From 4def99ccbaedb1ab733a3380417a72cd0b75307e Mon Sep 17 00:00:00 2001 From: eginer Date: Tue, 2 Apr 2019 16:23:05 +0200 Subject: [PATCH] updated manuscript --- Manuscript/G2-srDFT.tex | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/Manuscript/G2-srDFT.tex b/Manuscript/G2-srDFT.tex index 871e2c4..5f49d1c 100644 --- a/Manuscript/G2-srDFT.tex +++ b/Manuscript/G2-srDFT.tex @@ -220,8 +220,10 @@ We propose here to generalize this procedure to any WFT approach. The functional $\efuncbasisfci$ is not universal as it depends on the basis set $\basis$ used. A simple analytical form for such a functional is of course not known and we approximate it in two-steps. First, we define a real-space representation of the coulomb interaction projected in $\basis$, which is then fitted with a long-range interaction thanks to a range-separation parameter $\mu(r)$ varying in space (see \ref{sec:weff}). Then, we choose a specific class of short-range density functionals, namely the short-range correlation functionals with multi-determinantal reference (ECMD) introduced by Toulouse \textit{et al}\cite{Toulouse2005_ecmd}, that we evaluate at the FCI density $\denfci$ (see \ref{sec:ecmd}) and with the range-separation parameter $\mu(r)$ varying in space. -\subsection{Generalization to any single-reference WFT method} -The theory provided in \cite{GinPraFerAssSavTou-JCP-18} proposes a basis set correction to a FCI or selected CI wave function while ensuring the correct limit for a complete basis set. We propose here to generalize it to any single-reference WFT. +\subsection{Generalization to any WFT method} +The theory provided in \cite{GinPraFerAssSavTou-JCP-18} proposes a basis set correction to a FCI or selected CI wave function while ensuring the correct limit for a complete basis set. We propose here to generalize it to any WFT method. + +Consider a general WFT model $\mathcal{Y}$ which provides a reference wave function $\ket{\Psi_{\mathcal{Y}}^{(0)}}$ and an energy $E_{\mathcal{Y}}$. \subsection{Definition of a real-space representation of the coulomb operator truncated in a basis-set $\basis$}