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A&A
Volume 711, July 2026
Article Number A269
Number of page(s) 11
Section Interstellar and circumstellar matter
DOI https://doi.org/10.1051/0004-6361/202660371
Published online 22 July 2026

© The Authors 2026

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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1 Introduction

Sulfur, a crucial element for life on Earth, plays a vital role in various biological compounds such as cysteine and methionine, coenzyme A, vitamins B1 and biotin, as well as antioxidants such as glutathione (Voet et al. 2008). However, the role of sulfur in the interstellar medium (ISM), where stars and planets form, poses a challenge for astrochemists, particularly since the recognition of sulfur depletion in the ISM in the 1970s (Spitzer & Jenkins 1975; Gondhalekar 1985). While the gas-phase sulfur abundance in diffuse clouds (mostly in the form of S+) is consistent with the cosmic value, [S]/[H] = 1.8·10−5 (Anders & Grevesse 1989; Jenkins 2009), in more evolved environments (e.g., dense molecular clouds), its form remains uncertain and exhibits a depletion that depends on local conditions, typically by one to two orders of magnitude (Fuente et al. 2023), suggesting that atomic sulfur is predominant in chemically young cores (Hily-Blant et al. 2022), but it gradually becomes depleted as clouds evolve.

Freeze-out processes in MCs could lead to the adsorption of sulfur onto icy grain surfaces (Caselli et al. 1994), potentially forming compounds such as H2S. However, observations in MCs and young stellar objectices have mainly identified OCS and SO2 molecules (Boogert et al. 2015, 2022; McClure et al. 2023; Rocha et al. 2024), with only upper limits estimated for H2S (Smith 1991; McClure et al. 2023). A recent work by a group of our fellow authors showed that on a realistic amorphous water ice grain, even a small fraction of the formation energy of H2S suffices to desorb it, explaining the nondetection of this species in interstellar ices (Bariosco et al. 2024). Recent research indicates that sulfur could be found in organic species such as CS2 and the CnS (n = 2 – 3) carbon–sulfur chains (Laas & Caselli 2019), refractory residues such as H2Sn (3 ≤ n ≤ 8) and Sn chains (n = 2 – 3), and complex species such as hexathiepan (S6CH2), all of them formed through ice processing (Ferrante et al. 2008; Jiménez-Escobar & Caro 2011; Cazaux et al. 2022; Herath et al. 2025). Recent combined experimental and theoretical work, moreover, indicates that CS2 ices react efficiently with hydrogen atoms forming H2S, CH3SH, HC(S)SH, and CH2(SH)2 (Nguyen et al. 2026). The adsorption of 17 S-bearing molecules on crystalline and amorphous water ice has been reported by some of us, showing site-dependent binding energies (Perrero et al. 2022a). This was also extended to sulfur allotropes, Sn (n=1–8), generally finding low interactions and weak mid-infrared signatures on amorphous ice, consistent with S reservoirs that are difficult to detect (Perrero et al. 2024). In a recent work by some of our fellow authors (Saury et al. 2026), the binding energy distribution for OCS on water ice was presented, taking advantage of the OCS low binding energy and rotational lines in the millimeter was used to estimate the luminosity of embedded protostars in binary systems.

Comets, such as 67P/Churyumov–Gerasimenko, contain various S-bearing species, with the most common being H2S, OCS, SO, S2, SO2, and CS2, as well as S2, S3 and S4, CH3SH, C2H6SH, and CH3SCH3 (Calmonte et al. 2016; Hänni et al. 2024). could have been inherited from the prestellar and proto-stellar phases (Caselli & Ceccarelli 2012; Ceccarelli et al. 2023). Similarly, certain meteorites, such as chondrites, contain sulfur in minerals such as troilite (FeS) and pentlandite (Fe,Ni)9S8 (Kallemeyn et al. 1989; Gao & Thiemens 1993; Yabuta et al. 2007; Leroux et al. 2015), shedding light on the material feeding the formation of planets. Enstatite chondrites, on the other hand, are rich in sulfides such as niningerite (MgS) and alabandite (MnS) (Sears et al. 1982). However, a gap remains in terms of our understanding of the transition from gas-phase sulfur species in diffuse clouds to solid sulfides in protoplanetary disk remnants.

In recent decades, almost 30 S-bearing compounds originating from interstellar sources have been identified in the gas phase. Among them are carbon monosulfide (CS), thioformaldehyde (H2CS), and methyl mercaptan (also referred to as methanethiol; CH3 SH), along with various isotopes thereof (Penzias et al. 1971; Liszt et al. 1974; Linke et al. 1979; Marcelino et al. 2005; Müller et al. 2016; Bunn et al. 2025). Notably, all these compounds have been observed within starforming regions, including the Orion A and Barnard 1 molecular clouds, as well as hot molecular cores.

Recent proposals and modeling studies have suggested that CH3 SH can be formed on solid phase surfaces through the successive hydrogenation of CS (Majumdar et al. 2016; Müller et al. 2016; Vidal et al. 2017). The suggested surface synthesis is based on the presumed similarity between reaction networks involving H + CS and H + CO. Notably, methanol (CH3OH) can be efficiently produced via surface hydrogenation reactions of CO (Hiraoka et al. 1998; Watanabe & Kouchi 2002; Rimola 2014), which has proven significant in replicating interstellar methanol concentrations (Tielens & Hagen 1982; Charnley et al. 1992; Boogert et al. 2015; Walsh et al. 2016; An et al. 2017; Ceccarelli et al. 2023). Interestingly, the first solid-state detection of a CS-containing molecule in dense molecular clouds was OCS (Palumbo et al. 1997), suggesting the presence of this molecule in a layer rich in CH3OH, alongside H2CS and CH3SH. Interestingly, the outcome of the H2 addition to CS (resembling the industrial Fischer-Tropsch synthesis) occurring on a Fe13 nanocluster supported on silica (SiO2) surfaces has computationally been shown to depend on the state of the silica material (Pareras & Rimola 2026), whether as an open flat surface or presenting internal pores (in the cited work) of about 4 Å. In the former case, HCS formation is more favored, while in the latter case C-S cleavage takes place upon its adsorption on the metal nanocluster in favor of CH4 and H2 S formation, indicating genuine confinement effects.

In the reaction pathway starting from CS and progressing to the fully hydrogenated CH3SH by H addition, not only the stable H2CS compound emerges, but intermediate radicals (e.g., HCS, CH2SH, and CH3S) are also generated. Experimental data on surface reactions involving HCS-bearing species are scarce due to their chemical instability. Nguyen et al. (2023) investigated the interactions between solid CH3SH and H atoms on amorphous solid water using both experimental and computational methods. The primary finding was the production of H2 S + CH3 , which, under H addition conditions, facilitated the formation of CH4 . Additionally, small quantities of CH3 S and CH2SH were generated, which were subsequently converted back into CH3SH. Currently, there is a lack of low-temperature experimental data, measured unimolecular rate constants, or branching ratios for the reactions leading to the formation of H2CS and CH3SH through H addition to CS. On the theoretical front, Lamberts (2018) explored a H + CS reaction network involving 10 CS-bearing species and 29 reactions with atomic hydrogen, incorporating quantum tunneling effects. The chemical network was investigated in the absence of grain surfaces (namely, treated as gas-phase reactions) and the results indicated that CH3 SH formation occurs via key intermediate species such as HCS, CSH, CH2SH, and CH3 S radicals, corroborating the feasibility of H addition to CS to yield H2CS and CH3SH, akin to the CO hydrogenation reaction, namely, CS+H→HCS;Mathematical equation: &\ce{CS + H -> HCS}; \\(1) CS+H→CSH;Mathematical equation: &\ce{CS + H -> CSH}; \\(2) HCS+H→H2CS;Mathematical equation: &\ce{HCS + H -> H2CS}; \\(3) CSH+H→H2CS;Mathematical equation: &\ce{CSH + H -> H2CS}; \\(4) H2CS+H→H3CS;Mathematical equation: &\ce{H2CS + H -> H3CS}; \\(5) H2CS+H→CH2SH;Mathematical equation: &\ce{H2CS + H -> CH2SH}; \\(6) H3CS+H→CH3SH;Mathematical equation: &\ce{H3CS + H -> CH3SH}; \\(7) CH2SH+H→CH3SH.Mathematical equation: &\ce{CH2SH + H -> CH3SH}.(8)

However, the behavior of this reaction pathway on water ice surfaces remains unknown, even though a great deal of interstellar reactions are aided by the presence of grain surfaces covered in water ice. Therefore, our study aims to computationally simulate the CS hydrogenation reaction leading to H2CS and CH3 SH in the presence of interstellar water-ice mantles, using atomistic cluster models of varying sizes. This research thus offers a precise atomic-scale depiction of the series of reactions within the CS hydrogenation network on water ice surfaces, supplying quantitative structural, energetic, and kinetic data, including tunneling effects. These findings are pertinent to the astrochemical community as they furnish valuable parameters suited to future applications across large-scale astrochemical models.

2 Methods: Quantum chemical calculations

In this study, all calculations were carried out using the computational chemical software GAUSSIAN16 (Frisch et al. 2016). The first step of this work was to find density functional theory (DFT) methods that describe our chemical system accurately in a cost-effective way. A comprehensive list of DFT methods was prepared to do this benchmark study. The four tested methods were: M06-2X-D3 (Zhao & Truhlar 2008), PBE0-D3 (Adamo & Barone 1999), ωB97X-D (Chai & Head-Gordon 2008), and MPWB1K (Zhao & Truhlar 2004). These functionals were combined with Grimme’s D3 empirical dispersion corrections (Grimme 2006; Grimme et al. 2010), which account for long-range van der Waals interactions. These contributions are particularly important for properly describing weak inter-molecular interactions, such as hydrogen bonding and adsorption processes on water ice surfaces. The choice of these functionals was based on our previous experience in different works dealing with hydrogenation reactions on interstellar icy grain surfaces (Perrero et al. 2022b). The DFT functionals were benchmarked against the highly correlated coupled-cluster CCSD(T) method (Pople et al. 1987) with the aug-cc-pVTZ Dunning basis set (Dunning 1989). According to this benchmarking (see below), MPWB1K was chosen as the functional taken in this work due to its reliability and accuracy; thus, the geometry optimizations of reactants, products, and transition states was carried out with this method. Basis sets were also benchmarked for this functional, in which def2-TZVP was chosen as the most reliable and fast basis set. Previous studies about carbon monosulfide (Lamberts 2018) also prove that MPWB1K is a reliable and accurate functional for CS hydrogenations.

We carried out harmonic vibrational frequency calculations, at the same level of theory, to characterize the nature of each stationary point. Structures were classified as minima (reactants, intermediates, and products) when all frequencies were real, or as first-order saddle points (transition states) when precisely one (and only one) imaginary frequency was present. For each identified saddle point, intrinsic reaction coordinate (IRC) calculations (Gonzalez & Schlegel 1989, 1990) were then performed to ensure the connection between the transition states and their immediate corresponding reactants and products.

Radical-involved reactions were studied using the open-shell unrestricted formalism. The reactants, products, and transition states were characterized by calculating their frequencies (McQuarrie 1986). Frequency calculations were also used to compute thermochemical corrections to the potential energy values, particularly the vibrational zero-point energy (ZPE) correction.

2.1 Kinetics

To assess whether the studied processes are feasible under given interstellar conditions, we analyzed the kinetics of the hydrogenation reactions. To this end, rate constants associated with each elementary barrier were computed using Rice-Ramsperger-Kassel-Marcus (RRKM) theory (Marcus 1952), a microcanonical approach that assumes statistical population of the phase space. In this framework, tunneling effects are incorporated through the unsymmetrical Eckart potential barrier model (Eckart 1930). We used the calculated vibrational frequencies as the active degrees of freedom in the sum-of-state calculations. These kinetic computations were carried out with an in-house program implementing RRKM algorithms tailored for grain-surface processes, which is freely available from Enrique Romero & Rimola (2024).

To gain a first insight into the possibility of tunneling, we computed the cross-over temperature (Tx), which is the temperature below which tunneling effects become dominant. To this purpose, we used the Fermann & Auerbach formula (Fermann & Auerbach 2000), expressed as Tx=ℏω≠ΔU0≠/kB2πΔU0≠−ℏω≠ln⁡2,Mathematical equation: T_{x}=\frac{\hbar \omega^{\neq} \Delta U_{0}^{\neq} / k_{B}}{2 \pi \Delta U_{0}^{\neq}-\hbar \omega^{\neq} \ln 2},(9)

where ω≠ is the absolute value of the imaginary frequency corresponding to the transition state mode, ΔU0≠ the ZPE-corrected energy barrier including zero-point energy corrections, ℏ is the reduced Plank’s constant, and kB the Boltzmann’s constant. Frequencies data from the computed models of 18 and 33 water cluster were used to calculate Tx values.

Table 1

Gas-phase benchmark of DFT methods against CCSD(T) for CS hydrogenation.

3 Results

In this section, we present our quantum-chemical results for the studied reactions. First, results from the benchmarking of the DFT methods are shown, adopting the different gas-phase H additions to CS as model reactions. Second, results based on a 3-H2O ice cluster model are shown to refine the benchmarking. Finally, results of the same processes on larger water ice clusters (i.e., 18- and 33-H2O molecules) are reported.

3.1 Gas-phase benchmarking study

Here, we present the reaction energetics, that is, the reaction energies and energy barriers, obtained with the different DFT functionals and compared with those obtained with the CCSD(T) method. The energetics are referenced with respect to the corresponding prereactant complexes (PRCs), namely, structures in which the reactive species are in different binding sites but in close proximity to each other, establishing a specific geometry prior to the transition state. Table 1 gives the results of this benchmarking study and Figure 1 provides the related structures. It is worth noting that we omitted those reactions involving the hydrogenation of a radical species since they are barrierless n the gas phase.

Results show that the most suitable methods are M06-2X-D3 and MPWB1K (and hence that single-point calculations onto the optimized geometries with these functionals were calculated with CCSD(T). Nonetheless, for accuracy and performance efficiency, the MPWB1K method was the chosen method, as this functional provides faster results at similar levels of accuracy than the M06-2X-D3 one. To further validate the MPWB1K geometries and energetics, optimizations at the CCSD(T)/aug-cc-pVTZ level of theory for the first hydrogenation in the gas phase were also performed at the CCSD(T)/aug-cc-pVTZ level of theory (results shown in Figure A.1 and Table A.1 of the Appendix). Results calculated at the two methods are in good agreement, confirming the reliability of the chosen DFT method.

The energetics, including ZPE corrections, of the different successive H additions to CS calculated at MPWB1K are given in Table 2. These data serve to elucidate the intrinsic energetics of these reactions. Figures 2 and 3 also present the potential energy surfaces (including ZPE corrections) for the first and third H addition reactions in the gas phase, respectively. Clearly, the formation of HCS is energetically more favorable than CSH formation, given the lower energy barrier and more highly negative reaction energy. This is essentially because the HCS is more stable than its CSH isomer. In contrast, although CH3S formation is more favorable than CH2SH formation when the reaction energies are considered, the energy barriers display the opposite behavior.

Thumbnail: Fig. 1 Refer to the following caption and surrounding text. Fig. 1

MPWB1K/def2-TZVP-optimized geometries for: (a) first hydrogenation to the carbon atom leading to the formation of HCS; (b) first hydrogenation to the sulfur atom leading to the formation of CSH; (c) third hydrogenation leading to the formation of CH3S; and (d) third hydrogenation leading to the formation of CH2SH. The energetics of these reactions are shown in Table 1.
Table 2

Energetics of the gas-phase hydrogenation of CS.

Thumbnail: Fig. 2 Refer to the following caption and surrounding text. Fig. 2

MPWB1K/def2-TZVP PES (values in brackets, including ZPE corrections) for the first hydrogenation to CS in gas-phase: (a) hydrogenation on the carbon atom forming HCS; (b) hydrogenation on the sulfur atom forming CSH. Bond lengths are in Å, relative energies in kJ mol–1.

3.2 Reactions on the 3-H2O cluster

The hydrogenation reactions have been simulated in the presence of the 3-H2O cluster model (hereafter referred to as W3), as shown in Figure 4. Their energetics are summarized in Table 3. The W3 cluster corresponds to the global minimum structure of a three-water-molecule system, as reported in Petty et al. (2025).

The predominant interaction of CS with the ice cluster takes place between the C of CS and a dangling H atom of W3 (see first structure of Figures 4a and 4b). Any attempt to establish an interaction via the S atom has failed, as the system spontaneously evolves towards a CS interaction with the surface via its C end. As observed in the gas phase, the energetically most favorable hydrogenation path first leads to the formation of HCS. However, the potential energy barrier increases to 4.1 kJ mol–1 compared to the gas-phase process (2.9 kJ mol–1). This is because the interaction with the surface strengthened the C-S chemical bond (reflected by a shortening from 1.516 in the gas phase to 1.511 Å on W3), making the C atom less reactive. For this reaction, we also benchmarked DFT methods and confirmed that MPWB1K maintains good performance, even in the presence of 3W ice (see Appendix).

Figure 4 also shows the third hydrogenation, in this case on either the carbon atom (forming CH3S, see Figure 4c) or the sulfur atom (forming CH2SH, see Figure 4d). This trend is the same as that found in the gas phase: while the formation of CH3S is more favorable according to its reaction energy, the energy barrier is higher than formation of CH2SH, if ZPE corrections are considered.

Thumbnail: Fig. 3 Refer to the following caption and surrounding text. Fig. 3

MPWB1K/def2-TZVP PES (values in brackets, including ZPE corrections) for the third hydrogenation to CS in gas-phase: (a) hydrogenation on the carbon atom forming CH3CS; (b) hydrogenation on the sulfur atom forming CH2SH. Bond lengths are in Å, relative energies in kJ mol–1.
Table 3

Energetics of the CS hydrogenation processes on the three-water-molecule ice cluster.

3.3 Reactions on the 18- and 33-H2O clusters

In this section, our results for the reactions taking place on larger water ice clusters are given. These results are based on our investigation of the hydrogenation reactions on larger water ice cluster models, moving beyond the minimal W3 system towards a more extended representation of the ice surface.

Two water ice structures were considered, with 18 and 33 water molecules (referred to as W18 and W33, respectively), which are shown in Figures 5 and 6 and already used in previous works by a group of our fellow authors (e.g., Rimola (2014); Enrique-Romero et al. (2019); Gelli et al. (2025); Perrero et al. (2025). Figures 5 and 6 also present the potential energy surfaces (also including ZPE corrections) for the first H addition reactions on W18 and W33, respectively, while Figures 7 and 8 for the third H addition reactions on W18 and W33, respectively.

The first hydrogenation clearly shows how water ice affects the reactivity of CS. As in the W3 case, the interaction leads to a shortening of the C-S bond length (on both W18 and W33 to 1.505 Å) and, accordingly, to a strengthening of the chemical bond, which is reflected by an increase of the inertness of the C atom to react, leading to somewhat higher energy barriers (3.9 and 4.2 kJ mol–1) compared to the gas-phase (2.9 kJ mol–1). Figure 5b shows the first hydrogenation to the sulfur atom. As expected, according to previous results, this pathway is less favorable than hydrogenation on the carbon atom since the CSH isomer is less stable than HCS.

The third hydrogenation reveals a different scheme. In this case, H2CS establishes an H-bond through the S atom. This induces the polarization of the C-S chemical bond, reflected by an increase of its bond length (from 1.588 A in the gas-phase to 1.594 on W18 and 1.592 on W33). This makes the C atom more electrophilic and, accordingly, more prone to be hydrogenated by an incoming H atom to form CH3S, this way reducing the potential energy barrier (4.7 kJ mol–1 in the gas-phase while 3.7/4.1 kJ mol–1 on W18/W33). In contrast, for the formation of CH2SH, since the S atom is involved in the interaction with the surface acting as H-bond acceptor, losing electron density and thus increasing its nucleophilic character. Consequently, its hydrogenation presents higher potential energy barriers than the gas-phase process (2.0 kJ mol–1 in the gas phase, while 2.8/8.2 kJ mol–1 on W18/W33).

The interaction energy of CS and the formed products (i.e., HCS, H2CS, CH3S, and CH2SH) has been computed to show the affinity of the species to the water clusters. The aim is now to determine whether the species are strongly bound to water ice or are more likely to leave the surface. The computed binding energies are shown in Table 4.

The computed values are relatively higher than the energy barriers, but significantly lower than the reaction energies. However, due to the enhanced third body exerted by water ice surfaces (Pantaleone et al. 2020, 2021; Di Genova et al. 2025b), it is expected that the nascent reaction energies are dissipated throughout the water ice surfaces, allowing the newly formed products to stay attached to the surface.

According to our results, the water ice surface does not act as a classical chemical catalyst in the first hydrogenation reaction, since it does not substantially reduce the energy barrier. Instead, based on our recent works (Pantaleone et al. 2021, 2020; Ferrero et al. 2023), we assume it acts as a third body that dissipates the excess reaction energy, thereby stabilizing the newly formed species.

Thumbnail: Fig. 4 Refer to the following caption and surrounding text. Fig. 4

MPWB1K/def2-TZVP-optimized geometries for the hydrogenation of CS on the 3-H2O ice cluster model: (a) first hydrogenation to the carbon atom leading to the formation of HCS; (b) first hydrogenation to the sulfur atom leading to the formation of CSH; (c) third hydrogenation leading to the formation of CH3S; and (d) third hydrogenation leading to the formation of CH2SH.
Thumbnail: Fig. 5 Refer to the following caption and surrounding text. Fig. 5

MPWB1K/def2-TZVP PES (values in brackets, including ZPE corrections) for the first hydrogenation to CS on the W18 ice cluster: (a) hydrogenation on the carbon atom forming HCS; (b) hydrogenation on the sulfur atom forming CSH. Bond lengths are in Å, relative energies in kJ mol–1.
Thumbnail: Fig. 6 Refer to the following caption and surrounding text. Fig. 6

MPWB1K/def2-TZVP PES (values in brackets, including ZPE corrections) for the first hydrogenation to CS on the W33 ice cluster: (a) hydrogenation on the carbon atom forming HCS; (b) hydrogenation on the sulfur atom forming CSH. Bond lengths are in Å, relative energies in kJ mol–1.
Table 4

Binding energies of CS hydrogenation species on water ice clusters.

4 Discussion

4.1 Comparison with CO hydrogenation

Hydrogenation to CO is an analogous process to that for CS, leading to the formation of H2CO and CH3OH. Accordingly, a comparison between the two processes is done here. The calculated PESs of the first and third hydrogenation reaction of CO (leading to the formation of HCO and CH3O as the most favorable species (Rimola 2014)) on W18 and W33 are shown in Figures 9 and 10, respectively. The energetics of the gas-phase reactions are shown in Table 5. It is worth mentioning that these are new calculations performed for this work adopting similar structures as for CS. This is at variance with respect to the work of Rimola (2014), since the H additions were based on adopting an Eley-Rideal mechanism, whereas in this case, they render a Langmuir-Hinshelwood mechanism.

The first aspect to compare is the adsorption of the two reactive species (CS and CO) on the water ice clusters, the binding energies (BEs) of which are reported in Table 6. Results show that for both species the preferred interaction is always through the C atom. This is due to the fact that in both CS and CO, the H-bond with the cluster model induces a shortening of the C-S/C-O distance compared to the gas-phase value, strengthening the chemical bonds. This behavior is explained by the natural bond order (NBO) analysis of the H2O···CS/CO interaction. The NBO analysis reveals a donor-acceptor interaction between the lone pair of the C atom (LPC), and the antibonding σ∗ (O-H) orbital of the water ice surface (see Table C.1 in the Appendix).

This interaction is accompanied by an electron density transfer LPC → σ∗(O-H). This electron density redistribution strengthens the C-S bond, consistent with the observed bond shortening upon adsorption on the ice surface.

Although the BEs for CS and CO have been extensively investigated in previous works in a more rigorous way (namely, sampling different binding sites and providing BE ranges, (Ferrero et al. 2020; Perrero et al. 2022a), our calculated values indicate that BEs for CS on water ice are higher than for CO (e.g., on W18 23.2 vs. 7.3 kJ mol–1), which is in line with the previous works. Unfortunately, no experimental values for the BEs of CS are available and, thus, a comparison cannot be made.

Gas-phase calculations show that the most favorable path for CS hydrogenations is the same as that predicted by earlier studies (Lamberts 2018). The first reaction, H+CS, is favorable towards the formation of HCS at the detriment of CSH. This reaction presents a low energy barrier (ΔE≠ + ZPE = 2.6 kJ mol–1) and is highly exoergic (ΔEr + ZPE = −225.1 kJ mol–1). In comparison, the first CO hydrogenation forming HCO in the gas-phase is also the preferred path (against COH formation), but displaying a less exo-energetic character and a higher energy barrier than HCS formation (ΔEr +ZPE= −106.9 kJ mol–1 and ΔE≠ + ZPE = 12.6 kJ mol–1). The H + H2CS reaction can provide two isomeric products: CH3S and CH2SH. CH3S is thermodynamically favored over the formation of CH2SH but with energy barriers of ΔE≠ + ZPE = 6.3 kJ mol–1 and ΔE≠ + ZPE = 1.6 kJ mol–1, respectively. However, as pointed out in (Lamberts 2018), CH2SH can dissociate into H2CS + H again, thus leading to the formation of the more stable CH3S species. For the H + H2CO reaction, Rimola (2014) identified formation of CH3O to be energetically more favorable than CH2OH, here with ΔE≠ + ZPE = 15.9 kJ mol–1 and ΔEr + ZPE = –104.9 kJ mol–1. Trends in gas-phase reactions clearly indicate that H additions to CS are energetically more favorable than those to CO, with lower energy barriers and more favorable reaction energies. This can be due to the stability of the C-S/C-O chemical bonds. The bond dissociation energy of CS is 746 kJ mol–1, while for CO is 1072 kJ mol–1, indicating the greater inertness (and consequently less reactive) character of CO compared to CS.

With respect to water ice models, two distinctive behaviors can be observed, that is, when the molecules to hydrogenate are either CS/CO or H2CS/H2CO. As mentioned above, the interaction of CS/CO with water ice shortens the chemical bonds (and hence strengthens them). This makes the H additions energetically more difficult than in the gas phase with higher potential energy barriers (e.g., for HCS formation on W18, ΔE≠ = 3.9 kJ mol–1, while in the gas-phase it is ΔE≠ = 2.9 kJ mol–1).

However, when ZPE corrections are introduced, due to the vibrational coupling between the reactants and the water ice, the energy barriers in the presence of water ice become lower (e.g., on W18, ΔE≠ + ZPE = 0.1 kJ mol–1), thus favoring the reactions. In contrast, the interaction of the water ice surfaces with H2CS/H2CO induces an enlargement of the chemical bonds (and, hence, a weakening), making the C atom more nucleophilic and accordingly more prone to receiving a H atom to form CH3S/CH3O (e.g., for CH3S formation on W18, ΔE≠ + ZPE = 3.8 kJ mol–1 while in the gas-phase ΔE≠ + ZPE = 6.3 kJ mol–1). It is worth mentioning, however, that all these energy differences are within chemical accuracy (around 4 kJ mol–1) and, accordingly, not all the processes follow the same trend. Since the energy differences are so subtle, with numbers below such a level of chemical accuracy, it is reasonable to assume that the interaction with water ice has limited effects.

Thumbnail: Fig. 7 Refer to the following caption and surrounding text. Fig. 7

W18 water cluster reactions at MPWB1K/def2-TZVP level. (a) Third hydrogenation through the carbon atom. (b) Third, less favorable, hydrogenation to the sulfur atom. Bond lengths in Å. Energies in kJ mol–1. In square braces, the energy plus the ZPE correction.
Table 5

Energetics of the gas-phase hydrogenation of CO.

Thumbnail: Fig. 8 Refer to the following caption and surrounding text. Fig. 8

W33 water cluster reactions at MPWB1K/def2-TZVP level. (a) Third hydrogenation through the carbon atom. (b) Third, less favorable, hydrogenation to the sulfur atom. Bond lengths in Å. Energies in kJ mol–1. In square braces the energy plus the ZPE correction.
Table 6

Binding energies for CS and CO on water ice clusters.

Thumbnail: Fig. 9 Refer to the following caption and surrounding text. Fig. 9

W18 water cluster reactions at MPWB1K/def2-TZVP level. (a) Formation of HCO in W18. (b) Formation of H3CO in W18. Bond lengths in Å. Energies in kJ mol–1. In square braces the energy plus the ZPE correction.
Thumbnail: Fig. 10 Refer to the following caption and surrounding text. Fig. 10

W33 water cluster reactions at MPWB1K/def2-TZVP level. (a) Formation of HCO in W33. (b) Formation of H3CO in W33. Bond lengths in Å. Energies in kJ mol–1. In square braces, the energy plus the ZPE correction.
Table 7

Crossover temperatures and rate constants for CS and CO hydrogenation.

4.2 Kinetic analysis and astrophysical implications

To understand reaction kinetics and the relative astrophysical implications, rate constants have been calculated using the RRKM theory, incorporating tunneling effects via an Eckart model, while the crossover temperatures have been determined using the Fermann & Auerbach formula 9 (see above). The results are shown in Table 7.

Our results show that tunneling plays a decisive role in the hydrogenation of CS on interstellar ices. Despite nominally small activation barriers, the reactions occur at extremely low temperatures characteristic of dense clouds (∼10 K). Kinetic constants derived from tunneling-corrected calculations (Table 7) indicate that H-addition to CS remains highly efficient even at the coldest astrophysical conditions, with rates reaching up to 109 s−1 at 10 K. Consequently, CS hydrogenation is expected to proceed readily wherever CS is present on grain surfaces.

The influence of the icy substrate is not uniform across the hydrogenation sequence; rather, each step responds differently to grain-surface environments. Nevertheless, once tunneling is included, all hydrogenation steps remain efficient between 10 and 20 K, enabling the rapid conversion of CS into H2CS and, ultimately, into CH3SH on icy mantles. Laboratory studies have shown that a variety of S-bearing organics, including methanethiol and its larger homologous, have the capacity to form efficiently in irradiated or H-rich ices (Herath et al. 2026), demonstrating that solid-state reactions can channel sulfur into complex molecules at 10 K. Such grain-surface pathways can therefore contribute to building an unobservable reservoir of sulfur within icy mantles that becomes relevant during later evolutionary stages.

From an astrophysical standpoint, the formation of CH3SH is particularly significant. CH3SH has been detected in a wide range of environments, including regions such as SgrB2(OH) (rotational temperature of ∼9 K), hot cores such as G327.3–0.6, and the solar-type protostar IRAS 16293–2422, where excitation temperatures up to 180 K have been derived (Linke et al. 1979; Majumdar et al. 2016; Gibb et al. 2000). These observations show that CH3 SH is present in warm gas, consistent with an origin in grain-surface chemistry followed by desorption. H2CS has also been detected in colder environments, however, it has been shown that gas-phase reactions could be efficient in forming it (as it is the case for H2CO) such as protoplanetary disks and cold clouds in such conditions. Once in the gas phase, CH3SH can react with other species and form more complex molecules. This was demonstrated by Di Genova et al. (2025a) who studied the reactions involving neutral or protonated CH3SH to account for the formation of dimethyl sulfide, recently detected toward the galactic-center molecular cloud G+0.693-0.027 (Sanz-Novo et al. 2025).

Importantly, observational surveys with ALMA and single-dish facilities reveal that S-bearing organics such as methanethiol and ethanethiol. In addition, an even greater number of S-bearing species are formed in star-forming regions (Rodríguez-Almeida et al. 2021; Manna & Pal 2024). This supports the notion that grain-surface hydrogenation reactions, such as those explored here, feed directly into the gas-phase sulfur chemistry once materials are released from the ices. Consequently, the efficiency of the CS hydrogenation sequence implies that CH3SH and related thiols are expected to be present in regions where thermal or non-thermal desorption is active, offering concrete observational targets.

5 Conclusions

This study provides a comprehensive quantum chemical and kinetic investigation into the successive hydrogenation of CS on interstellar water ice surfaces, offering new atomistic insights into the formation of H2CS and CH3 SH. Our calculations reveal that CS interacts with water ice exclusively through the C atom, which results in a shortening and strengthening of the C-S bond. This interaction essentially inactivates the C atom, leading to higher potential energy barriers for the first hydrogenation step, as compared to the gas phase. Conversely, H2CS interacts with the ice via the S atom, which polarizes and weakens the C-S bond, thereby activating the C atom and reducing the energy barriers for subsequent hydrogenation towards CH3 SH formation.

A comparison with the CO hydrogenation network demonstrates that H additions to CS are energetically more favorable than those to CO, characterized by lower energy barriers and a more pronounced exoergic nature. This difference is largely attributed to the significantly higher bond dissociation energy of CO compared to CS, making the former more inert. Despite the presence of small activation barriers, our RRKM kinetic analysis identifies quantum tunneling as the dominant mechanism at the low temperatures (10 K) of dense molecular clouds. Tunneling ensures that the conversion of CS to CH3 SH remains highly efficient at low (≤10–20 K) temperatures.

While it is clear that water ice does not act as a traditional chemical catalyst for the initial hydrogenation, it presumably serves as a crucial third body that dissipates reaction energy, allowing newly formed species to remain stabilized on the grain surface. Furthermore, the quantitative energetic and kinetic data provided here are essential parameters for astrochemical models seeking to explain the chemical complexity observed in star-forming regions.

Acknowledgements

G.D.G., N.B., and C.C. thank the Italian MUR PRIN2020 (2020AFB3FX-Astrochemistry beyond the second period elements) and the European Union’s Horizon 2020 research and innovation program from the European Research Council (ERC) (project ‘The Dawn of Organic Chemistry’ DOC, grant agreement No 741002) for support. Support from the Italian Space Agency (Bando ASI Prot. n. DC-DSR-UVS-2022-231, Grant no. 2023-10-U.0 MIGLIORA) is also acknowledged. This project also received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 Research and Innovation Program (Grant Agreement 865657) for Project ‘Quantum Chemistry on Interstellar Grains’ (QUANTUMGRAIN). MICIN is also acknowledged for financing the projects PID2024-157971NB-C21 and CNS2023-144902. A.R. acknowledges Accademia delle Scienze di Torino for supporting the project ‘In silico interstellar grain-surface chemistry’. A.R. gratefully acknowledges support through a 2023 ICREA Award.

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Appendix A Validation of MPWB1K level against CCSD(T) calculations

Thumbnail: Fig. A.1 Refer to the following caption and surrounding text. Fig. A.1

Optimized geometries for the first hydrogenation of CS in the gas-phase at: i) CCSD(T)/aug-cc-pVTZ level of theory (bare values); and ii) MPWB1K/def2-TZVP level of theory (values in parenthesis). Bond lengths are in Å.
Table A.1

Energetics of the gas-phase processes at different levels of theory.

Appendix B 3-H2O ice cluster model benchmark

Table B.1

ZPE-noncorrected reaction energies and energy barriers for the hydrogenation of CS on the three-water-molecule cluster.

Appendix C NBO analysis

Table C.1

NBO second-order perturbation stabilization energies for CS and CO on water ice clusters.

All Tables

Table 1

Gas-phase benchmark of DFT methods against CCSD(T) for CS hydrogenation.

In the text
Table 2

Energetics of the gas-phase hydrogenation of CS.

In the text
Table 3

Energetics of the CS hydrogenation processes on the three-water-molecule ice cluster.

In the text
Table 4

Binding energies of CS hydrogenation species on water ice clusters.

In the text
Table 5

Energetics of the gas-phase hydrogenation of CO.

In the text
Table 6

Binding energies for CS and CO on water ice clusters.

In the text
Table 7

Crossover temperatures and rate constants for CS and CO hydrogenation.

In the text
Table A.1

Energetics of the gas-phase processes at different levels of theory.

In the text
Table B.1

ZPE-noncorrected reaction energies and energy barriers for the hydrogenation of CS on the three-water-molecule cluster.

In the text
Table C.1

NBO second-order perturbation stabilization energies for CS and CO on water ice clusters.

In the text

All Figures

Thumbnail: Fig. 1 Refer to the following caption and surrounding text. Fig. 1

MPWB1K/def2-TZVP-optimized geometries for: (a) first hydrogenation to the carbon atom leading to the formation of HCS; (b) first hydrogenation to the sulfur atom leading to the formation of CSH; (c) third hydrogenation leading to the formation of CH3S; and (d) third hydrogenation leading to the formation of CH2SH. The energetics of these reactions are shown in Table 1.
In the text
Thumbnail: Fig. 2 Refer to the following caption and surrounding text. Fig. 2

MPWB1K/def2-TZVP PES (values in brackets, including ZPE corrections) for the first hydrogenation to CS in gas-phase: (a) hydrogenation on the carbon atom forming HCS; (b) hydrogenation on the sulfur atom forming CSH. Bond lengths are in Å, relative energies in kJ mol–1.
In the text
Thumbnail: Fig. 3 Refer to the following caption and surrounding text. Fig. 3

MPWB1K/def2-TZVP PES (values in brackets, including ZPE corrections) for the third hydrogenation to CS in gas-phase: (a) hydrogenation on the carbon atom forming CH3CS; (b) hydrogenation on the sulfur atom forming CH2SH. Bond lengths are in Å, relative energies in kJ mol–1.
In the text
Thumbnail: Fig. 4 Refer to the following caption and surrounding text. Fig. 4

MPWB1K/def2-TZVP-optimized geometries for the hydrogenation of CS on the 3-H2O ice cluster model: (a) first hydrogenation to the carbon atom leading to the formation of HCS; (b) first hydrogenation to the sulfur atom leading to the formation of CSH; (c) third hydrogenation leading to the formation of CH3S; and (d) third hydrogenation leading to the formation of CH2SH.
In the text
Thumbnail: Fig. 5 Refer to the following caption and surrounding text. Fig. 5

MPWB1K/def2-TZVP PES (values in brackets, including ZPE corrections) for the first hydrogenation to CS on the W18 ice cluster: (a) hydrogenation on the carbon atom forming HCS; (b) hydrogenation on the sulfur atom forming CSH. Bond lengths are in Å, relative energies in kJ mol–1.
In the text
Thumbnail: Fig. 6 Refer to the following caption and surrounding text. Fig. 6

MPWB1K/def2-TZVP PES (values in brackets, including ZPE corrections) for the first hydrogenation to CS on the W33 ice cluster: (a) hydrogenation on the carbon atom forming HCS; (b) hydrogenation on the sulfur atom forming CSH. Bond lengths are in Å, relative energies in kJ mol–1.
In the text
Thumbnail: Fig. 7 Refer to the following caption and surrounding text. Fig. 7

W18 water cluster reactions at MPWB1K/def2-TZVP level. (a) Third hydrogenation through the carbon atom. (b) Third, less favorable, hydrogenation to the sulfur atom. Bond lengths in Å. Energies in kJ mol–1. In square braces, the energy plus the ZPE correction.
In the text
Thumbnail: Fig. 8 Refer to the following caption and surrounding text. Fig. 8

W33 water cluster reactions at MPWB1K/def2-TZVP level. (a) Third hydrogenation through the carbon atom. (b) Third, less favorable, hydrogenation to the sulfur atom. Bond lengths in Å. Energies in kJ mol–1. In square braces the energy plus the ZPE correction.
In the text
Thumbnail: Fig. 9 Refer to the following caption and surrounding text. Fig. 9

W18 water cluster reactions at MPWB1K/def2-TZVP level. (a) Formation of HCO in W18. (b) Formation of H3CO in W18. Bond lengths in Å. Energies in kJ mol–1. In square braces the energy plus the ZPE correction.
In the text
Thumbnail: Fig. 10 Refer to the following caption and surrounding text. Fig. 10

W33 water cluster reactions at MPWB1K/def2-TZVP level. (a) Formation of HCO in W33. (b) Formation of H3CO in W33. Bond lengths in Å. Energies in kJ mol–1. In square braces, the energy plus the ZPE correction.
In the text
Thumbnail: Fig. A.1 Refer to the following caption and surrounding text. Fig. A.1

Optimized geometries for the first hydrogenation of CS in the gas-phase at: i) CCSD(T)/aug-cc-pVTZ level of theory (bare values); and ii) MPWB1K/def2-TZVP level of theory (values in parenthesis). Bond lengths are in Å.
In the text

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