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url = {https://link.aps.org/doi/10.1103/PhysRevA.73.032506}
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}
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@article{HalHelJorKloKocOls-CPL-98,
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title = "Basis-set convergence in correlated calculations on Ne, N2, and H2O",
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journal = "Chemical Physics Letters",
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volume = "286",
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number = "3",
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pages = "243 - 252",
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year = "1998",
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issn = "0009-2614",
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doi = "https://doi.org/10.1016/S0009-2614(98)00111-0",
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url = "http://www.sciencedirect.com/science/article/pii/S0009261498001110",
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author = "Asger Halkier and Trygve Helgaker and Poul Jørgensen and Wim Klopper and Henrik Koch and Jeppe Olsen and Angela K. Wilson",
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abstract = "Valence and all-electron correlation energies of Ne, N2, and H2O at fixed experimental geometries are computed at the levels of second-order perturbation theory (MP2) and coupled cluster theory with singles and doubles excitations (CCSD), and singles and doubles excitations with a perturbative triples correction (CCSD(T)). Correlation-consistent polarized valence and core-valence basis sets up to sextuple zeta quality are employed. Guided by basis-set limits established by rij-dependent methods, a number of extrapolation schemes for use with the correlation-consistent basis sets are investigated. Among the schemes considered here, a linear least-squares procedure applied to the quintuple and sextuple zeta results yields the most accurate extrapolations."
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}
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@ -643,12 +643,14 @@ Therefore, we propose the following valence-only approximations for the compleme
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\section{Results}
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%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Comparison between the CIPSI and CCSD(T) models in the case of C$_2$, N$_2$, O$_2$, F$_2$}
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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$_2$, F$_2$ homo-nuclear diatomic molecules in the Dunning cc-pVXZ and cc-pCVXZ (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 $\basis$, the set of valence orbitals $\basisval$ involved in the definition of the valence interaction $\wbasisval$ and density $\onedmval$ refers to all MOs except the core.
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\subsection{Comparison between the CIPSI and CCSD(T) models in the case of N$_2$, O$_2$, F$_2$}
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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 $\basis$, the set of valence orbitals $\basisval$ involved in the definition of the valence interaction $\wbasisval$ and density $\onedmval$ refers to all MOs except the core.
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In order to estimate the CBS limit of each model we use the two-point extrapolation of \onlinecite{HalHelJorKloKocOls-CPL-98} for the correlation energies which are referred as $E_{Q5Z}^{\infty}$ and $E_{C(Q5)Z}^{\infty}$ 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.
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%\subsubsection{CIPSI calculations and the basis-set correction}
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%All CIPSI calculations were performed in two steps. First, a CIPSI calculation was performed until the zeroth-order wave function reaches $10^6$ Slater determinants, from which we extracted the natural orbitals. From this set of natural orbitals, we performed CIPSI calculations until the $\EexFCIbasis$ reaches about $0.1$ mH convergence for each systems. Such convergence criterion is more than sufficient for the CIPSI densities $\dencipsi$.
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%Regarding the wave function $\psibasis$ chosen to define the local range-separation parameter $\mur$, we take a single Slater determinant built with the natural orbitals of the first CIPSI calculation.
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\subsubsection{CCSD(T) calculations and the basis-set correction}
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\subsubsection{Comparison between the CIPSI}
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\begin{table*}
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\caption{
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@ -661,7 +663,7 @@ We begin the investigation of the behavior of the basis-set correction by the st
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\\
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\\
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\cline{3-6}
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Molecule & Method & \tabc{cc-pVDZ} & \tabc{cc-pVTZ} & \tabc{cc-pVQZ} & \tabc{cc-pV5Z} & \tabc{$E_{QZ5Z}^{\infty}$}
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Molecule & Method & \tabc{cc-pVDZ} & \tabc{cc-pVTZ} & \tabc{cc-pVQZ} & \tabc{cc-pV5Z} & \tabc{$E_{Q5Z}^{\infty}$}
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\\
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\\
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%\hline
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@ -672,15 +674,16 @@ We begin the investigation of the behavior of the basis-set correction by the st
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\hline
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& ex (FC)FCI+LDA-val & 143.0 & 145.4 & 146.4 & 146.0 & \\
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& ex (FC)FCI+PBE-val & 147.4 & 146.1 & 146.4 & 145.9 & \\
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% & exFCI+PBE-on-top-val & 143.3 & 144.7 & 145.7 & 145.6 & \\
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%%%%%%%% \hline
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%%%%%%%% & ex (FC)FCI+LDA & 141.9 & 142.8 & 145.8 & 146.2 & \\
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%%%%%%%% & ex (FC)FCI+PBE & 146.1 & 143.9 & 145.9 & 145.12 & \\
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%%%%%%%% \hline
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%%%%%%%% & exFCI+PBE-on-top& 142.7 & 142.7 & 145.3 & 144.9 & \\
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\hline
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\hline
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& (FC)CCSD(T) & 129.2 & 139.1 & 143.0 & 144.2 & 145.4 \\
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\hline
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& (FC)CCSD(T)+LDA-val & 139.1 & 143.7 & 145.9 & 145.9 & \\
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& (FC)CCSD(T)+PBE-val & 142.8 & 144.2 & 145.9 & 145.8 & \\
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\hline
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\\
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\cline{3-6}
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& & \tabc{cc-pCVDZ} & \tabc{cc-pCVTZ} & \tabc{cc-pCVQZ} & \tabc{cc-pCV5Z} & \tabc{ $E_{CQZC5Z}^{\infty}$ }
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& & \tabc{cc-pCVDZ} & \tabc{cc-pCVTZ} & \tabc{cc-pCVQZ} & \tabc{cc-pCV5Z} & \tabc{ $E_{C(Q5)Z}^{\infty}$ }
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\\
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\\
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% \hline
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@ -705,22 +708,22 @@ We begin the investigation of the behavior of the basis-set correction by the st
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& & \mc{4}{c}{Dunning's basis set}
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\\
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\cline{3-6}
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Molecule & Method & \tabc{cc-pVDZ} & \tabc{cc-pVTZ} & \tabc{cc-pVQZ} & \tabc{cc-pV5Z} & \tabc{$E_{QZ5Z}^{\infty}$}
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Molecule & Method & \tabc{cc-pVDZ} & \tabc{cc-pVTZ} & \tabc{cc-pVQZ} & \tabc{cc-pV5Z} & \tabc{$E_{Q5Z}^{\infty}$}
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\\
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\\
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\ce{N2} & ex (FC)FCI & 201.1 & 217.1 & 223.5 & 225.7 & 227.8 \\
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\hline
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& ex (FC)FCI+LDA-val & 217.9 & 225.9 & 228.0 & 228.6 & \\
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& ex (FC)FCI+PBE-val & 227.7 & 227.8 & 228.3 & 228.5 & \\
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& exFCI+PBE-on-top-val & 224.8 & 226.7 & 228.3 & 228.3 & \\
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% & exFCI+PBE-on-top-val & 224.8 & 226.7 & 228.3 & 228.3 & \\
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\hline
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\hline
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& (FC)CCSD(T) & 199.9 & 216.3 & 222.8 & 225.0 & 227.2 \\
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\hline
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%%%%%%%%& ex (FC)CCSD(T)+LDA & 214.7 & 221.9 & ----- & ----- & \\
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%%%%%%%%& ex (FC)CCSD(T)+PBE & 223.4 & 224.3 & ----- & ----- & \\
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& ex (FC)CCSD(T)+LDA-val & 216.3 & 224.8 & 227.2 & 227.8 & \\
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& ex (FC)CCSD(T)+PBE-val & 225.9 & 226.7 & 227.5 & 227.8 & \\
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& (FC)CCSD(T)+LDA-val & 216.3 & 224.8 & 227.2 & 227.8 & \\
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& (FC)CCSD(T)+PBE-val & 225.9 & 226.7 & 227.5 & 227.8 & \\
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\hline
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%%%%%%%%& ex (FC)FCI+LDA & 216.4 & 223.1 & 227.9 & 228.1 & \\
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%%%%%%%%& ex (FC)FCI+PBE & 225.4 & 225.6 & 228.2 & 227.9 & \\
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@ -728,7 +731,7 @@ We begin the investigation of the behavior of the basis-set correction by the st
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\\
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\\
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\cline{3-6}
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& & \tabc{cc-pCVDZ} & \tabc{cc-pCVTZ} & \tabc{cc-pCVQZ} & \tabc{cc-pCV5Z} & \tabc{$E_{QZ5Z}^{\infty}$}
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& & \tabc{cc-pCVDZ} & \tabc{cc-pCVTZ} & \tabc{cc-pCVQZ} & \tabc{cc-pCV5Z} & \tabc{$E_{Q5Z}^{\infty}$}
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\\
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\\
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%%%%%%%% & ex (FC)FCI & 201.7 & 217.9 & 223.7 & 225.7 & 228.8 \\
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@ -775,8 +778,8 @@ We begin the investigation of the behavior of the basis-set correction by the st
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\hline
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\hline
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& (FC)CCSD(T) & 103.9 & 113.6 & 117.1 & 118.6 & 120.0 \\
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& ex (FC)CCSD(T)+LDA-val & 110.6 & 117.2 & 119.2 & 119.8 & \\
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& ex (FC)CCSD(T)+PBE-val & 115.1 & 118.0 & 119.3 & 119.8 & \\
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& (FC)CCSD(T)+LDA-val & 110.6 & 117.2 & 119.2 & 119.8 & \\
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& (FC)CCSD(T)+PBE-val & 115.1 & 118.0 & 119.3 & 119.8 & \\
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\hline
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%%%%%%%% & exFCI+PBE-on-top & 115.0 & 118.4 & 120.2 & & \\
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%%%%%%%% & exFCI+PBE-on-top-val & 116.1 & 119.4 & 120.5 & & \\
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@ -795,8 +798,8 @@ We begin the investigation of the behavior of the basis-set correction by the st
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\hline
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\hline
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& (FC)CCSD(T) & 25.7 & 34.4 & 36.5 & 37.4 & 38.2 \\
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& ex (FC)CCSD(T)+LDA-val & 29.2 & 36.5 & 37.2 & 38.2 & \\
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& ex (FC)CCSD(T)+PBE-val & 31.5 & 37.1 & 37.8 & 38.2 & \\
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& (FC)CCSD(T)+LDA-val & 29.2 & 36.5 & 37.2 & 38.2 & \\
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& (FC)CCSD(T)+PBE-val & 31.5 & 37.1 & 37.8 & 38.2 & \\
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\end{tabular}
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\end{ruledtabular}
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