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Emmanuel Giner 2019-04-15 10:16:23 +02:00
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@ -164,7 +164,7 @@ To reduce further the computational cost and/or ease the transferability of the
Present-day DFT calculations are almost exclusively done within the so-called Kohn-Sham (KS) formalism, which corresponds to an exact dressed one-electron theory. \cite{KohSha-PR-65}
DFT's attractiveness originates from its very favorable cost/efficiency ratio as it can provide accurate energies and properties at a relatively low computational cost.
Thanks to this, KS-DFT \cite{HohKoh-PR-64, KohSha-PR-65} has become the workhorse of electronic structure calculations for atoms, molecules and solids. \cite{ParYan-BOOK-89}
In the present context, one of the interesting feature of density-based methods is their much faster convergence with respect to the size of the basis set. \cite{FraMusLupTou-JCP-15}
In the \manu{context of the present work}, one of the interesting feature of density-based methods is their much faster convergence with respect to the size of the basis set. \cite{FraMusLupTou-JCP-15}
%especially in the range-separated (RS) context where the WFT method is relieved from describing the short-range part of the correlation hole. \cite{TouColSav-PRA-04, FraMusLupTou-JCP-15}
%To obtain accurate results within DFT, one must develop the art of selecting the adequate exchange-correlation functional, which can be classified in various families depending on their physical input quantities. \cite{Bec-JCP-14}
Although there is no clear way on how to systematically improve density-functional approximations, \cite{Bec-JCP-14} climbing the Jacob's ladder of DFT is potentially the most satisfactory way forward. \cite{PerSch-AIPCP-01, PerRuzTaoStaScuCso-JCP-05}
@ -413,7 +413,7 @@ and the corresponding FC range-separation function
\label{eq:muval}
\rsmu{\Bas}{\FC}(\br{}) = \frac{\sqrt{\pi}}{2} \W{\Bas}{\FC}(\br{},\br{}).
\end{equation}
It is worth noting that, within the present definition, $\W{\Bas}{\FC}(\br{1},\br{2})$ still satisfies Eq.~\eqref{eq:lim_W}.
It is worth not\manu{ic}ing that, within the present definition, $\W{\Bas}{\FC}(\br{1},\br{2})$ still satisfies Eq.~\eqref{eq:lim_W}.
Defining $\n{\modZ}{\FC}$ as the FC (i.e.~valence-only) one-electron density obtained with a model $\modZ$, the FC contribution of the complementary functional is then evaluated as $\bE{\LDA}{\sr}[\n{\modZ}{\FC}(\br{}),\rsmu{\Bas}{\FC}(\br{})]$ or $\bE{\PBE}{\sr}[\n{\modZ}{\FC}(\br{}),\rsmu{\Bas}{\FC}(\br{})]$.
@ -516,8 +516,8 @@ Except for the carbon dimer where we have taken the experimental equilibrium bon
Frozen-core calculations are defined as such: an \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 spinorbitals $\BasFC$ involved in the definition of the effective interaction refers to the non-frozen spinorbitals.
The FC density-based correction is set consistently when the FC approximation was applied in WFT methods.
In order to estimate the complete basis set (CBS) limit for each model, we employ the two-point extrapolation proposed in Ref.~\onlinecite{HalHelJorKloKocOlsWil-CPL-98} for the correlation energies, and we refer to these as $\CBS$.
\titou{What about the HF energies?}
In order to estimate the complete basis set (CBS) limit for each model, \manu{following the work of Ref.~\onlinecite{HalHelJorKloKocOlsWil-CPL-98}},
we employ the two-point extrapolation for the correlation energies \manu{in quadruple- and quintuple-$\zeta$ basis sets, which is refered to as $\CBS$, and we add to these the HF energies in the largest basis sets, \textit{i.e.} in quintuple-$\zeta$ quality basis sets, to estimate the CBS FCI energies.}
%\subsection{Convergence of the atomization energies with the WFT models }
As the exFCI calculations are converged with a precision of about 0.1 {\kcal}, we can consider these atomization energies as near-FCI values, and they will be our references for \ce{C2}, \ce{N2}, \ce{O2} and \ce{F2}.