From 0ffa8557f4bb1133d2b2fef4032529a0089e5534 Mon Sep 17 00:00:00 2001 From: Emmanuel Fromager Date: Fri, 28 Feb 2020 16:24:33 +0100 Subject: [PATCH] Manu: minor changes in II A --- Manuscript/eDFT.tex | 7 +++++-- 1 file changed, 5 insertions(+), 2 deletions(-) diff --git a/Manuscript/eDFT.tex b/Manuscript/eDFT.tex index 27f991c..8a62861 100644 --- a/Manuscript/eDFT.tex +++ b/Manuscript/eDFT.tex @@ -254,7 +254,10 @@ Atomic units are used throughout. \subsection{GOK-DFT}\label{subsec:gokdft} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -The GOK ensemble energy~\cite{Gross_1988a,Oliveira_1988,Gross_1988b} is defined as +In this section we give a brief review of GOK-DFT and discuss the +extraction of individual energy levels \cite{Deur_2019,Fromager_2020} with a particular focus on exact +individual exchange energies. +Let us start by introducing the GOK ensemble energy~\cite{Gross_1988a}: \beq\label{eq:exact_GOK_ens_ener} \E{}{\bw}=\sum_{K \geq 0} \ew{K} \E{}{(K)}, \eeq @@ -271,7 +274,7 @@ They are normalized, \ie, so that only the weights $\bw \equiv \qty( \ew{1}, \ew{2}, \ldots, \ew{K}, \ldots )$ assigned to the excited states can vary independently. For simplicity we will assume in the following that the energies are not degenerate. Note that the theory can be extended to multiplets simply by assigning the same ensemble weight to all degenerate states~\cite{Gross_1988b}. -In the KS formulation of GOK-DFT, \manu{which is simply referred to as +In the KS formulation of GOK-DFT, {which is simply referred to as KS ensemble DFT (KS-eDFT) in the following}, the ensemble energy is determined variationally as follows~\cite{Gross_1988b}: \beq\label{eq:var_ener_gokdft} \E{}{\bw}