From 334aced980de09a3393737c456cdce120281a7c3 Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Fri, 22 Jan 2021 14:47:03 +0100 Subject: [PATCH] small typos --- Manuscript/sfBSE-control.bib | 15 --------------- Manuscript/sfBSE.tex | 9 ++++----- 2 files changed, 4 insertions(+), 20 deletions(-) delete mode 100644 Manuscript/sfBSE-control.bib diff --git a/Manuscript/sfBSE-control.bib b/Manuscript/sfBSE-control.bib deleted file mode 100644 index 5187ef4..0000000 --- a/Manuscript/sfBSE-control.bib +++ /dev/null @@ -1,15 +0,0 @@ -%% This BibTeX bibliography file was created using BibDesk. -%% http://bibdesk.sourceforge.net/ - -%% Created for Pierre-Francois Loos at 2021-01-19 16:50:57 +0100 - - -%% Saved with string encoding Unicode (UTF-8) - - - -@control{achemso-control, - ctrl-article-title = {yes}, - ctrl-chapter-title = {yes}, - ctrl-etal-firstonly = {yes}, - ctrl-etal-number = {30}} diff --git a/Manuscript/sfBSE.tex b/Manuscript/sfBSE.tex index 32c9143..5f55654 100644 --- a/Manuscript/sfBSE.tex +++ b/Manuscript/sfBSE.tex @@ -3,7 +3,6 @@ \usepackage[version=4]{mhchem} \usepackage{natbib} \bibliographystyle{achemso} -\AtBeginDocument{\nocite{achemso-control}} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} @@ -259,7 +258,7 @@ Unless otherwise stated, atomic units are used. Let us consider an electronic system consisting of $n = n_\up + n_\dw$ electrons (where $n_\up$ and $n_\dw$ are the number of spin-up and spin-down electrons, respectively) and $N$ one-electron basis functions. The number of spin-up and spin-down occupied orbitals are $O_\up = n_\up$ and $O_\dw = n_\dw$, respectively, and, assuming the absence of linear dependencies in the one-electron basis set, there is $V_\up = N - O_\up$ and $V_\dw = N - O_\dw$ spin-up and spin-down virtual (\ie, unoccupied) orbitals. The number of spin-conserved (sc) single excitations is then $S^\spc = S_{\up\up}^\spc + S_{\dw\dw}^\spc = O_\up V_\up + O_\dw V_\dw$, while the number of spin-flip (sf) excitations is $S^\spf = S_{\up\dw}^\spf + S_{\dw\up}^\spf = O_\up V_\dw + O_\dw V_\up$. -Let us denote as $\MO{p_\sig}(\br)$ the $p$th (spin)orbital with spin $\sig$ (where $\sig =$ $\up$ or $\dw$) and $\e{p_\sig}{}$ its one-electron energy. +Let us denote as $\MO{p_\sig}(\br)$ the $p$th spatial orbital associated with the spin-$\sig$ electrons (where $\sig =$ $\up$ or $\dw$) and $\e{p_\sig}{}$ its one-electron energy. It is important to understand that, in a spin-conserved excitation the hole orbital $\MO{i_\sig}$ and particle orbital $\MO{a_\sig}$ have the same spin $\sig$. In a spin-flip excitation, the hole and particle states, $\MO{i_\sig}$ and $\MO{a_\bsig}$, have opposite spins, $\sig$ and $\bsig$. We assume real quantities throughout this manuscript, $i$ and $j$ are occupied orbitals, $a$ and $b$ are unoccupied orbitals, $p$, $q$, $r$, and $s$ indicate arbitrary orbitals, and $m$ labels single excitations. @@ -269,7 +268,7 @@ Moreover, we consider systems with collinear spins and a spin-independent Hamilt \subsection{The dynamical screening} %================================ The pillar of Green's function many-body perturbation theory is the (time-ordered) one-body Green's function, which has poles at the charged excitations (i.e., ionization potentials and electron affinities) of the system. \cite{ReiningBook} -The spin-$\sig$ component of the one-body Green's function reads \cite{ReiningBook,Bruneval_2016a} +The spin-$\sig$ component of the one-body Green's function reads \cite{ReiningBook,Bruneval_2016} \begin{equation} \label{eq:G} G^{\sig}(\br_1,\br_2;\omega) @@ -504,7 +503,7 @@ The purpose of the underlying $GW$ calculation is to provide quasiparticle energ \label{sec:BSE} %================================ -Within the so-called static approximation of BSE, the Dyson equation that links the generalized four-point susceptibility $L^{\sig\sigp}(\br_1,\br_2;\br_1',\br_2';\omega)$ and the BSE kernel $\Xi^{\sig\sigp}(\br_3,\br_5;\br_4,\br_6)$ is \cite{ReiningBook,Bruneval_2016a} +Within the so-called static approximation of BSE, the Dyson equation that links the generalized four-point susceptibility $L^{\sig\sigp}(\br_1,\br_2;\br_1',\br_2';\omega)$ and the BSE kernel $\Xi^{\sig\sigp}(\br_3,\br_5;\br_4,\br_6)$ is \cite{ReiningBook,Bruneval_2016} \begin{multline} L^{\sig\sigp}(\br_1,\br_2;\br_1',\br_2';\omega) = L_{0}^{\sig\sigp}(\br_1,\br_2;\br_1',\br_2';\omega) @@ -1055,7 +1054,7 @@ Additional graphs comparing (SF-)TD-BLYP, (SF-)TD-B3LYP, and (SF-)dBSE with EOM- %The data that supports the findings of this study are available within the article and its supplementary material. %%%%%%%%%%%%%%%%%%%%%%%% -\bibliography{sfBSE,sfBSE-control} +\bibliography{sfBSE} %%%%%%%%%%%%%%%%%%%%%%%% \end{document}