From 31b6eb78ad4d8e0c14e548804e4a36016ecfed7a Mon Sep 17 00:00:00 2001 From: eginer Date: Thu, 17 Oct 2019 18:58:37 +0200 Subject: [PATCH] pouet --- Manuscript/srDFT_SC.tex | 7 ++++--- 1 file changed, 4 insertions(+), 3 deletions(-) diff --git a/Manuscript/srDFT_SC.tex b/Manuscript/srDFT_SC.tex index 0c43215..4909214 100644 --- a/Manuscript/srDFT_SC.tex +++ b/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}},