updated manuscript

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Emmanuel Giner 2019-03-25 18:39:39 +01:00
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@ -389,7 +389,7 @@ In order to correct such a defect, we propose here a new ECMD functional inspire
The exact behaviour of the $\ecmubis$ is known in the large $\mu$ limit\cite{pbeontop}:
\begin{equation}
\label{eq:ecmd_large_mu}
\ecmubis = \frac{2\sqrt{\pi}\left(1 - \sqrt{2}\right)}{3\,\mu^3} + \int \text{d}{\bf r} \,\, n^{(2)}({\bf} r)
\ecmubis = \frac{2\sqrt{\pi}\left(1 - \sqrt{2}\right)}{3\,\mu^3} \int \text{d}{\bf r} \,\, n^{(2)}({\bf} r)
\end{equation}
where $ n^{(2)}({\bf r}) $ is the \textit{exact} on-top pair density for the ground state of the system.
As the exact ground state on-top pair density $n^{(2)}({\bf} r)$ is not known, we propose here to approximate it by that of the UEG at the density of the system:
@ -414,7 +414,6 @@ with
\begin{equation}
\label{eq:epsilon_cmdpbe}
\bar{e}_{\text{c,md}}^\text{PBE}(n,\nabla n;\,\mu) = \frac{e_c^{PBE}(n,\nabla n)}{1 + \beta_{\text{c,md}\,\text{PBE}}(n,\nabla n;\,\mu)\mu^3 }
and
\end{equation}
\begin{equation}
\label{eq:epsilon_cmdpbe}
@ -453,26 +452,8 @@ Therefore, we propose the following valence-only approximations for the compleme
\section{Results}
%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{The case of C$_2$ and the comparison with the F12 methods.}
\subsection{The case of C$_2$, F$_2$, O$_2$, F$_2$ and the impact of the lack of basis functions adapted to core correlation }
\begin{table*}
\caption{Dissociation energy ($D_e$) in kcal/mol of the F$_2$ molecule computed using FCIQMC, CIPSI, FCIQMC+F$_{12}$, CIPSI+LDA$_{\rm HF}$ and CIPSI+LDA$_{\text{HF-val}}$ (valence only interaction and density) in the Dunnng cc-pVXZ (VXZ) basis sets. $^a$ Results from Ref\cite{PetTouUmr-JCP-12} taking into account the ZPE correction. }
\begin{ruledtabular}
\begin{tabular}{lccccc}
%\hline
& CIPSI & CIPSI+LDA$_{\text{HF}}$ & CIPSI+LDA${_\text{HF-val}}$ & CIPSI+PBE$_{\text{HF}}$ & CIPSI+PBE${_\text{HF-val}}$ \\
\hline
V2Z & 27.5 & 30.8 & 31.1 & 32.1 & 32.4 \\
V3Z & 35.4 & 37.0 & 37.5 & 37.5 & 37.8 \\
V4Z & 37.5 & 38.7 & 38.8 & 38.7 & 38.8 \\
V5Z & 38.0 & 38.7 & 38.8 & 38.7 & 38.8 \\
%\hline
& \multicolumn{5}{c}{Estimated exact} \\
& \multicolumn{5}{c}{ 38.2$^a$} \\
\end{tabular}
\end{ruledtabular}
\label{conv_He_table}
\end{table*}
\begin{table*}
\caption{
\label{tab:diatomics}
@ -540,6 +521,58 @@ V5Z & 38.0 & 38.7 & 38.8
\end{table*}
\begin{table*}
\caption{
\label{tab:diatomics}
Dissociation energy ($\De$) in kcal/mol of the \ce{C2}, \ce{O2}, \ce{N2} and \ce{F2} molecules computed with various methods and basis sets.
}
\begin{ruledtabular}
\begin{tabular}{llddddd}
& & \mc{4}{c}{Dunning's basis set}
\\
\cline{3-6}
Molecule & Method & \tabc{cc-pCVDZ} & \tabc{cc-pCVTZ} & \tabc{cc-pCVQZ} & \tabc{cc-pCV5Z} & \tabc{Exp.}
\\
\hline
\ce{C2} & ex (FC)FC-FCI & 130.5 & 140.5 & 143.8 & 144.9 &146.9(5)\fnm \\
\hline
& ex (FC)FCI+LDA & 140.9 & 145.7 & 146.6 & 146.4 & \\
& ex (FC)FCI+LDA-val & 141.3 & 145.6 & 146.5 & 146.4 & \\
\hline
& ex (FC)FCI+PBE & 144.5 & 145.9 & 146.4 & 146.3 & \\
& ex (FC)FCI+PBE -val & 145.2 & 145.9 & 146.4 & 146.3 & \\
\ce{C2} & ex FC-FCI & 131.0 & 141.5 & 145.1 & ----- & \\
\hline
& ex FCI+LDA & 141.4 & 146.7 & 147.8 & ----- & \\
& ex FCI+LDA-val & 141.8 & 146.6 & 147.7 & ----- & \\
\hline
& ex FCI+PBE & 145.1 & 147.0 & 147.7 & ----- & \\
& ex FCI+PBE -val & 145.7 & 147.0 & 147.6 & ----- & \\
\\
\ce{N2} & ex (FC)FCI & 201.6 & 217.9 & 223.7 & 226.0 & 228.5\fnm[2] \\
\hline
& ex (FC)FCI+LDA & 217.4 & 226.2 & 228.4 & 228.7 & \\
& ex (FC)FCI+LDA-val & 218.7 & 226.3 & 228.5 & 228.7 & \\
\hline
& ex (FC)FCI+PBE & 225.8 & 227.6 & 228.4 & 228.6 & \\
& ex (FC)FCI+PBE -val & 228.0 & 227.8 & 228.5 & 228.6 & \\
\ce{N2} & ex FCI & 202.0 & 218.5 & 224.3 & ----- & 228.5\fnm[2] \\
\hline
& ex FCI+LDA & 217.8 & 226.8 & 229.0 & ----- & \\
& ex FCI+LDA-val & 218.8 & 226.9 & 229.0 & ----- & \\
\hline
& ex FCI+PBE & 226.2 & 228.2 & 229.0 & ----- & \\
& ex FCI+PBE -val & 227.8 & 228.2 & 229.0 & ----- & \\
\\
\end{tabular}
\end{ruledtabular}
\fnt[1]{Results from Ref.~\onlinecite{BytLaiRuedenJCP05}.}
\fnt[2]{Results from Ref.~\onlinecite{PetTouUmr-JCP-12}.}
\end{table*}
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345.148 197.898 m 341.449 197.898 l S Q
BT
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/f-0-0 1 Tf
(-0.01)Tj
ET
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43.852 166.699 m 47.551 166.699 l S Q
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345.148 166.699 m 341.449 166.699 l S Q
BT
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/f-0-0 1 Tf
(-0.005)Tj
ET
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BT
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/f-0-0 1 Tf
( 0)Tj
ET
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345.148 197.898 m 345.148 194.199 l S Q
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245.949 135.648 l 246.199 135.602 l 249.301 135.602 l 249.551 135.551 l
261.199 135.551 l 261.449 135.5 l 311.801 135.5 l S Q
0 g
q 1 0 0 -1 0 216 cm
43.852 10.75 301.297 187.148 re S Q
Q Q
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