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correcting typos
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@mhjensen
mhjensen committed Nov 28, 2024
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Binary file modified doc/pub/week48/pdf/cc.pdf
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2 changes: 1 addition & 1 deletion doc/src/week47/LatexSlides/cctheory.tex
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Expand Up @@ -294,7 +294,7 @@ \section{Coupled Cluster theory}
\include{src/ccsd_H2summary}
\include{src/ccsd_H2diagrams}
\include{src/ccsd_barh_expansion}
\include{src/ccsd_factoring}
\include{src/ccsd_factoring01}
\include{src/ccsd_algorithm}
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79 changes: 76 additions & 3 deletions doc/src/week47/LatexSlides/src/ccsd_H2diagrams.tex
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Expand Up @@ -7,16 +7,89 @@
\input{src/ccsd_diagramderivation01}
\input{src/ccsd_diagramequations01}
\input{src/diagram_rules01}
\input{src/ccsd_algebraicequations01}

\begin{frame}{CCSD energy equation }
\note{Filename: ccsd\_algebraicequations02.tex}
\begin{equation*}
E_{CCSD} =
f_a^i t_i^a + \frac{1}{4} \bra{ij}\ket{ab} t_{ij}^{ab} + \frac{1}{2} \bra{ij}\ket{ab} t_i^a t_j^b
\end{equation*}

Note the implicit sum over repeated indices.



\end{frame}





\input{src/ccsd_diagramderivation02}
\input{src/ccsd_diagramequations02}
\input{src/diagram_rules01}
\input{src/ccsd_algebraicequations02}

\begin{frame}{CCSD $\op{T}_1$ amplitude equation }
\note{Filename: ccsd\_algebraicequations02.tex}

\begin{align*}
0 &= f_{i}^a + f_{e}^a t_i^e - f_{i}^mt_m^a + \bra{ma}\ket{ei} t_m^e
+ f_{e}^m t_{im}^{ae} + \frac{1}{2} \bra{am}\ket{ef} t_{im}^{ef} \\
&\, - \frac{1}{2} \bra{mn}\ket{ei} t_{mn}^{ea} - f_{e}^m t_i^e t_m^a
+ \bra{am}\ket{ef} t_i^e t_m^f - \bra{mn}\ket{ei} t_m^e t_n^a \\
& \quad + \bra{mn}\ket{ef} t_m^e t_{ni}^{fa}
- \frac{1}{2} \bra{mn}\ket{ef} t_i^e t_{mn}^{af}
- \frac{1}{2} \bra{mn}\ket{ef} t_n^a t_{mi}^{ef}\\
& \quad - \bra{mn}\ket{ef} t_i^e t_m^a t_n^f
\end{align*}


\end{frame}



\input{src/ccsd_diagramderivation03}
\input{src/ccsd_diagramequations03}
\input{src/diagram_rules02}
\input{src/ccsd_algebraicequations03}

\begin{frame}{CCSD $\op{T}_2$ amplitude equation }
\note{Filename: ccsd\_algebraicequations03.tex}
\scriptsize
\begin{align*}
0 &=
\bra{ab} \ket{ij}
+ P(ij) \bra{ab}\ket{ej} t_i^e
- P(ab) \bra{am} \ket{ij} t_m^b
+ P(ab) f_{e}^b t_{ij}^{ae}
- P(ij) f_{i}^m t_{mj}^{ab} \\
& + \, \frac{1}{2} \bra{ab}\ket{ef} t_{ij}^{ef}
+ \frac{1}{2} \bra{mn}\ket{ij} t_{mn}^{ab}
+ P(ij) P(ab) \bra{mb}\ket{ej} t_{im}^{ae} \\
& + \, \frac{1}{2} P(ij) \bra{ab}\ket{ef} t_i^e t_j^f
+ \frac{1}{2} P(ab) \bra{mn}\ket{ij} t_m^a t_n^b
- P(ij) P(ab) \bra{mb}\ket{ej} t_i^e t_m^a \\
& + \, \frac{1}{4} \bra{mn}\ket{ef} t_{ij}^{ef} t_{mn}^{ab}
+ \frac{1}{2} P(ij) P(ab) \bra{mn}\ket{ef} t_{im}^{ae} t_{nj}^{fb}
- \frac{1}{2} P(ab) \bra{mn}\ket{ef} t_{ij}^{ae} t_{mn}^{bf} \\
& - \, \frac{1}{2} P(ij) \bra{mn}\ket{ef} t_{mi}^{ef} t_{nj}^{ab}
- P(ij) f_{e}^m t_i^e t_{mj}^{ab}
- P(ab) f_{e}^m t_{ij}^{ae} t_m^b \\
& + \, P(ij) P(ab) \bra{am}\ket{ef} t_i^e t_{mj}^{fb}
- \frac{1}{2} P(ab) \bra{am}\ket{ef} t_{ij}^{ef} t_m^b
+ P(ab) \bra{bm}\ket{ef} t_{ij}^{ae} t_m^f \\
& - \, P(ij) P(ab) \bra{mn} \ket{ej} t_{im}^{ae} t_n^b
+ \frac{1}{2} P(ij) \bra{mn}\ket{ej} t_i^e t_{mn}^{ab}
-P(ij) \bra{mn}\ket{ei} t_m^e t_{nj}^{ab} \\
& - \, \frac{1}{2} P(ij) P(ab) \bra{am}\ket{ef} t_i^e t_j^f t_m^b
+ \frac{1}{2} P(ij) P(ab) \bra{mn}\ket{ej} t_i^e t_m^a t_n^b \\
& + \, \frac{1}{4} P(ij) \bra{mn}\ket{ef} t_i^e t_{mn}^{ab} t_j^f
- P(ij) P(ab) \bra{mn}\ket{ef} t_i^e t_m^a t_{nj}^{fb} \\
& + \, \frac{1}{4} P(ab) \bra{mn}\ket{ef} t_m^a t_{ij}^{ef} t_n^b
- P(ij) \bra{mn}\ket{ef} t_m^e t_i^f t_{nj}^{ab}
- P(ab) \bra{mn}\ket{ef} t_{ij}^{ae} t_m^b t_n^f \\
& + \, \frac{1}{4} P(ij) P(ab) \bra{mn}\ket{ef} t_i^e t_m^a t_j^f t_n^b \\
\end{align*}

\end{frame}


8 changes: 4 additions & 4 deletions doc/src/week47/LatexSlides/src/ccsd_H2summary02.tex
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Expand Up @@ -4,16 +4,16 @@
\begin{block}{Normal ordered Hamiltonian}
\begin{align*}
\op{H} &= \sum_{pq} f_q^p\left\{ a_p^\dagger a_q \right\} +
\frac{1}{4} \sum_{pqrs} \bra{pq} \ket{rs} \left\{ a_p^\dagger a_q^\dagger a_s a_r \right\} \\
\frac{1}{4} \sum_{pqrs} \bra{pq}\op{v} \ket{rs} \left\{ a_p^\dagger a_q^\dagger a_s a_r \right\} \\
& \quad + \mathrm{E}_0 \\
&= \op{F}_N + \op{V}_N + \mathrm{E}_0
= \op{H}_N + \mathrm{E}_0
\end{align*}
where
where (often used notations, see also Shavitt and Bartlett chapters 3-4)
\begin{align*}
f_q^p &= \bra{p} \op{t} \ket{q} + \sum_i \bra{pi} \op{v} \ket{qi} \\
f_q^p &= \bra{p} \op{h}_0 \ket{q} + \sum_i \bra{pi} \op{v} \ket{qi} \\
\bra{pq} \ket{rs} &= \bra{pq} \op{v} \ket{rs} \\
\mathrm{E}_0 &= \sum_i \bra{i} \op{t} \ket{i} + \frac{1}{2} \sum_{ij} \bra{ij} \op{v} \ket{ij}
\mathrm{E}_0 &= \sum_i \bra{i} \op{h}_0 \ket{i} + \frac{1}{2} \sum_{ij} \bra{ij} \op{v} \ket{ij}
\end{align*}
\end{block}

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110 changes: 107 additions & 3 deletions doc/src/week47/LatexSlides/src/ccsd_factoring01.tex
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Expand Up @@ -6,20 +6,124 @@
\begin{block}{Diagram (2.12)}
\begin{equation*}
\parbox{40mm}{\includegraphics[scale=0.5]{graphics/ccsd_hbar_13_12}}
= \frac{1}{4} \bra{mn}\ket{ef} t_{ij}^{ef} t_{mn}^{ab}
= \frac{1}{4} \bra{mn}\op{v}\ket{ef} t_{ij}^{ef} t_{mn}^{ab}
\end{equation*}
\end{block}
\begin{block}{Diagram (2.26)}
\begin{equation*}
\parbox{40mm}{\includegraphics[scale=0.5]{graphics/ccsd_hbar_13_26}}
= \frac{1}{4} P(ij) \bra{mn}\ket{ef} t_i^e t_{mn}^{ab} t_j^f
= \frac{1}{4} P(ij) \bra{mn}\op{v}\ket{ef} t_i^e t_{mn}^{ab} t_j^f
\end{equation*}
\end{block}
\begin{block}{Diagram (2.31)}
\begin{equation*}
\parbox{40mm}{\includegraphics[scale=0.5]{graphics/ccsd_hbar_13_31}}
= \frac{1}{4} P(ij) P(ab) \bra{mn}\ket{ef} t_i^e t_m^a t_j^f t_n^b
= \frac{1}{4} P(ij) P(ab) \bra{mn}\op{v}\ket{ef} t_i^e t_m^a t_j^f t_n^b
\end{equation*}
\end{block}
\end{frame}

\begin{frame}
\frametitle{Factoring, motivation}
\note{Filename: ccsd\_factoring02.tex}

\scriptsize
\begin{block}{Diagram (2.12)}
\begin{equation*}
\parbox{40mm}{\includegraphics[scale=0.5]{graphics/ccsd_hbar_13_12}}
= \frac{1}{4} \bra{mn}\op{v}\ket{ef} t_{ij}^{ef} t_{mn}^{ab}
\end{equation*}
\end{block}
Diagram cost: $n_p^4 n_h^4$
\begin{block}{Diagram (2.12) - Factored}
\small
\begin{align*}
\parbox{40mm}{\includegraphics[scale=0.5]{graphics/ccsd_hbar_13_12}}
&= \frac{1}{4} \bra{mn}\op{v}\ket{ef} t_{ij}^{ef} t_{mn}^{ab} \\
&= \frac{1}{4} \left(\bra{mn}\op{v}\ket{ef} t_{ij}^{ef}\right) t_{mn}^{ab} \\
&= \frac{1}{4} X_{ij}^{mn} t_{mn}^{ab}
\end{align*}
\end{block}
\end{frame}

\begin{frame}
\frametitle{Factoring, motivation}
\note{Filename: ccsd\_factoring03.tex}

\small
\begin{block}{Diagram (2.26)}
\begin{align*}
\parbox{40mm}{\includegraphics[scale=0.5]{graphics/ccsd_hbar_13_26}}
&= \frac{1}{4} P(ij) \bra{mn}\ket{ef} t_i^e t_{mn}^{ab} t_j^f
\end{align*}
\end{block}
Diagram cost: $n_p^4 n_h^4$
\begin{block}{Diagram (2.26) - Factored}
\begin{align*}
\parbox{40mm}{\includegraphics[scale=0.5]{graphics/ccsd_hbar_13_26}}
&= \frac{1}{4} P(ij) \bra{mn}\op{v}\ket{ef} t_i^e t_{mn}^{ab} t_j^f \\
&= \frac{1}{4} P(ij) t_{mn}^{ab} t_i^e X_{ej}^{mn} \\
&= \frac{1}{4} P(ij) t_{mn}^{ab} Y^{mn}_{ij}
\end{align*}
\end{block}
\end{frame}



\begin{frame}
\frametitle{Factoring, motivation}
\note{Filename: ccsd\_factoring04.tex}

\scriptsize
\begin{block}{Diagram (2.31)}
\begin{align*}
\parbox{40mm}{\includegraphics[scale=0.5]{graphics/ccsd_hbar_13_31}}
&= \frac{1}{4} P(ij) P(ab) \bra{mn}\op{v}\ket{ef} t_i^e t_m^a t_j^f t_n^b
\end{align*}
\end{block}
Diagram cost: $n_p^4 n_h^4$
\begin{block}{Diagram (2.31) - Factored}
\begin{align*}
\parbox{40mm}{\includegraphics[scale=0.4]{graphics/ccsd_hbar_13_31}}
&= \frac{1}{4} P(ij) P(ab) \bra{mn}\op{v}\ket{ef} t_i^e t_m^a t_j^f t_n^b \\
&= \frac{1}{4} P(ij) P(ab) t_m^a t_n^b t_i^e X_{ej}^{mn} \\
&= \frac{1}{4} P(ij) P(ab) t_m^a t_n^b Y_{ij}^{mn} \\
&= \frac{1}{4} P(ij) P(ab) t_m^a Z_{ij}^{mb}
\end{align*}
\end{block}
\end{frame}

\begin{frame}
\frametitle{Factoring, Classification}
\note{Filename: ccsd\_factoring05.tex}

A diagram is classified by how many hole and particle lines between a $\hat{T}_i$ operator and the interaction ($T_i(p^{np} h^{nh})$).
\begin{block}{Diagram (2.12) Classification}
\begin{equation*}
\parbox{40mm}{\includegraphics[scale=0.5]{graphics/ccsd_hbar_13_12}}
= \frac{1}{4} \bra{mn}\op{v}\ket{ef} t_{ij}^{ef} t_{mn}^{ab}
\end{equation*}
\end{block}
This diagram is classified as $T_2(p^2) \times T_2(h^2)$
\end{frame}

\begin{frame}
\frametitle{Factoring, Classification}
\note{Filename: ccsd\_factoring06.tex}

\begin{block}{Diagram (2.26)}
\begin{equation*}
\parbox{40mm}{\includegraphics[scale=0.5]{graphics/ccsd_hbar_13_26}}
= \frac{1}{4} P(ij) \bra{mn}\op{v}\ket{ef} t_i^e t_{mn}^{ab} t_j^f
\end{equation*}
\end{block}
This diagram is classified as $T_2(h^2) \times T_1(p) \times T_1(p)$
\begin{block}{Diagram (2.31)}
\begin{equation*}
\parbox{40mm}{\includegraphics[scale=0.5]{graphics/ccsd_hbar_13_31}}
= \frac{1}{4} P(ij) P(ab) \bra{mn}\op{v}\ket{ef} t_i^e t_m^a t_j^f t_n^b
\end{equation*}
\end{block}
This diagram is classified as $T_1(p) \times T_1(p) \times T_1(h) \times T_1(h)$
\end{frame}

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