680 lines
26 KiB
TeX
680 lines
26 KiB
TeX
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% Masters/Doctoral Thesis
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% LaTeX Template
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% Version 2.5 (27/8/17)
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%
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% This template was downloaded from:
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% http://www.LaTeXTemplates.com
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%
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% Version 2.x major modifications by:
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% Vel (vel@latextemplates.com)
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%
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% This template is based on a template by:
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% Steve Gunn (http://users.ecs.soton.ac.uk/srg/softwaretools/document/templates/)
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% Sunil Patel (http://www.sunilpatel.co.uk/thesis-template/)
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%
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% Template license:
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% CC BY-NC-SA 3.0 (http://creativecommons.org/licenses/by-nc-sa/3.0/)
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%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%----------------------------------------------------------------------------------------
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% PACKAGES AND OTHER DOCUMENT CONFIGURATIONS
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%----------------------------------------------------------------------------------------
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\documentclass[
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11pt, % The default document font size, options: 10pt, 11pt, 12pt
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%oneside, % Two side (alternating margins) for binding by default, uncomment to switch to one side
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english, % ngerman for German
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singlespacing, % Single line spacing, alternatives: onehalfspacing or doublespacing
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%draft, % Uncomment to enable draft mode (no pictures, no links, overfull hboxes indicated)
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%nolistspacing, % If the document is onehalfspacing or doublespacing, uncomment this to set spacing in lists to single
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%liststotoc, % Uncomment to add the list of figures/tables/etc to the table of contents
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%toctotoc, % Uncomment to add the main table of contents to the table of contents
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%parskip, % Uncomment to add space between paragraphs
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%nohyperref, % Uncomment to not load the hyperref package
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headsepline, % Uncomment to get a line under the header
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%chapterinoneline, % Uncomment to place the chapter title next to the number on one line
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%consistentlayout, % Uncomment to change the layout of the declaration, abstract and acknowledgements pages to match the default layout
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]{MastersDoctoralThesis} % The class file specifying the document structure
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%\usepackage[utf8]{inputenc} % Required for inputting international characters
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%\usepackage[T1]{fontenc} % Output font encoding for international characters
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\usepackage{mathpazo} % Use the Palatino font by default
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\usepackage[backend=bibtex,style=phys,natbib=true]{biblatex} % Use the bibtex backend with the authoryear citation style (which resembles APA)
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\addbibresource{HDR.bib} % The filename of the bibliography
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\usepackage[autostyle=true]{csquotes} % Required to generate language-dependent quotes in the bibliography
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\usepackage{graphicx,dcolumn,bm,xcolor,microtype,hyperref,multirow,amscd,amsmath,amssymb,amsfonts,physics}
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\usepackage[version=4]{mhchem}
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\usepackage{algorithmicx,algorithm,algpseudocode}
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\newcommand{\alert}[1]{\textcolor{red}{#1}}
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\newcommand{\cdash}{\multicolumn{1}{c}{---}}
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\newcommand{\mc}{\multicolumn}
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\newcommand{\mcc}[1]{\multicolumn{1}{c}{#1}}
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\newcommand{\mr}{\multirow}
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\DeclareMathOperator{\erfc}{erfc}
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%algorithm
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\algnewcommand\algorithmicswitch{\textbf{switch}}
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\algnewcommand\algorithmiccase{\textbf{case}}
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\algnewcommand\algorithmicassert{\texttt{assert}}
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\algnewcommand\Assert[1]{\State \algorithmicassert(#1)}
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\algdef{SE}[SWITCH]{Switch}{EndSwitch}[1]{\algorithmicswitch\ #1\ \algorithmicdo} {\algorithmicend\ \algorithmicswitch}
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\algdef{SE}[CASE]{Case}{EndCase}[1]{\algorithmiccase\ #1}{\algorithmicend\ \algorithmiccase}
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\algtext*{EndSwitch}
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\algtext*{EndCase}
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\algrenewcommand{\algorithmiccomment}[1]{$\triangleright$ \textit{#1}}
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\algnewcommand{\algorithmicgoto}{\textbf{go to}}%
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\algnewcommand{\Goto}[1]{\algorithmicgoto~\ref{#1}}%
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% wave functions
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\newcommand{\PsiT}{\Psi_\text{T}}
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\newcommand{\PsiEx}{\Psi_\text{ex}}
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\newcommand{\PsiHF}{\Psi_\text{HF}}
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\newcommand{\PsiCI}{\Psi_\text{CI}}
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\newcommand{\PsiCC}{\Psi_\text{CC}}
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\newcommand{\Js}{J}
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\newcommand{\sdet}{D}
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% orbitals
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\newcommand{\sMO}[1]{\psi_{#1}}
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\newcommand{\MO}[1]{\phi_{#1}}
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\newcommand{\GTO}[1]{\chi_{#1}}
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\newcommand{\AO}[1]{\chi_{#1}}
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% Operators
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\newcommand{\IdOp}{\Hat{I}}
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\newcommand{\HOp}{\Hat{H}}
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\newcommand{\POp}{\Hat{P}}
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\newcommand{\QOp}{\Hat{Q}}
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\newcommand{\TOp}{\Hat{T}}
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\newcommand{\VOp}{\Hat{V}}
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\newcommand{\DOp}{\Hat{D}}
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\newcommand{\FkOp}{\Hat{F}}
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\newcommand{\FOp}{\Hat{F}}
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\newcommand{\HcOp}{\Hat{H}^\text{c}}
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\newcommand{\JOp}{\Hat{J}}
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\newcommand{\KOp}{\Hat{K}}
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\newcommand{\TeOp}{\Hat{T}_\text{e}}
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\newcommand{\VenOp}{\Hat{V}_\text{en}}
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\newcommand{\VeeOp}{\Hat{V}_\text{ee}}
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\newcommand{\VnnOp}{\Hat{V}_\text{nn}}
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% Matrices
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\newcommand{\IdMat}{\bm{I}}
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\newcommand{\FkMat}{\bm{F}}
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\newcommand{\PMat}{\bm{P}}
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\newcommand{\HcMat}{\bm{H}^\text{c}}
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\newcommand{\HMat}{\bm{H}}
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\newcommand{\FMat}{\bm{F}}
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\newcommand{\SMat}{\bm{S}}
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\newcommand{\CMat}{\bm{C}}
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\newcommand{\GMat}{\bm{G}}
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\newcommand{\XMat}{\bm{X}}
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\newcommand{\UMat}{\bm{U}}
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\newcommand{\sMat}{\bm{s}}
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\newcommand{\MOevMat}{\bm{\varepsilon}}
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% matrix elements
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\newcommand{\FkEl}[2]{F_{#1 #2}}
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\newcommand{\PEl}[2]{P_{#1 #2}}
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\newcommand{\HcEl}[2]{H^\text{c}_{#1 #2}}
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\newcommand{\HEl}[2]{H_{#1 #2}}
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\newcommand{\FEl}[2]{F_{#1 #2}}
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\newcommand{\GEl}[2]{G_{#1 #2}}
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\newcommand{\SEl}[2]{S_{#1 #2}}
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\newcommand{\XEl}[2]{X_{#1 #2}}
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% bold symbols
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\newcommand{\br}{\bm{r}}
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\newcommand{\bx}{\bm{x}}
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\newcommand{\bs}{\bm{s}}
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\newcommand{\bR}{\bm{R}}
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\newcommand{\bN}{\bm{N}}
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\newcommand{\bX}{\bm{X}}
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\newcommand{\rA}{r_A}
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\newcommand{\rB}{r_B}
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\newcommand{\brA}{\br_A}
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\newcommand{\brB}{\br_B}
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\newcommand{\ri}{r_i}
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\newcommand{\rj}{r_j}
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\newcommand{\rij}{r_{ij}}
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\newcommand{\ree}{r_{12}}
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\newcommand{\bri}{\br_i}
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\newcommand{\brj}{\br_j}
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\newcommand{\bA}{\mathbf{A}}
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\newcommand{\bB}{\mathbf{B}}
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\newcommand{\bC}{\mathbf{C}}
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\newcommand{\bO}{\mathbf{0}}
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% coefficients
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\newcommand{\cCI}[2]{c_{#1}^{#2}}
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\newcommand{\cMO}[2]{c_{#1 #2}}
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% energies
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\newcommand{\EHF}{E_\text{HF}}
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\newcommand{\EKS}{E_\text{KS}}
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\newcommand{\ECI}{E_\text{CI}}
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\newcommand{\ECC}{E_\text{CC}}
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\newcommand{\Ec}{E_\text{c}}
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\newcommand{\Eee}{E_\text{ee}}
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\newcommand{\Ts}{T_\text{s}}
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\newcommand{\J}{J}
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\newcommand{\Ex}{E_\text{x}}
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\newcommand{\Exc}{E_\text{xc}}
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\newcommand{\Ene}{E_\text{ne}}
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\newcommand{\EVMC}{E_\text{VMC}}
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\newcommand{\EDMC}{E_\text{DMC}}
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\newcommand{\MOev}[1]{\varepsilon_{#1}}
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% potentials
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\newcommand{\vxc}{v_\text{xc}}
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% Determinants
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\newcommand{\ExDet}[2]{\Psi_{#1}^{#2}}
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% others
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\newcommand{\nuc}{\text{nuc}}
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\newcommand{\occ}{\text{occ}}
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\newcommand{\virt}{\text{virt}}
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% DFT
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\newcommand{\Fx}{F_{\text{x}}}
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%
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\newcommand{\gX}{gX}
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\newcommand{\HgX}{HgX}
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\newcommand{\GX}{GX}
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\newcommand{\HGX}{HGX}
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\newcommand{\PBEGX}{PBE-GX}
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%
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\newcommand{\FxgX}{F_{\text{x}}^\text{\gX}}
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\newcommand{\FxHgX}{F_{\text{x}}^\text{\HgX}}
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\newcommand{\FxGX}{F_{\text{x}}^\text{\GX}}
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\newcommand{\FxHGX}{F_{\text{x}}^\text{\HGX}}
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\newcommand{\FxPBEGX}{F_{\text{x}}^\text{\PBEGX}}
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%
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\newcommand{\ExLDA}{E_{\text{x}}^\text{LDA}}
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\newcommand{\FxGGA}{F_{\text{x}}^\text{GGA}}
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\newcommand{\FxGLDA}{F_{\text{x}}^\text{GLDA}}
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\newcommand{\FxMGGA}{F_{\text{x}}^\text{MGGA}}
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\newcommand{\FxFMGGA}{F_{\text{x}}^\text{FMGGA}}
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\newcommand{\ExsLDA}{E_{\text{x},\sigma}^\text{LDA}}
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\newcommand{\ExsGGA}{E_{\text{x},\sigma}^\text{GGA}}
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\newcommand{\ExsGLDA}{E_{\text{x},\sigma}^\text{GLDA}}
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\newcommand{\exsLDA}{e_{\text{x},\sigma}^\text{LDA}}
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\newcommand{\exsGGA}{e_{\text{x},\sigma}^\text{GGA}}
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\newcommand{\exsGLDA}{e_{\text{x},\sigma}^\text{GLDA}}
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\newcommand{\exsMGGA}{e_{\text{x},\sigma}^\text{MGGA}}
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\newcommand{\exsFMGGA}{e_{\text{x},\sigma}^\text{FMGGA}}
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\newcommand{\CxLDA}{C_\text{x}^\text{LDA}}
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\newcommand{\CxGLDA}{C_\text{x}^\text{GLDA}}
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\newcommand{\Cx}{C_\text{x}}
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\newcommand{\Cf}{C_\text{F}}
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\newcommand{\rs}{\rho_\sigma}
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\newcommand{\xs}{x_\sigma}
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\newcommand{\ts}{\tau_\sigma}
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\newcommand{\as}{\alpha_\sigma}
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\newcommand{\ns}{n_\sigma}
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\newcommand{\Ls}{L_\sigma}
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\newcommand\upa{\uparrow}
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\newcommand\dwa{\downarrow}
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% integrals
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\usepackage[version=4]{mhchem}
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\newcommand{\sba}{\mathring{a}}
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\newcommand{\sbb}{\mathring{b}}
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\newcommand{\sbp}{\mathring{p}}
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\newcommand{\sbz}{\mathring{z}}
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\newcommand{\sbd}{\mathring{\delta}}
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\newcommand{\sbD}{\mathring{\Delta}}
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\newcommand{\sbzeta}{\mathring{\zeta}}
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\newcommand*\elide{\textup{[\,\dots]}}
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\newcommand{\Db}{\check{\Delta}}
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\newcommand{\sbR}{\mathring{R}}
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\newcommand{\sbY}{\mathring{Y}}
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\newcommand{\sbZ}{\mathring{Z}}
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\newcommand{\bAB}{\mathbf{AB}}
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\newcommand{\bG}{\mathbf{G}}
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\newcommand{\bY}{\mathbf{Y}}
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\newcommand{\bZ}{\mathbf{Z}}
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\newcommand{\la}{\lambda}
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\newcommand{\eps}{\varepsilon}
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\newcommand{\Lo}{L}
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\newcommand{\bo}{\mathbf{0}}
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\newcommand{\barS}{\Bar{S}}
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\newcommand{\ba}{\bm{a}}
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\newcommand{\bb}{\bm{b}}
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\newcommand{\Po}{\mathcal{P}}
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\newcommand{\ssc}{\scriptscriptstyle}
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\newcommand{\Rb}{\mathcal{R}}
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\newcommand{\purple}[1]{\textcolor{purple}{#1}}
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\newcommand{\orange}[1]{\textcolor{orange}{#1}}
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\newcommand{\green}[1]{\textcolor{green}{#1}}
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\newcommand{\blue}[1]{\textcolor{blue}{#1}}
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\newcommand{\alphaup}{\hat{\alpha}}
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\newcommand{\Lup}{\hat{a}}
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\newcommand{\hztup}{\hat{\hzt}}
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\newcommand{\hztdw}{\check{\hzt}}
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\newcommand{\Deltaup}{\hat{\Delta}}
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\newcommand{\Deltadw}{\check{\Delta}}
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\newcommand{\deltadw}{\check{\delta}}
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\newcommand{\Lambdaup}{\hat{\Lambda}}
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\newcommand{\Lambdadw}{\check{\Lambda}}
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\newcommand{\hzt}{\xi}
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\newcommand{\sbra}[1]{[ #1 |}
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\newcommand{\sket}[1]{| #1 ]}
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\newcommand{\sexpval}[1]{[ #1 ]}
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\newcommand{\sbraket}[2]{[ #1 | #2 ]}
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\newcommand{\smel}[3]{[ #1 | #2 | #3 ]}
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\newcommand{\shield}{\sigma}
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\newcommand{\mfac}{\sexpval{\widehat{1}}}
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\newcommand{\cfac}{\sexpval{\widetilde{1}}}
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\newcommand{\shopt}{\mathring{\sigma}}
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\newcommand{\shO}{\mathring{\omega}_{1}}
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\newcommand{\shOij}{\mathring{\omega}_{1ij}}
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\newcommand{\cmax}[1]{\langle\widehat{#1}\rangle}
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% Dressed CI
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\newcommand{\oH}{\mathring{H}}
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\newcommand{\EPT}{E_\text{PT2}}
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\newcommand{\NGG}{N_\text{GG}}
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\newcommand{\mA}{\mathcal{A}}
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\newcommand{\mC}{\mathcal{C}}
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\newcommand{\mD}{\mathcal{D}}
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\newcommand{\mE}{\mathcal{E}}
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\newcommand{\mK}{\mathcal{K}}
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\newcommand{\mF}{\mathcal{F}}
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\newcommand{\mL}{\mathcal{L}}
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\newcommand{\kA}{\ket{A}}
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\newcommand{\kD}{\ket{D}}
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\newcommand{\kI}{\ket{I}}
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\newcommand{\kJ}{\ket{J}}
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\newcommand{\kE}{\ket{E}}
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\newcommand{\kK}{\ket{K}}
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\newcommand{\kL}{\ket{L}}
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\newcommand{\kF}{\ket{F}}
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\newcommand{\kO}{\ket{0}}
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% Dressed e-n cusp
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\newcommand{\DrSym}[1]{\Tilde{#1}}
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% wave functions and orbitals
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\newcommand{\ExactPsi}{\Phi}
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\newcommand{\MOsA}[1]{\mathring{\MO{#1}}}
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\newcommand{\STO}[2]{{\DrSym{\chi}_{#1}}^{#2}}
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\newcommand{\ccedMO}[1]{\DrSym{\MO{#1}}}
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\newcommand{\ccingMO}[1]{\varphi_{#1}}
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% coefficients
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\newcommand{\cGTO}[2]{c_{#1 #2}}
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\newcommand{\cSTO}[2]{\DrSym{c}_{#1 #2}}
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\newcommand{\bcGTO}{\bm{c}}
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\newcommand{\bcSTO}{\DrSym{\bm{c}}}
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% exponents
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\newcommand{\expSTOa}{\DrSym{\alpha}}
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\newcommand{\expSTOb}{\DrSym{\beta}}
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% hat operators
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\newcommand{\hFk}{\Hat{f}}
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\newcommand{\hHc}{\Hat{h}}
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% matrices
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\newcommand{\bFk}{\bm{F}}
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\newcommand{\bHc}{\bm{h}}
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\newcommand{\bP}{\bm{P}}
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\newcommand{\bDrFkOp}[1]{\DrSym{\bm{F}}^{#1}}
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\newcommand{\bDr}[1]{\bm{D}^{#1}}
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\newcommand{\bDrFk}[1]{\DrSym{\bm{F}}^{#1}}
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\newcommand{\bDrHc}[1]{\DrSym{\bm{h}}^{#1}}
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\newcommand{\bDrKi}[1]{\DrSym{\bm{T}}^{#1}}
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\newcommand{\bDrPo}[1]{\DrSym{\bm{V}}^{#1}}
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\newcommand{\bDrOv}[1]{\DrSym{\bm{S}}^{#1}}
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\newcommand{\bMOeigval}{\bm{\varepsilon}}
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\newcommand{\bDrMOeigval}{\DrSym{\bm{\varepsilon}}}
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% matrix elements
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\newcommand{\DrFkEl}[3]{\DrSym{F}_{#1 #2}^{#3}}
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\newcommand{\DrFkOpEl}[3]{\DrSym{F}_{#1 #2}^{#3}}
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\newcommand{\DrHcEl}[3]{\DrSym{h}_{#1 #2}^{#3}}
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\newcommand{\DrKiEl}[3]{\DrSym{T}_{#1 #2}^{#3}}
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\newcommand{\DrPoEl}[3]{\DrSym{V}_{#1 #2}^{#3}}
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\newcommand{\DrOvEl}[3]{\DrSym{S}_{#1 #2}^{#3}}
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\newcommand{\DrEl}[2]{\DrSym{D}_{#1}^{#2}}
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\newcommand{\MOeigval}[1]{\varepsilon_{#1}}
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\newcommand{\DrMOeigval}[1]{\DrSym{\varepsilon}_{#1}}
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%----------------------------------------------------------------------------------------
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% MARGIN SETTINGS
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%----------------------------------------------------------------------------------------
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\geometry{
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paper=a4paper, % Change to letterpaper for US letter
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inner=2.5cm, % Inner margin
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outer=3.8cm, % Outer margin
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bindingoffset=.5cm, % Binding offset
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top=1.5cm, % Top margin
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bottom=1.5cm, % Bottom margin
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%showframe, % Uncomment to show how the type block is set on the page
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}
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%----------------------------------------------------------------------------------------
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% THESIS INFORMATION
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%----------------------------------------------------------------------------------------
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\thesistitle{Functionals, Integrals, Spheres \& Cusps} % Your thesis title, this is used in the title and abstract, print it elsewhere with \ttitle
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\supervisor{} % Your supervisor's name, this is used in the title page, print it elsewhere with \supname
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\examiner{} % Your examiner's name, this is not currently used anywhere in the template, print it elsewhere with \examname
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\degree{Habilitation \`a diriger les recherches} % Your degree name, this is used in the title page and abstract, print it elsewhere with \degreename
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\author{Pierre-Fran{\c c}ois Loos} % Your name, this is used in the title page and abstract, print it elsewhere with \authorname
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\addresses{} % Your address, this is not currently used anywhere in the template, print it elsewhere with \addressname
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\subject{Theoretical Chemistry} % Your subject area, this is not currently used anywhere in the template, print it elsewhere with \subjectname
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\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
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\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
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\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
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\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
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\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
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\AtBeginDocument{
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\hypersetup{pdftitle=\ttitle} % Set the PDF's title to your title
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\hypersetup{pdfauthor=\authorname} % Set the PDF's author to your name
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\hypersetup{pdfkeywords=\keywordnames} % Set the PDF's keywords to your keywords
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}
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\begin{document}
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\frontmatter % Use roman page numbering style (i, ii, iii, iv...) for the pre-content pages
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\pagestyle{plain} % Default to the plain heading style until the thesis style is called for the body content
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%----------------------------------------------------------------------------------------
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% TITLE PAGE
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%----------------------------------------------------------------------------------------
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\begin{titlepage}
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\begin{center}
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\vspace*{.06\textheight}
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{\scshape\LARGE \univname\par}\vspace{1.5cm} % University name
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\textsc{\Large Habilitation \`a diriger les recherches}\\[0.5cm] % Thesis type
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\HRule \\[0.4cm] % Horizontal line
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{\huge \bfseries \ttitle\par}\vspace{0.4cm} % Thesis title
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\HRule \\[1.5cm] % Horizontal line
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\begin{minipage}[t]{0.4\textwidth}
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\begin{flushleft} \large
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\emph{Author:}\\
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\href{http://www.irsamc.ups-tlse.fr/loos/}{\authorname} % Author name - remove the \href bracket to remove the link
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\end{flushleft}
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\end{minipage}
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\begin{minipage}[t]{0.5\textwidth}
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\begin{flushright} \large
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\emph{Panel:} \\
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\href{http://www.lpt.ups-tlse.fr/spip.php?article49&lang=en}{Pierre Pujol} (president) \\
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\href{https://www.quantummatter.eu}{Paola Gori-Giorgi} (reviewer) \\
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\href{https://quantique.u-strasbg.fr/doku.php?id=en:pageperso:ef:welcome}{Emmanuel Fromager} (reviewer) \\
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\href{http://www.lct.jussieu.fr/pagesperso/toulouse/}{Julien Toulouse} (reviewer) \\
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\href{http://qmcchem.ups-tlse.fr/index.php?title=Michel_Caffarel}{Michel Caffarel} (supervisor)
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\end{flushright}
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\end{minipage}\\[1cm]
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\vfill
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\large \textit{A thesis submitted in fulfillment of the requirements\\ for the degree of \degreename}\\[0.3cm] % University requirement text
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\textit{in the}\\[0.4cm]
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\groupname\\\deptname\\[2cm] % Research group name and department name
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\vfill
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{\large January 25, 2018}\\[4cm] % Date
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%\includegraphics{Logo} % University/department logo - uncomment to place it
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\vfill
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\end{center}
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\end{titlepage}
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%----------------------------------------------------------------------------------------
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% DECLARATION PAGE
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%----------------------------------------------------------------------------------------
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%\begin{declaration}
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%\addchaptertocentry{\authorshipname} % Add the declaration to the table of contents
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%\noindent I, \authorname, declare that this thesis titled, \enquote{\ttitle} and the work presented in it are my own. I confirm that:
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%\begin{itemize}
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%\item This work was done wholly or mainly while in candidature for a research degree at this University.
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%\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.
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%\item Where I have consulted the published work of others, this is always clearly attributed.
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%\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.
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%\item I have acknowledged all main sources of help.
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%\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.\\
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%\end{itemize}
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%\noindent Signed:\\
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%\rule[0.5em]{25em}{0.5pt} % This prints a line for the signature
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%\noindent Date:\\
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%\rule[0.5em]{25em}{0.5pt} % This prints a line to write the date
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%\end{declaration}
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%\cleardoublepage
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%----------------------------------------------------------------------------------------
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% QUOTATION PAGE
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%----------------------------------------------------------------------------------------
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%\vspace*{0.2\textheight}
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%
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%\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
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%
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%\hfill Marco Siffredi
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%----------------------------------------------------------------------------------------
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% ABSTRACT PAGE
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%----------------------------------------------------------------------------------------
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\begin{abstract}
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%\addchaptertocentry{\abstractname} % Add the abstract to the table of contents
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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.
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First, I describe succinctly several studies we have been doing on model two-electron systems.
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In particular, we introduced a novel class a quasi-exactly solvable systems that we have been studying exhaustively in several papers.
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Following this work, we shed new lights on the universality of correlation effects in two-electrons systems.
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The discovery we have made are discussed.
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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.
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Third, new recurrence relations for three- and four-electron integrals as well as their fundamental integrals and upper bounds are discussed.
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In particular, our strategy to bound rigorously and efficiently these many-electron integrals is presented.
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This new way of calculating many-electron integrals represents an interesting alternative to what is currently done in explicitly-correlated methods.
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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.
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\end{abstract}
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%----------------------------------------------------------------------------------------
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% ACKNOWLEDGEMENTS
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%----------------------------------------------------------------------------------------
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%\begin{acknowledgements}
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%\addchaptertocentry{\acknowledgementname} % Add the acknowledgements to the table of contents
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%I would like to thank... absolutely nobody!
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%\end{acknowledgements}
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%----------------------------------------------------------------------------------------
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% LIST OF CONTENTS/FIGURES/TABLES PAGES
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%----------------------------------------------------------------------------------------
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\tableofcontents % Prints the main table of contents
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%\listoffigures % Prints the list of figures
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%\listoftables % Prints the list of tables
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%----------------------------------------------------------------------------------------
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% ABBREVIATIONS
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%----------------------------------------------------------------------------------------
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%\begin{abbreviations}{ll} % Include a list of abbreviations (a table of two columns)
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%
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%\textbf{LAH} & \textbf{L}ist \textbf{A}bbreviations \textbf{H}ere\\
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%\textbf{WSF} & \textbf{W}hat (it) \textbf{S}tands \textbf{F}or\\
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%
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%\end{abbreviations}
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%----------------------------------------------------------------------------------------
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|
% PHYSICAL CONSTANTS/OTHER DEFINITIONS
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%----------------------------------------------------------------------------------------
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%\begin{constants}{lr@{${}={}$}l} % The list of physical constants is a three column table
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% The \SI{}{} command is provided by the siunitx package, see its documentation for instructions on how to use it
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%Speed of Light & $c_{0}$ & \SI{2.99792458e8}{\meter\per\second} (exact)\\
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%Constant Name & $Symbol$ & $Constant Value$ with units\\
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%\end{constants}
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%----------------------------------------------------------------------------------------
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|
% SYMBOLS
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|
%----------------------------------------------------------------------------------------
|
|
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|
%\begin{symbols}{lll} % Include a list of Symbols (a three column table)
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|
|
|
%$a$ & distance & \si{\meter} \\
|
|
%$P$ & power & \si{\watt} (\si{\joule\per\second}) \\
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|
%Symbol & Name & Unit \\
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|
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%\addlinespace % Gap to separate the Roman symbols from the Greek
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%$\omega$ & angular frequency & \si{\radian} \\
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%\end{symbols}
|
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%----------------------------------------------------------------------------------------
|
|
% DEDICATION
|
|
%----------------------------------------------------------------------------------------
|
|
|
|
%\dedicatory{A mon v\'elo \dots}
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|
|
|
%----------------------------------------------------------------------------------------
|
|
% THESIS CONTENT - CHAPTERS
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|
%----------------------------------------------------------------------------------------
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|
\mainmatter % Begin numeric (1,2,3...) page numbering
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|
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\pagestyle{thesis} % Return the page headers back to the "thesis" style
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|
|
|
% Include the chapters of the thesis as separate files from the Chapters folder
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|
% Uncomment the lines as you write the chapters
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|
|
|
%----------------------------------------------------------------
|
|
% 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}
|
|
|
|
%----------------------------------------------------------------------------------------
|
|
% THESIS CONTENT - APPENDICES
|
|
%----------------------------------------------------------------------------------------
|
|
|
|
%\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}
|
|
|
|
%----------------------------------------------------------------------------------------
|
|
% BIBLIOGRAPHY
|
|
%----------------------------------------------------------------------------------------
|
|
|
|
\printbibliography[heading=bibintoc]
|
|
|
|
%----------------------------------------------------------------------------------------
|
|
|
|
\end{document}
|