diff --git a/Manuscript/G2-srDFT.pdf b/Manuscript/G2-srDFT.pdf index 216937a..c14b048 100644 Binary files a/Manuscript/G2-srDFT.pdf and b/Manuscript/G2-srDFT.pdf differ diff --git a/Manuscript/G2-srDFT.tex b/Manuscript/G2-srDFT.tex index 57b09f7..fca1722 100644 --- a/Manuscript/G2-srDFT.tex +++ b/Manuscript/G2-srDFT.tex @@ -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*} + + % diff --git a/plots/N2.ezfio.ec_in_z b/plots/N2.ezfio.ec_in_z deleted file mode 100644 index 8b7cdbb..0000000 --- a/plots/N2.ezfio.ec_in_z +++ /dev/null @@ -1,1000 +0,0 @@ - -5.5370816972 -0.0000000898 0.0000418227 0.0006530010 - -5.5250816972 -0.0000000913 0.0000431084 0.0006758482 - -5.5130816972 -0.0000000903 0.0000444568 0.0006994239 - -5.5010816972 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