diff --git a/JPCL_revision/G2-srDFT.tex b/JPCL_revision/G2-srDFT.tex index ae7c630..6c62094 100644 --- a/JPCL_revision/G2-srDFT.tex +++ b/JPCL_revision/G2-srDFT.tex @@ -227,7 +227,7 @@ where \titou{$\E{\CCSDT}{}$ is the $\CCSDT$ energy} in the CBS limit. %In the case where $\modY = \FCI$ in Eq.~\eqref{eq:limitfunc}, we have a strict equality as $\E{\FCI}{} = \E{}{}$. In the case where \titou{$\CCSDT$ is replaced by $\FCI$} in Eq.~\eqref{eq:limitfunc}, we have a strict equality as $\E{\FCI}{} = \E{}{}$. %Provided that the functional $\bE{}{\Bas}[\n{}{}]$ is known exactly, the only sources of error at this stage lie in the potential approximate nature of the methods $\modY$ and $\modZ$, and the lack of self-consistency in the present scheme. -Provided that the functional $\bE{}{\Bas}[\n{}{}]$ is known exactly, the only sources of error at this stage lie in the potential approximate nature of the \titou{$\CCSDT$ and $\HF$ methods}, and the lack of self-consistency in the present scheme. +Provided that the functional $\bE{}{\Bas}[\n{}{}]$ is known exactly, the only sources of error at this stage lie in the approximate nature of the \titou{$\CCSDT$ and $\HF$ methods}, and the lack of self-consistency of the present scheme. The functional $\bE{}{\Bas}[\n{}{}]$ is obviously \textit{not} universal as it depends on $\Bas$. Moreover, as $\bE{}{\Bas}[\n{}{}]$ aims at fixing the incompleteness of $\Bas$, its main role is to correct @@ -429,7 +429,7 @@ We begin our investigation of the performance of the basis-set correction by com 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. -As \titou{a ``reference'' method}, we employ either CCSD(T) or exFCI. +\titou{We employ either CCSD(T) or exFCI to compute the energy of these systems.} Here, exFCI stands for extrapolated FCI energies computed with the CIPSI algorithm. \cite{HurMalRan-JCP-73, GinSceCaf-CJC-13, GinSceCaf-JCP-15} We refer the interested reader to Refs.~\onlinecite{HolUmrSha-JCP-17, SceGarCafLoo-JCTC-18, LooSceBloGarCafJac-JCTC-18, SceBenJacCafLoo-JCP-18, LooBogSceCafJAc-JCTC-19} for more details. %In the case of the CCSD(T) calculations, we have $\modZ = \ROHF$ as we use the restricted open-shell HF (ROHF) one-electron density to compute the complementary basis-set correction energy. @@ -463,8 +463,8 @@ In most cases, the basis-set corrected triple-$\zeta$ atomization energies are o \begin{figure} \includegraphics[width=0.5\linewidth]{fig2} \caption{ - $\rsmu{}{\Bas}$ (top) and $\n{}{} \times \be{\text{c,md}}{\sr,\PBE}$ (bottom) along the molecular axis ($z$) for \ce{N2} in various basis sets. - The two nitrogen atoms are located at $z=0$ and $z=2.076$ bohr. + \titou{$\rsmu{}{\Bas}$ (top) and $\n{}{} \times \be{\text{c,md}}{\sr,\PBE}$ (bottom) along the molecular axis ($z$) for \ce{N2} in various basis sets. + The two nitrogen atoms are located at $z=0$ and $z=2.076$ bohr.} \label{fig:N2}} \end{figure} @@ -524,7 +524,7 @@ The ``plain'' CCSD(T) atomization energies as well as the corrected \titou{CCSD( The raw data \titou{(as well as the corresponding LDA results)} can be found in the {\SI}. A statistical analysis of these data is also provided in Table \ref{tab:stats}, where we report the mean absolute deviation (MAD), root-mean-square deviation (RMSD), and maximum deviation (MAX) with respect to the CCSD(T)/CBS atomization energies. Note that the MAD of our CCSD(T)/CBS atomization energies is only 0.37 {\kcal} compared to the values extracted from Ref.~\onlinecite{HauKlo-JCP-12} which corresponds to frozen-core non-relativistic atomization energies obtained at the CCSD(T)(F12)/cc-pVQZ-F12 level of theory corrected for higher-excitation contributions ($E_\text{CCSDT(Q)/cc-pV(D+d)Z} - E_\text{CCSD(T)/cc-pV(D+d)Z})$. -From double-$\zeta$ to quintuple-$\zeta$ basis, the MAD associated with the CCSD(T) atomization energies goes down slowly from 14.29 to 1.28 {\kcal}. +From the double- to the quintuple-$\zeta$ basis, the MAD associated with the CCSD(T) atomization energies goes down slowly from 14.29 to 1.28 {\kcal}. For a commonly used basis like cc-pVTZ, the MAD of CCSD(T) is still 6.06 {\kcal}. Applying the basis-set correction drastically reduces the basis-set incompleteness error. %Already at the CCSD(T)+LDA/cc-pVDZ and CCSD(T)+PBE/cc-pVDZ level, the MAD is reduced to 3.24 and 1.96 {\kcal}.