pouet

Manuscript/srDFT_SC.tex

@@ -497,9 +497,8 @@ Such a property is also important in the context of covalent bond breaking where
 
 \subsubsection{Condition for the functional $\efuncdenpbe{\argebasis}$ to obtain $S_z$ invariance}
 A sufficient condition to achieve $S_z$ invariance is to eliminate all dependency to $S_z$, which in the case of $\ecmd(\argecmd)$ is the spin polarisation $\zeta(\br{})$ involved in the correlation energy density $\varepsilon_{\text{c,PBE}}(\argepbe)$ (see equation \eqref{eq:def_ecmdpbe}). 
-Of course, the dependency on the spin polarisation of the functionals can be thought as an aterfact 
-A possible way to eliminate the $S_z$ dependency would be to simply set $\zeta(\br{})=0$, but this would lower the accuracy of the usual PBE correlation functional $\varepsilon_{\text{c,PBE}}(\argepbe)$. 
-Therefore, we use the effective spin polarisation introduced by Scuseria and co-workers\cite{GarBulHenScu-PCCP-15}  which depends on the on-top pair density and the total density of a general multi configurational wave function $\psibasis$: 
+As originally shown by Perdew and co-workers\cite{PerSavBur-PRA-95}, the dependence on the spin polarisation in the KS-DFT framework can be removed by the reformulating the spin polarisation of a single Slater determinant with the on-top pair density and the total density. In other terms, the spin density dependence of the correlation functionals usually try to mimic the on-top pair density of a given system. 
+Based on this reasoning, a similar approach has been used in the context of multi configurational DFT approaches where an effective spin density is introduced
 \begin{equation}
  \label{eq:def_effspin}
  \tilde{\zeta}(n,\ntwo_{\psibasis}) =  
@@ -508,6 +507,8 @@ Therefore, we use the effective spin polarisation introduced by Scuseria and co-
                                0              & \text{otherwise.}
     \end{cases}
 \end{equation}
+A possible way to eliminate the $S_z$ dependency would be to simply set $\zeta(\br{})=0$, but this would lower the accuracy of the usual PBE correlation functional $\varepsilon_{\text{c,PBE}}(\argepbe)$. 
+Therefore, we use the effective spin polarisation introduced by Scuseria and co-workers\cite{GarBulHenScu-PCCP-15}  which depends on the on-top pair density and the total density of a general multi configurational wave function $\psibasis$: 
 If the density $n$ and on-top pair density $\ntwo_{\psibasis}$ are obtained from a single HF determinant, the definition \eqref{eq:def_effspin} is equivalent to the usual one
 \begin{equation}
  \tilde{\zeta}(n^{\text{HF}},\ntwohf) = n_{\alpha}^{\text{HF}} - n_{\beta}^{\text{HF}},