loos/SRGGW
2
0
Fork 0
Code Issues Pull Requests Projects Releases Wiki Activity

saving work in results

Browse Source
This commit is contained in:
Pierre-Francois Loos 2023-02-14 18:06:36 -05:00
parent d5960011ab
commit 39b874f305
1 changed files with 11 additions and 10 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

21
Manuscript/SRGGW.tex
View File

@ -647,7 +647,7 @@ However, in order to perform a black-box comparison, these parameters have been
The results section is divided into two parts. The results section is divided into two parts.
The first step will be to analyze in depth the behavior of the two static self-energy approximations in a few test cases. The first step will be to analyze in depth the behavior of the two static self-energy approximations in a few test cases.
Then the accuracy of the IP yielded by the traditional and SRG schemes will be statistically gauged over a test set of molecules. Then, the accuracy of the principal IPs and EAs produced by the qs$GW$ and SRG-qs$GW$ schemes are statistically gauged over the test set of molecules described in Sec.~\ref{sec:comp_det}.
%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%
\subsection{Flow parameter dependence of the SRG-qs$GW$ scheme} \subsection{Flow parameter dependence of the SRG-qs$GW$ scheme}
@ -675,18 +675,19 @@ Then the accuracy of the IP yielded by the traditional and SRG schemes will be s
\end{figure*} \end{figure*}
%%% %%% %%% %%% %%% %%% %%% %%%
This section starts by considering a prototypical molecular system, \ie the water molecule, in the aug-cc-pVTZ cartesian basis set. This section starts by considering a prototypical molecular system, \ie the water molecule, in the aug-cc-pVTZ basis set.
Figure \ref{fig:fig2} shows the error of various methods for the principal IP with respect to the CCSD(T) reference value. Figure \ref{fig:fig2} shows the error of various methods for the principal IP with respect to the CCSD(T) reference value.
The HF IP (dashed black line) is overestimated; this is a consequence of the missing correlation and the lack of orbital relaxation for the cation, a result that is well understood. \cite{SzaboBook,Lewis_2019} The IP at the HF level (dashed black line) is overestimated; this is a consequence of the missing correlation and the lack of orbital relaxation for the cation, a result that is well understood. \cite{SzaboBook,Lewis_2019}
The usual qs$GW$ scheme (dashed blue line) brings a quantitative improvement as the IP is now within \SI{0.3}{\electronvolt} of the reference. The usual qs$GW$ scheme (dashed blue line) brings a quantitative improvement as the IP is now within \SI{0.3}{\eV} of the reference.
Figure~\ref{fig:fig2} also displays the SRG-qs$GW$ IP as a function of the flow parameter (blue curve). Figure \ref{fig:fig2} also displays the IP at the SRG-qs$GW$ level as a function of the flow parameter (blue curve).
At $s=0$, the IP is equal to its HF counterpart as expected from the discussion of Sec.~\ref{sec:srggw}. At $s=0$, the SRG-qs$GW$ IP is equal to its HF counterpart as expected from the discussion of Sec.~\ref{sec:srggw}.
For $s\to\infty$, the IP reaches a plateau at an error that is significantly smaller than their $s=0$ starting point. As $s\to\infty$, the IP reaches a plateau at an error that is significantly smaller than their $s=0$ starting point.
Even more, the value associated with this plateau is slightly more accurate than its qs$GW$ counterpart. Furthermore, the value associated with this plateau is slightly more accurate than its qs$GW$ counterpart.
However, the SRG-qs$GW$ error do not decrease smoothly between the initial HF value and the $s\to\infty$ limit as for small $s$ values it is actually worst than the HF starting point. However, the SRG-qs$GW$ error does not decrease smoothly between the initial HF value and the $s\to\infty$ limit.
For small $s$, it is actually worse than the HF starting point.
This behavior as a function of $s$ can be approximately rationalized by applying matrix perturbation theory on Eq.~(\ref{eq:GWlin}). This behavior as a function of $s$ can be understood by applying matrix perturbation theory on Eq.~\eqref{eq:GWlin}.
Through second order in the coupling block, the principal IP is Through second order in the coupling block, the principal IP is
\begin{equation} \begin{equation}
\label{eq:2nd_order_IP} \label{eq:2nd_order_IP}