Merge branch 'master' of https://github.com/pfloos/srDFT_G2

Manuscript/G2-srDFT.tex

@@ -609,7 +609,7 @@ which scales as $\Nb^2\times N_{elec}^2 \times \Ng$ and is embarassingly paralle
 When the four-index transformation become prohibitive, by performing successive matrix multiplications, one could rewrite the equations directly in the AO basis where it scales formally as $\order{\Ng \Nb^4}$  but where one can take advantage of the sparsity atomic-orbital-based algorithms to significantly speed up the calculations.  
 
 
-To conclude this theory session, it is important to notice that the basis set correction proposed here has the folowing properties whatever the approximations made in the DFT part: i) it can be applied to any wave function models that provide an energy and density, ii) it vanishes for one-electron systems, 
+To conclude this theory session, it is important to notice that the basis set correction proposed here has the folowing properties whatever the approximations made in the DFT part: i) it can be applied to any WFT model that provides an energy and a density, ii) it vanishes for one-electron systems, 
 iii) it vanishes in the limit of a complete basis set and thus garentees the correct CBS limit of the WFT model. 
 %, because of the behaviour of the effective interaction [see \eqref{eq:lim_W}], the range separation function $\rsmu{\wf{}{\Bas}}{}(\br{})$ tends to infinity. Therefore, in the limit of a complete basis set, according to equation \eqref{eq:large_mu_ecmd}, the complementary functional tends to zero \textit{whatever the approximated functional} used for the DFT part. 
 
@@ -664,7 +664,7 @@ iii) it vanishes in the limit of a complete basis set and thus garentees the cor
 							&	CCSD(T)+PBE\fnm[1]	&	31.5 	(-6.7	)	&	37.1 	(-1.1	)	&	37.8 	(-0.4	)	&	38.2 	(+0.0	)	&					\\	
 		\end{tabular}
 	\end{ruledtabular}
-	\fnt[1]{Fronzen core calculations. Only valence spinorbitals are taken into account in the basis set correction.}
+	\fnt[1]{Frozen core calculations. Only valence spinorbitals are taken into account in the basis set correction.}
 	\fnt[2]{``Full'' calculation, i.e., all electrons are correlated. All spinorbitals are taken into account in the basis set correction.}
 \end{table*}
 
@@ -708,7 +708,7 @@ iii) it vanishes in the limit of a complete basis set and thus garentees the cor
 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 sets (X $=$ D, T, Q and 5).
 In the case of \ce{C2} and \ce{N2}, we also perform calculations with the cc-pCVXZ family.
 \ce{N2}, \ce{O2} and \ce{F2} are weakly correlated systems and belong to the G2 set, whereas \ce{C2} already contains a non-negligible amount of strong correlation. \cite{BooCleThoAla-JCP-11} 
-In a second time, we compute the entire atomization energies of the G2 set \cite{CurRagTruPop-JCP-91} composed by 55 molecules with the cc-pVXZ family, except for Li, Be and Na for which we use the cc-pCVXZ basis sets.
+In a second time, we compute the entire atomization energies of the G2 set \cite{CurRagTruPop-JCP-91} composed by 55 molecules with the cc-pVXZ family of basis sets.
 This molecular set has been exhausively 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,PetTouUmr-JCP-12,FelPet-JCP-13,KesSylKohTewMar-JCP-18}).
 %The reference values for the atomization energies are extracted from Ref.~\onlinecite{HauKlo-JCP-12} and 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 ($E_\text{CCSDT(Q)/cc-pV(D+d)Z} - E_\text{CCSD(T)/cc-pV(D+d)Z})$.
 As a method $\modX$ we employ either CCSD(T) or exFCI.
@@ -720,7 +720,7 @@ The CCSD(T) calculations have been performed with Gaussian09 with standard thres
 RS-DFT and exFCI calculations are performed with {\QP}. \cite{QP2}
 For the quadrature grid, we employ the radial and angular points of the SG2 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.
-Frozen core calculations are defined as such: an \ce{He} core is frozen from \ce{B} to \ce{Mg}, while a \ce{Ne} core is frozen from \ce{Al} to \ce{Xe}.
+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 valence spinorbitals $\Val$ involved in the definition of the effective interaction refers to the non-frozen spinorbitals.
 The ``valence'' correction was used consistently when the FC approximation was applied.
 In order to estimate the complete basis set (CBS) limit for each model, we employed the two-point extrapolation proposed in Ref.~\onlinecite{HalHelJorKloKocOlsWil-CPL-98} for the correlation energies.