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52
Manuscript/sfBSE.bib
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@ -1,13 +1,55 @@
%% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/
%% Created for Pierre-Francois Loos at 2021-01-11 09:47:39 +0100
%% Created for Pierre-Francois Loos at 2021-01-13 09:41:10 +0100
%% Saved with string encoding Unicode (UTF-8)
@article{Becke_1993b,
author = {Becke,Axel D.},
date-added = {2021-01-13 09:37:07 +0100},
date-modified = {2021-01-13 09:40:17 +0100},
doi = {10.1063/1.464304},
journal = {J. Chem. Phys.},
number = {2},
pages = {1372-1377},
title = {A new mixing of Hartree--Fock and local density‐functional theories},
volume = {98},
year = {1993},
Bdsk-Url-1 = {https://doi.org/10.1063/1.464304}}
@article{Lee_1988,
author = {C. Lee and W. Yang and R. G. Parr},
date-added = {2021-01-13 09:35:39 +0100},
date-modified = {2021-01-13 09:35:47 +0100},
doi = {10.1103/PhysRevB.37.785},
issue = {2},
journal = {Phys. Rev. B},
month = {Jan},
pages = {785},
publisher = {American Physical Society},
title = {Development of the Colle--Salvetti correlation-energy formula into a functional of the electron density},
url = {http://link.aps.org/doi/10.1103/PhysRevB.37.785},
volume = {37},
year = {1988},
Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevB.37.785},
Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.37.785}}
@article{Becke_1988,
author = {A. D. Becke},
date-added = {2021-01-13 09:34:25 +0100},
date-modified = {2021-01-13 09:34:25 +0100},
doi = {10.1103/PhysRevA.38.3098},
journal = {Phys. Rev. A},
pages = {3098},
title = {Density-functional exchange-energy approximation with correct asymptotic behavior},
volume = {38},
year = {1988},
Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevA.38.3098}}
@article{Koch_1994,
author = {Koch,Henrik and Kobayashi,Rika and Sanchez de Mer{\'a}s,Alfredo and Jorgensen, Poul},
date-added = {2021-01-11 09:32:50 +0100},
@ -8699,9 +8741,9 @@
Bdsk-Url-1 = {http://dx.doi.org/10.1080/00268976.2014.1003621}}
@article{Koch_1990,
author = {Koch, Henrik and Jensen, Hans Jo/rgen Aa. and Jo/rgensen, Poul and Helgaker, Trygve},
author = {Koch, Henrik and Jensen, Hans Jorgen Aa. and Jorgensen, Poul and Helgaker, Trygve},
date-added = {2020-01-01 21:36:51 +0100},
date-modified = {2021-01-11 09:32:58 +0100},
date-modified = {2021-01-13 09:40:51 +0100},
doi = {10.1063/1.458815},
journal = {J. Chem. Phys.},
number = {5},
@ -13435,10 +13477,10 @@
year = {2016},
Bdsk-Url-1 = {https://doi.org/10.1063/1.4963749}}
@article{Becke_1993,
@article{Becke_1993a,
author = {A. D. Becke},
date-added = {2018-07-04 21:18:18 +0000},
date-modified = {2018-07-18 13:08:55 +0000},
date-modified = {2021-01-13 09:37:24 +0100},
doi = {10.1063/1.464913},
journal = {J. Chem. Phys.},
pages = {5648--5652},

38
Manuscript/sfBSE.tex
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@ -577,10 +577,12 @@ In the following, all linear response calculations are performed within the TDA
%\titou{As one-electron basis sets, we employ Pople's 6-31G basis or the Dunning families cc-pVXZ and aug-cc-pVXZ (X = D, T, and Q) defined with cartesian Gaussian functions.}
Finally, the infinitesimal $\eta$ is set to $100$ meV for all calculations.
All the static and dynamic BSE calculations have been performed with the software \texttt{QuAcK}, \cite{QuAcK} developed in our group and freely available on \texttt{github}.
The SF-ADC, EOM-SF-CC and SF-TD-DFT calculations have been performed with Q-CHEM 5.2.1 \cite{qchem4} and the EOM-CCSD calculation with Gaussian 09. \cite{g09}
As a consistency check, we systematically perform the SF-CIS calculations with both \texttt{QuAcK} and Q-CHEM, and make sure that they yield identical excitation energies.
Throughout this work, all spin-flip calculations have been performed with a UHF reference.
All the static and dynamic BSE calculations (labeled in the following as SF-BSE and SF-dBSE respectively) are performed with the software \texttt{QuAcK}, \cite{QuAcK} developed in our group and freely available on \texttt{github}.
The standard and extended spin-flip ADC(2) calculations [SF-ADC(2)-s and SF-ADC(2)-x, respectively] as well as the SF-ADC(3) \cite{Lefrancois_2015} are performed with Q-CHEM 5.2.1. \cite{qchem4}
Spin-flip TD-DFT calculations \cite{Shao_2003} considering the BLYP, \cite{Becke_1988,Lee_1988} B3LYP, \cite{Becke_1988,Lee_1988,Becke_1993a} and BH\&HLYP \cite{Lee_1988,Becke_1993b} functionals with contains $0\%$, $20\%$, and $50\%$ of exact exchange are labeled as SF-TD-BLYP, SF-TD-B3LYP, and SF-TD-BH\&HLYP, respectively, and are also performed with Q-CHEM 5.2.1.
EOM-CCSD excitation energies \cite{Koch_1990,Stanton_1993,Koch_1994} are computed with Gaussian 09. \cite{g09}
As a consistency check, we systematically perform the SF-CIS calculations \cite{Krylov_2001a} with both \texttt{QuAcK} and Q-CHEM, and make sure that they yield identical excitation energies.
Throughout this work, all spin-flip calculations are performed with a UHF reference.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Results}
@ -625,9 +627,9 @@ The excitation energies corresponding to the first singlet and triplet single ex
FCI\fnm[3] & 2.862 & 6.577 & 7.669 & 8.624 \\
\end{tabular}
\end{ruledtabular}
\fnt[1]{Excitation energies extracted from Ref.~\onlinecite{Casanova_2020}.}
\fnt[1]{Values from Ref.~\onlinecite{Casanova_2020}.}
\fnt[2]{This work.}
\fnt[3]{Excitation energies taken from Ref.~\onlinecite{Krylov_2001a}.}
\fnt[3]{Values from Ref.~\onlinecite{Krylov_2001a}.}
\end{table}
\end{squeezetable}
%%% %%% %%% %%%
@ -637,7 +639,7 @@ The excitation energies corresponding to the first singlet and triplet single ex
\includegraphics[width=\linewidth]{Be}
\caption{
Excitation energies [with respect to the $^1S(1s^2 2s^2)$ singlet ground state] of \ce{Be} obtained with the 6-31G basis for various levels of theory:
SD-TD-DFT \cite{Casanova_2020} (red), SF-BSE (blue), SF-CIS \cite{Krylov_2001a} and SF-ADC (orange), and FCI \cite{Krylov_2001a} (black).
SF-TD-DFT \cite{Casanova_2020} (red), SF-BSE (blue), SF-CIS \cite{Krylov_2001a} and SF-ADC (orange), and FCI \cite{Krylov_2001a} (black).
All the spin-flip calculations have been performed with a UHF reference.
\label{fig:Be}}
\end{figure}
@ -797,7 +799,8 @@ All of them have been obtained with a UHF reference like the SF-BSE calculations
%%% TABLE ?? %%%
\begin{table}
\caption{
Vertical excitation energies (with respect to the singlet $X\,{}^1A_{g}$ ground state) of the $1\,{}^3B_{1g}$, $1\,{}^1B_{1g}$, and $2\,{}^1A_{1g}$ states at the $D_{2h}$ rectangular equilibrium geometry of the $X\,{}^1 A_{g}$ singlet ground state.
Vertical excitation energies (with respect to the singlet $\text{X}\,{}^1A_{g}$ ground state) of the $1\,{}^3B_{1g}$, $1\,{}^1B_{1g}$, and $2\,{}^1A_{1g}$ states at the $D_{2h}$ rectangular equilibrium geometry of the $X\,{}^1 A_{g}$ singlet ground state.
All the spin-flip calculations have been performed with a UHF reference.
\label{tab:CBD_D2h}}
\begin{ruledtabular}
\begin{tabular}{lccc}
@ -812,12 +815,12 @@ All of them have been obtained with a UHF reference like the SF-BSE calculations
SF-ADC(2)-s\fnm[2] & 1.572& 3.201& 4.241\\
SF-ADC(2)-x\fnm[2] &1.576 &3.134 &3.792 \\
SF-ADC(3)\fnm[2] & 1.455&3.276 &4.328 \\
SF-BSE@{\GOWO}@UHF\fnm[3] & 1.438 & 2.704 &4.540 \\
SF-dBSE@{\GOWO}@UHF\fnm[3] & 1.403 &2.883 &4.621 \\
SF-BSE@{\GOWO}\fnm[3] & 1.438 & 2.704 &4.540 \\
SF-dBSE@{\GOWO}\fnm[3] & 1.403 &2.883 &4.621 \\
\end{tabular}
\end{ruledtabular}
\fnt[1]{Value from Ref.~\onlinecite{Manohar_2008} using a UHF reference.}
\fnt[2]{Value from Ref.~\onlinecite{Lefrancois_2015} using a UHF reference.}
\fnt[1]{Spin-flip EOM-CC values from Ref.~\onlinecite{Manohar_2008}.}
\fnt[2]{Value from Ref.~\onlinecite{Lefrancois_2015}.}
\fnt[3]{This work.}
\end{table}
%%% %%% %%% %%%
@ -825,7 +828,8 @@ All of them have been obtained with a UHF reference like the SF-BSE calculations
%%% TABLE ?? %%%
\begin{table}
\caption{
Vertical excitation energies (with respect to the singlet $X\,{}^1B_{1g}$ ground state) of the $1\,{}^3A_{2g}$, $2\,{}^1A_{1g}$, and $1\,{}^1B_{2g}$ states at the $D_{4h}$ square-planar equilibrium geometry of the $X\,{}^1B_{1g}$ singlet ground state.
Vertical excitation energies (with respect to the singlet $\text{X}\,{}^1B_{1g}$ ground state) of the $1\,{}^3A_{2g}$, $2\,{}^1A_{1g}$, and $1\,{}^1B_{2g}$ states at the $D_{4h}$ square-planar equilibrium geometry of the $X\,{}^1B_{1g}$ singlet ground state.
All the spin-flip calculations have been performed with a UHF reference.
\label{tab:CBD_D2h}}
\begin{ruledtabular}
\begin{tabular}{lccc}
@ -840,12 +844,12 @@ All of them have been obtained with a UHF reference like the SF-BSE calculations
SF-ADC(2)-s\fnm[2] & & & \\
SF-ADC(2)-x\fnm[2] & & & \\
SF-ADC(3)\fnm[2] & & & \\
SF-BSE@{\GOWO}@UHF\fnm[3] & -0.049 & 1.189 & 1.480 \\
SF-dBSE@{\GOWO}@UHF\fnm[3] & 0.012 & 1.507 & 1.841 \\
SF-BSE@{\GOWO}\fnm[3] & -0.049 & 1.189 & 1.480 \\
SF-dBSE@{\GOWO}\fnm[3] & 0.012 & 1.507 & 1.841 \\
\end{tabular}
\end{ruledtabular}
\fnt[1]{Value from Ref.~\onlinecite{Manohar_2008} using a UHF reference.}
\fnt[2]{Value from Ref.~\onlinecite{Lefrancois_2015} using a UHF reference.}
\fnt[1]{Spin-flip EOM-CC values from Ref.~\onlinecite{Manohar_2008}.}
\fnt[2]{Value from Ref.~\onlinecite{Lefrancois_2015}.}
\fnt[3]{This work.}
\end{table}
%%% %%% %%% %%%