From 6ee0204b3e3e700ed55f9e087b8f01a96b7357d1 Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Fri, 10 May 2019 18:53:25 +0200 Subject: [PATCH] DONE with revision --- JPCL_revision/G2-srDFT.tex | 11 ++++++----- JPCL_revision/fig2.pdf | Bin 232124 -> 232741 bytes 2 files changed, 6 insertions(+), 5 deletions(-) diff --git a/JPCL_revision/G2-srDFT.tex b/JPCL_revision/G2-srDFT.tex index aeba4b0..bcf7a4f 100644 --- a/JPCL_revision/G2-srDFT.tex +++ b/JPCL_revision/G2-srDFT.tex @@ -198,8 +198,8 @@ We refer the interested reader to Ref.~\onlinecite{GinPraFerAssSavTou-JCP-18} fo %Let us assume we have both the energy $\E{\modY}{\Bas}$ and density $\n{\modZ}{\Bas}$ of a $\Ne$-electron system described by two methods $\modY$ and $\modZ$ (potentially identical) in an incomplete basis set $\Bas$. %According to Eq.~(15) of Ref.~\onlinecite{GinPraFerAssSavTou-JCP-18}, assuming that $\E{\modY}{\Bas}$ and $\n{\modZ}{\Bas}$ are reasonable approximations of the FCI energy and density within $\Bas$, the exact ground state energy $\E{}{}$ may be approximated as Let us assume -\titou{that we have reasonable approximations of the FCI energy and density of a $\Ne$-electron system in an incomplete basis set $\Bas$, say the CCSD(T) energy $\E{\CCSDT}{\Bas}$ and the Hartree-Fock (HF) density $\n{\HF}{\Bas}$. According to Eq.~(15) of Ref.~\onlinecite{GinPraFerAssSavTou-JCP-18}, the exact ground-state energy $\E{}{}$ may be approximated as -} +\titou{that we have reasonable approximations of the FCI energy and density of a $\Ne$-electron system in an incomplete basis set $\Bas$, say the CCSD(T) energy $\E{\CCSDT}{\Bas}$ and the Hartree-Fock (HF) density $\n{\HF}{\Bas}$. +According to Eq.~(15) of Ref.~\onlinecite{GinPraFerAssSavTou-JCP-18}, the exact ground-state energy $\E{}{}$ may be approximated as} %we have both the energy \titou{$\E{\CCSDT}{\Bas}$ and density $\n{\HF}{\Bas}$ of a $\Ne$-electron system in an incomplete basis set $\Bas$.} %According to Eq.~(15) of Ref.~\onlinecite{GinPraFerAssSavTou-JCP-18}, assuming that \titou{$\E{\CCSDT}{\Bas}$ and $\n{\HF}{\Bas}$} are reasonable approximations of the FCI energy and density within $\Bas$, the exact ground state energy $\E{}{}$ may be approximated as \begin{equation} @@ -428,7 +428,7 @@ iii) vanishes in the CBS limit, hence guaranteeing an unaltered CBS limit for a We begin our investigation of the performance of the basis-set correction by computing the atomization energies of \ce{C2}, \ce{N2}, \ce{O2} and \ce{F2} obtained with Dunning's cc-pVXZ basis (X $=$ D, T, Q and 5). -\ce{N2}, \ce{O2} and \ce{F2} are weakly correlated systems and belong to the G2 set \cite{CurRagTruPop-JCP-91} (see below), whereas \ce{C2} already contains a non-negligible amount of strong correlation. \cite{BooCleThoAla-JCP-11} +%\ce{N2}, \ce{O2} and \ce{F2} are weakly correlated systems and belong to the G2 set \cite{CurRagTruPop-JCP-91} (see below), whereas \ce{C2} already contains a non-negligible amount of strong correlation. \cite{BooCleThoAla-JCP-11} In a second time, we compute the atomization energies of the entire G2 set \cite{CurRagTruPop-JCP-91} composed by 55 molecules with the cc-pVXZ basis set family. This molecular set has been intensively studied in the last 20 years (see, for example, Refs.~\onlinecite{FelPetDix-JCP-08, Gro-JCP-09, FelPet-JCP-09, NemTowNee-JCP-10, FelPetHil-JCP-11, HauKlo-JCP-12, PetTouUmr-JCP-12, FelPet-JCP-13, KesSylKohTewMar-JCP-18}) and can be considered as a representative set of small organic and inorganic molecules. %As a method $\modY$ we employ either CCSD(T) or exFCI. @@ -442,7 +442,7 @@ 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} Apart from 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 systematically performed and 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 [see Eq.~\eqref{eq:WFC}] 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 [see Eq.~\eqref{eq:WFC}] refers to the non-frozen MOs. The FC density-based correction is used consistently with the FC approximation 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. @@ -467,7 +467,8 @@ In most cases, the basis-set corrected triple-$\zeta$ atomization energies are o \includegraphics[width=0.5\linewidth]{fig2} \caption{ \titou{$\rsmu{}{\Bas}$ (top) and $\n{}{} \times \be{\text{c,md}}{\sr,\PBE}$ (bottom) along the molecular axis ($z$) for \ce{N2} for various basis sets. - The two nitrogen nuclei are located at $z=0$ and $z=2.076$ bohr.} + The two nitrogen nuclei are located at $z=0$ and $z=2.076$ bohr. + The calculations have been performed in the FC approximation.} \label{fig:N2}} \end{figure} diff --git a/JPCL_revision/fig2.pdf b/JPCL_revision/fig2.pdf index 72bc3d648e4b6e91a564416c460c10e4d4e72613..efc184480433a2c6501502ffc99b678cf6de3f1e 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