HDR/Manuscript/main/HDR.tex
2021-05-20 15:13:48 +02:00

680 lines
26 KiB
TeX

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Masters/Doctoral Thesis
% LaTeX Template
% Version 2.5 (27/8/17)
%
% This template was downloaded from:
% http://www.LaTeXTemplates.com
%
% Version 2.x major modifications by:
% Vel (vel@latextemplates.com)
%
% This template is based on a template by:
% Steve Gunn (http://users.ecs.soton.ac.uk/srg/softwaretools/document/templates/)
% Sunil Patel (http://www.sunilpatel.co.uk/thesis-template/)
%
% Template license:
% CC BY-NC-SA 3.0 (http://creativecommons.org/licenses/by-nc-sa/3.0/)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%----------------------------------------------------------------------------------------
% PACKAGES AND OTHER DOCUMENT CONFIGURATIONS
%----------------------------------------------------------------------------------------
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11pt, % The default document font size, options: 10pt, 11pt, 12pt
%oneside, % Two side (alternating margins) for binding by default, uncomment to switch to one side
english, % ngerman for German
singlespacing, % Single line spacing, alternatives: onehalfspacing or doublespacing
%draft, % Uncomment to enable draft mode (no pictures, no links, overfull hboxes indicated)
%nolistspacing, % If the document is onehalfspacing or doublespacing, uncomment this to set spacing in lists to single
%liststotoc, % Uncomment to add the list of figures/tables/etc to the table of contents
%toctotoc, % Uncomment to add the main table of contents to the table of contents
%parskip, % Uncomment to add space between paragraphs
%nohyperref, % Uncomment to not load the hyperref package
headsepline, % Uncomment to get a line under the header
%chapterinoneline, % Uncomment to place the chapter title next to the number on one line
%consistentlayout, % Uncomment to change the layout of the declaration, abstract and acknowledgements pages to match the default layout
]{MastersDoctoralThesis} % The class file specifying the document structure
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% orbitals
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% Operators
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% matrix elements
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% bold symbols
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% coefficients
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% energies
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\newcommand{\EKS}{E_\text{KS}}
\newcommand{\ECI}{E_\text{CI}}
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% potentials
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% Determinants
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% others
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\newcommand{\occ}{\text{occ}}
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% DFT
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%
\newcommand{\gX}{gX}
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\newcommand{\HGX}{HGX}
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%
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%
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\newcommand{\ns}{n_\sigma}
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\newcommand\upa{\uparrow}
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% integrals
\usepackage[version=4]{mhchem}
\newcommand{\sba}{\mathring{a}}
\newcommand{\sbb}{\mathring{b}}
\newcommand{\sbp}{\mathring{p}}
\newcommand{\sbz}{\mathring{z}}
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% Dressed CI
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\newcommand{\kO}{\ket{0}}
% Dressed e-n cusp
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% wave functions and orbitals
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% coefficients
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\newcommand{\bcGTO}{\bm{c}}
\newcommand{\bcSTO}{\DrSym{\bm{c}}}
% exponents
\newcommand{\expSTOa}{\DrSym{\alpha}}
\newcommand{\expSTOb}{\DrSym{\beta}}
% hat operators
\newcommand{\hFk}{\Hat{f}}
\newcommand{\hHc}{\Hat{h}}
% matrices
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\newcommand{\bHc}{\bm{h}}
\newcommand{\bP}{\bm{P}}
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\newcommand{\bDrFk}[1]{\DrSym{\bm{F}}^{#1}}
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\newcommand{\bDrKi}[1]{\DrSym{\bm{T}}^{#1}}
\newcommand{\bDrPo}[1]{\DrSym{\bm{V}}^{#1}}
\newcommand{\bDrOv}[1]{\DrSym{\bm{S}}^{#1}}
\newcommand{\bMOeigval}{\bm{\varepsilon}}
\newcommand{\bDrMOeigval}{\DrSym{\bm{\varepsilon}}}
% matrix elements
\newcommand{\DrFkEl}[3]{\DrSym{F}_{#1 #2}^{#3}}
\newcommand{\DrFkOpEl}[3]{\DrSym{F}_{#1 #2}^{#3}}
\newcommand{\DrHcEl}[3]{\DrSym{h}_{#1 #2}^{#3}}
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%----------------------------------------------------------------------------------------
% MARGIN SETTINGS
%----------------------------------------------------------------------------------------
\geometry{
paper=a4paper, % Change to letterpaper for US letter
inner=2.5cm, % Inner margin
outer=3.8cm, % Outer margin
bindingoffset=.5cm, % Binding offset
top=1.5cm, % Top margin
bottom=1.5cm, % Bottom margin
%showframe, % Uncomment to show how the type block is set on the page
}
%----------------------------------------------------------------------------------------
% THESIS INFORMATION
%----------------------------------------------------------------------------------------
\thesistitle{Functionals, Integrals, Spheres \& Cusps} % Your thesis title, this is used in the title and abstract, print it elsewhere with \ttitle
\supervisor{} % Your supervisor's name, this is used in the title page, print it elsewhere with \supname
\examiner{} % Your examiner's name, this is not currently used anywhere in the template, print it elsewhere with \examname
\degree{Habilitation \`a diriger les recherches} % Your degree name, this is used in the title page and abstract, print it elsewhere with \degreename
\author{Pierre-Fran{\c c}ois Loos} % Your name, this is used in the title page and abstract, print it elsewhere with \authorname
\addresses{} % Your address, this is not currently used anywhere in the template, print it elsewhere with \addressname
\subject{Theoretical Chemistry} % Your subject area, this is not currently used anywhere in the template, print it elsewhere with \subjectname
\keywords{correlation energy; quasi-exactly solvable models; uniform electron gas; many-electron integrals, density-functional theory; explicitly-correlated methods; quantum Monte Carlo methods} % Keywords for your thesis, this is not currently used anywhere in the template, print it elsewhere with \keywordnames
\university{\href{http://www.university.com}{Universit\'e Toulouse III, Paul Sabatier}} % Your university's name and URL, this is used in the title page and abstract, print it elsewhere with \univname
\department{\href{http://www.lcpq.ups-tlse.fr}{Laboratoire de Chimie et Physique Quantiques}} % Your department's name and URL, this is used in the title page and abstract, print it elsewhere with \deptname
\group{\href{http://researchgroup.university.com}{Universit\'e de Toulouse, CNRS, UPS, France}} % Your research group's name and URL, this is used in the title page, print it elsewhere with \groupname
\faculty{\href{http://faculty.university.com}{}} % Your faculty's name and URL, this is used in the title page and abstract, print it elsewhere with \facname
\AtBeginDocument{
\hypersetup{pdftitle=\ttitle} % Set the PDF's title to your title
\hypersetup{pdfauthor=\authorname} % Set the PDF's author to your name
\hypersetup{pdfkeywords=\keywordnames} % Set the PDF's keywords to your keywords
}
\begin{document}
\frontmatter % Use roman page numbering style (i, ii, iii, iv...) for the pre-content pages
\pagestyle{plain} % Default to the plain heading style until the thesis style is called for the body content
%----------------------------------------------------------------------------------------
% TITLE PAGE
%----------------------------------------------------------------------------------------
\begin{titlepage}
\begin{center}
\vspace*{.06\textheight}
{\scshape\LARGE \univname\par}\vspace{1.5cm} % University name
\textsc{\Large Habilitation \`a diriger les recherches}\\[0.5cm] % Thesis type
\HRule \\[0.4cm] % Horizontal line
{\huge \bfseries \ttitle\par}\vspace{0.4cm} % Thesis title
\HRule \\[1.5cm] % Horizontal line
\begin{minipage}[t]{0.4\textwidth}
\begin{flushleft} \large
\emph{Author:}\\
\href{http://www.irsamc.ups-tlse.fr/loos/}{\authorname} % Author name - remove the \href bracket to remove the link
\end{flushleft}
\end{minipage}
\begin{minipage}[t]{0.5\textwidth}
\begin{flushright} \large
\emph{Panel:} \\
\href{http://www.lpt.ups-tlse.fr/spip.php?article49&lang=en}{Pierre Pujol} (president) \\
\href{https://www.quantummatter.eu}{Paola Gori-Giorgi} (reviewer) \\
\href{https://quantique.u-strasbg.fr/doku.php?id=en:pageperso:ef:welcome}{Emmanuel Fromager} (reviewer) \\
\href{http://www.lct.jussieu.fr/pagesperso/toulouse/}{Julien Toulouse} (reviewer) \\
\href{http://qmcchem.ups-tlse.fr/index.php?title=Michel_Caffarel}{Michel Caffarel} (supervisor)
\end{flushright}
\end{minipage}\\[1cm]
\vfill
\large \textit{A thesis submitted in fulfillment of the requirements\\ for the degree of \degreename}\\[0.3cm] % University requirement text
\textit{in the}\\[0.4cm]
\groupname\\\deptname\\[2cm] % Research group name and department name
\vfill
{\large January 25, 2018}\\[4cm] % Date
%\includegraphics{Logo} % University/department logo - uncomment to place it
\vfill
\end{center}
\end{titlepage}
%----------------------------------------------------------------------------------------
% DECLARATION PAGE
%----------------------------------------------------------------------------------------
%\begin{declaration}
%\addchaptertocentry{\authorshipname} % Add the declaration to the table of contents
%\noindent I, \authorname, declare that this thesis titled, \enquote{\ttitle} and the work presented in it are my own. I confirm that:
%\begin{itemize}
%\item This work was done wholly or mainly while in candidature for a research degree at this University.
%\item Where any part of this thesis has previously been submitted for a degree or any other qualification at this University or any other institution, this has been clearly stated.
%\item Where I have consulted the published work of others, this is always clearly attributed.
%\item Where I have quoted from the work of others, the source is always given. With the exception of such quotations, this thesis is entirely my own work.
%\item I have acknowledged all main sources of help.
%\item Where the thesis is based on work done by myself jointly with others, I have made clear exactly what was done by others and what I have contributed myself.\\
%\end{itemize}
%\noindent Signed:\\
%\rule[0.5em]{25em}{0.5pt} % This prints a line for the signature
%\noindent Date:\\
%\rule[0.5em]{25em}{0.5pt} % This prints a line to write the date
%\end{declaration}
%\cleardoublepage
%----------------------------------------------------------------------------------------
% QUOTATION PAGE
%----------------------------------------------------------------------------------------
%\vspace*{0.2\textheight}
%
%\noindent\enquote{\itshape Dans la poudreuse, on est tous champion du monde. [...] Y'en pas pu un d\`es que c'est raide et un peu gel\'e.}\bigbreak
%
%\hfill Marco Siffredi
%----------------------------------------------------------------------------------------
% ABSTRACT PAGE
%----------------------------------------------------------------------------------------
\begin{abstract}
%\addchaptertocentry{\abstractname} % Add the abstract to the table of contents
In this memoir, after a brief introduction of the various quantum chemistry methods considered here, I summarise some of the projects we have been working on in the last ten years.
First, I describe succinctly several studies we have been doing on model two-electron systems.
In particular, we introduced a novel class a quasi-exactly solvable systems that we have been studying exhaustively in several papers.
Following this work, we shed new lights on the universality of correlation effects in two-electrons systems.
The discovery we have made are discussed.
Second, I present the work we performed on the mathematical properties of a new family of uniform electron gases as well as the development of a new class of density functionals based on this new paradigm.
Third, new recurrence relations for three- and four-electron integrals as well as their fundamental integrals and upper bounds are discussed.
In particular, our strategy to bound rigorously and efficiently these many-electron integrals is presented.
This new way of calculating many-electron integrals represents an interesting alternative to what is currently done in explicitly-correlated methods.
Finally, I present two lines of research we have been pursuing recently, namely the development of explicitly-correlated configuration interaction methods and a self-consistent correction to enforce the electron-nucleus cusp in molecular orbitals.
\end{abstract}
%----------------------------------------------------------------------------------------
% ACKNOWLEDGEMENTS
%----------------------------------------------------------------------------------------
%\begin{acknowledgements}
%\addchaptertocentry{\acknowledgementname} % Add the acknowledgements to the table of contents
%I would like to thank... absolutely nobody!
%\end{acknowledgements}
%----------------------------------------------------------------------------------------
% LIST OF CONTENTS/FIGURES/TABLES PAGES
%----------------------------------------------------------------------------------------
\tableofcontents % Prints the main table of contents
%\listoffigures % Prints the list of figures
%\listoftables % Prints the list of tables
%----------------------------------------------------------------------------------------
% ABBREVIATIONS
%----------------------------------------------------------------------------------------
%\begin{abbreviations}{ll} % Include a list of abbreviations (a table of two columns)
%
%\textbf{LAH} & \textbf{L}ist \textbf{A}bbreviations \textbf{H}ere\\
%\textbf{WSF} & \textbf{W}hat (it) \textbf{S}tands \textbf{F}or\\
%
%\end{abbreviations}
%----------------------------------------------------------------------------------------
% PHYSICAL CONSTANTS/OTHER DEFINITIONS
%----------------------------------------------------------------------------------------
%\begin{constants}{lr@{${}={}$}l} % The list of physical constants is a three column table
% The \SI{}{} command is provided by the siunitx package, see its documentation for instructions on how to use it
%Speed of Light & $c_{0}$ & \SI{2.99792458e8}{\meter\per\second} (exact)\\
%Constant Name & $Symbol$ & $Constant Value$ with units\\
%\end{constants}
%----------------------------------------------------------------------------------------
% SYMBOLS
%----------------------------------------------------------------------------------------
%\begin{symbols}{lll} % Include a list of Symbols (a three column table)
%$a$ & distance & \si{\meter} \\
%$P$ & power & \si{\watt} (\si{\joule\per\second}) \\
%Symbol & Name & Unit \\
%\addlinespace % Gap to separate the Roman symbols from the Greek
%$\omega$ & angular frequency & \si{\radian} \\
%\end{symbols}
%----------------------------------------------------------------------------------------
% DEDICATION
%----------------------------------------------------------------------------------------
%\dedicatory{A mon v\'elo \dots}
%----------------------------------------------------------------------------------------
% THESIS CONTENT - CHAPTERS
%----------------------------------------------------------------------------------------
\mainmatter % Begin numeric (1,2,3...) page numbering
\pagestyle{thesis} % Return the page headers back to the "thesis" style
% Include the chapters of the thesis as separate files from the Chapters folder
% Uncomment the lines as you write the chapters
%----------------------------------------------------------------
% INTRODUCTION
%----------------------------------------------------------------
\chapter*{
\label{chap:intro}
Introduction}
\addchaptertocentry{Introduction}
%----------------------------------------------------------------
\input{../Intro/intro.tex}
\input{../Intro/publications.tex}
%----------------------------------------------------------------
% CHAPTER 1
%----------------------------------------------------------------
\chapter{
\label{chap:method}
Methods}
%----------------------------------------------------------------
\input{../Chapter1/chapter1.tex}
%----------------------------------------------------------------
% CHAPTER 2
%----------------------------------------------------------------
\chapter{
\label{chap:two-electron}
Correlation in two-electron systems}
%----------------------------------------------------------------
\input{../Chapter2/chapter2.0.tex}
\input{../Chapter2/chapter2.1.tex}
\input{../Chapter2/chapter2.2.tex}
\input{../Chapter2/summary.tex}
%----------------------------------------------------------------
% CHAPTER 3
%----------------------------------------------------------------
\chapter{
\label{chap:DFT-UEG}
DFT using finite uniform electron gases}
%----------------------------------------------------------------
\input{../Chapter3/chapter3.0.tex}
\input{../Chapter3/chapter3.1.tex}
\input{../Chapter3/chapter3.2.tex}
\input{../Chapter3/summary.tex}
%----------------------------------------------------------------
% CHAPTER 4
%----------------------------------------------------------------
\chapter{
\label{chap:ManyElectronIntegrals}
Many-electron integrals involving Gaussian geminals}
%----------------------------------------------------------------
\input{../Chapter4/chapter4.0.tex}
\input{../Chapter4/chapter4.1.tex}
\input{../Chapter4/chapter4.2.tex}
\input{../Chapter4/chapter4.3.tex}
\input{../Chapter4/chapter4.4.tex}
\input{../Chapter4/chapter4.5.tex}
\input{../Chapter4/chapter4.6.tex}
\input{../Chapter4/summary.tex}
%----------------------------------------------------------------
% CHAPTER 5
%----------------------------------------------------------------
\chapter{
\label{chap:future}
Future directions}
%----------------------------------------------------------------
\input{../Chapter5/chapter5.0.tex}
\input{../Chapter5/chapter5.1.tex}
\input{../Chapter5/chapter5.2.tex}
\input{../Chapter5/summary.tex}
%----------------------------------------------------------------
% CONCLUSION
%----------------------------------------------------------------
\chapter*{
\label{chap:conclusion}
Conclusion}
\addchaptertocentry{Conclusion}
%----------------------------------------------------------------
\input{../Conclusion/conclusion.tex}
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% THESIS CONTENT - APPENDICES
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%\appendix % Cue to tell LaTeX that the following "chapters" are Appendices
% Include the appendices of the thesis as separate files from the Appendices folder
% Uncomment the lines as you write the Appendices
%\include{Appendices/AppendixA}
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% BIBLIOGRAPHY
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\printbibliography[heading=bibintoc]
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\end{document}