4 id="org9a98a25"><span class="section-number-4">2.1.5</span> Exercise 5</h4>
<div class="outline-text-4" id="text-2-1-5"> <div class="outline-text-4" id="text-2-1-5">
<div class="exercise"> <div class="exercise">
<p> <p>
@ -821,8 +820,8 @@ Find the theoretical value of \(a\) for which \(\Psi\) is an eigenfunction of \(
</div> </div>
</div> </div>
<div id="outline-container-org78ac743" class="outline-3"> <div id="outline-container-org4dc200a" class="outline-3">
<h3 id="org78ac743"><span class="section-number-3">2.2</span> Plot of the local energy along the \(x\) axis</h3> <h3 id="org4dc200a"><span class="section-number-3">2.2</span> Plot of the local energy along the \(x\) axis</h3>
<div class="outline-text-3" id="text-2-2"> <div class="outline-text-3" id="text-2-2">
<p> <p>
The program you will write in this section will be written in The program you will write in this section will be written in
@ -853,8 +852,8 @@ In Fortran, you will need to compile all the source files together:
</div> </div>
</div> </div>
<div id="outline-container-org674310c" class="outline-4"> <div id="outline-container-org57af737" class="outline-4">
<h4 id="org674310c"><span class="section-number-4">2.2.1</span> Exercise</h4> <h4 id="org57af737"><span class="section-number-4">2.2.1</span> Exercise</h4>
<div class="outline-text-4" id="text-2-2-1"> <div class="outline-text-4" id="text-2-2-1">
<div class="exercise"> <div class="exercise">
<p> <p>
@ -950,8 +949,8 @@ plot './data' index 0 using 1:2 with lines title 'a=0.1', \
</div> </div>
</div> </div>
<div id="outline-container-org79e713c" class="outline-3"> <div id="outline-container-orgf856ad9" class="outline-3">
<h3 id="org79e713c"><span class="section-number-3">2.3</span> Numerical estimation of the energy</h3> <h3 id="orgf856ad9"><span class="section-number-3">2.3</span> Numerical estimation of the energy</h3>
<div class="outline-text-3" id="text-2-3"> <div class="outline-text-3" id="text-2-3">
<p> <p>
If the space is discretized in small volume elements \(\mathbf{r}_i\) If the space is discretized in small volume elements \(\mathbf{r}_i\)
@ -981,8 +980,8 @@ The energy is biased because:
</div> </div>
<div id="outline-container-orgb32b9f2" class="outline-4"> <div id="outline-container-org5b336d3" class="outline-4">
<h4 id="orgb32b9f2"><span class="section-number-4">2.3.1</span> Exercise</h4> <h4 id="org5b336d3"><span class="section-number-4">2.3.1</span> Exercise</h4>
<div class="outline-text-4" id="text-2-3-1"> <div class="outline-text-4" id="text-2-3-1">
<div class="exercise"> <div class="exercise">
<p> <p>
@ -1055,8 +1054,8 @@ To compile the Fortran and run it:
</div> </div>
</div> </div>
<div id="outline-container-orgcd32e90" class="outline-3"> <div id="outline-container-orgcf8dd2d" class="outline-3">
<h3 id="orgcd32e90"><span class="section-number-3">2.4</span> Variance of the local energy</h3> <h3 id="orgcf8dd2d"><span class="section-number-3">2.4</span> Variance of the local energy</h3>
<div class="outline-text-3" id="text-2-4"> <div class="outline-text-3" id="text-2-4">
<p> <p>
The variance of the local energy is a functional of \(\Psi\) The variance of the local energy is a functional of \(\Psi\)
@ -1083,8 +1082,8 @@ energy can be used as a measure of the quality of a wave function.
</p> </p>
</div> </div>
<div id="outline-container-org56c6c46" class="outline-4"> <div id="outline-container-org1932bf3" class="outline-4">
<h4 id="org56c6c46"><span class="section-number-4">2.4.1</span> Exercise (optional)</h4> <h4 id="org1932bf3"><span class="section-number-4">2.4.1</span> Exercise (optional)</h4>
<div class="outline-text-4" id="text-2-4-1"> <div class="outline-text-4" id="text-2-4-1">
<div class="exercise"> <div class="exercise">
<p> <p>
@ -1095,8 +1094,8 @@ Prove that :
</div> </div>
</div> </div>
</div> </div>
<div id="outline-container-orge76103e" class="outline-4"> <div id="outline-container-org7e92320" class="outline-4">
<h4 id="orge76103e"><span class="section-number-4">2.4.2</span> Exercise</h4> <h4 id="org7e92320"><span class="section-number-4">2.4.2</span> Exercise</h4>
<div class="outline-text-4" id="text-2-4-2"> <div class="outline-text-4" id="text-2-4-2">
<div class="exercise"> <div class="exercise">
<p> <p>
@ -1175,8 +1174,8 @@ To compile and run:
</div> </div>
</div> </div>
<div id="outline-container-orgd2b410e" class="outline-2"> <div id="outline-container-org344d166" class="outline-2">
<h2 id="orgd2b410e"><span class="section-number-2">3</span> Variational Monte Carlo</h2> <h2 id="org344d166"><span class="section-number-2">3</span> Variational Monte Carlo</h2>
<div class="outline-text-2" id="text-3"> <div class="outline-text-2" id="text-3">
<p> <p>
Numerical integration with deterministic methods is very efficient Numerical integration with deterministic methods is very efficient
@ -1192,8 +1191,8 @@ interval.
</p> </p>
</div> </div>
<div id="outline-container-org7e2d1ab" class="outline-3"> <div id="outline-container-org7557f27" class="outline-3">
<h3 id="org7e2d1ab"><span class="section-number-3">3.1</span> Computation of the statistical error</h3> <h3 id="org7557f27"><span class="section-number-3">3.1</span> Computation of the statistical error</h3>
<div class="outline-text-3" id="text-3-1"> <div class="outline-text-3" id="text-3-1">
<p> <p>
To compute the statistical error, you need to perform \(M\) To compute the statistical error, you need to perform \(M\)
@ -1233,8 +1232,8 @@ And the confidence interval is given by
</p> </p>
</div> </div>
<div id="outline-container-org202952d" class="outline-4"> <div id="outline-container-org2e5da03" class="outline-4">
<h4 id="org202952d"><span class="section-number-4">3.1.1</span> Exercise</h4> <h4 id="org2e5da03"><span class="section-number-4">3.1.1</span> Exercise</h4>
<div class="outline-text-4" id="text-3-1-1"> <div class="outline-text-4" id="text-3-1-1">
<div class="exercise"> <div class="exercise">
<p> <p>
@ -1276,8 +1275,8 @@ input array.
</div> </div>
</div> </div>
<div id="outline-container-org8009dba" class="outline-3"> <div id="outline-container-org6d5f40f" class="outline-3">
<h3 id="org8009dba"><span class="section-number-3">3.2</span> Uniform sampling in the box</h3> <h3 id="org6d5f40f"><span class="section-number-3">3.2</span> Uniform sampling in the box</h3>
<div class="outline-text-3" id="text-3-2"> <div class="outline-text-3" id="text-3-2">
<p> <p>
We will now perform our first Monte Carlo calculation to compute the We will now perform our first Monte Carlo calculation to compute the
@ -1338,8 +1337,8 @@ compute the statistical error.
</p> </p>
</div> </div>
<div id="outline-container-org2827619" class="outline-4"> <div id="outline-container-org29364d9" class="outline-4">
<h4 id="org2827619"><span class="section-number-4">3.2.1</span> Exercise</h4> <h4 id="org29364d9"><span class="section-number-4">3.2.1</span> Exercise</h4>
<div class="outline-text-4" id="text-3-2-1"> <div class="outline-text-4" id="text-3-2-1">
<div class="exercise"> <div class="exercise">
<p> <p>
@ -1443,8 +1442,8 @@ well as the index of the current step.
</div> </div>
</div> </div>
<div id="outline-container-org0de0313" class="outline-3"> <div id="outline-container-orgd8b523a" class="outline-3">
<h3 id="org0de0313"><span class="section-number-3">3.3</span> Metropolis sampling with \(\Psi^2\)</h3> <h3 id="orgd8b523a"><span class="section-number-3">3.3</span> Metropolis sampling with \(\Psi^2\)</h3>
<div class="outline-text-3" id="text-3-3"> <div class="outline-text-3" id="text-3-3">
<p> <p>
We will now use the square of the wave function to sample random We will now use the square of the wave function to sample random
@ -1563,8 +1562,8 @@ All samples should be kept, from both accepted <i>and</i> rejected moves.
</div> </div>
<div id="outline-container-orgdf21cbc" class="outline-4"> <div id="outline-container-org3f8f8a0" class="outline-4">
<h4 id="orgdf21cbc"><span class="section-number-4">3.3.1</span> Optimal step size</h4> <h4 id="org3f8f8a0"><span class="section-number-4">3.3.1</span> Optimal step size</h4>
<div class="outline-text-4" id="text-3-3-1"> <div class="outline-text-4" id="text-3-3-1">
<p> <p>
If the box is infinitely small, the ratio will be very close If the box is infinitely small, the ratio will be very close
@ -1599,8 +1598,8 @@ the same variable later on to store a time step.
</div> </div>
<div id="outline-container-org7e22285" class="outline-4"> <div id="outline-container-org0bb36e4" class="outline-4">
<h4 id="org7e22285"><span class="section-number-4">3.3.2</span> Exercise</h4> <h4 id="org0bb36e4"><span class="section-number-4">3.3.2</span> Exercise</h4>
<div class="outline-text-4" id="text-3-3-2"> <div class="outline-text-4" id="text-3-3-2">
<div class="exercise"> <div class="exercise">
<p> <p>
@ -1711,8 +1710,8 @@ Can you observe a reduction in the statistical error?
</div> </div>
</div> </div>
<div id="outline-container-orgcfba2cf" class="outline-3"> <div id="outline-container-orgd2b8682" class="outline-3">
<h3 id="orgcfba2cf"><span class="section-number-3">3.4</span> Generalized Metropolis algorithm</h3> <h3 id="orgd2b8682"><span class="section-number-3">3.4</span> Generalized Metropolis algorithm</h3>
<div class="outline-text-3" id="text-3-4"> <div class="outline-text-3" id="text-3-4">
<p> <p>
One can use more efficient numerical schemes to move the electrons by choosing a smarter expression for the transition probability. One can use more efficient numerical schemes to move the electrons by choosing a smarter expression for the transition probability.
@ -1833,8 +1832,8 @@ The algorithm of the previous exercise is only slighlty modified as:
</ol> </ol>
</div> </div>
<div id="outline-container-org32d2aaa" class="outline-4"> <div id="outline-container-orgd0861e4" class="outline-4">
<h4 id="org32d2aaa"><span class="section-number-4">3.4.1</span> Gaussian random number generator</h4> <h4 id="orgd0861e4"><span class="section-number-4">3.4.1</span> Gaussian random number generator</h4>
<div class="outline-text-4" id="text-3-4-1"> <div class="outline-text-4" id="text-3-4-1">
<p> <p>
To obtain Gaussian-distributed random numbers, you can apply the To obtain Gaussian-distributed random numbers, you can apply the
@ -1898,8 +1897,8 @@ In Python, you can use the <a href="https://numpy.org/doc/stable/reference/rando
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<div id="outline-container-org0f3c095" class="outline-4"> <div id="outline-container-org0cf72a5" class="outline-4">
<h4 id="org0f3c095"><span class="section-number-4">3.4.2</span> Exercise 1</h4> <h4 id="org0cf72a5"><span class="section-number-4">3.4.2</span> Exercise 1</h4>
<div class="outline-text-4" id="text-3-4-2"> <div class="outline-text-4" id="text-3-4-2">
<div class="exercise"> <div class="exercise">
<p> <p>
@ -1942,8 +1941,8 @@ Write a function to compute the drift vector \(\frac{\nabla \Psi(\mathbf{r})}{\P
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<div id="outline-container-org2493e9d" class="outline-4"> <div id="outline-container-orgb298efc" class="outline-4">
<h4 id="org2493e9d"><span class="section-number-4">3.4.3</span> Exercise 2</h4> <h4 id="orgb298efc"><span class="section-number-4">3.4.3</span> Exercise 2</h4>
<div class="outline-text-4" id="text-3-4-3"> <div class="outline-text-4" id="text-3-4-3">
<div class="exercise"> <div class="exercise">
<p> <p>
@ -2042,8 +2041,8 @@ Modify the previous program to introduce the drift-diffusion scheme.
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<div id="outline-container-org15f595a" class="outline-2"> <div id="outline-container-orgd5eecd6" class="outline-2">
<h2 id="org15f595a"><span class="section-number-2">4</span> Project</h2> <h2 id="orgd5eecd6"><span class="section-number-2">4</span> Project</h2>
<div class="outline-text-2" id="text-4"> <div class="outline-text-2" id="text-4">
<p> <p>
Change your PDMC code for one of the following: Change your PDMC code for one of the following:
@ -2060,88 +2059,28 @@ And compute the ground state energy.
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<div id="outline-container-orge21458a" class="outline-2"> <div id="outline-container-orgdf684f7" class="outline-2">
<h2 id="orge21458a"><span class="section-number-2">5</span> <span class="todo TODO">TODO</span> Last things to do&#xa0;&#xa0;&#xa0;<span class="tag"><span class="noexport">noexport</span></span></h2> <h2 id="orgdf684f7"><span class="section-number-2">5</span> Acknowledgments</h2>
<div class="outline-text-2" id="text-5"> <div class="outline-text-2" id="text-5">
<ul class="org-ul">
<li class="off"><code>[&#xa0;]</code> Prepare 4 questions for the exam: multiple-choice questions <div class="figure">
with 4 possible answers. Questions should be independent because <p><img src="https://trex-coe.eu/sites/default/files/inline-images/euflag.jpg" alt="euflag.jpg" />
they will be asked in a random order.</li> </p>
</ul>
</div>
</div> </div>
<div id="outline-container-org56dd2e2" class="outline-2"> <p>
<h2 id="org56dd2e2"><span class="section-number-2">6</span> Schedule</h2> <a href="https://trex-coe.eu">TREX</a> : Targeting Real Chemical Accuracy at the Exascale project
<div class="outline-text-2" id="text-6"> has received funding from the European Union’s Horizon 2020 - Research and
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides"> Innovation program - under grant agreement no. 952165. The content of this
document does not represent the opinion of the European Union, and the European
Union is not responsible for any use that might be made of such content.
<colgroup> </p>
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<thead>
<tr>
<th scope="col" class="org-left"><span class="timestamp-wrapper"><span class="timestamp">&lt;2021-02-04 Thu 09:00&gt;&#x2013;&lt;2021-02-04 Thu 10:30&gt;</span></span></th>
<th scope="col" class="org-right">Lecture</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left"><span class="timestamp-wrapper"><span class="timestamp">&lt;2021-02-04 Thu 10:45&gt;&#x2013;&lt;2021-02-04 Thu 11:10&gt;</span></span></td>
<td class="org-right">2.1</td>
</tr>
<tr>
<td class="org-left"><span class="timestamp-wrapper"><span class="timestamp">&lt;2021-02-04 Thu 11:10&gt;&#x2013;&lt;2021-02-04 Thu 11:30&gt;</span></span></td>
<td class="org-right">2.2</td>
</tr>
<tr>
<td class="org-left"><span class="timestamp-wrapper"><span class="timestamp">&lt;2021-02-04 Thu 11:30&gt;&#x2013;&lt;2021-02-04 Thu 12:15&gt;</span></span></td>
<td class="org-right">2.3</td>
</tr>
<tr>
<td class="org-left"><span class="timestamp-wrapper"><span class="timestamp">&lt;2021-02-04 Thu 12:15&gt;&#x2013;&lt;2021-02-04 Thu 12:30&gt;</span></span></td>
<td class="org-right">2.4</td>
</tr>
</tbody>
<tbody>
<tr>
<td class="org-left"><span class="timestamp-wrapper"><span class="timestamp">&lt;2021-02-04 Thu 14:00&gt;&#x2013;&lt;2021-02-04 Thu 14:10&gt;</span></span></td>
<td class="org-right">3.1</td>
</tr>
<tr>
<td class="org-left"><span class="timestamp-wrapper"><span class="timestamp">&lt;2021-02-04 Thu 14:10&gt;&#x2013;&lt;2021-02-04 Thu 14:30&gt;</span></span></td>
<td class="org-right">3.2</td>
</tr>
<tr>
<td class="org-left"><span class="timestamp-wrapper"><span class="timestamp">&lt;2021-02-04 Thu 14:30&gt;&#x2013;&lt;2021-02-04 Thu 15:30&gt;</span></span></td>
<td class="org-right">3.3</td>
</tr>
<tr>
<td class="org-left"><span class="timestamp-wrapper"><span class="timestamp">&lt;2021-02-04 Thu 15:30&gt;&#x2013;&lt;2021-02-04 Thu 16:30&gt;</span></span></td>
<td class="org-right">3.4</td>
</tr>
<tr>
<td class="org-left"><span class="timestamp-wrapper"><span class="timestamp">&lt;2021-02-04 Thu 16:30&gt;&#x2013;&lt;2021-02-04 Thu 18:30&gt;</span></span></td>
<td class="org-right">4.5</td>
</tr>
</tbody>
</table>
</div> </div>
</div> </div>
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Anthony Scemama, Claudia Filippi</p> <p class="author">Author: Anthony Scemama, Claudia Filippi</p>
<p class="date">Created: 2021-02-03 Wed 16:26</p> <p class="date">Created: 2021-02-03 Wed 16:59</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p> <p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div> </div>
</body> </body>