## 1 Introduction  
The main protease (M\({}^{\text{pro}}\)) and papain-like protease (PL\({}^{\text{pro}}\)) of SARS-CoV-2 are suitable targets for the pharmacological action against its viral replication [1]. Both enzymes are Cysteine (Cys) proteases [2, 3], and in the case of M\({}^{\text{pro}}\), the mechanism closely resembles the well-studied mechanism of Serine protease. M\({}^{\text{pro}}\) works via a catalytic dyad formed by a nucleophilic Cysteine (Cys145) activated by a Histidine (His41) residue. After a preliminary proton transfer from Cys145 to His41, through which the nucleophilic strength of the former residue is strongly enhanced, M\({}^{\text{pro}}\) preferentially attacks peptide bonds after a glutamine residue [4], leading to a tetrahedral intermediate from which the actual peptide bond cleavage occurs, due to the back-proton-transfer from His45 leading to a thioester (Scheme 1a). After that, the thioester is hydrolyzed, regenerating the active enzyme. EbSe is supposed to covalently inhibit SARS-CoV-2 M\({}^{\text{pro}}\) via the formation of a selenylsulfide (Se-S) adduct with Cys145 (Scheme 1b). The formation of a selenyl-sulfide bond with Cys residues was also postulated five years ago in order to explain the antiviral activity of EbSe against HIV [12]. However, to the best of our knowledge, the precise chemical mechanism has never been investigated in protein and it might provide insight into the rational engineering of existing organoselenides (e.g., diphenyl diselenide), ebselen derivatives [13, 14] or the design of new selenium-based antivirals. In a recent preprint, [PERSON] et al. [15] reported interesting results indicating that the inhibitory capacity of organoselenium compounds towards M\({}^{\text{pro}}\) is greatly reduced upon dimerization to diselenides, and [PERSON] et al. recently demonstrated that, under reducing conditions, i.e., in the presence of 1,4-dithiothreitol (DTT) and/or glutathione (GSH), EbSe is not able to effectively inhibit SARS-CoV-2 M\({}^{\text{pro}}\) as well as a panel of other Cys proteases [16, 17]. Particularly, all the ebselen-like scaffolds investigated by [PERSON] al. were 1-2 orders of magnitude less efficient at inhibiting M\({}^{\text{pro}}\) after dimerization to diselenides. Moreover, the decrease in the inhibitory potency of EbSe in the presence of DTT and GSH raises the problem of formation of ebselen-low-molecular mass thiol adducts in vivo (i.e., adducts with free Cys and GSH). Further investigation is thus important to understand the true antiviral potential of organoselenium compounds, starting from the chemical mechanism, and then progressively moving to realistic biological conditions. For this reason, we thoroughly analyzed, in silico, the chemical mechanism of Se-S bond formation between EbSe and Cys145, which is at the basis of the protease inhibition, and we extended our analysis to the Se-S bond formation starting from ebselen enthalolate (EbSeS) (Scheme 2) as a model of the adduct of EbSe with endogenous thiol molecules. In fact, since it is unlikely that the reactive N-Se bond of EbSe reaches M\({}^{\text{pro}}\) unmodified, EbSeS was taken as a general model of ebselen selenyl sulfides, which are expected to be present in the biological environment. EbSe actually travels through the plasma bonded to the free Cys of albumin and/or other low-molecular-containing thiol molecules (Cys and GSH) [18; 19]. Thus, EbSe is suitable for the description of in vitro inhibition and EbSeS is a simplified model for the description of in vivo inhibition of M\({}^{\text{pro}}\). In early 2020, a high-throughput screening discovered ebselen (EbSe, Scheme 2), one of the most famous organoselenides, as a potent inhibitor of SARS-CoV-2 M\({}^{\text{pro}}\) (IC\({}_{50}\) = 0.67 uM) [6]. EbSe is known to interact with a plethora of biologically relevant cysteines [7; 8; 9], implying both pharmacological interest and toxicological concern.