Electronic spectra of (H₂S)_n⁺ (n = 2–6) and [(H₂S)₂–(H₂O)_m]⁺ (m = 1–2) in the gas phase

Abstract

A hemibond, a two-center, three-electron non-classical covalent bond, forms between a singly occupied and a fully-occupied non-bonding orbital. Hemibonded species exhibit a strong absorption in the near-ultraviolet (UV) to visible region, known as the charge resonance (CR) band, which serves as a well-established marker band for hemibond formation. Despite its significance, the influence of solvation effects on the CR band has not been fully understood due to the scarcity of direct comparison between condensed and gas phases. In this study, we investigated the CR band of hemibonded radical cation clusters, (H₂S)_n⁺ (n = 2–6) and [(H₂S)₂–(H₂O)_m]⁺ (m = 1–2), in the gas phase using mass-selected UV-vis photodissociation spectroscopy. For the (H₂S)_n⁺ clusters, the maximum absorption wavelength (λ_max) of the CR band displayed a blue-shift as the cluster size increased. The λ_max shift converged at n = 6, which corresponds to the completion of the first solvation shell around the hemibonded (H₂S)₂⁺ ion core. A comparison with the previously reported CR band in aqueous solution suggests that the first solvation shell plays a predominant role in influencing the electronic transition of the ion core. For the [(H₂S)₂–(H₂O)_m]⁺ clusters, the hemibonded ion core (H₂S)₂⁺ was disrupted upon the addition of two water molecules. Implications of the gas phase spectra for the previously observed spectrum in aqueous solution are discussed.

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1. Introduction

Hemibonds (two-center, three-electron bonds) are a type of non-classical covalent bond.^1–14 They form when a radical cation's non-bonding orbital, which contains a hole, overlaps with a neutral molecule's fully-occupied non-bonding orbital. This overlap leads to the creation σ and σ* orbitals. When three electrons occupy these σ and σ* orbitals, an effective bond with a bond order of 1/2 is formed. Hemibonds have been extensively studied in radiation chemistry due to their significant contribution to the initial stages of ionization. Recently, their role in the oxidation (or ionization) of various biomolecules has garnered considerable attention.^15–23

Molecules containing third-period elements, especially sulfur, readily form hemibonds and are the most frequently observed examples.^{2–10,15–37} Among sulfur-containing molecules, H₂S is the simplest and its hemibond can be considered as a prototype for hemibond research. A transient absorption spectroscopy study of an H₂S aqueous solution has been conducted by Asmus and coworkers using pulse radiolysis.²⁷ In this measurement, a broad absorption was observed in the near-ultraviolet (UV) to visible region. This absorption is attributed to the σ–σ* transition of the hemibonded ion-core (H₂S)₂⁺_(aq.). Such a σ–σ* transition is often referred to as the charge resonance (CR) band and is well-known as a marker band for hemibond formation.^{2,24–29,31,35,38–55} Because the upper state of the CR transition is a dissociative state, the CR transition manifests as a broadened, structureless band. This characteristic feature has facilitated the observation of transient hemibond formation in the condensed phase and the structural characterization of hemibonded cluster cations in the gas phase.

Further research was conducted on the H₂S hemibond. Infrared photodissociation (IRPD) spectroscopy of (H₂S)_n⁺ (n = 3–6) has revealed the stable existence of a hemibonded ion core, (H₂S∴SH₂)⁺, which is solvated by H₂S molecules via hydrogen bonds.^56,57 However, the bare ion core (n = 2) could not be observed using IRPD spectroscopy due to its high dissociation energy. Regarding the microsolvation of the hemibonded ion core by water, IRPD spectroscopy of [(H₂S)₂–H₂O]⁺ showed that the hemibond remains stable with the addition of a single water molecule.⁵⁸ In contrast, for methanol and ethanol, which have higher proton affinities than water, the addition of just one molecule leads to proton transfer, disrupting the hemibond.⁵⁸ IRPD spectroscopy of CH₃SH radical cation clusters reported similar results to H₂S.^59,60

Gas phase clusters are also valuable for understanding the solvation effect on the hemibonded ion core in the condensed phase at a microscopic level.^43–71 By incrementally varying the number of molecules solvating the hemibonded ion core (i.e., cluster size), we can track the changes in the CR band as microsolvation progresses.^{47,49,50,54,70} Furthermore, comparing these results with the condensed phase allows us to observe the convergence process from the gas phase and determine the size of the effective solvation shell. However, our knowledge regarding the effect of solvation on the CR band remains limited. To the best of our knowledge, comparisons between the gas and condensed phases are particularly rare for hemibonds strongly solvated by hydrogen bonds in protic solvents.

In this study, we performed UV-visible photodissociation (UV-vis PD) spectroscopy of (H₂S)_n⁺ (n = 2–6) and [(H₂S)₂(H₂O)_m]⁺ (m = 1–2). Unlike IRPD spectroscopy, UV-vis PD spectroscopy is expected to allow the direct observation of the hemibond in the dimer cation due to its higher photon energy. The observed spectra provided clear evidence of hemibond formation, shedding light on the stability of the hemibonded structure upon microsolvation, and the accompanying changes in its electronic structure. By comparing these results to the previously reported transient absorption spectrum in the aqueous solution, we discuss the nature of the absorption of hemibonded ion core (H₂S∴SH₂)⁺ in the condensed phase.

2. Experimental and computational methods

Details of the experimental setup for dissociation spectroscopy using a tandem quadrupole mass spectrometer have been described elsewhere.⁷² We generated the (H₂S)_n⁺ (n = 2–6) and [(H₂S)₂(H₂O)_m]⁺ (m = 1–2) radical cation clusters via discharge in a supersonic expansion of an Ar/H₂S/H₂O gaseous mixture. The generated cluster cations were mass-selected by the first quadrupole mass spectrometer with the mass resolution set to Δm/z ≤ 1 to remove protonated clusters. Subsequently, the size-selected clusters were irradiated with UV-vis light in the octopole ion guide, inducing photodissociation and generating fragment ions. UV-vis spectra were then recorded by monitoring these fragment ions at the second quadrupole mass spectrometer while scanning the UV-vis light wavelength. The UV-vis light source was an optical parametric oscillator (EKSPLA, NT342).

Quantum chemical computations were performed using the Gaussian 16 program package.⁷³ Energy-optimized structure searches were conducted at the BHandHLYP/aug-cc-pVTZ level. This level well reproduces low energy isomers of (H₂S)_n⁺ obtained at the MP2/aug-cc-pVDZ level, which have successfully aligned with experimental observations from IRPD spectroscopy.⁵⁶ Additionally, excited-state calculations were performed at the TD-BHandHLYP/aug-cc-pVTZ level to determine vertical excitation energies and oscillator strengths. For calculating the CR band in hemibonded systems, this level shows good agreement with experimental results seen in the hemibonded (H₂O–Ar)⁺ system.⁷⁴ For an isomerization barrier evaluation, reaction path searches were performed by the global reaction route mapping (GRRM) method.^75–77

3. Results and discussion

3.1 (H₂S)_n⁺ (n = 2–6)

Fig. 1(a)–(e) displays the observed gas phase UV-vis spectra of (H₂S)_n⁺ (n = 2–6), respectively. The spectral gap around 410 nm is attributed to the extreme depletion of the laser power in this region. Fig. 1(f) reproduces the transient absorption spectrum of an H₂S aqueous solution previously reported by Asmus and co-workers.²⁷ They observed this spectrum via pulsed radiolysis of the H₂S aqueous solution. A broad absorption (maximum absorption wavelength, λ_max, is 370 nm) was assigned to the hemibonded (H₂S)₂⁺_(aq.).

Fig. 1 (a)–(e) Observed UV-vis PD spectra of (H₂S)_n⁺ (n = 2–6) in the gas phase, obtained by detecting the H₂S⁺ fragment channel and normalized by laser power and maximum intensities. (f) Transient absorption spectrum of an H₂S aqueous solution following γ-ray radiolysis. Reprinted with permission from ref. 27 with modification. The blue line serves as a guide, indicating the maximum absorption wavelength (λ_max = 370 nm) of the hemibonded (H₂S)₂⁺ in the aqueous solution. The gap in spectra (a)–(e) around 410 nm is attributed to the extreme depletion of the output power of the light source.

All gas phase cluster spectra were obtained by detecting the H₂S⁺ fragment channel, which was the predominant dissociation pathway for all cluster sizes. A broad, structureless band is commonly observed in the spectrum for each size. λ_max of the band shows a slight shift with increasing cluster size. Furthermore, the observed transitions of the gas phase clusters well correspond to that in the aqueous solution. A detailed comparison between the gas phase cluster spectra and the condensed phase spectrum will be discussed in Section 3.3.

Fig. 2 presents the observed and simulated UV-vis spectra of (H₂S)₂⁺. The simulated spectra were generated based on two optimized stable isomers: the hemibonded type (S2_H), characterized by a hemibond formed between the S atoms, and the proton-transferred type (S2_P), which consists of an H₃S⁺ ion core and an SH radical formed via proton transfer (PT) between two H₂S molecules. Isomer S2_H is 56.3 kJ mol⁻¹ more stable than isomer S2_P. The observed spectrum has a broad band in the UV region (λ_max = 390 nm) that extends into the visible region. For isomer S2_H, the simulated spectrum predicts two absorptions in the UV region, and the transition at 360 nm is attributed to the σ–σ* transition (CR band). In contrast, the simulated spectrum for isomer S2_P predicts one absorption at 304 nm, attributed to the SH radical moiety. Comparing the observed and simulated spectra, the observed band position is better reproduced by the CR band calculated for isomer S2_H. We confirmed that the same level of computation (BHandHLYP/aug-cc-pVTZ) applied to the well-established CR band of hemibonded (H₂O–Ar)⁺ also exhibits ∼30 nm blueshift from its observed absorption maximum (at 320 nm).⁷⁴ Therefore, when considering this systematic error, the calculated result for isomer S2_H is in good agreement with the observed absorption maximum. Moreover, the σ–σ* transition of the hemibonded type is expected to exhibit a long tail extending into the longer wavelength region, which is attributed to the Franck–Condon projection from the bound potential of the ground state to the repulsive potential of the (σ, σ*) excited state. This characteristic of the σ–σ* transition effectively explains the observed band feature. On the other hand, the transition for isomer S2_P, attributed to the SH radical moiety, is predicted to be located at the edge of the observed wavelength region (the band origin of the bare SH radical was observed in 326 nm).⁷⁸ Additionally, the transition in the SH radical moiety is expected to exhibit vibronic transitions in the shorter wavelength region, making it difficult to explain the band shape of the observed spectrum with the transition of isomer S2_P. Moreover, the isomer population is expected to be dominated by S2_H, as it is much more stable than S2_P. We also note that the oscillator strength of the CR band of S2_H is about 100 times greater than that of the S2_P transition. For these reasons, we conclude that the CR band of the hemibonded type isomer exclusively contributes to the observed spectrum for n = 2.

Fig. 2 (a) Observed and (b) and (c) simulated spectra of (H₂S)₂⁺ at the BHandHLYP/aug-cc-pVTZ level. Schematic stable isomer structures are also shown. Numbers in parentheses are zero-point energy corrected relative energies.

Previous IR spectroscopic studies of gas phase (H₂S)_n⁺ clusters were unable to determine the structure of (H₂S)₂⁺ due to difficulties in spectral measurements for this size, attributed to its large dissociation energy.⁵⁶ In the present experiment, clear evidence of hemibond formation in (H₂S)₂⁺ has been obtained.

The observed spectra of (H₂S)_n⁺ (n = 3–6) exhibit bands similar to that in (H₂S)₂⁺. As with the n = 2 case, these spectra are well-explained by the σ–σ* transitions (CR bands) predicted for hemibonded isomers. Spectral simulations of stable isomers for n = 3–6 and their comparison with the observed spectra are summarized in Fig. S1–S4 in SI. Fig. 3 displays the schematic structure of the most stable isomer at each size, whose simulated spectrum aligns well with the observed spectrum. These structures feature a hemibonded ion core (H₂S∴SH₂)⁺ hydrogen-bonded to other H₂S molecules. Previous IR spectroscopic studies, using the same ion source as this experiment, reported the observation of the hemibonded structures of (H₂S)_n⁺ (n = 3–6).⁵⁶ Therefore, the present results, showing CR band observation due to the hemibonded structures for n = 3–6, are consistent with the conclusions of those previous IR studies.

Fig. 3 The most stable isomer structures of (H₂S)_n⁺ (n = 3–6), which have the hemibonded (H₂S)₂⁺ ion core. All the calculations were performed at the BHandHLYP/aug-cc-pVTZ level. These structures are essentially the same as those determined in the previous infrared study on (H₂S)_n⁺ (ref. 56).

The observed spectra of (H₂S)_n⁺ (n = 2–6) in Fig. 1 were normalized by the laser power and their maximum intensities. This allowed for a direct comparison of the λ_max and bandwidth of the CR band across different cluster sizes. As cluster size increases, the bandwidth becomes smaller and the intensity in the visible region decreases. This change in band shape is likely attributed to reduction in hot bands. A CR band represents a bound-continuum transition, and its band shape reflects the Franck–Condon overlap between the ground (bound) and excited (dissociative) states. Vibrational excitation of the S∴S (hemibond) stretching mode (the dissociation coordinate) in the ground state broadens the Franck–Condon region of the excited state, which extends the absorption to longer wavelengths. With increasing cluster size, the hemibonded ion core undergoes solvation by H₂S molecules. Consequently, hydrogen bonds in the solvation shell weaken due to the anti-cooperative effect in ion solvation.^79–81 This weakening makes evaporation cooling more effective in larger-sized clusters, which more efficiently suppresses hot bands. This, in turn, leads to the narrowing of the CR band in larger-sized clusters.

The λ_max of the CR band exhibits a gradual blue-shift as solvation progresses. The λ_max for n = 6 is blue-shifted by approximately 20 nm compared to that of n = 2, and the magnitude of shift appears to converge at n = 6. A λ_max value for a σ–σ* transition corresponds to the vertical excitation energy. Solvation influences both the ground and excited states by altering their stability and potential shapes, and by shifting their potential energy curves along the internuclear distance axis. Consequently, these changes lead to a shift in the vertical excitation energy. For the calculated ground state isomers, we confirmed a trend of hemibond (S∴S) distance shortening, from 2.82 Å in n = 2 to 2.77 Å in n = 6, with the progression of the solvation. This shortening, which also suggests the enhancement of the hemibond binding energy, would act to increase the vertical excitation energy. However, since other factors, especially the excited state behavior, are not clear, it is difficult to identify the dominant factor for the blue-shift observed in this system at the present stage.

Direct dissociation of the hemibond is expected via the CR (σ–σ*) transition of the hemibonded structure. Upon direct dissociation, a larger fragment would likely retain a positive charge and be detected. For example, in direct dissociation of (H₂S)₃⁺, (H₂S)₂⁺ is the plausible fragment in this simple discussion. However, H₂S⁺ monomer fragments were predominantly observed for all cluster sizes in the present experiment. This is likely due to the cage effect during cluster dissociation: collisions between the hemibonded core fragment and solvent molecules lead to a highly vibrationally excited ground state of the cluster, leading to the monomer H₂S⁺ cation by the stepwise evaporation of all solvent molecules.^82,83 An alternative interpretation suggests the possibility that the recoil force exerted on the fragment cation is strong enough to cause dissociation by shedding the other solvating (hydrogen-bonded) molecules. To further explore the fragmentation mechanism of the hemibond, we are currently planning first-principle molecular dynamics simulations.

3.2 [(H₂S)₂–(H₂O)_m]⁺ (m = 1–2)

Fig. 4 displays the observed UV-vis spectra of [(H₂S)₂–(H₂O)_m]⁺ (m = 0–2). The spectrum of m = 0 is a reproduction of Fig. 1(a), included for comparison with the m = 1 and m = 2 spectra. All observed spectra were obtained by detecting H₂S⁺ fragments, which were the predominant dissociation channel. For m = 1 and m = 2, a broad band similar to that in m = 0 was observed, suggesting the presence of the hemibonded structures. The spectra in Fig. 4 were normalized by the laser power, parent ion intensity, and detector sensitivity, enabling the comparison of the relative intensity across different sizes. For m = 0 and m = 1, the relative band intensities are nearly identical. In contrast, for m = 2, the band intensity decreases drastically, though the band shape remains similar. This change suggests a significant reduction in the population of the hemibonded type for m = 2, due to the addition of two water molecules to (H₂S)₂⁺.

Fig. 4 (a)–(c) Observed spectra of [(H₂S)₂–(H₂O)_m]⁺ (m = 0–2) obtained by detecting the H₂S⁺ fragment channel and normalized by the laser power, parent ion intensity, and detector sensitivity. The spectrum of m = 0 is a reproduction of Fig. 1(a).

Fig. 5 compares the observed spectrum with simulated spectra of four stable isomers of [(H₂S)₂–H₂O]⁺. Isomer H1 is the most stable. In this isomer, a hemibond forms between the H₂S molecules, and the H₂O molecule is hydrogen-bonded to the (H₂S)₂⁺ ion core as a double accepter. Isomer P1 possesses the H₃O⁺ ion core, forming hydrogen bonds with H₂S and the SH radical. Meanwhile, isomer P2 has an H₃S⁺ ion core, which forms hydrogen bonds with H₂O and the SH radical. Isomer H2 features a “hetero” hemibonded ion core, (H₂O∴SH₂)⁺, where H₂S is hydrogen-bonded to another H₂S. Comparing the observed and simulated spectra reveals that the observed band is best reproduced by the CR band (349 nm) for the most stable isomer H1. This band has the nearly equal oscillator strength to that of (H₂S)₂⁺ (isomer S2_H, as seen in Fig. 2). Furthermore, the other isomers are much higher in energy (over ∼20 kJ mol⁻¹) and their oscillator strengths are one or two orders of magnitude lower than that of isomer H1. Therefore, we conclude that only H1 is experimentally observed, and the contribution of other isomers is negligible. Consequently, the hemibonded structure of (H₂S)₂⁺ is retained upon the addition of one H₂O. This finding aligns with previous IRPD spectroscopic studies using the same ion source, which assigned isomer H1 to the observed structure of [(H₂S)₂–H₂O]⁺.⁵⁸

Fig. 5 (a) Observed and (b)–(e) simulated spectra of [(H₂S)₂–H₂O]⁺ at the BHandHLYP/aug-cc-pVTZ level. Schematic stable isomer structures are also shown. Numbers in parentheses are zero-point energy corrected relative energies.

Fig. 6 compares the observed spectrum and the simulated spectra of five main isomers for [(H₂S)₂–(H₂O)₂]⁺. Isomer P1-1 is the most stable structure, featuring an H₃O⁺ ion core that forms hydrogen bonds with H₂O, H₂S, and the SH radical. Notably, the most stable structure shifts from the hemibonded type to the proton-transferred type upon the addition of two water molecules to (H₂S)₂⁺. Isomer P1-2 also possesses an H₃O⁺ ion core, and a hemibond is formed between the neutral pair of H₂S and the SH radical. Isomer H1, H2, and H3 are the hemibonded types, forming hemibonds between H₂S molecules, between H₂S and H₂O molecules, and between H₂O molecules, respectively. These hemibonded ion cores are hydrogen bonded with other solvent molecules. Although the most stable structure is isomer P1-1, which forms the protonated ion core, its major calculated bands fall outside the experimentally scanned range. Additionally, their oscillator strengths are approximately 100 times weaker than the CR band for the hemibonded type. In contrast, in the observed spectra, the integrated absorption strength for [(H₂S)₂–(H₂O)₂]⁺ is approximately 30% of that of (H₂S)₂⁺. Moreover, no signal was obtained by monitoring the H₃O⁺ fragment channel, as shown in Fig. S5 in the SI. Thus, the contribution of P1-1 to the observed spectrum would be negligible. Instead, the observed band would be attributed to minor isomer(s) of the hemibonded type (e.g., P1-2 and H1).

Fig. 6 (a) Observed and (b)–(f) simulated spectra of [(H₂S)₂(H₂O)₂]⁺ at the BHandHLYP/aug-cc-pVTZ level. Schematic stable isomer structures are also shown. Numbers in parentheses are zero-point energy corrected relative energies.

In the observed spectra of [(H₂S)₂–(H₂O)_m]⁺, the integrated strength ratio for the CR band is 10 : 7 : 3 for m = 0, 1, and 2, respectively. Given the constant oscillator strength for the CR bands shown in the calculation, the population ratio of the hemibond type for m = 2 is roughly estimated to be approximately 30% of that for m = 0 (100%). Based on this population ratio, and assuming a cluster temperature of 200 K (this is typical value for ionic clusters produced by the present ion source),^84,85 the relative energy of the hemibonded isomer to the most stable (proton-transferred type) isomer is roughly estimated to be approximately 2 kJ mol⁻¹. This result, however, shows a large discrepancy compared to the isomer search results, where the hemibonded type is approximately 10–20 kJ mol⁻¹ higher in energy. (We note that the calculated Gibbs energy difference at 200 K is in the 10–25 kJ mol⁻¹ range, consistent with the electronic energy difference.) While a more quantitative discussion is difficult, the clear suppression of the CR band intensity in the observed spectrum for m = 2 indicates that the major isomer shifts to the PT type, which exhibits no absorption in the observed region. Therefore, for m = 2, the hemibonded structure is suggested to be disrupted due to this shift in the most stable structure as supported by the structural search results. In previous IRPD studies, [(H₂S)₂(H₂O)₂]⁺ could not be observed due to its low signal intensity.⁵⁸ Conversely, for microsolvation of (H₂S)₂⁺ by methanol and ethanol, which possess higher proton affinities (PA) than water, the hemibonded structure is disrupted by a single solvent molecule.⁵⁸ Because the PA of water is largely enhanced by its dimerization to a magnitude comparable to that of methanol and ethanol monomers,⁸⁶ these findings are consistent with the observed structural change for [(H₂S)₂(H₂O)₂]⁺.

Finally, we note that the microsolvation of (H₂S)₂⁺ by H₂O also causes a blue-shift trend in the peak position of the CR band. This trend is similar to what is observed during the microsolvation of (H₂S)₂⁺ by H₂S, as shown in Fig. 1. For the hemibonded type isomers, the solvation of the (H₂S)₂⁺ ion core by H₂O occurs through hydrogen bond formation with the ion core. Therefore, the similar CR band shift behavior is reasonably expected for solvation by both H₂S and H₂O.

Additionally, we attempted to measure the UV-vis spectrum of (H₂S–H₂O)⁺ as the simplest model of hetero hemibond (S∴O).^{29,58,87–91} However, no spectra were observed in this experiment. Details are discussed in Fig. S6 in the SI.

3.3 Comparison with the aqueous solution

In this section, we discuss the absorption of the hemibonded ion core (H₂S∴SH₂)⁺ observed in the condensed phase, drawing implications from the present gas phase study. A transient absorption spectrum of H₂S in aqueous solution after pulsed radiolysis, reported by Asmus and coworkers,²⁷ is reproduced in Fig. 1(f) alongside the gas phase spectra of (H₂S)_n⁺ (n = 2–6) in Fig. 1(a)–(e). The CR band for gas phase (H₂S)_n⁺ is gradually blue-shifts as microsolvation progresses, eventually converging with the absorption in the aqueous solution. Therefore, the band in the aqueous solution is unequivocally attributed to hemibonded (H₂S)₂⁺_(aq.). Its λ_max is blue-shifted compared to that of bare gas phase (H₂S)₂⁺ due to its solvated structure. Furthermore, in gas phase, the magnitude of the CR band shift converges when the size of (H₂S)_n⁺ reaches n = 6. This suggests that, even in the aqueous solution, the first solvation shell predominantly stabilizes the hemibonded ion core in both its ground and excited states.

Given the similar proton affinities of H₂O (691 kJ mol⁻¹) and H₂S (705 kJ mol⁻¹),⁹² it seems reasonable that solvation by both H₂S and H₂O would lead to the similar CR band shift convergence value. This would hold true if the first solvation shell structure commonly forms through four hydrogen bonds to four SH groups in the (H₂S)₂⁺ ion core. However, our current experiment clearly shows that the hemibonded ion core (H₂S)₂⁺ is disrupted and shifts to a proton-transferred type ion core (H₃O⁺) upon the addition of just two water molecules. Asmus and coworkers reported lifetime of ca. 60 µs for (H₂S)₂⁺ in the aqueous solution.²⁷ This longevity of (H₂S)₂⁺_(aq.) becomes puzzling when considering the instability of the hemibonded ion core to (micro)hydration.

A possible interpretation to explain this inconsistency is the existence of an isomerization barrier between the hemibonded and the proton-transferred types for hydrated (H₂S)₂⁺. For [(H₂S)₂–(H₂O)₂]⁺, the most stable isomer P1-1 (proton-transferred type) is 18.3 kJ mol⁻¹ more stable than isomer H1 (the most stable hemibonded type). We searched for the isomerization path from isomer H1 to P1-1 by the GRRM method,^75–77 and found an isomerization barrier of 19.1 kJ mol⁻¹, as seen in Fig. 7. This barrier arises from the instability of TS2, where a proton has just transferred from the (H₂S)₂⁺ moiety to the (H₂O)₂ moiety. In TS2, the produced H₃O⁺ is not fully solvated (one OH is free from a hydrogen bond), which is clearly the origin of the instability of TS2. The subsequent rearrangement of H₂S to solvate the free OH of the H₃O⁺ largely stabilizes the system, leading to the stable PT type isomer formation. As the number of water molecules increases, the transient state corresponding to TS2, where proton transfer just occurs, becomes even more stable. This is because the water molecule that accepts the proton from (H₂S)₂⁺ is already fully solvated at the time of proton transfer, meaning the produced H₃O⁺ is also fully-solvated. Therefore, the barrier from a hemibonded type to a PT type would largely decrease in aqueous solutions. Although estimating the reaction rate for isomerization in aqueous solutions is quite challenging and beyond the scope of the present study, it is questionable whether the hemibonded ion core exhibits a 60 µs lifetime due to this isomerization barrier.

Fig. 7 Energy diagram of the reaction path of [(H₂S)₂–(H₂O)₂]⁺. The reaction path from the hemibonded structure was searched by the GRRM program at the B3LYP-D3/6-31+G* level. Relative energies are evaluated by geometry re-optimization of the stable structures at the BHandHLYP/aug-cc-pVTZ level and recalculation of the transition-state structures at the same level.

In their report on the aqueous solution,²⁷ Asmus and coworkers proposed the following reaction mechanism for the formation of the hemibonded (H₂S)₂⁺_(aq.) after pulsed radiolysis:

SH˙ + H₂S + H⁺_(aq.) → (H₂S∴SH₂)⁺_(aq.)

If we assume this formation mechanism, the formation rate could govern the lifetime of hemibonded (H₂S)₂⁺_(aq.). However, this reaction corresponds the isomerization from a proton transferred type (which includes H₃O⁺) to a hemibonded type. As shown in the present isomer search results, this is clearly an endothermic reaction. Therefore, it is hard to accept this reaction mechanism at this point.

Another, somewhat bolder, explanation is that the (first) solvation shell for (H₂S)₂⁺ in aqueous solutions is composed of H₂S, leading to its long lifetime. In aqueous solution experiments, H₂S, introduced by bubbling or so on, is macroscopically dissolved in water. However, given the low acidity of the thiol group in H₂S and the predominance of dispersion force in its intermolecular interactions,^93–96 (a part of) H₂S in water might form nanometer-sized aggregates driven by hydrophobic effects. When such an H₂S aggregate is ionized by radiolysis, H₂S-solvated (H₂S)₂⁺ (i.e., (H₂S)_n⁺) is generated. As our present study shows, these hemibonded (H₂S)_n⁺ species are stable, which would account for the long lifetime of the hemibonded (H₂S)₂⁺ ion core in the aqueous solution. However, the acidity of H₂S solvating the ion core is enhanced by a positive charge of the ion core, leading to stronger interaction with water at the cluster surface. The eventual substitution of the solvation shell by H₂O would then lead to the isomerization to the proton-transferred-type. In this interpretation, the lifetime of the hemibonded ion core is governed by the distraction of the H₂S solvation shell (i.e., substitution by H₂O). It is worth noting that, to the best of our knowledge, there is currently no available information regarding the aggregation of H₂S in aqueous solutions. These interpretations are based on the current experiment and would require more detailed examination.

In summary, in aqueous solutions, the CR band is blue-shifted due to the solvation of the hemibonded (H₂S)₂⁺ ion core, primarily influenced by the first solvation shell. While a few interpretations have been examined to account for the observed long lifetime of the hemibonded ion core in aqueous solutions, it is difficult to reach an unequivocal conclusion regarding these interpretations.

4. Conclusion

In the present study, we performed UV-vis PD spectroscopy to examine the radical cation clusters of (H₂S)_n⁺ (n = 2–6) and [(H₂S)₂–(H₂O)_m]⁺ (m = 1–2). These clusters serve as effective models for a hemibonded ion core and its microsolvation. The observed spectra of (H₂S)_n⁺ (n = 2–6) consistently displayed CR bands across all cluster sizes, providing unequivocal evidence of hemibond formation. Significantly, this electronic spectroscopy firmly confirmed the hemibonded structure for n = 2, which had not been definitely established by previous IR studies.⁵⁶ Furthermore, the λ_max of the CR band exhibited a blue-shift with increasing cluster size. The shift converges at n = 6, a point corresponding to the completion of the first solvation shell around the hemibonded (H₂S)₂⁺ ion core. On the other hand, in the observed spectra of [(H₂S)₂–(H₂O)_m]⁺ (m = 1–2), the relative intensity of the CR band for m = 2 drastically decreased compared to m = 0 and m = 1. This reduction indicated that the hemibonded ion core (H₂S)₂⁺ is no longer the most stable form with the addition of just two water molecules. For [(H₂S)₂–(H₂O)₂]⁺, quantum chemical simulations further corroborated this finding, demonstrating a shift in the most stable form from a hemibonded type to a proton-transferred type, that is consistent with the experimental results. A comparison between the present gas-phase spectra and the previously reported transient absorption spectrum in the aqueous solution revealed that, in the aqueous solution, the CR band is blue-shifted due to the solvation of the hemibonded (H₂S)₂⁺ ion core, with this effect predominantly influenced by the first solvation shell.²⁷ Furthermore, this study allowed us to interpret the origin of the long lifetime of the hemibonded (H₂S)₂⁺ ion core in the aqueous solution, and enabled us to propose the possibility of neutral (H₂S)_n aggregates formation in aqueous solutions.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data supporting this article are included in the supplementary information (SI). Supplementary information is available. See DOI: https://doi.org/10.1039/d5cp03758a.

Acknowledgements

This study was supported by a Grant-in-Aid for Scientific Research (Project No. 21H04671 and 25K03402) from JSPS. A part of the computation was performed at the Research Center for Computational Science, Okazaki, Japan.

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