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Pierre-Francois Loos 2019-07-01 16:41:03 +02:00
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3
Manuscript/Ex-srDFT.tex
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@ -361,7 +361,6 @@ For a given $\tn{2}{}(\br{})$, some of the authors proposed the following functi
As illustrated in the context of RS-DFT, \cite{FerGinTou-JCP-19} such a functional form is able to treat both weakly and strongly correlated systems thanks to the explicit inclusion of $\e{\text{c}}{\PBE}$ and $\tn{2}{}$, respectively. As illustrated in the context of RS-DFT, \cite{FerGinTou-JCP-19} such a functional form is able to treat both weakly and strongly correlated systems thanks to the explicit inclusion of $\e{\text{c}}{\PBE}$ and $\tn{2}{}$, respectively.
Therefore, in the present context, we introduce the general form of the $\PBE$-based complementary functional within a given basis set $\Bas$ Therefore, in the present context, we introduce the general form of the $\PBE$-based complementary functional within a given basis set $\Bas$
\begin{multline} \begin{multline}
\label{eq:def_pbe_tot}
\bE{\PBE}{\Bas}[\n{}{},\tn{2}{},\rsmu{}{\Bas}] = \bE{\PBE}{\Bas}[\n{}{},\tn{2}{},\rsmu{}{\Bas}] =
\int \n{}{}(\br{}) \int \n{}{}(\br{})
\\ \\
@ -371,7 +370,6 @@ which has an explicit dependency on both the range-separation function $\rsmu{}{
In Ref.~\onlinecite{LooPraSceTouGin-JPCL-19}, some of the authors introduced a version of the $\PBE$-based functional, here-referred as $\PBEUEG$ In Ref.~\onlinecite{LooPraSceTouGin-JPCL-19}, some of the authors introduced a version of the $\PBE$-based functional, here-referred as $\PBEUEG$
\begin{equation} \begin{equation}
\label{eq:def_pbe_tot}
\bE{\PBEUEG}{\Bas} \bE{\PBEUEG}{\Bas}
\equiv \equiv
\bE{\PBE}{\Bas}[\n{}{},\n{2}{\UEG},\rsmu{}{\Bas}], \bE{\PBE}{\Bas}[\n{}{},\n{2}{\UEG},\rsmu{}{\Bas}],
@ -395,7 +393,6 @@ Therefore, as in Ref.~\onlinecite{FerGinTou-JCP-19}, we define a better approxim
which directly follows from the large-$\mu$ extrapolation of the exact on-top pair density proposed by Gori-Giorgi and Savin \cite{GorSav-PRA-06} in the context of RS-DFT. which directly follows from the large-$\mu$ extrapolation of the exact on-top pair density proposed by Gori-Giorgi and Savin \cite{GorSav-PRA-06} in the context of RS-DFT.
Using this new ingredient, we propose here the ``$\PBE$-ontop'' (\PBEot) functional Using this new ingredient, we propose here the ``$\PBE$-ontop'' (\PBEot) functional
\begin{equation} \begin{equation}
\label{eq:def_pbe_tot}
\bE{\PBEot}{\Bas} \bE{\PBEot}{\Bas}
\equiv \equiv
\bE{\PBE}{\Bas}[\n{}{},\ttn{2}{\Bas},\rsmu{}{\Bas}]. \bE{\PBE}{\Bas}[\n{}{},\ttn{2}{\Bas},\rsmu{}{\Bas}].

107
Manuscript/SI/Ex-srDFT-SI.tex
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@ -157,7 +157,7 @@
\title{Supporting Information for ``Chemically Accurate Excitation Energies With Small Basis Sets''} \title{Supporting Information for ``Chemically Accurate Excitation Energies With Small Basis Sets''}
\author{Emmanuel Giner} \author{Emmanuel Giner}
\email[Corresponding author: \jt{JTcomment: I propose to also put EG as a corresponding author}]{emmanuel.giner@lct.jussieu.fr} \email[Corresponding author: ]{emmanuel.giner@lct.jussieu.fr}
\affiliation{\LCT} \affiliation{\LCT}
\author{Anthony Scemama} \author{Anthony Scemama}
\affiliation{\LCPQ} \affiliation{\LCPQ}
@ -336,7 +336,7 @@ Here, we report the absolute energetic corrections for each state of each molecu
& -39.04124(1) & -39.04124(1)
& -39.00044(1) \\ & -39.00044(1) \\
\\ \\
exFCI+$\PBE$ & AVDZ & -39.07282(1) exFCI+$\PBEUEG$ & AVDZ & -39.07282(1)
& -39.06150(1) & -39.06150(1)
& -39.02181(1) & -39.02181(1)
& -38.97873(1) \\ & -38.97873(1) \\
@ -361,24 +361,8 @@ Here, we report the absolute energetic corrections for each state of each molecu
& -39.07959(2) & -39.07959(2)
& -39.04267(1) & -39.04267(1)
& -39.00135(1) \\ & -39.00135(1) \\
\\
SHCI\fnm[1] & AVQZ & -39.08849(1)
& -39.07404(1)
& -39.03711(1)
& -38.99603(1) \\
CR-EOMCC (2,3)D\fnm[2]& AVQZ& -39.08817
& -39.07303
& -39.03450
& -38.99457 \\
FCI\fnm[3] & TZ2P & -39.066738
& -39.048984
& -39.010059
& -38.968471 \\
\end{tabular} \end{tabular}
\end{ruledtabular} \end{ruledtabular}
\fnt[1]{Semistochastic heat-bath CI (SHCI) calculations from Ref.~\onlinecite{ChiHolAdaOttUmrShaZim-JPCA-18}.}
\fnt[2]{Completely-renormalized equation-of-motion coupled cluster (CR-EOMCC) calculations from Refs.~\onlinecite{SheLeiVanSch-JCP-98, JenBun-JCP-88}.}
\fnt[3]{Reference \onlinecite{SheLeiVanSch-JCP-98}.}
\end{table*} \end{table*}
\end{squeezetable} \end{squeezetable}
%%% %%% %%% %%% %%% %%% %%% %%%
@ -388,14 +372,14 @@ Here, we report the absolute energetic corrections for each state of each molecu
\begin{squeezetable} \begin{squeezetable}
\begin{table*}[h] \begin{table*}[h]
\caption{ \caption{
Basis set energetic corrections (in hartree) on absorption energies for excited states of ammonia, carbon dimer, water, and ethylene for various methods and basis sets.} Basis set energetic corrections (in hartree) on absorption energies for excited states of water, ammonia, carbon dimer and ethylene for various methods and basis sets.}
\begin{ruledtabular}{} \begin{ruledtabular}{}
\begin{tabular}{llddddddddd} \begin{tabular}{llddddddddd}
& & \mc{9}{c}{Deviation with respect to TBE} & & \mc{9}{c}{Deviation with respect to TBE}
\\ \\
\cline{3-11} \cline{3-11}
& & \mc{3}{c}{exFCI+$\PBEot$} & & \mc{3}{c}{exFCI+$\PBEot$}
& \mc{3}{c}{exFCI+$\PBE$} & \mc{3}{c}{exFCI+$\PBEUEG$}
& \mc{3}{c}{exFCI+$\LDA$} & \mc{3}{c}{exFCI+$\LDA$}
\\ \\
\cline{3-5} \cline{6-8} \cline{9-11} \cline{3-5} \cline{6-8} \cline{9-11}
@ -405,6 +389,42 @@ Here, we report the absolute energetic corrections for each state of each molecu
& \tabc{AVDZ} & \tabc{AVTZ} & \tabc{AVQZ} & \tabc{AVDZ} & \tabc{AVTZ} & \tabc{AVQZ}
\\ \\
\hline \hline
Water & $1\,^{1}A_1$
& -0.058\,765 & -0.024\,014 & -0.011\,990
& -0.066\,603 & -0.027\,236 & -0.013\,127
& -0.059\,660 & -0.027\,777 & -0.014\,274
\\
& $1\,^{1}B_1$
& -0.052\,137 & -0.021\,369 & -0.010\,611
& -0.061\,033 & -0.025\,180 & -0.012\,076
& -0.054\,803 & -0.025\,596 & -0.013\,154
\\
& $1\,^{1}A_2$
& -0.052\,102 & -0.021\,325 & -0.010\,591
& -0.061\,406 & -0.025\,263 & -0.012\,114
& -0.055\,215 & -0.025\,776 & -0.013\,270
\\
& $2\,^{1}A_1$
& -0.052\,995 & -0.021\,690 & -0.010\,852
& -0.061\,959 & -0.025\,457 & -0.012\,258
& -0.055\,301 & -0.025\,786 & -0.013\,304
\\
& $1\,^{3}B_1$
& -0.051\,161 & -0.020\,974 & -0.010\,117
& -0.057\,882 & -0.023\,791 & -0.011\,280
& -0.052\,744 & -0.024\,500 & -0.012\,358
\\
& $1\,^{3}A_2$
& -0.051\,244 & -0.020\,982 & -0.010\,115
& -0.058\,090 & -0.023\,847 & -0.011\,302
& -0.052\,729 & -0.024\,611 & -0.012\,398
\\
& $1\,^{3}A_1$
& -0.052\,193 & -0.021\,398 & -0.010\,401
& -0.059\,073 & -0.024\,272 & -0.011\,595
& -0.053\,409 & -0.024\,840 & -0.012\,699
\\
\\
Ammonia & $1\,^{1}A_{1}$ Ammonia & $1\,^{1}A_{1}$
& -0.044\,635 & -0.016\,982 & -0.008\,134 & -0.044\,635 & -0.016\,982 & -0.008\,134
& -0.051\,254 & -0.019\,468 & -0.008\,997 & -0.051\,254 & -0.019\,468 & -0.008\,997
@ -452,53 +472,6 @@ Here, we report the absolute energetic corrections for each state of each molecu
& -0.049\,208 & -0.021\,292 & -0.01\,0257 & -0.049\,208 & -0.021\,292 & -0.01\,0257
\\ \\
\\ \\
% Carbon monoxyde & $1\,^{1}\Sigma^+$
% & -0.074\,328 & -0.031\,117 & -0.015\,510
% & -0.084\,655 & -0.035\,318 & -0.017\,142
% & -0.076\,668 & -0.077\,437 & -0.018\,768
% \\
% & $1\,^{1}\Pi$
% & -0.075\,790 & -0.031\,456 & -0.016\,083
% & -0.085\,494 & -0.035\,255 & -0.017\,182
% & -0.036\,301 & -0.036\,359 & -0.018\,855
% \\
% \\
Water & $1\,^{1}A_1$
& -0.058\,765 & -0.024\,014 & -0.011\,990
& -0.066\,603 & -0.027\,236 & -0.013\,127
& -0.059\,660 & -0.027\,777 & -0.014\,274
\\
& $1\,^{1}B_1$
& -0.052\,137 & -0.021\,369 & -0.010\,611
& -0.061\,033 & -0.025\,180 & -0.012\,076
& -0.054\,803 & -0.025\,596 & -0.013\,154
\\
& $1\,^{1}A_2$
& -0.052\,102 & -0.021\,325 & -0.010\,591
& -0.061\,406 & -0.025\,263 & -0.012\,114
& -0.055\,215 & -0.025\,776 & -0.013\,270
\\
& $2\,^{1}A_1$
& -0.052\,995 & -0.021\,690 & -0.010\,852
& -0.061\,959 & -0.025\,457 & -0.012\,258
& -0.055\,301 & -0.025\,786 & -0.013\,304
\\
& $1\,^{3}B_1$
& -0.051\,161 & -0.020\,974 & -0.010\,117
& -0.057\,882 & -0.023\,791 & -0.011\,280
& -0.052\,744 & -0.024\,500 & -0.012\,358
\\
& $1\,^{3}A_2$
& -0.051\,244 & -0.020\,982 & -0.010\,115
& -0.058\,090 & -0.023\,847 & -0.011\,302
& -0.052\,729 & -0.024\,611 & -0.012\,398
\\
& $1\,^{3}A_1$
& -0.052\,193 & -0.021\,398 & -0.010\,401
& -0.059\,073 & -0.024\,272 & -0.011\,595
& -0.053\,409 & -0.024\,840 & -0.012\,699
\\
\\
Ethylene & $1\,^{1}A_{1g}$ Ethylene & $1\,^{1}A_{1g}$
& -0.057\,559 & -0.022\,007 & & -0.057\,559 & -0.022\,007 &
& -0.066\,251 & -0.024\,599 & & -0.066\,251 & -0.024\,599 &