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Manuscript/G2-srDFT.tex
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@ -671,8 +671,10 @@ Therefore, we propose the following valence-only approximations for the compleme
\section{Results} \section{Results}
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\subsection{Comparison between the CIPSI and CCSD(T) models in the case of N$_2$, O$_2$, F$_2$} \subsection{Comparison between the CIPSI and CCSD(T) models in the case of C$_2$, N$_2$, O$_2$, F$_2$}
We begin the investigation of the behavior of the basis-set correction by the study of the atomization energies of the N$_2$, O$_2$, F$_2$ homo-nuclear diatomic molecules in the Dunning cc-pVXZ and cc-pCVXZ in the case of N$_2$ (X=D,T,Q,5) using both the CIPSI algorithm and the CCSD(T). All through this work, we follow the frozen core (FC) convention of Klopper \textit{et. al}\cite{HauKlo-JCP-12} which consists in all-electron calculations for Li-Be, a He core for B-Na atoms and a Ne core for the Al-Cl series. In the context of the DFT correction for the basis-set, this implies that, for a given system in a given basis set $\Bas$, the set of valence orbitals $\Basval$ involved in the definition of the valence interaction $\wbasisval$ and density $\onedmval$ refers to all MOs except the core. We begin the investigation of the behavior of the basis-set correction by the study of the atomization energies of the C$_2$, N$_2$, O$_2$ and F$_2$ homo-nuclear diatomic molecules in the Dunning cc-pVXZ and cc-pCVXZ in the case of N$_2$ (X=D,T,Q,5) using both the CIPSI algorithm and the CCSD(T). N$_2$, O$_2$ and F$_2$ belong to the G2 set and can be considered as weakly correlated, whereas C$_2$ contains already a non negligible non dynamic correlation component.
All through this work, we follow the frozen core (FC) convention of Klopper \textit{et. al}\cite{HauKlo-JCP-12} which consists in all-electron calculations for Li-Be, a He core for B-Na atoms and a Ne core for the Al-Cl series. In the context of the DFT correction for the basis-set, this implies that, for a given system in a given basis set $\Bas$, the set of valence orbitals $\Basval$ involved in the definition of the valence interaction $\wbasisval$ and density $\onedmval$ refers to all MOs except the core.
In order to estimate the CBS limit of each model we use the two-point extrapolation of Ref. \onlinecite{HalHelJorKloKocOls-CPL-98} for the correlation energies and report the corresponding atomization energy which are referred as $D_e^{Q5Z}$ and $D_e^{C(Q5)Z}$ for the cc-pVXZ and cc-pCVXZ basis sets, respectively. All through this work, the valence interaction and density was used when the frozen core approximation was done on the WFT model. In order to estimate the CBS limit of each model we use the two-point extrapolation of Ref. \onlinecite{HalHelJorKloKocOls-CPL-98} for the correlation energies and report the corresponding atomization energy which are referred as $D_e^{Q5Z}$ and $D_e^{C(Q5)Z}$ for the cc-pVXZ and cc-pCVXZ basis sets, respectively. All through this work, the valence interaction and density was used when the frozen core approximation was done on the WFT model.
\subsection{Convergence of the atomization energies with the WFT models } \subsection{Convergence of the atomization energies with the WFT models }
@ -682,7 +684,7 @@ The same behaviours hold for the CCSD(T) model, and one can notice that the atom
\subsection{The effect of the basis set correction within the LDA and PBE approximation} \subsection{The effect of the basis set correction within the LDA and PBE approximation}
Regarding the effect of the basis set correction, both for the CIPSI and CCSD(T) models, several observations can be done. Regarding the effect of the basis set correction, both for the CIPSI and CCSD(T) models, several observations can be done.
First, in a given basis set, the addition of the basis set correction, both at the LDA and PBE level, improves the result even if it can overestimates the atomization energies in some cases. First, in a given basis set, the addition of the basis set correction, both at the LDA and PBE level, improves the result even if it can overestimates the estimated CBS atomization energies by a few tens of kcal/mol (the largest deviation being 0.6 kcal/mol for N$_2$ at the (FC)CCSD(T)+PBE-val level in the cc-pv5z basis). Nevertheless, the deviations observed in the largest basis sets are typically in the range of the accuracy of the atomization energies computed with the CBS extrapolation technique.
Also, the values obtained with the largest basis sets tends to converge toward a value close to the estimated CBS values. Also, one can observe that the sensitivity to the functional is quite large for the double- and triple-zeta basis sets, where clearly the PBE functional performs better. Nevertheless, from the quadruple-zeta basis set, the LDA and PBE functional agrees within a few tens of kcal/mol. Also, the values obtained with the largest basis sets tends to converge toward a value close to the estimated CBS values. Also, one can observe that the sensitivity to the functional is quite large for the double- and triple-zeta basis sets, where clearly the PBE functional performs better. Nevertheless, from the quadruple-zeta basis set, the LDA and PBE functional agrees within a few tens of kcal/mol.
\begin{table*} \begin{table*}