diff --git a/CCvsMBPT.bib b/CCvsMBPT.bib index 8e11367..b228f27 100644 --- a/CCvsMBPT.bib +++ b/CCvsMBPT.bib @@ -1,7 +1,7 @@ %% This BibTeX bibliography file was created using BibDesk. %% https://bibdesk.sourceforge.io/ -%% Created for Pierre-Francois Loos at 2022-11-16 22:07:19 +0100 +%% Created for Pierre-Francois Loos at 2022-12-05 18:48:30 +0100 %% Saved with string encoding Unicode (UTF-8) @@ -314,14 +314,13 @@ @article{Knysh_2022, author = {Knysh,Iryna and Duchemin,Ivan and Blase,X. and Jacquemin,Denis M.}, date-added = {2022-10-11 13:26:25 +0200}, - date-modified = {2022-10-11 13:26:41 +0200}, + date-modified = {2022-12-05 18:47:40 +0100}, doi = {10.1063/5.0121121}, journal = {J. Chem. Phys.}, - number = {ja}, - pages = {null}, + pages = {194102}, title = {Modelling of excited state potential energy surfaces with the Betheāˆ’Salpeter equation formalism: The 4-(dimethylamino)benzonitrile twist}, - volume = {0}, - year = {0}, + volume = {157}, + year = {2022}, bdsk-url-1 = {https://doi.org/10.1063/5.0121121}} @article{Loos_2022, diff --git a/CCvsMBPT.tex b/CCvsMBPT.tex index ed990cd..c1e7305 100644 --- a/CCvsMBPT.tex +++ b/CCvsMBPT.tex @@ -15,7 +15,7 @@ \newcommand{\ie}{\textit{i.e.}} \newcommand{\eg}{\textit{e.g.}} -\newcommand{\alert}[1]{\textcolor{red}{#1}} +\newcommand{\alert}[1]{\textcolor{black}{#1}} \usepackage[normalem]{ulem} \newcommand{\titou}[1]{\textcolor{red}{#1}} \newcommand{\trashPFL}[1]{\textcolor{\red}{\sout{#1}}} @@ -438,7 +438,7 @@ However, there is a significant difference with RPAx as the BSE involves $GW$ qu In other words, in the spirit of the Brueckner version of CCD, \cite{Handy_1989} \alert{the $GW$ pre-treatment renormalizes the bare one-electron energies and, consequently, incorporates mosaic \cite{Scuseria_2008,Scuseria_2013} as well as additional diagrams, \cite{Lange_2018} a process named Brueckner-like dressing in Ref.~\onlinecite{Berkelbach_2018}.} This observation evidences clear similitudes between BSE@$GW$ and the similarity-transformed EOM-CC (STEOM-CC) method introduced by Nooijen, \cite{Nooijen_1997c,Nooijen_1997b,Nooijen_1997a} where one performs a second similarity transformation to partially decouple the 1h determinants from the 2h1p ones in the ionization potential (IP) sector and the 1p determinants from the 1h2p ones in the electron affinity (EA) sector. -At the CCSD level, for example, this is achieved by performing IP-EOM-CCSD \cite{Stanton_1994,Musial_2003a} (up to 2h1p) and EA-EOM-CCSD \cite{Nooijen_1995,Musial_2003b} (up to 2p1h) calculations prior to the EOM-CC treatment, which can then be reduced to the 1h1p sector thanks to this partial decoupling. +At the CC with singles and doubles (CCSD) level, for example, this is achieved by performing IP-EOM-CCSD \cite{Stanton_1994,Musial_2003a} (up to 2h1p) and EA-EOM-CCSD \cite{Nooijen_1995,Musial_2003b} (up to 2p1h) calculations prior to the EOM-CC treatment, which can then be reduced to the 1h1p sector thanks to this partial decoupling. (An extended version of STEOM-CC has been proposed where the EOM treatment is pushed up to 2h2p. \cite{Nooijen_2000}) Following the same philosophy, in BSE@$GW$, one performs first a $GW$ calculation (which corresponds to an approximate and simultaneous treatment of the IP and EA sectors up to 2h1p and 2p1h \cite{Lange_2018,Monino_2022}) in order to renormalize the one-electron energies (see Sec.~\ref{sec:GW} for more details). Then, a static BSE calculation is performed in the 1h1p sector with a two-body term dressed with correlation stemming from $GW$. @@ -605,7 +605,7 @@ that can be converted to the following CC-like residual equations \end{split} \end{align} \end{subequations} -with $\Delta_{ija,p}^{\text{2h1p}} = \e{i}{} + \e{j}{} - \e{a}{} - \e{p}{}$ and $\Delta_{iab,p}^{\text{2p1h}} = \e{a}{} + \e{b}{} - \e{i}{} - \e{p}{}$. +with $\Delta_{ija,p}^{\text{2h1p}} = \e{i}{\GW} + \e{j}{\GW} - \e{a}{\GW} - \e{p}{}$ and $\Delta_{iab,p}^{\text{2p1h}} = \e{a}{\GW} + \e{b}{\GW} - \e{i}{\GW} - \e{p}{}$. To determine the 2h1p and 2p1h amplitudes, $t_{ija,p}^{\text{2h1p}}$ and $t_{iab,p}^{\text{2p1h}} $, one can then rely on the usual quasi-Newton iterative procedure to solve these quadratic equations by updating the amplitudes via \begin{subequations} \begin{align} @@ -659,9 +659,1363 @@ Data sharing is not applicable to this article as no new data were created or an %%%%%%%%% %\appendix %%%%%%%%% - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\bibliography{CCvsMBPT} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%merlin.mbs aipnum4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked +%Control: key (0) +%Control: author (8) initials jnrlst +%Control: editor formatted (1) identically to author +%Control: production of article title (-1) disabled +%Control: page (0) single +%Control: year (1) truncated +%Control: production of eprint (0) enabled +\begin{thebibliography}{143}% +\makeatletter +\providecommand \@ifxundefined [1]{% + \@ifx{#1\undefined} +}% +\providecommand \@ifnum [1]{% + \ifnum #1\expandafter \@firstoftwo + \else \expandafter \@secondoftwo + \fi +}% +\providecommand \@ifx [1]{% + \ifx #1\expandafter \@firstoftwo + \else \expandafter \@secondoftwo + \fi +}% +\providecommand \natexlab [1]{#1}% +\providecommand \enquote [1]{``#1''}% +\providecommand \bibnamefont [1]{#1}% +\providecommand \bibfnamefont [1]{#1}% +\providecommand \citenamefont [1]{#1}% +\providecommand \href@noop [0]{\@secondoftwo}% +\providecommand \href [0]{\begingroup \@sanitize@url \@href}% +\providecommand \@href[1]{\@@startlink{#1}\@@href}% +\providecommand \@@href[1]{\endgroup#1\@@endlink}% +\providecommand \@sanitize@url [0]{\catcode `\\12\catcode `\$12\catcode + `\&12\catcode `\#12\catcode `\^12\catcode `\_12\catcode `\%12\relax}% +\providecommand \@@startlink[1]{}% +\providecommand \@@endlink[0]{}% +\providecommand \url [0]{\begingroup\@sanitize@url \@url }% +\providecommand \@url [1]{\endgroup\@href {#1}{\urlprefix }}% +\providecommand \urlprefix [0]{URL }% +\providecommand \Eprint [0]{\href }% +\providecommand \doibase [0]{http://dx.doi.org/}% +\providecommand \selectlanguage [0]{\@gobble}% +\providecommand \bibinfo [0]{\@secondoftwo}% +\providecommand \bibfield [0]{\@secondoftwo}% +\providecommand \translation [1]{[#1]}% +\providecommand \BibitemOpen [0]{}% +\providecommand \bibitemStop [0]{}% +\providecommand \bibitemNoStop [0]{.\EOS\space}% +\providecommand \EOS [0]{\spacefactor3000\relax}% +\providecommand \BibitemShut [1]{\csname bibitem#1\endcsname}% +\let\auto@bib@innerbib\@empty +% +\bibitem [{\citenamefont {Bohm}\ and\ \citenamefont {Pines}(1951)}]{Bohm_1951}% + \BibitemOpen + \bibfield {author} {\bibinfo {author} {\bibfnamefont {D.}~\bibnamefont + {Bohm}}\ and\ \bibinfo {author} {\bibfnamefont {D.}~\bibnamefont {Pines}},\ + }\href {\doibase 10.1103/PhysRev.82.625} {\bibfield {journal} {\bibinfo + {journal} {Phys. 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Rev.}\ }\textbf {\bibinfo {volume} {175}},\ + \bibinfo {pages} {1283} (\bibinfo {year} {1968})}\BibitemShut {NoStop}% +\bibitem [{\citenamefont {Ring}\ and\ \citenamefont + {Schuck}(2004)}]{Schuck_book}% + \BibitemOpen + \bibfield {author} {\bibinfo {author} {\bibfnamefont {P.}~\bibnamefont + {Ring}}\ and\ \bibinfo {author} {\bibfnamefont {P.}~\bibnamefont {Schuck}},\ + }\href@noop {} {\emph {\bibinfo {title} {The Nuclear Many-Body Problem}}}\ + (\bibinfo {publisher} {Springer},\ \bibinfo {year} {2004})\BibitemShut + {NoStop}% +\bibitem [{Note1()}]{Note1}% + \BibitemOpen + \bibinfo {note} {The factor $1/4$ in Eq.~\protect \textup {\hbox + {\mathsurround \z@ \protect \normalfont (\ignorespaces \ref + {eq:EcRPAx}\unskip \@@italiccorr )}} is sometimes replaced by a factor $1/2$, + which corresponds to a different choice for the interaction kernel. See + Ref.~\protect \rev@citealpnum {Angyan_2011} for more details}\BibitemShut + {NoStop}% +\bibitem [{\citenamefont {Furche}\ and\ \citenamefont {{Van + Voorhis}}(2005)}]{Furche_2005}% + \BibitemOpen + \bibfield {author} {\bibinfo {author} {\bibfnamefont {F.}~\bibnamefont + {Furche}}\ and\ \bibinfo {author} {\bibfnamefont {T.}~\bibnamefont {{Van + Voorhis}}},\ }\href {\doibase 10.1063/1.1884112} {\bibfield {journal} + {\bibinfo {journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {122}},\ + \bibinfo {pages} {164106} (\bibinfo {year} {2005})}\BibitemShut {NoStop}% +\bibitem [{\citenamefont {Stanton}\ and\ \citenamefont + {Bartlett}(1993)}]{Stanton_1993}% + \BibitemOpen + \bibfield {author} {\bibinfo {author} {\bibfnamefont {J.~F.}\ \bibnamefont + {Stanton}}\ and\ \bibinfo {author} {\bibfnamefont {R.~J.}\ \bibnamefont + {Bartlett}},\ }\href {\doibase 10.1063/1.464746} {\bibfield {journal} + {\bibinfo {journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {98}},\ + \bibinfo {pages} {7029} (\bibinfo {year} {1993})}\BibitemShut {NoStop}% +\bibitem [{\citenamefont {Emrich}(1981)}]{Emrich_1981}% + \BibitemOpen + \bibfield {author} {\bibinfo {author} {\bibfnamefont {K.}~\bibnamefont + {Emrich}},\ }\href {\doibase https://doi.org/10.1016/0375-9474(81)90179-2} + {\bibfield {journal} {\bibinfo {journal} {Nuc. Phys. A}\ }\textbf {\bibinfo + {volume} {351}},\ \bibinfo {pages} {379} (\bibinfo {year} + {1981})}\BibitemShut {NoStop}% +\bibitem [{\citenamefont {Runge}\ and\ \citenamefont + {Gross}(1984)}]{Runge_1984}% + \BibitemOpen + \bibfield {author} {\bibinfo {author} {\bibfnamefont {E.}~\bibnamefont + {Runge}}\ and\ \bibinfo {author} {\bibfnamefont {E.~K.~U.}\ \bibnamefont + {Gross}},\ }\href {\doibase 10.1103/PhysRevLett.52.997} {\bibfield {journal} + {\bibinfo {journal} {Phys. Rev. Lett.}\ }\textbf {\bibinfo {volume} {52}},\ + \bibinfo {pages} {997} (\bibinfo {year} {1984})}\BibitemShut {NoStop}% +\bibitem [{\citenamefont {Casida}(1995)}]{Casida_1995}% + \BibitemOpen + \bibfield {author} {\bibinfo {author} {\bibfnamefont {M.~E.}\ \bibnamefont + {Casida}},\ }\enquote {\bibinfo {title} {Time-dependent density functional + response theory for molecules},}\ \ (\bibinfo {publisher} {World Scientific, + Singapore},\ \bibinfo {year} {1995})\ pp.\ \bibinfo {pages} + {155--192}\BibitemShut {NoStop}% +\bibitem [{Note2()}]{Note2}% + \BibitemOpen + \bibinfo {note} {\protect \leavevmode {\color {black}To the best of our + knowledge, the trace (or plasmon) formula has been first introduced by Sawada + \cite {Sawada_1957a} to calculate the correlation energy of the uniform + electron gas as an alternative to the Gell-Mann-Brueckner formulation \cite + {Gell-Mann_1957} where one integrates along the adiabatic connection path. + More precisely, the trace formula can be justified via the introduction of a + quadratic Hamiltonian made of boson transition operators (quasiboson + approximation). See Ref.~\protect \rev@citealpnum {Li_2020} for more + details}.}\BibitemShut {Stop}% +\bibitem [{\citenamefont {Li}\ \emph {et~al.}(2020)\citenamefont {Li}, + \citenamefont {Duchemin}, \citenamefont {Blase},\ and\ \citenamefont + {Olevano}}]{Li_2020}% + \BibitemOpen + \bibfield {author} {\bibinfo {author} {\bibfnamefont {J.}~\bibnamefont + {Li}}, \bibinfo {author} {\bibfnamefont {I.}~\bibnamefont {Duchemin}}, + \bibinfo {author} {\bibfnamefont {X.}~\bibnamefont {Blase}}, \ and\ \bibinfo + {author} {\bibfnamefont {V.}~\bibnamefont {Olevano}},\ }\href {\doibase + 10.21468/SciPostPhys.8.2.020} {\bibfield {journal} {\bibinfo {journal} + {SciPost Phys.}\ }\textbf {\bibinfo {volume} {8}},\ \bibinfo {pages} {20} + (\bibinfo {year} {2020})}\BibitemShut {NoStop}% +\bibitem [{\citenamefont {Li}\ and\ \citenamefont {Olevano}(2021)}]{Li_2021}% + \BibitemOpen + \bibfield {author} {\bibinfo {author} {\bibfnamefont {J.}~\bibnamefont + {Li}}\ and\ \bibinfo {author} {\bibfnamefont {V.}~\bibnamefont {Olevano}},\ + }\href {\doibase 10.1103/PhysRevA.103.012809} {\bibfield {journal} {\bibinfo + {journal} {Phys. 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