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57
SlideToulouse/SlideToulouse.bib
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@ -1,27 +1,18 @@
@article{gill_why_1988, @article{gill_why_1988,
title = {Why does unrestricted Mo/ller–Plesset perturbation theory converge so slowly for spin‐contaminated wave functions?}, title = {Why does unrestricted Møller–Plesset perturbation theory converge so slowly for spin‐contaminated wave functions?},
volume = {89}, volume = {89},
issn = {0021-9606},
url = {https://aip.scitation.org/doi/abs/10.1063/1.455312},
doi = {10.1063/1.455312},
pages = {7307--7314}, pages = {7307--7314},
number = {12}, number = {12},
journaltitle = {The Journal of Chemical Physics}, journaltitle = {The Journal of Chemical Physics},
shortjournal = {J. Chem. Phys.}, shortjournal = {J. Chem. Phys.},
author = {Gill, Peter M. W. and Pople, John A. and Radom, Leo and Nobes, Ross H.}, author = {Gill, Peter M. W. and Pople, John A. and Radom, Leo and Nobes, Ross H.},
urldate = {2020-06-10}, date = {1988-12-15}
date = {1988-12-15},
note = {Publisher: American Institute of Physics},
file = {Snapshot:/home/amarie/Zotero/storage/4SDW37YN/1.html:text/html}
} }
@article{sergeev_nature_2005, @article{sergeev_nature_2005,
title = {On the nature of the Møller-Plesset critical point}, title = {On the nature of the Møller-Plesset critical point},
volume = {123}, volume = {123},
issn = {0021-9606},
url = {https://aip.scitation.org/doi/10.1063/1.1991854},
doi = {10.1063/1.1991854},
pages = {064105}, pages = {064105},
number = {6}, number = {6},
journaltitle = {The Journal of Chemical Physics}, journaltitle = {The Journal of Chemical Physics},
@ -36,69 +27,59 @@
@article{sergeev_singularities_2006, @article{sergeev_singularities_2006,
title = {Singularities of Møller-Plesset energy functions}, title = {Singularities of Møller-Plesset energy functions},
volume = {124}, volume = {124},
issn = {0021-9606},
url = {https://aip.scitation.org/doi/10.1063/1.2173989},
doi = {10.1063/1.2173989},
pages = {094111}, pages = {094111},
number = {9}, number = {9},
journaltitle = {The Journal of Chemical Physics}, journaltitle = {The Journal of Chemical Physics},
shortjournal = {J. Chem. Phys.}, shortjournal = {J. Chem. Phys.},
author = {Sergeev, Alexey V. and Goodson, David Z.}, author = {Sergeev, Alexey V. and Goodson, David Z.},
urldate = {2020-06-10}, date = {2006-03-07}
date = {2006-03-07},
note = {Publisher: American Institute of Physics},
file = {Snapshot:/home/amarie/Zotero/storage/IP28R6TR/1.html:text/html}
} }
@article{olsen_divergence_2000, @article{olsen_divergence_2000,
title = {Divergence in Møller–Plesset theory: A simple explanation based on a two-state model}, title = {Divergence in Møller–Plesset theory: A simple explanation based on a two-state model},
volume = {112}, volume = {112},
issn = {0021-9606},
url = {https://aip.scitation.org/doi/10.1063/1.481611},
doi = {10.1063/1.481611},
shorttitle = {Divergence in Møller–Plesset theory}, shorttitle = {Divergence in Møller–Plesset theory},
pages = {9736--9748}, pages = {9736--9748},
number = {22}, number = {22},
journaltitle = {The Journal of Chemical Physics}, journaltitle = {The Journal of Chemical Physics},
shortjournal = {J. Chem. Phys.}, shortjournal = {J. Chem. Phys.},
author = {Olsen, Jeppe and Jørgensen, Poul and Helgaker, Trygve and Christiansen, Ove}, author = {Olsen, Jeppe and Jørgensen, Poul and Helgaker, Trygve and Christiansen, Ove},
urldate = {2020-06-10}, date = {2000-05-31}
date = {2000-05-31},
note = {Publisher: American Institute of Physics},
file = {Snapshot:/home/amarie/Zotero/storage/NNNBDR3R/1.html:text/html}
} }
@article{loos_ground_2009, @article{loos_ground_2009,
title = {Ground state of two electrons on a sphere}, title = {Ground state of two electrons on a sphere},
volume = {79}, volume = {79},
url = {https://link.aps.org/doi/10.1103/PhysRevA.79.062517},
doi = {10.1103/PhysRevA.79.062517},
abstract = {We have performed a comprehensive study of the singlet ground state of two electrons on the surface of a sphere of radius R. We have used electronic structure models ranging from restricted and unrestricted Hartree-Fock theories to explicitly correlated treatments, the last of which leads to near-exact wave functions and energies for any value of R. Møller-Plesset energy corrections (up to fifth-order) are also considered, as well as the asymptotic solution in the large-R regime.}, abstract = {We have performed a comprehensive study of the singlet ground state of two electrons on the surface of a sphere of radius R. We have used electronic structure models ranging from restricted and unrestricted Hartree-Fock theories to explicitly correlated treatments, the last of which leads to near-exact wave functions and energies for any value of R. Møller-Plesset energy corrections (up to fifth-order) are also considered, as well as the asymptotic solution in the large-R regime.},
pages = {062517}, pages = {062517},
number = {6}, number = {6},
journaltitle = {Physical Review A}, journaltitle = {Physical Review A},
shortjournal = {Phys. Rev. A}, shortjournal = {Phys. Rev. A},
author = {Loos, Pierre-François and Gill, Peter M. W.}, author = {Loos, Pierre-François and Gill, Peter M. W.},
urldate = {2020-06-11}, date = {2009-06-30}
date = {2009-06-30},
note = {Publisher: American Physical Society},
file = {APS Snapshot:/home/amarie/Zotero/storage/WWCNWCPS/PhysRevA.79.html:text/html;Submitted Version:/home/amarie/Zotero/storage/5DIQ69YK/Loos and Gill - 2009 - Ground state of two electrons on a sphere.pdf:application/pdf}
} }
@article{gill_deceptive_1986, @article{gill_deceptive_1986,
title = {Deceptive convergence in møller-plesset perturbation energies}, title = {Deceptive convergence in Møller-plesset perturbation energies},
volume = {132}, volume = {132},
issn = {0009-2614},
url = {http://www.sciencedirect.com/science/article/pii/0009261486806868},
doi = {10.1016/0009-2614(86)80686-8},
abstract = {Meller-Plesset perturbation calculations ({MPn}) up to fiftieth order, within both the restricted ({RHF}) and unrestricted Hartree-Fock ({UHF}) frameworks, have been used to examine the He2+2 ground-state potential curve. The bond lengths of the equilibrium and transition structures have been optimized at all orders of perturbation theory. It is found that {RMP} n describes the homolytic dissociation better than {UMPn} for all n {\textgreater} 2. This unexpected behaviour may be attributed to spin contamination in the {UHF} wavefunction. The {UMPn} barriers deceptively appear convergent for small n and the results may be indicative of dangers inherent generally in using the {UMP} approach with significantly spin-contaminated wavefunctions.}, abstract = {Meller-Plesset perturbation calculations ({MPn}) up to fiftieth order, within both the restricted ({RHF}) and unrestricted Hartree-Fock ({UHF}) frameworks, have been used to examine the He2+2 ground-state potential curve. The bond lengths of the equilibrium and transition structures have been optimized at all orders of perturbation theory. It is found that {RMP} n describes the homolytic dissociation better than {UMPn} for all n {\textgreater} 2. This unexpected behaviour may be attributed to spin contamination in the {UHF} wavefunction. The {UMPn} barriers deceptively appear convergent for small n and the results may be indicative of dangers inherent generally in using the {UMP} approach with significantly spin-contaminated wavefunctions.},
pages = {16--22}, pages = {16--22},
number = {1}, number = {1},
journaltitle = {Chemical Physics Letters}, journaltitle = {Chemical Physics Letters},
shortjournal = {Chemical Physics Letters}, shortjournal = {Chemical Physics Letters},
author = {Gill, Peter M. W. and Radom, Leo}, author = {Gill, Peter M. W. and Radom, Leo},
urldate = {2020-06-28},
date = {1986-11-28}, date = {1986-11-28},
langid = {english}, langid = {english}
file = {ScienceDirect Snapshot:/home/amarie/Zotero/storage/YV2LVWML/0009261486806868.html:text/html;Submitted Version:/home/amarie/Zotero/storage/U8VEPSSU/Gill and Radom - 1986 - Deceptive convergence in møller-plesset perturbati.pdf:application/pdf} }
@article{stillinger_mollerplesset_2000,
title = {Møller–Plesset convergence issues in computational quantum chemistry},
volume = {112},
pages = {9711--9715},
number = {22},
journaltitle = {The Journal of Chemical Physics},
shortjournal = {J. Chem. Phys.},
author = {Stillinger, Frank H.},
date = {2000-05-31}
} }

40
SlideToulouse/main.tex
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@ -2,8 +2,6 @@
%% General document %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% General document %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{graphicx} \usepackage{graphicx}
\usepackage{tikz}
\usetikzlibrary{decorations.fractals}
\usepackage{mathpazo} \usepackage{mathpazo}
\usepackage[english]{babel} \usepackage[english]{babel}
\usepackage[T1]{fontenc} \usepackage[T1]{fontenc}
@ -13,11 +11,12 @@
\usepackage{graphicx} \usepackage{graphicx}
\usepackage{physics} \usepackage{physics}
\usepackage{multimedia} \usepackage{multimedia}
\usepackage{subfigure}
\usepackage[absolute,overlay]{textpos} \usepackage[absolute,overlay]{textpos}
\usepackage{ragged2e} \usepackage{ragged2e}
\usepackage{amssymb} \usepackage{amssymb}
\usepackage[version=4]{mhchem} \usepackage[version=4]{mhchem}
\usepackage[style=verbose,backend=bibtex]{biblatex}
\bibliography{SlideToulouse}
@ -150,16 +149,20 @@ In physics perturbation theory is often a good way to improve the obtained resul
\begin{beamerboxesrounded}[scheme=foncé]{} \begin{beamerboxesrounded}[scheme=foncé]{}
\centering \centering
Full Configuration Interaction gives access to high-order terms of the perturbation series! Full Configuration Interaction gives access to high-order terms of the perturbation series!
\end{beamerboxesrounded} \end{beamerboxesrounded}
\end{frame} \end{frame}
\begin{frame}{Deceptive or slow convergences} \begin{frame}{Deceptive or slow convergences\footcite{gill_deceptive_1986}}
\begin{figure} \begin{figure}
\centering \centering
\includegraphics[width=0.5\textwidth]{gill1986.png}
\includegraphics[width=0.45\textwidth]{gill1986.png}
\caption{\centering Barriers to homolytic fission of \ce{He2^2+} at MPn/STO-3G level ($n = 1$--$20$).} \caption{\centering Barriers to homolytic fission of \ce{He2^2+} at MPn/STO-3G level ($n = 1$--$20$).}
\label{fig:my_label} \label{fig:my_label}
\end{figure} \end{figure}
@ -167,7 +170,7 @@ Full Configuration Interaction gives access to high-order terms of the perturbat
\end{frame} \end{frame}
\begin{frame}{Multi-reference and spin contamination} \begin{frame}{Multi-reference and spin contamination\footcite{gill_why_1988}}
\begin{table} \begin{table}
\centering \centering
\begin{tabular}{c c c c c c c} \begin{tabular}{c c c c c c c}
@ -184,7 +187,6 @@ Full Configuration Interaction gives access to high-order terms of the perturbat
\label{tab:my_label} \label{tab:my_label}
\end{table} \end{table}
\footnotetext{\tiny{Gill et al. Why does unrestricted M{\o}ller-Plesset perturbation theory converge so slowly for spin-contaminated wave functions, \textit{Journal of chemical physics}, 1988}}
\end{frame} \end{frame}
@ -193,12 +195,10 @@ Full Configuration Interaction gives access to high-order terms of the perturbat
\begin{figure} \begin{figure}
\centering \centering
\includegraphics[width=0.6\textwidth]{The-energy-corrections-for-HF-at-stretched-geometry-in-the-cc-pVDZ-basis.png} \includegraphics[width=0.6\textwidth]{The-energy-corrections-for-HF-at-stretched-geometry-in-the-cc-pVDZ-basis.png}
\caption{The energy corrections for HF at stretched geometry in the cc-pVDZ basis.} \caption{The energy corrections for HF at stretched geometry in the cc-pVDZ basis. \footcite{olsen_divergence_2000}}
\label{fig:my_label} \label{fig:my_label}
\end{figure} \end{figure}
\footnotetext{\tiny{Olsen et al. Divergence in Møller–Plesset theory: A simple explanation based on a two-state model, \textit{Journal of chemical physics}, 2000}}
\end{frame} \end{frame}
\section{The complex plane} \section{The complex plane}
@ -316,7 +316,7 @@ The \textcolor{red}{radius of convergence} of the Taylor expansion of a function
\end{frame} \end{frame}
\begin{frame}{A two-state model} \begin{frame}{A two-state model\footcite{olsen_divergence_2000}}
\begin{columns} \begin{columns}
@ -342,24 +342,20 @@ The \textcolor{red}{radius of convergence} of the Taylor expansion of a function
\vspace{1cm} \vspace{1cm}
\end{columns} \end{columns}
\footnotetext{\tiny{Olsen et al. Divergence in Møller–Plesset theory: A simple explanation based on a two-state model, \textit{Journal of chemical physics}, 2000}}
\end{frame} \end{frame}
\begin{frame}{Two-state model} \begin{frame}{Two-state model\footcite{olsen_divergence_2000}}
\begin{figure} \begin{figure}
\centering \centering
\includegraphics[width=0.6\textwidth]{figure-fig14.png} \includegraphics[width=0.6\textwidth]{figure-fig14.png}
\caption{\centering The energy corrections for HF at stretched geometry in the aug'-cc-pVDZ basis with the two-state model.\textsuperscript{a}} \caption{\centering The energy corrections for HF at stretched geometry in the aug'-cc-pVDZ basis with the two-state model.}
\label{fig:my_label} \label{fig:my_label}
\end{figure} \end{figure}
\footnotetext{\tiny{Olsen et al. Divergence in Møller–Plesset theory: A simple explanation based on a two-state model, \textit{Journal of chemical physics}, 2000}}
\end{frame} \end{frame}
\begin{frame}{Existence of a critical point} \begin{frame}{Existence of a critical point\footcite{stillinger_mollerplesset_2000}}
For $\lambda<0$: For $\lambda<0$:
@ -367,8 +363,6 @@ For $\lambda<0$:
H(\lambda)=\sum\limits_{j=1}^{2n}\left[ \underbrace{-\frac{1}{2}\grad_j^2 - \sum\limits_{k=1}^{N} \frac{Z_k}{|\vb{r}_j-\vb{R}_k|}}_{\text{Independant of }\lambda} + \overbrace{(1-\lambda)V_j^{(scf)}}^{\textcolor{red}{Repulsive}}+\underbrace{\lambda\sum\limits_{j<l}^{2n}\frac{1}{|\vb{r}_j-\vb{r}_l|}}_{\textcolor{blue}{Attractive}} \right] H(\lambda)=\sum\limits_{j=1}^{2n}\left[ \underbrace{-\frac{1}{2}\grad_j^2 - \sum\limits_{k=1}^{N} \frac{Z_k}{|\vb{r}_j-\vb{R}_k|}}_{\text{Independant of }\lambda} + \overbrace{(1-\lambda)V_j^{(scf)}}^{\textcolor{red}{Repulsive}}+\underbrace{\lambda\sum\limits_{j<l}^{2n}\frac{1}{|\vb{r}_j-\vb{r}_l|}}_{\textcolor{blue}{Attractive}} \right]
\end{equation*} \end{equation*}
\footnote{stillinger, sergeev, baker}
\end{frame} \end{frame}
\begin{frame}{Critical point in a finite basis set} \begin{frame}{Critical point in a finite basis set}
@ -395,7 +389,7 @@ The singularities occur in complex conjugate pairs with non-zero imaginary parts
\end{frame} \end{frame}
\begin{frame}{Singularities $\alpha$ and $\beta$} \begin{frame}{Singularities $\alpha$ and $\beta$ \footcite{sergeev_singularities_2006}}
\pause[1] \pause[1]
@ -423,8 +417,6 @@ We can separate singularities in two parts.
\end{itemize} \end{itemize}
\end{beamerboxesrounded} \end{beamerboxesrounded}
\footnote{sergeev}
\end{frame} \end{frame}
@ -451,7 +443,7 @@ Proof of the existence of this group of sharp avoided crossings for Ne, He and H
\section{The spherium model} \section{The spherium model}
\begin{frame}{Spherium: a theoretical playground} \begin{frame}{Spherium: a theoretical playground\footcite{loos_ground_2009}}
\begin{beamerboxesrounded}[scheme=foncé]{\centering Two electrons on a sphere Hamiltonian} \begin{beamerboxesrounded}[scheme=foncé]{\centering Two electrons on a sphere Hamiltonian}
\begin{equation*} \begin{equation*}