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mhjensen committed Nov 26, 2024
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90 changes: 87 additions & 3 deletions doc/pub/week48/html/week48-bs.html
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Original file line number Diff line number Diff line change
Expand Up @@ -39,10 +39,34 @@
'sections': [('Week 48, November 25-29, 2024',
2,
None,
'week-48-november-25-29-2024')]}
'week-48-november-25-29-2024'),
('CCSD with twobody Hamiltonian',
2,
None,
'ccsd-with-twobody-hamiltonian'),
('Two-body normal-ordered Hamiltonian',
2,
None,
'two-body-normal-ordered-hamiltonian')]}
end of tocinfo -->

<body>



<script type="text/x-mathjax-config">
MathJax.Hub.Config({
TeX: {
equationNumbers: { autoNumber: "AMS" },
extensions: ["AMSmath.js", "AMSsymbols.js", "autobold.js", "color.js"]
}
});
</script>
<script type="text/javascript" async
src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
</script>


<!-- Bootstrap navigation bar -->
<div class="navbar navbar-default navbar-fixed-top">
<div class="navbar-header">
Expand All @@ -59,6 +83,8 @@
<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
<ul class="dropdown-menu">
<!-- navigation toc: --> <li><a href="#week-48-november-25-29-2024" style="font-size: 80%;">Week 48, November 25-29, 2024</a></li>
<!-- navigation toc: --> <li><a href="#ccsd-with-twobody-hamiltonian" style="font-size: 80%;">CCSD with twobody Hamiltonian</a></li>
<!-- navigation toc: --> <li><a href="#two-body-normal-ordered-hamiltonian" style="font-size: 80%;">Two-body normal-ordered Hamiltonian</a></li>

</ul>
</li>
Expand All @@ -84,7 +110,7 @@ <h1>Week 48: Coupled cluster theory and summary of course </h1>
</center>
<br>
<center>
<h4>Week 48, November 25-29</h4>
<h4>November 25-29, 2024</h4>
</center> <!-- date -->
<br>

Expand All @@ -100,13 +126,71 @@ <h2 id="week-48-november-25-29-2024" class="anchor">Week 48, November 25-29, 202
<li> How to write your own coupled-cluster theory code, pairing model example</li>
<li> Coupled cluster theory, singles and doubles excitations, diagrammatic expansion</li>
</ol>
<li> Firday:
<li> Friday:
<ol type="a"></li>
<li> Coupled cluster theory for singles and doubles excitations using a diagrammatic derivation</li>
<li> Summary of course and discussion of final oral exam</li>
</ol>
<li> Lecture material: Lecture notes and Shavitt and Bartlett chapters 9 and 10. See also slides at <a href="https://github.com/ManyBodyPhysics/FYS4480/blob/master/doc/pub/week48/pdf/cc.pdf" target="_self"><tt>https://github.com/ManyBodyPhysics/FYS4480/blob/master/doc/pub/week48/pdf/cc.pdf</tt></a></li>
</ol>
<!-- !split -->
<h2 id="ccsd-with-twobody-hamiltonian" class="anchor">CCSD with twobody Hamiltonian </h2>

<p>Truncating the cluster operator \( \hat{T} \) at the \( n=2 \) level, defines
CCSD approximation to the Coupled Cluster wavefunction. The
coupled cluster wavefunction is now given by
</p>

$$
\begin{equation*}
\vert \Psi_{CC}\rangle = e^{\hat{T}_1 + \hat{T}_2} \vert \Phi_0\rangle,
\end{equation*}
$$

<p>where </p>
$$
\begin{align*}
\hat{T}_1 &=
\sum_{ia}
t_{i}^{a} a_{a}^\dagger a_i \\
\hat{T}_2 &= \frac{1}{4}
\sum_{ijab}
t_{ij}^{ab} a_{a}^\dagger a_{b}^\dagger a_{j} a_{i}.
\end{align*}
$$


<!-- !split -->
<h2 id="two-body-normal-ordered-hamiltonian" class="anchor">Two-body normal-ordered Hamiltonian </h2>

$$
\begin{align*}
\hat{H} &= \sum_{pq} f_q^p\left\{ a_p^\dagger a_q \right\} +
\frac{1}{4} \sum_{pqrs} \langle pq \vert \hat{v} \vert rs \rangle \left\{ a_p^\dagger a_q^\dagger a_s a_r \right\} \\
& \quad + \mathrm{E}_0 \\
&= \hat{F}_N + \hat{V}_N + \mathrm{E}_0
= \hat{H}_N + \mathrm{E}_0,
\end{align*}
$$

<p>where</p>
$$
\begin{align*}
f_q^p &= \langle p\vert \hat{t} \vert q\rangle + \sum_i \langle pi\vert \hat{v} \vert qi\rangle \\
\langle pq \vert \vert rs \rangle &= \langle pq \vert \hat{v} \vert rs \rangle \\
\mathrm{E}_0 &= \sum_i \langle i\vert \hat{t} \vert i\rangle + \frac{1}{2} \sum_{ij} \langle ij\vert \hat{v} \vert ij\rangle.
\end{align*}
$$


<!-- %\input{src/ccsd_summary02} -->
<!-- %\input{src/ccsd_summary03} -->

<!-- \include{src/ccsd_H2diagrams} -->
<!-- \include{src/ccsd_barh_expansion} -->
<!-- \include{src/ccsd_factoring} -->
<!-- \include{src/ccsd_algorithm} -->

<!-- ------------------- end of main content --------------- -->
</div> <!-- end container -->
<!-- include javascript, jQuery *first* -->
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87 changes: 85 additions & 2 deletions doc/pub/week48/html/week48-reveal.html
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Expand Up @@ -149,6 +149,22 @@




<script type="text/x-mathjax-config">
MathJax.Hub.Config({
TeX: {
equationNumbers: { autoNumber: "none" },
extensions: ["AMSmath.js", "AMSsymbols.js", "autobold.js", "color.js"]
}
});
</script>
<script type="text/javascript" async
src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
</script>




<section>
<!-- ------------------- main content ---------------------- -->
<center>
Expand All @@ -165,7 +181,7 @@ <h1 style="text-align: center;">Week 48: Coupled cluster theory and summary of c
</center>
<br>
<center>
<h4>Week 48, November 25-29</h4>
<h4>November 25-29, 2024</h4>
</center> <!-- date -->
<br>

Expand All @@ -185,7 +201,7 @@ <h2 id="week-48-november-25-29-2024">Week 48, November 25-29, 2024 </h2>
<p><li> Coupled cluster theory, singles and doubles excitations, diagrammatic expansion</li>
</ol>
<p>
<p><li> Firday:
<p><li> Friday:
<ol type="a"></li>
<p><li> Coupled cluster theory for singles and doubles excitations using a diagrammatic derivation</li>
<p><li> Summary of course and discussion of final oral exam</li>
Expand All @@ -195,6 +211,73 @@ <h2 id="week-48-november-25-29-2024">Week 48, November 25-29, 2024 </h2>
</ol>
</section>

<section>
<h2 id="ccsd-with-twobody-hamiltonian">CCSD with twobody Hamiltonian </h2>

<p>Truncating the cluster operator \( \hat{T} \) at the \( n=2 \) level, defines
CCSD approximation to the Coupled Cluster wavefunction. The
coupled cluster wavefunction is now given by
</p>

<p>&nbsp;<br>
$$
\begin{equation*}
\vert \Psi_{CC}\rangle = e^{\hat{T}_1 + \hat{T}_2} \vert \Phi_0\rangle,
\end{equation*}
$$
<p>&nbsp;<br>

<p>where </p>
<p>&nbsp;<br>
$$
\begin{align*}
\hat{T}_1 &=
\sum_{ia}
t_{i}^{a} a_{a}^\dagger a_i \\
\hat{T}_2 &= \frac{1}{4}
\sum_{ijab}
t_{ij}^{ab} a_{a}^\dagger a_{b}^\dagger a_{j} a_{i}.
\end{align*}
$$
<p>&nbsp;<br>
</section>

<section>
<h2 id="two-body-normal-ordered-hamiltonian">Two-body normal-ordered Hamiltonian </h2>

<p>&nbsp;<br>
$$
\begin{align*}
\hat{H} &= \sum_{pq} f_q^p\left\{ a_p^\dagger a_q \right\} +
\frac{1}{4} \sum_{pqrs} \langle pq \vert \hat{v} \vert rs \rangle \left\{ a_p^\dagger a_q^\dagger a_s a_r \right\} \\
& \quad + \mathrm{E}_0 \\
&= \hat{F}_N + \hat{V}_N + \mathrm{E}_0
= \hat{H}_N + \mathrm{E}_0,
\end{align*}
$$
<p>&nbsp;<br>

<p>where</p>
<p>&nbsp;<br>
$$
\begin{align*}
f_q^p &= \langle p\vert \hat{t} \vert q\rangle + \sum_i \langle pi\vert \hat{v} \vert qi\rangle \\
\langle pq \vert \vert rs \rangle &= \langle pq \vert \hat{v} \vert rs \rangle \\
\mathrm{E}_0 &= \sum_i \langle i\vert \hat{t} \vert i\rangle + \frac{1}{2} \sum_{ij} \langle ij\vert \hat{v} \vert ij\rangle.
\end{align*}
$$
<p>&nbsp;<br>


<!-- %\input{src/ccsd_summary02} -->
<!-- %\input{src/ccsd_summary03} -->

<!-- \include{src/ccsd_H2diagrams} -->
<!-- \include{src/ccsd_barh_expansion} -->
<!-- \include{src/ccsd_factoring} -->
<!-- \include{src/ccsd_algorithm} -->
</section>



</div> <!-- class="slides" -->
Expand Down
88 changes: 85 additions & 3 deletions doc/pub/week48/html/week48-solarized.html
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Original file line number Diff line number Diff line change
Expand Up @@ -40,10 +40,34 @@
'sections': [('Week 48, November 25-29, 2024',
2,
None,
'week-48-november-25-29-2024')]}
'week-48-november-25-29-2024'),
('CCSD with twobody Hamiltonian',
2,
None,
'ccsd-with-twobody-hamiltonian'),
('Two-body normal-ordered Hamiltonian',
2,
None,
'two-body-normal-ordered-hamiltonian')]}
end of tocinfo -->

<body>



<script type="text/x-mathjax-config">
MathJax.Hub.Config({
TeX: {
equationNumbers: { autoNumber: "AMS" },
extensions: ["AMSmath.js", "AMSsymbols.js", "autobold.js", "color.js"]
}
});
</script>
<script type="text/javascript" async
src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
</script>


<!-- ------------------- main content ---------------------- -->
<center>
<h1>Week 48: Coupled cluster theory and summary of course </h1>
Expand All @@ -59,7 +83,7 @@ <h1>Week 48: Coupled cluster theory and summary of course </h1>
</center>
<br>
<center>
<h4>Week 48, November 25-29</h4>
<h4>November 25-29, 2024</h4>
</center> <!-- date -->
<br>

Expand All @@ -72,13 +96,71 @@ <h2 id="week-48-november-25-29-2024">Week 48, November 25-29, 2024 </h2>
<li> How to write your own coupled-cluster theory code, pairing model example</li>
<li> Coupled cluster theory, singles and doubles excitations, diagrammatic expansion</li>
</ol>
<li> Firday:
<li> Friday:
<ol type="a"></li>
<li> Coupled cluster theory for singles and doubles excitations using a diagrammatic derivation</li>
<li> Summary of course and discussion of final oral exam</li>
</ol>
<li> Lecture material: Lecture notes and Shavitt and Bartlett chapters 9 and 10. See also slides at <a href="https://github.com/ManyBodyPhysics/FYS4480/blob/master/doc/pub/week48/pdf/cc.pdf" target="_blank"><tt>https://github.com/ManyBodyPhysics/FYS4480/blob/master/doc/pub/week48/pdf/cc.pdf</tt></a></li>
</ol>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="ccsd-with-twobody-hamiltonian">CCSD with twobody Hamiltonian </h2>

<p>Truncating the cluster operator \( \hat{T} \) at the \( n=2 \) level, defines
CCSD approximation to the Coupled Cluster wavefunction. The
coupled cluster wavefunction is now given by
</p>

$$
\begin{equation*}
\vert \Psi_{CC}\rangle = e^{\hat{T}_1 + \hat{T}_2} \vert \Phi_0\rangle,
\end{equation*}
$$

<p>where </p>
$$
\begin{align*}
\hat{T}_1 &=
\sum_{ia}
t_{i}^{a} a_{a}^\dagger a_i \\
\hat{T}_2 &= \frac{1}{4}
\sum_{ijab}
t_{ij}^{ab} a_{a}^\dagger a_{b}^\dagger a_{j} a_{i}.
\end{align*}
$$


<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="two-body-normal-ordered-hamiltonian">Two-body normal-ordered Hamiltonian </h2>

$$
\begin{align*}
\hat{H} &= \sum_{pq} f_q^p\left\{ a_p^\dagger a_q \right\} +
\frac{1}{4} \sum_{pqrs} \langle pq \vert \hat{v} \vert rs \rangle \left\{ a_p^\dagger a_q^\dagger a_s a_r \right\} \\
& \quad + \mathrm{E}_0 \\
&= \hat{F}_N + \hat{V}_N + \mathrm{E}_0
= \hat{H}_N + \mathrm{E}_0,
\end{align*}
$$

<p>where</p>
$$
\begin{align*}
f_q^p &= \langle p\vert \hat{t} \vert q\rangle + \sum_i \langle pi\vert \hat{v} \vert qi\rangle \\
\langle pq \vert \vert rs \rangle &= \langle pq \vert \hat{v} \vert rs \rangle \\
\mathrm{E}_0 &= \sum_i \langle i\vert \hat{t} \vert i\rangle + \frac{1}{2} \sum_{ij} \langle ij\vert \hat{v} \vert ij\rangle.
\end{align*}
$$


<!-- %\input{src/ccsd_summary02} -->
<!-- %\input{src/ccsd_summary03} -->

<!-- \include{src/ccsd_H2diagrams} -->
<!-- \include{src/ccsd_barh_expansion} -->
<!-- \include{src/ccsd_factoring} -->
<!-- \include{src/ccsd_algorithm} -->

<!-- ------------------- end of main content --------------- -->
<center style="font-size:80%">
<!-- copyright --> &copy; 1999-2024, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
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