loos/eDFT_FUEG
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

Manu: minor changes in the introduction

Browse Source
This commit is contained in:
Emmanuel Fromager 2020-03-11 15:29:29 +01:00
parent 74caf1a604
commit f0874a96ad
1 changed files with 7 additions and 6 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

13
Manuscript/eDFT.tex
View File

@ -188,7 +188,7 @@ Interestingly, a similar approach exists in DFT. Referred to as
Gross--Oliveira--Kohn (GOK) DFT, \cite{Gross_1988a,Gross_1988b,Oliveira_1988} it was proposed at the end of the 80's as a generalization Gross--Oliveira--Kohn (GOK) DFT, \cite{Gross_1988a,Gross_1988b,Oliveira_1988} it was proposed at the end of the 80's as a generalization
of Theophilou's DFT for equiensembles. \cite{Theophilou_1979} of Theophilou's DFT for equiensembles. \cite{Theophilou_1979}
In GOK-DFT, the ensemble xc energy is a functional of the In GOK-DFT, the ensemble xc energy is a functional of the
density but also a density {\it and} a
function of the ensemble weights. Note that, unlike in conventional function of the ensemble weights. Note that, unlike in conventional
Boltzmann ensembles, \cite{Pastorczak_2013} the ensemble weights (each state in the ensemble Boltzmann ensembles, \cite{Pastorczak_2013} the ensemble weights (each state in the ensemble
is assigned a given and fixed weight) are allowed to vary is assigned a given and fixed weight) are allowed to vary
@ -213,12 +213,13 @@ or atoms. \cite{Yang_2014,Yang_2017,Gould_2019_insights}
Despite all these efforts, it is still unclear how weight dependencies Despite all these efforts, it is still unclear how weight dependencies
can be incorporated into density-functional approximations. This problem is actually central not can be incorporated into density-functional approximations. This problem is actually central not
only in GOK-DFT but also in conventional (ground-state) DFT as the infamous derivative only in GOK-DFT but also in conventional (ground-state) DFT as the infamous derivative
discontinuity problem that ocurs when crossing an integral number of discontinuity problem that occurs when crossing an integral number of
electrons can be recast into a weight-dependent ensemble electrons can be recast into a weight-dependent ensemble
one. \cite{Senjean_2018,Senjean_2020} one. \cite{Senjean_2018,Senjean_2020}
The present work is an attempt to address this problem, The present work is an attempt to address the ensemble weight dependence problem
with the ambition to turn, in the forthcoming future, GOK-DFT into a in GOK-DFT,
with the ambition to turn the theory, in the forthcoming future, into a
(low-cost) practical computational method for modeling excited states in molecules and extended systems. (low-cost) practical computational method for modeling excited states in molecules and extended systems.
Starting from the ubiquitous local-density approximation (LDA), we Starting from the ubiquitous local-density approximation (LDA), we
design a weight-dependent ensemble correction based on a finite uniform design a weight-dependent ensemble correction based on a finite uniform
@ -239,13 +240,13 @@ In these extreme conditions, where magnetic effects compete with Coulombic force
The paper is organized as follows. The paper is organized as follows.
Exact and approximate formulations of GOK-DFT are discussed in Sec.~\ref{sec:eDFT}, Exact and approximate formulations of GOK-DFT are discussed in Sec.~\ref{sec:eDFT},
with a particular emphasis on the calculation of individual energy levels. with a particular emphasis on the extraction of individual energy levels.
In Sec.~\ref{sec:eDFA}, we detail the construction of the In Sec.~\ref{sec:eDFA}, we detail the construction of the
weight-dependent local correlation functional specially designed for the weight-dependent local correlation functional specially designed for the
computation of single and double excitations within GOK-DFT. computation of single and double excitations within GOK-DFT.
Computational details needed to reproduce the results of the present work are reported in Sec.~\ref{sec:comp_details}. Computational details needed to reproduce the results of the present work are reported in Sec.~\ref{sec:comp_details}.
In Sec.~\ref{sec:res}, we illustrate the accuracy of the present eLDA functional by computing single and double excitations in 1D many-electron systems in the weak, intermediate and strong correlation regimes. In Sec.~\ref{sec:res}, we illustrate the accuracy of the present eLDA functional by computing single and double excitations in 1D many-electron systems in the weak, intermediate and strong correlation regimes.
Finally, we draw our conclusion in Sec.~\ref{sec:conclusion}. Finally, we draw our conclusions in Sec.~\ref{sec:conclusion}.
Atomic units are used throughout. Atomic units are used throughout.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%