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{To the Editors of the Journal of Chemical Physics}

\opening{Dear Editors,}

\justifying
Please find enclosed our manuscript entitled \textit{``Dynamical Kernels for Optical Excitations''}, which we would like you to consider as a Regular Article in the \textit{Journal of Chemical Physics}.
This contribution fits nicely in the section \textit{``Theoretical Methods and Algorithms''}. 
This contribution has never been submitted in total nor in parts to any other journal, and has been seen and approved by all authors.

In the present manuscript, we discuss, in a pedagogical way, the physics of dynamical (i.e., frequency-dependent) kernels for the computation of optical excitations within linear response theory.
In particular, we consider three dynamical kernels, namely i) an a priori built kernel inspired by the dressed TD-DFT kernel of Maitra and coworkers, ii) the dynamical kernel stemming from the BSE formalism derived originally by Strinati, and iii) the second-order BSE kernel derived first by the group of Weitao Yang. 
The principal take-home message of the present paper is that dynamical kernels have much more to give that one would think. 
In more scientific terms, dynamical kernels can provide, thanks to their frequency-dependent nature, additional excitations that can be associated to higher-order excitations (such as the infamous double excitations).
However, they sometimes give too much, and generate spurious excitations, i.e., excitation which does not corresponds to any physical excited state.
Using a simple two-model system, prototypical examples of valence, charge-transfer, and Rydberg excitations are studied.
From these, we have observed that, overall, the dynamical correction usually improves the static excitation energies, and that, if one has no interest in double excitations, a perturbative treatment is an excellent alternative to a non-linear resolution of the dynamical equations.

We expect this work to be of interest to a wide audience within the chemistry and physics communities.
We suggest Paola Gori-Giorgi, Neepa Maitra, Valerio Olevano, Patrick Rinke, Weitao Yang, Michael Rohlfing, and Lucia Reining as potential referees.
We look forward to hearing from you soon.

\closing{Sincerely, the authors.}


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