diff --git a/Manuscript/BSE_JPCL.tex b/Manuscript/BSE_JPCL.tex index 146acd0..054351d 100644 --- a/Manuscript/BSE_JPCL.tex +++ b/Manuscript/BSE_JPCL.tex @@ -89,7 +89,7 @@ \newcommand{\EA}{A} \newcommand{\HOMO}{\text{HOMO}} \newcommand{\LUMO}{\text{LUMO}} -\newcommand{\Eg}{E_\text{gap}} +\newcommand{\Eg}{E_\text{g}} \newcommand{\EgFun}{\Eg^\text{fund}} \newcommand{\EgOpt}{\Eg^\text{opt}} \newcommand{\EB}{E_B} @@ -247,9 +247,16 @@ An important conclusion drawn from these calculations was that the quality of th \end{equation} with the experimental (photoemission) fundamental gap \cite{Bredas_2014} \begin{equation} - \EgFun = I - A, + \EgFun = I^N - A^N, \end{equation} -where $I = E_0^{N-1} - E_0^N$ and $A = E_0^{N+1} - E_0^N$ are the ionization potential and the electron affinity of the $N$-electron system, $E_s^{N}$ is the total energy of the $s$th excited state of the $N$-electron system, and $E_0^N$ corresponds to the $N$-electron ground-state energy. +where $I^N = E_0^{N-1} - E_0^N$ and $A^N = E_0^{N+1} - E_0^N$ are the ionization potential and the electron affinity of the $N$-electron system, $E_s^{N}$ is the total energy of the $s$th excited state of the $N$-electron system, and $E_0^N$ corresponds to the $N$-electron ground-state energy (see Fig.~\ref{fig:gaps}). + +\begin{figure*} + \includegraphics[width=0.7\linewidth]{gaps} + \caption{ + Optical and fundamental gaps. + \label{fig:gaps}} +\end{figure*} Standard $G_0W_0$ calculations starting with Kohn-Sham (KS) eigenstates generated with (semi)local functionals yield much larger HOMO-LUMO gaps than the input KS gap \begin{equation} diff --git a/Manuscript/gaps.png b/Manuscript/gaps.png new file mode 100644 index 0000000..e3da4c2 Binary files /dev/null and b/Manuscript/gaps.png differ diff --git a/gaps.svg b/gaps.svg new file mode 100644 index 0000000..c7e31e1 --- /dev/null +++ b/gaps.svg @@ -0,0 +1,2929 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + image/svg+xml + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +