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\begin{letter}%
{To the Editors of the Journal of Chemical Theory and Computation}

\opening{Dear Editors,}

\justifying
Please find enclosed our manuscript entitled
\begin{quote}
\textit{``A Density-Based Basis Set Correction for GW Methods''}, 
\end{quote}
which we would like you to consider as a Regular Article in the \textit{Journal of Chemical Theory and Computation}.
This contribution nicely fits in the \textit{``Quantum Electronic Structure''} section.  

One of the most fundamental drawbacks of conventional electron correlation methods is the slow convergence of energies and properties with respect to the one-electron basis set.
Similar to other electron correlation methods, many-body perturbation theory methods based on Green functions, such as the so-called $GW$ approximation, suffer from the same pathological slow convergence.
As proposed by Kutzelnigg more than thirty years ago, one can introduce explicitly the interelectronic distance $r_{12}$ to significantly speed up the convergence.
However, significant computational overheads are introduced by the large auxiliary basis used to resolve three- and four-electron integrals.
Moreover, to the best of our knowledge, a F12-based correction for $GW$ has not been designed yet.
In this manuscript, we describe a drastically different approach which combines density-functional theory (DFT) and Green function based methods.
The present universal, density-based basis set incompleteness correction relies on short-range correlation density functionals from range-separated DFT to estimate the basis set incompleteness error.
The performance of this density-based correction is illustrated by computing the ionization potentials of molecules of the GW100 test set at the perturbative GW level.
In particular, we evidence that the present basis set correction significantly speeds up the convergence of ionization potentials for small and larger molecules towards the complete basis set limit. 

We suggest Xavier Blase, Lucia Reining, Timothy Berkelbach, Michel van Setten,Patrick Rinke, Valerio Olevano, Seiichiro Ten-no, Wim Klopper, and David Tew as potential referees.
This contribution has never been submitted in total nor in parts to any other journal, and has been seen and approved by all authors.
We look forward to hearing from you.

\closing{Sincerely, the authors.}


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