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Pierre-Francois Loos 2019-04-23 14:53:18 +02:00
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Manuscript/G2-srDFT.tex
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@ -363,6 +363,7 @@ Depending on the functional choice, the complementary functional $\bE{}{\Bas}[\n
As most WFT calculations are performed within the frozen-core (FC) approximation, it is important to define an effective interaction within a subset of MOs. As most WFT calculations are performed within the frozen-core (FC) approximation, it is important to define an effective interaction within a subset of MOs.
We then naturally split the basis set as $\Bas = \Cor \bigcup \BasFC$ (where $\Cor$ and $\BasFC$ are the sets of core and active MOs, respectively) and define the FC version of the effective interaction as We then naturally split the basis set as $\Bas = \Cor \bigcup \BasFC$ (where $\Cor$ and $\BasFC$ are the sets of core and active MOs, respectively) and define the FC version of the effective interaction as
\begin{equation} \begin{equation}
\label{eq:WFC}
\WFC{}{\Bas}(\br{1},\br{2}) = \WFC{}{\Bas}(\br{1},\br{2}) =
\begin{cases} \begin{cases}
\fFC{}{\Bas}(\br{1},\br{2})/\nFC{2}{\Bas}(\br{1},\br{2}), & \text{if $\nFC{2}{\Bas}(\br{1},\br{2}) \ne 0$}, \fFC{}{\Bas}(\br{1},\br{2})/\nFC{2}{\Bas}(\br{1},\br{2}), & \text{if $\nFC{2}{\Bas}(\br{1},\br{2}) \ne 0$},
@ -475,7 +476,7 @@ CCSD(T) energies are computed with Gaussian09 using standard threshold values, \
For the numerical quadratures, we employ the SG-2 grid. \cite{DasHer-JCC-17} For the numerical quadratures, we employ the SG-2 grid. \cite{DasHer-JCC-17}
Except for the carbon dimer where we have taken the experimental equilibrium bond length (\InAA{1.2425}), all geometries have been extracted from Ref.~\onlinecite{HauJanScu-JCP-09} and have been obtained at the B3LYP/6-31G(2df,p) level of theory. Except for the carbon dimer where we have taken the experimental equilibrium bond length (\InAA{1.2425}), all geometries have been extracted from Ref.~\onlinecite{HauJanScu-JCP-09} and have been obtained at the B3LYP/6-31G(2df,p) level of theory.
Frozen-core calculations are defined as such: a \ce{He} core is frozen from \ce{Li} to \ce{Ne}, while a \ce{Ne} core is frozen from \ce{Na} to \ce{Ar}. Frozen-core calculations are defined as such: a \ce{He} core is frozen from \ce{Li} to \ce{Ne}, while a \ce{Ne} core is frozen from \ce{Na} to \ce{Ar}.
In the context of the basis-set correction, the set of active MOs $\BasFC$ involved in the definition of the effective interaction refers to the non-frozen MOs. In the context of the basis-set correction, the set of active MOs, $\BasFC$, involved in the definition of the effective interaction \titou{[see Eq.~\eqref{eq:WFC}]} refers to the non-frozen MOs.
The FC density-based correction is used consistently when the FC approximation was applied in WFT methods. The FC density-based correction is used consistently when the FC approximation was applied in WFT methods.
To estimate the CBS limit of each method, following Ref.~\onlinecite{HalHelJorKloKocOlsWil-CPL-98}, we perform a two-point X$^{-3}$ extrapolation of the correlation energies using the quadruple- and quintuple-$\zeta$ data that we add up to the HF energies obtained in the largest (i.e.~quintuple-$\zeta$) basis. To estimate the CBS limit of each method, following Ref.~\onlinecite{HalHelJorKloKocOlsWil-CPL-98}, we perform a two-point X$^{-3}$ extrapolation of the correlation energies using the quadruple- and quintuple-$\zeta$ data that we add up to the HF energies obtained in the largest (i.e.~quintuple-$\zeta$) basis.