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Pierre-Francois Loos 2021-01-13 21:39:31 +01:00
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TrUEGs.bib
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@ -1,13 +1,43 @@
%% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/
%% Created for Pierre-Francois Loos at 2021-01-12 16:47:17 +0100
%% Created for Pierre-Francois Loos at 2021-01-13 21:07:52 +0100
%% Saved with string encoding Unicode (UTF-8)
@article{Becke_1993b,
author = {Becke,Axel D.},
date-added = {2021-01-13 21:07:34 +0100},
date-modified = {2021-01-13 21:07:34 +0100},
doi = {10.1063/1.464304},
journal = {J. Chem. Phys.},
number = {2},
pages = {1372-1377},
title = {A new mixing of Hartree--Fock and local density‐functional theories},
volume = {98},
year = {1993},
Bdsk-Url-1 = {https://doi.org/10.1063/1.464304}}
@article{Lee_1988,
author = {C. Lee and W. Yang and R. G. Parr},
date-added = {2021-01-13 21:06:49 +0100},
date-modified = {2021-01-13 21:06:49 +0100},
doi = {10.1103/PhysRevB.37.785},
issue = {2},
journal = {Phys. Rev. B},
month = {Jan},
pages = {785},
publisher = {American Physical Society},
title = {Development of the Colle--Salvetti correlation-energy formula into a functional of the electron density},
url = {http://link.aps.org/doi/10.1103/PhysRevB.37.785},
volume = {37},
year = {1988},
Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevB.37.785},
Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.37.785}}
@article{Wigner_1934,
author = {Wigner, E.},
date-added = {2021-01-12 16:22:53 +0100},
@ -13718,10 +13748,10 @@
year = {2016},
Bdsk-Url-1 = {https://doi.org/10.1063/1.4963749}}
@article{Becke_1993,
@article{Becke_1993a,
author = {A. D. Becke},
date-added = {2018-07-04 21:18:18 +0000},
date-modified = {2018-07-18 13:08:55 +0000},
date-modified = {2021-01-13 21:07:37 +0100},
doi = {10.1063/1.464913},
journal = {J. Chem. Phys.},
pages = {5648--5652},

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TrUEGs.nb
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TrUEGs.tex
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@ -64,7 +64,7 @@ Indeed, apart from very few exceptions, most density-functional approximations a
Thanks to the construction of exchange-correlation LDA functionals \cite{Slater_1951,Vosko_1980,Perdew_1981,Perdew_1992,Chachiyo_2016} which can be loosely seen as a one-to-one mapping between a given value of the electron density and the exchange-correlation energy of the UEG, one can then straightforwardly compute, within KS-DFT, the electronic ground-state energy and properties of any molecules or materials with, nonetheless, a certain degree of approximation inherently associated with the approximate nature of the exchange-correlation LDA functional.
One can also access excited states via the time-dependent version of DFT. \cite{Runge_1984,Casida_1995,Petersilka_1996,UllrichBook}
As commonly done, the LDA can be refined by adding up new ingredients, such as the gradient of the density $\nabla \rho$ [which defines the generalized gradient approximation (GGA)], \cite{Perdew_1986,Becke_1988,Perdew_1996} the kinetic energy density $\tau$ (meta-GGA), \cite{Becke_1988b,Sun_2015} exact Hartree-Fock exchange (yielding the so-called hybrid functionals), \cite{Becke_1993,Adamo_1999} and others.
As commonly done, the LDA can be refined by adding up new ingredients, such as the gradient of the density $\nabla \rho$ [which defines the generalized gradient approximation (GGA)], \cite{Perdew_1986,Becke_1988,Lee_1988,Perdew_1996} the kinetic energy density $\tau$ (meta-GGA), \cite{Becke_1988b,Sun_2015} exact Hartree-Fock exchange (yielding the so-called hybrid functionals), \cite{Becke_1993a,Becke_1993b,Adamo_1999} and others.
Each of these quantities defines a new rung of the well-known Jacob ladder of DFT \cite{Perdew_2001} that is supposed to bring electronic structure theory calculations from the evil Hartree world to the chemical accuracy heaven.
The UEG, also known as jellium in some context, \cite{Loos_2016} is a hypothetical infinite substance where an infinite number of electrons ``bathe'' in a (uniform) positively charged jelly of infinite volume. \cite{ParrBook,Loos_2016}
@ -141,7 +141,7 @@ For the other electronic states corresponding to higher total angular momentum,
\includegraphics[width=\linewidth]{3P}
\caption{
$c_0 - 2 c_1/3 + c_2/5$ as a function of the radius of the sphere $R$ for various states of $^3P$ symmetry.
The root associated to each state is located by a marker.
The root associated to each state (which corresponds to the value of $R$ for which the electron density is uniform) is located by a marker.
\label{fig:3P}}
\end{figure}
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