2024 files

This commit is contained in:
Pierre-Francois Loos 2024-06-17 10:07:19 +02:00
parent 0f33fecfa0
commit 51290a9b8f
52 changed files with 4078 additions and 14 deletions

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@ -7,6 +7,7 @@
\usetheme{Pittsburgh}
\usecolortheme{seahorse}
\usepackage{mathpazo,libertine}
\usepackage[normalem]{ulem}
\usepackage{algorithmicx,algorithm,algpseudocode}
\algnewcommand\algorithmicassert{\texttt{assert}}
@ -152,11 +153,11 @@ decoration={snake,
\item Generalities on correlation methods
\begin{itemize}
\item Configuration Interaction (CI) \pub{[Szabo \& Ostlund, Modern Quantum Chemistry]}
\item Perturbation theory
\item Coupled-cluster (CC) theory
\item Perturbation theory \pub{[Szabo \& Ostlund, Modern Quantum Chemistry]}
\item Coupled-cluster (CC) theory \pub{[Jensen, Introduction to Computational Chemistry]}
\end{itemize}
\bigskip
\item Computing the 2th-order M{\o}ller-Plesset (MP2) correlation energy
\item Computing the 2nd-order M{\o}ller-Plesset (MP2) correlation energy
\begin{itemize}
\item Atomic orbital (AO) to molecular orbital (MO) transformation \pub{[Frisch et al. CPL 166 (1990) 281]}
\item Laplace transform \pub{[Alml{\"o}f, CPL 181 (1991) 319]}
@ -200,6 +201,24 @@ decoration={snake,
\end{columns}
\end{frame}
%
%-----------------------------------------------------
\begin{frame}{Assumptions \& Notations}
\begin{block}{Let's talk about notations}
\begin{itemize}
\bigskip
\item Number of \green{occupied orbitals} $O$
\item Number of \alert{vacant orbitals} $V$
\item \violet{Total number of orbitals} $N = O + V$
\bigskip
\item $i,j,k,l$ are \green{occupied orbitals}
\item $a,b,c,d$ are \alert{vacant orbitals}
\item $p,q,r,s$ are \violet{arbitrary (occupied or vacant) orbitals}
\item $\mu,\nu,\lambda,\sigma$ are \purple{basis function indexes}
\bigskip
\end{itemize}
\end{block}
\end{frame}
%-----------------------------------------------------
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{One- and two-electron integrals}
@ -226,18 +245,18 @@ decoration={snake,
( \mu \nu | \lambda \sigma )
= \iint \phi_\mu(\alert{\br_1}) \phi_\nu(\alert{\br_1}) \frac{1}{r_{12}} \phi_\lambda(\blue{\br_2}) \phi_\sigma(\blue{\br_2}) d\red{\br_1} d\blue{\br_2}
\end{equation}
\begin{equation}
( \mu \blue{\nu} \orange{||} \lambda \red{\sigma} ) = ( \mu \blue{\nu} | \lambda \red{\sigma} ) - ( \mu \red{\sigma} | \lambda \blue{\nu} )
\end{equation}
% \begin{equation}
% ( \mu \blue{\nu} \orange{||} \lambda \red{\sigma} ) = ( \mu \blue{\nu} | \lambda \red{\sigma} ) - ( \mu \red{\sigma} | \lambda \blue{\nu} )
% \end{equation}
\end{block}
\begin{block}{Physicist/Dirac notation for two-electron integrals (p.~68)}
\begin{equation}
\langle \mu \nu | \lambda \sigma \rangle
= \iint \phi_\mu(\alert{\br_1}) \phi_\nu(\blue{\br_2}) \frac{1}{r_{12}} \phi_\lambda(\alert{\br_1}) \phi_\sigma(\blue{\br_2}) d\red{\br_1} d\blue{\br_2}
\end{equation}
\begin{equation}
\langle \mu \nu \orange{||} \blue{\lambda} \red{\sigma} \rangle = \langle \mu \nu | \blue{\lambda} \red{\sigma} \rangle - \langle \mu \nu | \red{\sigma} \blue{\lambda} \rangle
\end{equation}
% \begin{equation}
% \langle \mu \nu \orange{||} \blue{\lambda} \red{\sigma} \rangle = \langle \mu \nu | \blue{\lambda} \red{\sigma} \rangle - \langle \mu \nu | \red{\sigma} \blue{\lambda} \rangle
% \end{equation}
\end{block}
\end{frame}
@ -702,7 +721,7 @@ decoration={snake,
\end{frame}
\begin{frame}{Computation of DFT exchange}
\begin{block}{LDA exchange (in theory) = cf Julien's lectures}
\begin{block}{LDA exchange (in theory) = cf \sout{Julien's} Manu's lectures}
\begin{gather}
K_{\mu\nu}^\text{LDA}
= \int \phi_{\mu}(\br) \violet{v_\text{x}^\text{LDA}}(\br) \phi_{\nu}(\br) d\br
@ -752,7 +771,7 @@ decoration={snake,
\bigskip
\item \alert{Multireference methods}: MCSCF, CASSCF, RASSCF, MRCI, MRCC, CASPT2, NEVPT2, etc. (C.~Angeli \& S. Knecht)
\bigskip
\item \alert{Density-functional theory}: DFT, TDDFT, etc. (J. Toulouse, F. Sottile)
\item \alert{Density-functional theory}: DFT, TDDFT, etc. (J. Toulouse/E. Fromager, F. Sottile)
\bigskip
\item \alert{Quantum Monte Carlo}: VMC, DMC, FCIQMC, etc. (M.~Caffarel)
\end{enumerate}
@ -1446,10 +1465,10 @@ decoration={snake,
\\
& = \hI + \hT{1}{}
+ \qty( \underbrace{\hT{2}{}}_{\text{\green{connected}}} + \frac{1}{2} \underbrace{\hT{1}{2}}_{\text{\alert{disconnected}}} )
+ \qty( \hT{3}{} + \hT{2}{} \hT{1}{} + \frac{1}{6} \hT{3}{} )
+ \qty( \hT{3}{} + \hT{2}{} \hT{1}{} + \frac{1}{6} \hT{1}{3} )
\\
& + \qty( \hT{4}{} + \hT{3}{} \hT{1}{} + \frac{1}{2} \underbrace{\hT{2}{2}}_{\text{\blue{two pairs of electrons}}} + \frac{1}{2} \hT{2}{} \hT{1}{2} + \frac{1}{24} \underbrace{\hT{4}{}}_{\text{
\purple{four electrons}}} )
& + \qty( \underbrace{\hT{4}{}}_{\text{
\purple{four electrons}}} + \hT{3}{} \hT{1}{} + \frac{1}{2} \underbrace{\hT{2}{2}}_{\text{\blue{two pairs of electrons}}} + \frac{1}{2} \hT{2}{} \hT{1}{2} + \frac{1}{24} \hT{1}{4} )
+ \ldots
\end{split}
\end{equation}
@ -1607,6 +1626,12 @@ decoration={snake,
= \cre{p} \delta_{qa} \ani{i} - \cre{a} \delta_{ip} \ani{q}
\end{equation}
\end{block}
\begin{itemize}
\item At the \blue{TCC} level, the BCH expansion \blue{truncates naturally after the first five terms}
\item At the \alert{VCC} level, the BCH expansion \alert{does not truncate but terminates}
\item At the \purple{UCC} level, the BCH expansion \purple{does not terminate}
\end{itemize}
\bigskip
For more details about normal-ordered operators, Wick's theorem, and diagrammatic techniques, see
\pub{Crawford \& Schaefer, Reviews in Computational Chemistry, Vol.~14, Chap.~2, 2000.}
\end{frame}

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\documentclass{standalone}
\usepackage{amsmath,amssymb,amsfonts,pgfpages,graphicx,subfigure,xcolor,bm,multirow,microtype,wasysym,multimedia,hyperref,tabularx,amscd,pgfgantt,mhchem,physics}
\usetikzlibrary{shapes.gates.logic.US,trees,positioning,arrows}
\usepackage{tgchorus}
\usepackage[T1]{fontenc}
\begin{document}
\begin{tikzpicture}
\begin{scope}[very thick,
node distance=5cm,on grid,>=stealth',
theo1/.style={rectangle,draw,fill=red!20},
theo2/.style={rectangle,draw,fill=orange!20},
theo3/.style={rectangle,draw,fill=green!40},
exp1/.style={rectangle,draw,fill=cyan!40},
exp2/.style={rectangle,draw,fill=violet!40}]
\node [theo1, text width=7cm, align=center] (KS)
{\textbf{\LARGE Kohn-Sham DFT}
$$
\qty[ -\frac{\nabla^2}{2} + v_\text{ext} + V^{\text{Hxc}} ] \phi_p^{\text{KS}} = \varepsilon^{\text{KS}}_p \phi_p^{\text{KS}}
$$
};
\node [theo2, text width=7cm, align=center] (GW) [below=of KS, yshift=2cm]
{\textbf{\LARGE $GW$ approximation}
$$
\varepsilon_p^{GW} = \varepsilon_p^{\text{KS}} +
\mel{\phi_p^{\text{KS}}}{\Sigma^{GW}(\varepsilon_p^{GW}) - V^{\text{xc}}}{\phi_p^{\text{KS}}}
$$
};
\node [theo3, text width=7cm, align=center] (BSE) [below=of GW, yshift=2cm]
{\textbf{\LARGE Bethe-Salpeter equation}
$$
\begin{pmatrix}
\bm{A} & \bm{B} \\
-\bm{B}^* & -\bm{A}^{*}
\end{pmatrix}
\begin{pmatrix}
\bm{X}_m \\
\bm{Y}_m
\end{pmatrix}
=
\Omega_{m}
\begin{pmatrix}
\bm{X}_m \\
\bm{Y}_m
\end{pmatrix}
$$
};
\node [exp1, align=center] (photo) [right=of GW, xshift=3cm]
{\LARGE (Inverse) \\ \LARGE photoemission \\ \LARGE spectroscopy};
\node [exp2, align=center] (abs) [right=of BSE, xshift=3cm]
{\LARGE Optical \\ \LARGE spectroscopy};
\path
(KS) edge [->,color=black] node [right,black] {\LARGE Fundamental gap} (GW)
(GW) edge [->,color=black] node [right,black] {\LARGE Excitonic effect} (BSE)
(photo) edge [<->,color=black] node [above,black] {Ionization potentials} node [below,black] {Electron affinities} (GW)
(abs) edge [<->,color=black] node [above,black] {Optical excitations} (BSE)
;
\end{scope}
\end{tikzpicture}
\end{document}

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\documentclass{standalone}
%\usepackage[top=3cm,left=0cm,right=0cm,bottom=3cm]{geometry}
\usepackage{mathtools,physics,bm,xcolor}
\usepackage{tikz}
% shadows only for title
\usetikzlibrary{decorations.pathmorphing,shadows}
\pagestyle{empty}
\begin{document}
% colors
\definecolor{turquoise}{rgb}{0 0.41 0.41}
\definecolor{rouge}{rgb}{0.79 0.0 0.1}
\definecolor{vert}{rgb}{0.15 0.4 0.1}
\definecolor{mauve}{rgb}{0.6 0.4 0.8}
\definecolor{violet}{rgb}{0.58 0. 0.41}
\definecolor{orange}{rgb}{0.8 0.4 0.2}
\definecolor{bleu}{rgb}{0.39, 0.58, 0.93}
\begin{center}
\begin{tikzpicture}
% styles
\tikzstyle{elec} = [line width=2pt,draw=black!80]
\tikzstyle{vib} = [thick,draw=black!30]
\tikzstyle{trans} = [line width=2pt,->]
\tikzstyle{transCI} = [trans,dashed,draw=vert]
\tikzstyle{transCS} = [trans,dashed,draw=violet]
\tikzstyle{relax} = [draw=orange,ultra thick,decorate,decoration=snake]
\tikzstyle{rv} = [rotate=90,text=orange,pos=0.5,yshift=3mm]
% fondamental
\path[elec] (0,0) -- ++ (14,0)
node[below,pos=0.5,yshift=-1mm] {\large Ground state $S_0$};
\path[vib] (0,0.2) -- ++ (14,0);
\path[vib] (0,0.4) -- ++ (13,0);
\foreach \i in {1,2,...,30} {
\path[vib] (0,0.4 + \i*0.2) -- ++ ({2 + 10*exp(-0.2*\i)},0);
}
% T1
\path[elec] (11,4) -- ++ (3,0) node[anchor=south west] {\large $T_1$};
\foreach \i in {1,2,...,6} {
\path[vib] (11,4 + \i*0.2) -- ++ (3,0);
}
% S1
\path[elec] (4,5) node[anchor=south east] {\large $S_1$} -- ++ (5,0);
\foreach \i in {1,2,...,6} {
\path[vib] (4,5 + \i*0.2) -- ++ (5,0);
}
\foreach \i in {1,2,...,12} {
\path[vib] ({7.5 - 1*exp(-0.3*\i)},6.2+\i*0.2) -- (9,6.2+\i*0.2);
}
% S2
\path[elec] (4,8) node[anchor=south east] {\large $S_2$} -- ++ (2,0);
\foreach \i in {1,2,...,6} {
\path[vib] (4,8 + \i*0.2) -- ++ (2,0);
}
% absorption
\path[trans,draw=turquoise] (4.5,0) -- ++(0,9)
node[rotate=90,pos=0.35,text=turquoise,yshift=-3mm] {\large Absorption};
% fluo
\path[trans,draw=rouge](7,5) -- ++(0,-4.4)
node[rotate=90,pos=0.5,text=rouge,yshift=-3mm] {\large Fluorescence};
% phosphorescence
\path[trans,draw=mauve] (13,4) -- ++(0,-3.4)
node[rotate=90,pos=0.5,text=mauve,yshift=-3mm] {\large Phosphorescence};
% Conversion interne
\path[transCI] (4,5) -- ++(-1.9,0) node[below,pos=0.5,text=vert] {\large IC};
\path[transCI] (6,8) -- ++(1.3,0) node[above,pos=0.5,text=vert] {\large IC};
% Croisement intersysteme
\path[transCS] (9,5) -- ++(2,0) node[below,pos=0.5,text=violet] {\large ISC};
\path[transCS] (11,4) -- ++(-2.5,0) node[below,pos=0.5,text=violet] {\large ISC};
% relaxation vib
\path[relax] (5.5,8.8) -- ++(0,-0.8) node[rv] {\textbf{VR}};
\path[relax] (8,8) -- ++(0,-3) node[rv] {\textbf{VR}};
\path[relax] (1,5) -- ++(0,-5) node[rv] {\textbf{VR}};
\path[relax] (11.5,5) -- ++(0,-1) node[rv] {\textbf{VR}};
\end{tikzpicture}
\end{center}
\begin{itemize}
\item[] \tikz {\path[line width=2pt,->,dashed,draw=vert]
(0,0) -- (1,0) node[above,pos=0.5,text=vert] {IC};} Internal Conversion,
$S_i\,\longrightarrow\,S_j$ non radiative transition.
\item[] \tikz {\path[line width=2pt,->,dashed,draw=violet]
(0,0) -- (1,0) node[above,pos=0.5,text=violet] {ISC};} InterSystem Crossing,
$S_i\,\longrightarrow\,T_j$ non radiative transition.
\item[] \tikz {\path[line width=2pt,draw=orange,ultra thick,
decorate,decoration=snake] (0,0) -- (1,0) node[above,pos=0.5,text=orange] {RV};}
Vibrationnal Relaxation.
\end{itemize}
\end{document}

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@ -0,0 +1,120 @@
\documentclass{standalone}
\usepackage{tikz}
\usepackage{siunitx}
\usepackage{mathtools,physics,bm,xcolor}
%\usetikzlibrary{arrows.meta}
%\tikzset{myarr/.style={
% {Triangle[width=4pt, length=4pt]}-{Triangle[width=4pt, length=4pt]},
%}}
\usepackage{tikz}
\usetikzlibrary{intersections}
\usepackage{pgfplots}
\usepgfplotslibrary{fillbetween}
\definecolor{darkgreen}{RGB}{0, 180, 0}
\begin{document}
\begin{tikzpicture}[scale=2]
% x axis
\draw [->] (0,0) -- (0,4);
\node [left] at (0,4) {Energy};
% x axis
\draw [->] (0,0) -- (4,0);
\node [below] at (4,0) {Nuclear coordinates};
% absorption
\draw [thick, blue, <->] (1,1) -- (1,3);
% emission
\draw [thick, red, <->] (2,1.5) node[along]{$E^{fluo}$} -- (2,2.5);
% adiabatic
\draw [thick, darkgreen, <->] (2.5,1) node[right]{$E^\text{adia}$} -- (2.5,2.5);
% 0-0
\draw [thick, blue, <->] (3,1.1) node[along]{$E^{0-0}$} -- (3,2.7);
% \node [right] at (2.65,-2) {$\theta$};
% \draw [thick] (-2,-2.05) node[below]{\SI{70}{\degree}} -- (-2,-1.95);
% \draw [thick] (0,-2.05) node[below]{\SI{90}{\degree}} -- (0,-1.95);
% \draw [thick] (2,-2.05) node[below]{\SI{110}{\degree}} -- (2,-1.95);
% Theta = 75 rectangular
% \node[draw,circle,minimum size=85pt,opacity=0.3,thick] (a) at (-2,-1) {};
% \node [above] at (-2,-0.2) {$D_{2h}$};
% \draw [thick] (a.35) -- (a.145) -- (a.-145) -- (a.-35) -- (a.35);
% \node[fill,draw,circle, label=above right:H, minimum size=3pt,inner sep=0pt] at (a.35) {};
% \node[fill,draw,circle, label=below right:H, minimum size=3pt,inner sep=0pt] at (a.-35) {};
% \node[fill,draw,circle, label=below left:H, minimum size=3pt,inner sep=0pt] at (a.-145) {};
% \node[fill,draw,circle, label=above left:H, minimum size=3pt,inner sep=0pt] at (a.145) {};
% \draw [dashed,thick] (-2,-1) -- (a.35);
% \draw [dashed,thick] (-2,-1) -- (a.-35);
% \draw [thick] (-1.8,-1) arc [start angle=0,end angle=35,radius=0.2];
% \draw [thick] (-1.8,-1) arc [start angle=0,end angle=-35,radius=0.2];
% \node [right] at (-1.8,-1) {$\theta$};
% Theta = 90 square
% \node[draw,circle,minimum size=85pt,opacity=0.3,thick] (b) at (0,-1) {};
% \node [above] at (0,-0.2) {$D_{4h}$};
% \draw [thick] (b.45) -- (b.135) -- (b.-135) -- (b.-45) -- (b.45);
% \node[fill,draw,circle, label=above right:H, minimum size=3pt,inner sep=0pt] at (b.45) {};
% \node[fill,draw,circle, label=below right:H, minimum size=3pt,inner sep=0pt] at (b.-45) {};
% \node[fill,draw,circle, label=below left:H, minimum size=3pt,inner sep=0pt] at (b.-135) {};
% \node[fill,draw,circle, label=above left:H, minimum size=3pt,inner sep=0pt] at (b.135) {};
% \draw [thick,myarr,dashed] (b.-135) -- (b.45);
% \node [above left] at (0,-1) {$d$};
% Theta = 105 rectangular
% \node[draw,circle,minimum size=85pt,opacity=0.3,thick] (c) at (2,-1) {};
% \node [above] at (2,-0.2) {$D_{2h}$};
% \draw [thick] (c.55) -- (c.125) -- (c.-125) -- (c.-55) -- (c.55);
% \node[fill,draw,circle, label=above right:H, minimum size=3pt,inner sep=0pt] at (c.55) {};
% \node[fill,draw,circle, label=below right:H, minimum size=3pt,inner sep=0pt] at (c.-55) {};
% \node[fill,draw,circle, label=below left:H, minimum size=3pt,inner sep=0pt] at (c.-125) {};
% \node[fill,draw,circle, label=above left:H, minimum size=3pt,inner sep=0pt] at (c.125) {};
% \draw [dashed,thick] (2,-1) -- (c.55);
% \draw [dashed,thick] (2,-1) -- (c.-55);
% \draw [thick] (2.2,-1) arc [start angle=0,end angle=55,radius=0.2];
% \draw [thick] (2.2,-1) arc [start angle=0,end angle=-55,radius=0.2];
% \node [right] at (2.2,-1) {$\theta$};
%%%%%%% Define Potential Function %%%%%%%
% \pgfmathsetmacro{\DeGS}{1}
% \pgfmathsetmacro{\RoGS}{1}
% \pgfmathsetmacro{\alphaGS}{1}
% \pgfmathsetmacro{\DeES}{1.2}
% \pgfmathsetmacro{\RoES}{1.2}
% \pgfmathsetmacro{\alphaES}{1.2}
% \pgfmathdeclarefunction{GS}{1}{%
% \pgfmathparse{%
% \DeGS*((1-exp(-\alphaGS*(#1-\RoGS)))^2-1)%
% }%
% }%
% \pgfmathdeclarefunction{ES}{1}{%
% \pgfmathparse{%
% \DeES*((1-exp(-\alphaES*(#1-\RoES)))^2-1)%
% }%
% }%
%%%%%%%% Energy Levels %%%%%%%
% \pgfmathdeclarefunction{energyGS}{1}{%
% \pgfmathparse{%
% -\DeGS+(#1+.5) - (#1+.5)^2/(1*\DeGS)
% }%
% }%
% \pgfmathdeclarefunction{energyES}{1}{%
% \pgfmathparse{%
% -\DeES+(#1+.5) - (#1+.5)^2/(1*\DeES)
% }%
% }%
%
% \begin{axis}[
% axis lines=none,
% smooth,
% no markers,
% domain=0:4,
% xmax=10,
% ymax=10,
% scale=1
% ]
% \addplot [black, samples=50, name path global=GSCurve] {GS(x)};
% \addplot [black, samples=50, name path global=ESCurve] {ES(x)};
% \end{axis}
\end{tikzpicture}
\end{document}

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