diff --git a/TrUEGs.bib b/TrUEGs.bib index 22be327..084b247 100644 --- a/TrUEGs.bib +++ b/TrUEGs.bib @@ -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. 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100644 --- a/TrUEGs.tex +++ b/TrUEGs.tex @@ -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} %%% %%% %%% %%%