From a32b33ff922a591be82f99935fc089424662f525 Mon Sep 17 00:00:00 2001 From: Emmanuel Giner Date: Mon, 15 Apr 2019 10:16:23 +0200 Subject: [PATCH] minor push --- Manuscript/G2-srDFT.tex | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/Manuscript/G2-srDFT.tex b/Manuscript/G2-srDFT.tex index a3ed518..5c9d158 100644 --- a/Manuscript/G2-srDFT.tex +++ b/Manuscript/G2-srDFT.tex @@ -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}.