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Pierre-Francois Loos 2022-04-28 19:20:38 +02:00
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Manuscript/ufGW.tex
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@ -15,7 +15,7 @@
\newcommand{\ie}{\textit{i.e.}}
\newcommand{\eg}{\textit{e.g.}}
\newcommand{\alert}[1]{\textcolor{red}{#1}}
\newcommand{\alert}[1]{\textcolor{black}{#1}}
\usepackage[normalem]{ulem}
\newcommand{\titou}[1]{\textcolor{red}{#1}}
\newcommand{\trashPFL}[1]{\textcolor{r\ed}{\sout{#1}}}
@ -464,9 +464,10 @@ In particular, we compute, with and without regularization, the total energy at
These results are compared to high-level coupled-cluster \alert{(CC)} calculations extracted from the same work: \alert{CC with singles and doubles (CCSD) \cite{Purvis_1982} and the non-perturbative third-order approximate CC method (CC3). \cite{Christiansen_1995b}}
As already shown in Ref.~\onlinecite{Loos_2020e}, the potential energy surface of \ce{F2} at the BSE@{\GOWO}@HF (blue curve) is very ``bumpy'' around the equilibrium bond length and it is clear that the regularization scheme (black curve computed with $\alert{\kappa} = \SI{1}{\hartree}$) allows to smooth it out without significantly altering the overall accuracy.
Moreover, while it is extremely challenging to perform self-consistent $GW$ calculations without regularization, it is now straightforward to compute the BSE@ev$GW$@HF potential energy surface (gray curve).
\alert{For the sake of completeness, a similar graph for $\kappa = \SI{10}{\hartree}$ is reported as {\SupMat}.
Interestingly, for this rather large value of $\kappa$, the smooth BSE@{\GOWO}@HF and BSE@ev$GW$@HF curves are superposed, and of very similar quality as CCSD.
It is therefore clear that a smaller value of $\kappa$ is more suitable.}
\alert{For the sake of completeness, similar graphs for $\kappa = \SI{0.1}{\hartree}$ and $\kappa = \SI{10}{\hartree}$ are reported as {\SupMat}.
For $\kappa = \SI{0.1}{\hartree}$, one still has issues.
In particular, the BSE@ev$GW$@HF calculations do not converge for numerous values of the internuclear distance.
Interestingly, for $\kappa = \SI{10}{\hartree}$, the smooth BSE@{\GOWO}@HF and BSE@ev$GW$@HF curves are superposed, and of very similar quality as CCSD.}
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\section{Concluding remarks}