The Nature of the Hydrated Proton H_(aq)⁺ in Organic Solvents

Abstract

The nature of H(H₂O)_n⁺ cations for n = 3 – 8 with weakly basic carborane counterions has been studied by IR spectroscopy in benzene and dichloroethane solution. Contrary to general expectation, neither Eigen-type H₃O·3H₂O⁺ nor Zundel-type H₅O₂⁺·4H₂O ions are present. Rather, the core species is the H₇O₃⁺ ion.

Introduction

The current state of knowledge of the aquated proton H_(aq)⁺ is in a curious position. In water, the “excess proton” is widely believed to exist in two limiting forms, the Eigen-type H₃O⁺ ion¹ and the Zundel-type H₅O₂⁺ ion,² coexisting in a dynamic equilibrium. These ions are well characterized in crystalline salts,^3,4 organic solvents^5–7 and the gas phase^8–10 but the extent to which they represent H_(aq)⁺ in water has not been determined experimentally. The belief that H_(aq)⁺ is an approx. 60:40 ratio of hydrated Eigen:Zundel ions is based on theory.^11,12

The problem of developing an accurate molecular description of H⁺ in water lies in the difficulty of accurately separating its spectroscopic signature(s) from those of the background water, and in interpreting the resulting spectra. Infrared is the spectroscopy of choice because of its sensitivity and fast timescale but the IR spectrum of H_(aq)⁺ is notoriously broad. A poorly understood continuous broad absorption (cba) associated with the vibrations of the excess proton extends over the much of the useful IR range. These difficulties have shifted attention to the gas phase. The underlying assumption is that an accurate molecular description of each ion-selected hydrate H(H₂O)_n⁺ via step-by-step increasing n will ultimately lead to an understanding of H_(aq)⁺ in bulk water. Indeed, experiment and theory in vacuo come together very nicely to establish that the trihydrated Eigen ion (H₉O₄⁺ i.e. H₃O⁺·3H₂O) and the tetra-hydrated Zundel ion (H₁₃O₆⁺ i.e. H₅O₂⁺·4H₂O) have extra stability in the gas phase.^13,14 Other “magic number” clusters such as H(H₂O)₂₁⁺ have distinctive structural characteristics and heightened stability compared to their near n neighbors.^15–18

While gas phase studies have obvious and direct importance in atmospheric chemistry there are reasons to doubt such a close relationship will hold in condensed phases – where so much acid chemistry is carried out. Gas phase ion chemistry (and theory) is carried out in the absence of counterions whereas all condensed phase chemistry must deal with the necessity of a conjugate base. Even strong acids that fully ionize in a solvent are subject to ion pairing. The uni-directional electric field created by the proximity of an anion will affect the structures of the H(H₂O)_n⁺ cations. Structural isomers of H(H₂O)_n⁺ for n = 5–8 values are calculated in vacuo to be very close in energy^10,19–22 so their structures should be quite sensitive to environmental influences in condensed media.

In the solid state, X-ray crystal structures of hydrated acids were studied quite extensively in the late 1970s.²³ In favorable circumstances they can be expected to reflect the structures of ions in other phases. For example, if an H(H₂O)_n⁺ ion is surrounded in a crystal by a spherically symmetric anion field, it might be expected to reflect the gas phase structure of the cation. In anion fields of lower symmetry, an H(H₂O)_n⁺ ion might be expected to reflect ion-paired structures of hydrated acids in solution.

Given these considerations, as well as the importance of the hydrated proton in acid catalysis, fuel cell electrolytes and acid/base chemistry in general, we are focusing on the nature of the hydrated proton in organic solvents, where studies are few. Just as in the gas phase, water molecules can be controlled and sequentially attached to the proton forming H(H₂O)_n⁺ clusters. The ease of formation, structure and composition of these cations depends strongly on the basicity of the solvent and the basicity of the anion, i.e. the strength of the conjugate acid. In weakly basic solvents like CH₂Cl₂, acids such as HCl are hydrated mainly without proton transfer to H₂O molecules.²⁴ Simple H-bonded solvates of the type HA·(H₂O)_n prevail rather than ionized H(H₂O)_n⁺ clusters. With solvents of higher basicity such as tributylphosphate (TBP), whose basicity is close to that of water, proton transfer to H₂O becomes possible but is accompanied by waterless TBP·HA monosolvates.²⁵ Stronger acids such as perchloric and triflic acid certainly protonate water in weakly basic solvents but the solubilities of the ionized species are low and often insufficient to study their full hydration by IR. Thus, only the mono- and dihydrates of triflic acid, H₃O⁺OTf⁻ and H₅O₂⁺OTf⁻, have been studied in dichloroethane.²⁶ With increasing solvent basicity, the solubilities of strong acids increase. In TBP for example, HClO₄ and HFeCl₄ form a set of H(H₂O)_n⁺ clusters with step-by-step increasing n up to aggregates with high n that are like reverse nanomicelles.^27,28 The protons are located in the water core of these micelles near the boundary with the TBP solvation shell in the form of tetrasolvated H₅O₂⁺ ions, [H₅O₂⁺·2H₂O·2TBP]. The counterions are weakly ion paired to the water micelle in the case of ClO₄⁻ but remote and non-interacting in the case of the more weakly basic FeCl₄⁻ anion. These observations highlight the need for a strong acid whose H(H₂O)_n⁺ salts are soluble in low basicity solvents and whose anion will have minimal influence on the structures of the H(H₂O)_n⁺ cations.

Suitable acids have recently become available in carborane superacids, H(CHB₁₁R₅X₆) (R = H, Cl, Br, I; X = Cl, Br, I; see Figure 1).²⁹ They are presently the strongest known pure acids^30,31 and their conjugate base anions impart good solubility to salts in low basicity solvents. Their large, non-polarizable anions are expected to have the weakest influence on the structure of the cations, possibly leading to H(H₂O)_n⁺ cations that reflect those in the gas phase. We have previously used carborane acids to establish the nature of the H₃O⁺ and H₅O₂⁺ ions under controlled conditions of minimal water content.^5,7 We now apply these methods to the more normal laboratory conditions of wet organic solvents where higher hydrates prevail. Benzene and dichloroethane are chosen because they are common solvents for synthetic chemistry.

Figure 1.

The conjugate base carborane anions of the type CHB₁₁X₅Hal₆⁻ used in this work (X/Hal = H/Br, Cl/Cl, I/I).

Experimental Section

Carborane acids H(CHB₁₁H₅Br₆), H(CHB₁₁Cl₁₁) and H(CHB₁₁I₁₁) (abbrev. H{H₅Br₆}, H{Cl₁₁} and H{I₁₁}) and their arenium ion salts were prepared as previously described.³⁰ Chlorinated cobalt(III) dicarbollide, Co(C₂B₉H₈Cl₃)₂⁻, (abbrev. {CCD⁻}) (90% in H-form and 10% in Na-form) with an analysis of 9.35% Co, and 29.05% Cl was received from KatChem (Czech Republic) and converted into 100% H-form H{CCD} by shaking a dichloroethane (DCE) solution with 3M H₂SO₄ aqueous solution for 5 min and retaining the DCE layer. Benzene and DCE were purified and dried according to literature methods.³² H⁺(H₂O)_n{H₅Br₆} solutions in DCE were prepared by mixing calculated volumes of dry DCE, water-saturated DCE containing 0.1M H₂O, and 0.025M C₆Me₆H⁺{H₅Br₆⁻} or C₆H₇⁺{H₅Br₆⁻} solutions in DCE to obtain solutions with constant acid concentration C_HCarb, and defined water concentration C⁰_H2O. For solutions with H₂O/acid molar ratio equal to 2–3, the C_HCarb was 0.015M. For H₂O/acid > 3, C_HCarb was 0.01M. Solutions with the largest fixed H₂O/acid molar ratios were obtained by dissolving weighed portions of C₆H₇⁺{H₅Br₆⁻} in DCE containing 0.1M H₂O. Benzene solutions of H⁺(H₂O)_n{H₅Br₆⁻} and H⁺(H₂O)_n{Cl₁₁⁻} were prepared in a similar manner to the DCE solutions, using water-saturated benzene (0.2M) and weighed quantities of mesitylenium or hexamethylbenzenium salts dissolved in water-saturated benzene. The final benzene solutions contained 0.004M H⁺(H₂O)_n{H₅Br₆} or 0.005M H⁺(H₂O)_n{Cl₁₁}. The spectrum of free hexamethylbenzene or mesitylene (formed in solution) was digitally subtracted. Water-saturated H⁺(H₂O)_nCarb⁻ solutions with Carb⁻ = {H₅Br₆⁻}, {Cl₁₁⁻}, {I₁₁⁻} and {CCD⁻} were obtained by extraction of the acids from aqueous solutions. The concentrations of all acids were measured by the intensity of the anion absorption bands in IR spectra.

The IR spectra of these solutions consist of overlapping spectra of the following components: (i) solvent, (ii) water dissolved in the solvent, and (iii) hydrated acid, H(H₂O)_n⁺Carb⁻. To isolate the spectrum of a particular H⁺(H₂O)_nCarb⁻ species, the spectrum of the solvent and dissolved water were successively subtracted from the initial spectrum. Figure 2 shows a typical example of this procedure. Subtraction of the dissolved water using spectra of 0.1M water-saturated DCE or 0.2M water-saturated benzene with a scaling factor f_i allowed determination of the concentration of “free” water dissolved in the solutions under study: C_H2O^free = f_i·C^sat, where C^sat = 0.1 or 0.2M for DCE and benzene, respectively. The concentration of the water involved in H(H₂O)_n⁺ cation is determined from the difference C_H2O^Cat = C⁰_H2O - C_H2O^free, where C⁰_H2O is the total water concentration, known from the conditions of preparation. The ratio N = C_H2O^Cat/C_HCarb gives the average stoichiometry of H(H₂O)_n⁺ cations formed in solution. This method of spectral subtraction to determine the concentration of water (or methanol)³³ bound with H⁺ and the average N stoichiometry of the formed H⁺·L_N cations has been previously described in detail.^27,28,34

Figure 2.

IR spectrum of H(H₂O)_n⁺{H₅Br₆⁻} in DCE solution with N = 3.7 after sequential subtraction of dry DCE and hexamethylbenzene (black), then free dissolved water, resulting in the final spectrum (red). For reference, the spectrum of 0.1 M water in DCE (after subtracting DCE) is shown in dashed blue.

The water-saturated DCE solutions of H(H₂O)_n⁺{I₁₁⁻} and H(H₂O)_n⁺{CCD⁻} acids were prepared by extraction from water solution of their Cs{I₁₁} or H/Na{CCD} salts containing 2–4 M H₂SO₄. The separated organic phase was washed 4–5 times with 1–2 M H₂SO₄ and then with distilled water. The molar concentrations of the acids were determined from the intensity of IR absorption of the {I₁₁⁻} and {CCD⁻} anions compared to standard DCE solutions of (Oct)₃NH⁺{I₁₁⁻} or (Oct)₃NH⁺{CCD⁻}. The total water concentration was determined using ¹H NMR. The initial DCE solvent was made 0.2 M in chloroform as an internal standard. In the NMR spectra of water-saturated DCE solutions, the signal integrations of chloroform (at 7.26 ppm) and water (at 1.49 ppm) give the ratio 1.00:1.03, in good agreement with known water content of 0.1 M.³⁵ In the spectra of H(H₂O)_n⁺{I₁₁⁻} and H(H₂O)_n⁺{CCD⁻}, the ratio of these signals allowed determination of the total water concentration, C⁰_H2O, and the molar ratio N = (C⁰_H2O – 0.1)C_Hcarb.

With the exception of water-saturated solvents, all solutions were prepared in a Vacuum Atmospheres Corp. glove box under nitrogen (O₂, H₂O < 0.5 ppm). IR spectra in the 4000–450 cm⁻¹ range were run on a Shimadzu-8300 FT-IR spectrometer housed inside a glovebox. A cell with Si windows having 0.036 mm separation at the beam transmission point was used. To avoid interference effects, the cell configuration was wedge-shaped. IR data were manipulated using GRAMMS software. NMR spectra were run on Varian INOVA 400.

X-ray crystals of [H₇O₃⁺][CHB₁₁Cl₁₁] were grown from o-dichlorobenzene under conditions of slow solvent evaporation at low pressure. Crystals of [H(CH₃OH)₃⁺][CHB₁₁Cl₁₁⁻] were grown from benzene solution with a 1:3 MeOH/H{Cl₁₁} mole ratio.³³ Crystals of [H₉O₄⁺][CHB₁₁Cl₁₁⁻] were grown from water-saturated H[CHB₁₁Cl₁₁] solution in a desiccator over CaCl₂. CCDC 687306, 687307 and 687308 contain the supplementary crystallographic data for these salts. These data can be obtained free of charge in the Supporting Information or from The Cambridge Crystallographic Data Centre at www.ccdc.cam.ac.uk/data_request/cif.

Results and Discussion

IR spectra of benzene and DCE solutions of carborane acids with different water/acid mole ratios N = H₂/H(carborane) change regularly with increasing N, indicating sequential of hydration of H⁺. In addition, water molecules may be involved with solvation of the carborane anions. In order to examine this possibility we studied dichloroethane extracts of cesium carborane salts from water solutions. In addition to the bands from the carborane anions and dissolved water, IR spectra of these extracts developed two new narrow OH stretching bands ν_as at 3655 and ν_s at 3578 cm⁻¹, arising from H₂O molecules with free OH groups. Since these frequencies are independent of the nature of the carborane anion and are red shifted compared to those for dissolved monomeric water molecules in DCE (3675 and 3591 cm⁻¹, respectively) they are assigned to H₂O molecules bound to the Cs⁺ cation via the O-atom. Thus, there are no water molecules involved with hydrating the carborane anions. Taking into account that the νOH frequencies of the H(H₂O)_n⁺ cations discussed below are also independent of the nature of carborane anion, we can conclude that the OH groups of the cations are not H-bonded with counterion. This is consistent with our earlier studies on the H₅O₂⁺·4Solv cations⁷ where, although there is good evidence for ion pairing, H-bonding of the cation occurs only with solvent molecules. Thus, solvent separated ion pairs of the type [H⁺(H₂O)_n·mSolv]Carb⁻ are formulated in the present work.

DCE solutions

IR spectra of H(H₂O)_n⁺{H₅Br₆⁻} solutions with water/acid mole ratios N ≥ 2 have been studied. The spectrum of the solution with N = 2 belongs to the H₅O₂⁺·4DCE cation.⁷ With gradually increasing N to 3, the intensity of the H₅O₂⁺ spectrum decreases and disappears. At the same time the spectrum of the H₇O₃⁺ cation appears and reaches a maximum at N = 3. As shown in Figure 3, there is an isosbestic point at 3494 cm⁻¹ up to N = 2.9, confirming that in this range only two cations, H₅O₂⁺ and H₇O₃⁺, are formed (i.e. N = n). As N = 3 is approached, there is a peculiar step change in the H₇O₃⁺ spectrum (Figure 3). This change is consistently reproducible and indicates the existence of two forms of the H₇O₃⁺ cation, the α isomer at N < 3 and the β isomer at N > 3. Their individual spectra are shown in Figure 4 and, as discussed in more detail below, are ascribed to different degrees of ion pairing. With further increase of N from 3 to 5.2 the spectrum of β-H₇O₃⁺ is transformed into that for the more highly hydrated H(H₂O)_n⁺ cations with isosbestic points at 3542 and 3467 cm⁻¹ (Figure 5). This means either that H₇O₃⁺ is transformed into a single H(H₂O)_n⁺ cation with constant n, which seems improbable, or that a set of spectroscopically indistinguishable compounds with variable n ≥ 4 are formed, which will need a specific explanation.

Figure 3.

IR spectra of H(H₂O)_n⁺ cations with n = 2.0, 2.16, 2.30, 2.45, 2.75, 2.85 and 3.06 in DCE solutions. The initial spectrum (black) belongs to H₅O₂⁺. The red spectrum belongs to the α-H₇O₃⁺ isomer, the final (blue dashed) spectrum to the β-H₇O₃⁺ isomer.

Figure 4.

IR spectra of H₇O₃⁺ isomers α (red) and β (blue).

Figure 5.

IR spectra of H(H₂O)_n⁺ cations with n = 3.02–5.22.

Proton hydrates can be followed as a function of N via the change in frequency of ν_asH₂O from the terminal H₂O molecules, i.e. the “free” OH groups that are H-bonded to solvent. The ν_asH₂O band is chosen over ν_sH₂O for this analysis because it does not overlap with bands from other types of vibrations. As shown in Figure 6, for N = 2–3 the ν_asH₂O frequency of α-H₇O₃⁺ is constant. At about N ∼ 3, the α → β isomerism of H₇O₃⁺ takes place and ν_asOH jumps steeply. In the range N > 3, n_asH₂O of β-H₇O₃⁺ and higher H(H₂O)_n⁺ hydrates are strongly overlapped and their joint maximum weakly increases in frequency as cations with n > 3 are formed. The procedures necessary to obtain samples of known water concentration (see Exp. Sect.) do not allow the total water concentration to exceed that of water-saturated DCE (0.1M) and maximum N value we can study is 5.2. On the other hand, a DCE extract from aqueous H{H₅Br₆} has a higher total concentration of water and the ν_asOH frequency is 3636±1 cm⁻¹. Extrapolation using the Figure 6 dependence indicates that this frequency corresponds on average to the H(H₂O)₆⁺ cation.

Figure 6.

The dependence of ν_asH₂O on the stoichiometry n of H(H₂O)_n⁺.

If successive H(H₂O)_n⁺ cations have strongly differing stability constants K_n, then the dependence of the free dissolved water concentration C_H2O^free on n should be stepped since in accordance with equilibria

$${\mathrm{H}}^{+}{({\mathrm{H}}_2\mathrm{O})}_{\mathrm{n}-1}+{\mathrm{H}}_2\mathrm{O}\to {\mathrm{H}}^{+}{({\mathrm{H}}_2\mathrm{O})}_{\mathrm{n}}$$

the equilibrium constant K_n = C_n/C_n−1·C_H2O^free includes, in addition to C_n and C_n−1 concentrations of H(H₂O)_n⁺ and H(H₂O)_n−1⁺ cations respectively, the concentration of free dissolved water C_H2O^free. However, as shown in Figure 7, the dependence of C_H2O^free on n shows only one step at n = 3, when formation of H₇O₃⁺ cation is complete and a detectable concentration of free dissolved water appears. With further increasing n, the dependence increases steeply and linearly, indicating that the K_n constants for cations with n ≥ 4 are low and do not differ significantly. Extrapolation to water-saturated DCE (C_H2O^free = 0.1 M) results in n = 6, confirming that the highest formed proton hydrate is the H(H₂O)₆⁺ ion. The dependence of C_H2O^free on n allows the determination of K_n values for cations with n ≥ 4. For equal concentrations of H⁺(H₂O)_n and H⁺(H₂O)_n+1 cations K_n = 1/C'_H2O, where C'_H2O is the free water concentration for solutions with C_n = C_n−1. From C^free_H2O = f(n) one can determine that C'_H2O = 0.0385, 0.0628 and 0.0876M respectively for solutions with N = 3.5, 4.5 and 5.5. Then K₄ = 26.0, K₅ = 15.9 and K₆ = 11.4. The K₃ value, for the formation of the H₇O₃⁺ cation, cannot be determined since the C'_H2O concentration required for calculation is below the threshold of IR detectability.

Figure 7.

The dependence of the concentration of free dissolved water on stoichiometry of the H(H₂O)_n⁺ cations formed.

For all H(H₂O)_n⁺ cations with n ≥ 3 the frequency of the δ_H2O terminal water bending vibration is practically the same, 1608 cm⁻¹. Its intensity (I₁₆₀₈) increases linearly with increasing H₇O₃⁺ cation concentration in solutions as N increases from 2 to 3 and extrapolates to zero at N = 2 (Figure 8). This confirms a peculiarity established earlier, namely, that in the IR spectrum of the H₅O₂⁺ cation the δ_H2O band is not observed.⁷ At N ∼ 3 the I₁₆₀₈ dependence on N changes slope and then continues to grow with increasing n in line with the increasing number of terminal water molecules in H(H₂O)_n⁺ cations. They can contain two types of terminal H₂O: type (i) with both OH groups free or type (ii) with one free and the second H-bonded. Their δ_H2O frequencies coincide because the addition of a single H-bond in (ii) has minimal effect on the force constant of this vibration.

Figure 8.

Dependence of the δ_H2O band intensity on the stoichiometry of the H(H₂O)_n⁺ cations.

On the other hand, when both O-H groups are H-bonded to additional water molecules as in coordination type (iii), the δ_H2O frequency is detectably higher.

In summary, IR spectra of DCE solutions show that only the H₅O₂⁺ and H₇O₃⁺ cations have specific identities. H(H₂O)_n⁺ cations with n = 4–6 develop as a single family of compounds with spectroscopic properties sufficiently similar that it is impossible to detect their successive formation. They only differ slightly in the bands arising from their terminal water molecules.

Benzene solutions

The IR spectra of H(H₂O)_n⁺ cations in benzene solution are quite similar to those for DCE and are essentially independent of the nature of the counterion, {Cl₁₁⁻} or {Me₅Br₆⁻}. Therefore, we will discuss the spectra of solutions of the H{Cl₁₁} acid, whose hydrates are more soluble in benzene.

The spectrum of the cation formed in solution with N = 2 belongs to H₅O₂⁺.⁷ With N increasing to 3 the intensity of the H₅O₂⁺ spectrum decreases as the spectrum of the H₇O₃⁺ cation increases with an isosbestic point at 3447 cm⁻¹ (Figure 9). However, in the range of N = 2.6–2.9 the spectrum of H₇O₃⁺ cation changes rapidly such that at N = 3 the spectrum does not cross the isosbestic point. Just as in DCE solution, the H₇O₃⁺ cation must exist in two isomeric forms in benzene solution: α (N = 2–2.6) and β (N ≥ 2.9). Their spectra are given in Figure 10.

Figure 9.

IR spectra of H(H₂O)_n⁺ cations with n = 1.99, 2.35, 2.55, 2.91 in benzene solution in the frequency range of νOH of the terminal OH groups. The initial spectrum (black) belongs to H₅O₂⁺. The red spectrum belongs to the β-H₇O₃⁺ isomer.

Figure 10.

IR spectra of α (red) and β (blue) isomers of the H₇O₃⁺ ion, equalized to unit intensity of the {Cl₁₁}⁻ anion, and the difference spectrum (brown) with hatching showing positive and negative intensity.

With increasing N from 3 to 4, the spectra change with a new isosbestic point at 3544 cm⁻¹ indicating transformation of the H₇O₃⁺ cation into H(H₂O)_n⁺ (Figure 11). The spectra with N > 4 do not cross exactly at 3544 cm⁻¹ indicating that the H(H₂O)₄⁺ cation may differ slightly more from cations with n ≥ 5 in benzene compared to DCE.

Figure 11.

Spectra of H⁺(H₂O)_n{Cl₁₁} in benzene solutions with N = 3.2; 3.42; 3.46; 3.91 and 4.52. The red spectrum is close to water saturated with undetermined N. The bands from {Cl₁₁} anion were subtracted using the spectrum of (Oct)₃NH{Cl₁₁} solution in benzene.

Spectra and structures of the H(H₂O)_n⁺ cations

H₇O³⁺

IR spectra of the α and β isomers of the H₇O₃⁺ cation are both in agreement with the symmetrical cation structure I.

They show two types of OH stretching vibrations from terminal OH groups: firstly, ν_sH₂O and ν_asH₂O from the two equivalent H₂O molecules and secondly, a lower frequency ν band from the group labeled OH* in I. The deconvolution is shown in Figure 12 and the data are listed in Table 1. The δH₂O bend is at 1608 cm⁻¹. Vibrations from the conjugated (O⋯H−O−H⋯O)⁺ group develop as a continuous broad absorption (cba) in the range 1400–3100 cm⁻¹ (Figure 4 and Figure 10) with a particular shape (discussed below). The OH stretching frequencies of the terminal OH groups of the α isomer are somewhat red shifted compared with those for β isomer and band intensity is slightly higher (Figure 4, Figure 10 and Figure 12). This means that the α isomer experiences a somewhat stronger interaction with its environment. It is likely that α-H₇O₃⁺ forms mixed ion associates of the type (H₇O₃⁺)_x(H₅O₂⁺)_yCarb⁻_x+y since the α isomer exists only in the presence of H₅O₂⁺ when N < 3. The destruction of these mixed associates as N approaches 3 can be understood in terms of the disappearance of the H₅O₂⁺ ion, resulting in the formation of the β isomer. Related associates were found in reverse nano-micelles formed in wet tributylphosphate solutions of HFeCl₄ and HCl.²⁸ They have a specific HFeCl₄/HCl mole ratio and are destroyed when this molar ratio is not supplied.

Figure 12.

Deconvolution of the IR spectra of the α and β isomers of H₇O₃⁺ in benzene in the frequency range of the terminal OH groups.

Table 1.

Frequencies of terminal OH stretching vibrations in H₇O₃⁺.

Solvent	Band	Frequency		Δν(β - α)
		α isomer	β isomer
DCE	νasH2O	3595	3612	17
	νsH2O	3520	3535	14
	νOH*	†	†	†
Benzene	νasH2O	3576	3597	21
	νsH2O	3501	3523	21
	νOH*	3416	3458	42

^†Cannot be determined with reliable accuracy

The distinctive continuous broad absorption (cba) in the spectrum of H₇O₃⁺ in the 1400–3100 cm⁻¹ frequency range, which notably is absent in the spectrum of H₅O₂⁺ cation,⁷ derives from the (O⋯H−O−H⋯O)⁺ group vibrations. A similar feature is observed in the spectra of all other compounds containing the O−H⋯O group as long as the condition of O⋯O distance in the range 2.51–2.60 Å is fulfilled. As shown in Table 2, this group of compounds includes dimers of dialkylphosphoric and dialkylphosphinic acids, the salts of carboxylic acids with organic basics, and a variety of other acid salts. The IR spectra of compounds containing a conjugated (biprotonic) group of the (X⋯H−O−H⋯X)⁺ type with X = heteroatom, whose stretching and bending vibrations are strongly coupling, nevertheless develop the same cba.^48,49 The shape of the cba is quite specific having so-called A (∼2600–2800), B (∼2200) and C (1700–1800 cm⁻¹) structure.⁵⁰

Table 2.

The frequencies of O-H⋯O groups for some compounds developed in IR spectra the OH stretching as a broad absorption with A, B and C contours.

Type of O-H⋯O group	Compound	Method	Stretching vibration			Bending vibration		RO⋯O, Å	Ref
			A	B	C	δ(OHO)	γ(OHO)
(C)O-H⋯O(X)	H-complexes of carboxylic acids	IR	2800	2500	1900	1200–1600	900–1100		36–38
(O3P)O-H⋯O(PO3)	K2HPO4·3H2O	IR	2700	2330 2265	1670 1700	1220 1212	800	2.578	39
(O3P)O-H⋯O(PO3)	Ca(H2PO4)2·H2O	IR	2920	2375	1700	*	*	2.596	40
(S)O-H⋯O(S)	CsHSO4	IR, Raman	2850	2500	1680	1252	884	2.572	41
(Se)O-H⋯O(Se)	CsHSeO4	IR, Raman	2840	2415	1600	1258	805	2.603	42
(Se)O-H⋯O(Se)	C6H5SeOOH	IR	2740	2270	1650	*	*	2.52	43
(P)O-H⋯O(P)	dialkylphosphoric and dialkylphosphinic acids	IR44,45	2600–2800	2200–2400	1610–1700	*	*	2.5346 2.5147

There are different points of views on the interpretation of the A, B, C structure of the cba band⁵¹ but Fermi resonance between the νOH stretch and the overtones of low frequency vibrations of the O−⋯ group, namely, with the first overtones of the in-plane δ(OHO) (A and B bands) and out-of-plane γ(OHO) (C band) vibrations is gaining wide acceptance.^{36–38,52,53} The Fermi resonance nature of the A, B and C bands and the correct assignments of the δ(OHO) and γ(OHO) bands have been rigorously confirmed based on polarization data in the IR and Raman bands in the spectra of acid sulfates, phosphates and selenates of potassium and cesium at 300 and 20 K.^39,41,42

Since the cba represents a very broad OH stretching band, and its shape is distorted by Fermi resonance, νOH is determined as the centre of gravity of cba absorption.^37,38 The cba does not significantly depend on the energy/enthalpy of the H-bonding, the temperature (80–550 K) or the state of matter.⁴⁵ However, the center of gravity (i.e. νOH) depends on O⋯O distance. With O⋯O decreasing to 2.41–2.42 Å, as in H₅O₂⁺ cation^3,4 or to 2.39 Å as in proton disolvates L-H⁺-L with L = strong base,⁵⁴ νOH decreases in frequency. As O⋯O decreases, bands A and B decrease in intensity and disappear when H₇O₃⁺ becomes H₅O₂⁺. Band C is retained and new bands in the low frequency 800–1200 cm⁻¹ region appear in the spectrum of H₅O₂⁺.⁷

In crystalline H₇O₃⁺{Cl₁₁} the H₇O₃⁺ cation is asymmetric with one O⋯O distance longer, 2.518(2) Å, and the second shorter, 2.439(2) Å, reflecting the asymmetrical environment of {Cl₁₁⁻} anions. Such asymmetry is common for H₇O₃⁺ cations in the crystalline state e.g. [H₇O₃·(15-crown-5)][AuCl₄]⁵⁵ has 2.536(7) and 2.423(7) Å O⋯O distances). The proximity of shorter distance to that in the H₅O₂⁺ cation (2.40–2.42 Å)^3,4,7 suggests formulation of these salts as H₅O₂⁺ monohydrates, H₅O₂⁺·H₂O. However, the IR spectrum of the distorted H₇O₃⁺ cation in crystalline H₇O₃⁺{Cl₁₁} shows a strong cba with A,B,C structure, not seen for the H₅O₂⁺ cation, arising from the O⋯H−O−H⋯O chromophore (Figure 13). Thus, it has a separate identity. Since its IR spectrum differs considerably from that in solution (Figure 13) we should compare it to that in a more symmetrical crystalline environment.

Figure 13.

Comparison of IR spectrum of α-H₇O₃⁺ cation in benzene solution (red) with that of solid H(CH₃OH)₃⁺{Cl₁₁⁻} (blue) and crystalline H₇O₃⁺{Cl₁₁} (black dashed). The red and black spectra are normalized to unit absorption of the {Cl₁₁-} anion.

The structure reported to have the most symmetrical H₇O₃⁺ cation is found in [H₇O₃⁺][H₉O₄⁺]Br⁻₂·H₂O where the O⋯O distances are 2.47(1) and 2.50(1) Å (ave. 2.481 Å).⁵⁶ The symmetry arises from a nearly symmetrical anion/hydrate field as shown in (iv).

The proton labeled H* is more tightly H-bonded to bromide than those from the terminal water molecules, reflecting its closer proximity to the positive charge. The interaction with two water solvate molecules is weak. Unfortunately, because of the presence of H₉O₄⁺ (and H₂O) in these crystals, they are not suitable for IR investigation of the H₇O₃⁺ ion. Lacking good hydrates for structure/spectra correlation, we turn to the methanol analogue of the H₃O₃⁺ ion, namely the H(CH₃OH)₃⁺ cation, which has a similar cba band and has been characterized by X-ray crystallography.

The structure of the H(CH₃OH)₃⁺ cation in crystalline H(CH₃OH)₃⁺{Cl₁₁⁻} with O⋯O distances 2.446(2) and 2.491(2) Å is shown in Figure 14.

Figure 14.

X-ray crystal structure of one cation of [H(MeOH)₃][CHB₁₁Cl₁₁] in the unit cell. Thermal ellipsoids are shown at the 50% probability level.

The overall average O⋯O distance of 2.455 Å is close to the average of 2.481 Å in the nearly symmetrical H₇O₃⁺ cation in [H₇O₃⁺][H₉O₄⁺]Br⁻₂ ·H₂O.⁵⁶ The spectrum of the H(CH₃OH)₃⁺ cation in benzene solution and in the crystal phase as the {Cl₁₁}⁻ salt is essentially the same so the structure of the cation must be very similar in both phases. Since the O⋯O distances in the H(CH₃OH)₃⁺ cation are shorter than those in compounds containing isolated O−H⋯O groups (Table 2), the νOH frequency (cba center of gravity, 1920±40 cm⁻¹) is lower than, for example, in phosphinic acid dimers (2000–2070 cm⁻¹).⁴⁵ Comparing the spectrum of the H(CH₃OH)₃⁺ cation with the α-H₇O₃⁺ cation in benzene solution (Figure 13) close similarity can be seen.

The bands at ∼1300 and 1732 cm⁻¹ in α-H₇O₃⁺ cation correspond to those at ∼960 and ∼1655 cm⁻¹ in H(CH₃OH)₃⁺ and the center of gravity of the cba of α-H₇O₃⁺ practically coincides with that of H(CH₃OH)₃⁺, but in case of β-H₇O₃⁺ it is higher (Table 3). Therefore, the O⋯O distance of α-H₇O₃⁺ must be close to that of 2.455 Å in H⁺(CH₃OH)₃ cation while that in β-H₇O₃⁺ must be longer, approaching the value of 2.481 Å observed in the H₇O₃⁺ ion of [H₇O₃⁺][H₉O₄⁺]Br₂⁻·H₂O. This demonstration of diminished H-bond strength in the (O⋯H−O−H⋯O)⁺ group of β-H₇O₃⁺ compared to that in H(CH₃OH)₃⁺ can be understood in terms of the weaker intrinsic basicity of water versus methanol. Nevertheless, the availability of five terminal OH groups in H₇O₃⁺ instead of two in H(CH₃OH)₃⁺ for H-bonding with the environment must also play an important role. The H₇O₃⁺ cation can more effectively transfer positive charge from (O⋯H−O−H⋯O)⁺ group to the environment via a greater number of H-bonds.

Table 3.

νOH of H(H₂O)_n⁺ and H(CH₃OH)₃⁺ cations determined from the cba center of gravity.

Sample	Solvent	νOH
α-H7O3+{Cl11−}	benzene	1911 ± 40
α-H7O3+{H5Br6−}	DChE	2110 ± 40
β-H7O3+{H5Br6−}	DChE	2285 ± 40
H3O+(H2O)3{Cl11−}	crystal	2390 ± 40
H7O3+·H2O{Cl11−}	benzene	2270 ± 40
H(CH3OH)3+{Cl11−}	benzene	1920 ± 40

A weak blue shift of the cba center of gravity and the νOH frequencies of the terminal OH groups of the β isomer of H₇O₃⁺ compared to those for the α isomer (Table 1, Table 3) indicates a slight weakening of both the internal O⋯H−O−H⋯O core H-bonds and the external H-bonds with the environment in the β isomer. This may reflect different H₇O₃⁺/anion interactions. If aggregates of α-H₇O₃⁺{Cl₁₁⁻} ion pairs are associated with H₅O₂⁺{Cl₁₁⁻} ion pairs, α-H₇O₃⁺ may experience a more spherically symmetric anion field than the unidirectional field of the simple ion paired structure of β-H₇O₃⁺{Cl₁₁⁻}. As shown schematically by II, the polarization of the β cation by the anion weakens its interaction with environment.

H(H₂O)_n⁺ cations with n ≥ 4

The formation of the H(H₂O)₄⁺ cation as an individual entity is detected with higher certainty in the lower permittivity solvent, benzene rather than DCE. As shown in Figure 15, its IR spectrum is very similar to that of β-H₇O₃⁺. The two differences are (a) the νOH* band of the “free” OH* group at 3458 cm⁻¹ is red shifted to the region of ∼3200 cm⁻¹ and (b) there is an increase in the intensity of the ν_asH₂O, ν_sH₂O and δ_H2O (1610 cm⁻¹) bands from an added peripheral H₂O molecule. These changes are readily understood in terms of structure III.

Figure 15.

Spectrum of H(H₂O)₄⁺ (red) compared to β-H₇O₃⁺ (blue) after subtraction of solvent (benzene) and counterion {Cl₁₁⁻}.

Compared to H₇O₃⁺, the OH* group is now H-bonded to H₂O rather than solvent so the νOH* frequency is decreases. The fourth water molecule is not equivalent to the other two peripheral H₂O groups and ν_asH₂O and ν_sH₂O develop as one broad asymmetric band. The absorptions from the core (O⋯H−O−H⋯O)⁺ group are retained nearly unchanged indicating that the H₇O₃⁺ ion remains the fundamental building block. The H₇O₃⁺−H₂O interaction is relatively weak so the H(H₂O)₄⁺ cation is more correctly represented as the monohydrated H₇O₃⁺ cation, i.e. H₇O₃⁺·H₂O.

As noted earlier, the close similarity of the spectroscopic properties of H(H₂O)_n⁺ cations with n ≥ 4 means that these cations all belong to one family of compounds. Their spectra show isosbestic points and the only significant differences arise from absorptions from the increasing number of peripheral water molecules (Figure 16). All the data can be rationalized by the sequential attachment of three water molecules to the H₇O₃⁺ cation in structures III, IV and V for n = 4, 5 and 6 respectively (L = solvent). In each cation, the (O⋯H−O−H⋯O)⁺ structural unit of the H₇O₃⁺ ion is retained as the basic building block.

Figure 16.

IR spectra (red through black) of DCE solutions of H(H₂O)_n⁺{H₅Br₆⁻} with n = 3.02; 3.1; 3.4; 3.7; 4.2; 5.2.

Consistent with these structures, only the spectra for N = 5 and 6 show an increase in intensity of the broad band νOH at 3327 cm⁻¹ (Figure 16) arising from the H-bonded OH groups of semi-hydrated water molecules (designated earlier as type (ii) and indicated in blue in IV and V). This is accompanied by a Fermi resonance band at 3180 cm⁻¹ from the overtone of 2δ_H2O. Finally, the constancy of the δ_H2O frequency at 1608–1610 cm⁻¹ for all cations with n = 3–6 that is in agreement with structures IV and V since they contain closely related peripheral water molecules only of types (i) and (ii).

The H(H₂O)₆⁺ cation with {H₅Br₆⁻} counterion is formed in DCE solution under conditions of water saturation. However, by using alternative carborane acids and extracting them from aqueous solution at varying temperatures, H(H₂O)_n⁺ cations with n > 6 may by obtained. Figure 17 presents the spectra of cations from aqueous H{CCD} extracts with N varying from 5.5–6.5 as well as the spectrum of an H{I₁₁} extract in which N reaches 8.2. In all spectra the absorptions from the core (O⋯H−O−H⋯O)⁺ group remain unchanged as indicated by the constancy of the cba from 3000-1500 cm⁻¹.

Figure 17.

IR spectra of H(H₂O)_n⁺ cations in water-saturated DCE: black, n = 5.5; green, n = 6.0; red, n = 6.5; blue, N = 8.2. The anion is {CCD}⁻ in the black, green and red spectra, {I₁₁}⁻ in the blue. In the inset, the difference of the spectra with n = 8.2 and 5.5 is given to show with higher certainty the appearance of the δH₂O band at 1634 cm⁻¹ of the water molecules of type (iii) in cation VI.

Let us now consider the interaction between the terminal water molecules and H₇O₃⁺ group in more detail. Figure 18 shows the difference spectrum of cations with n = 4 and n = 4.74 in order to reveal the bands associated with the fifth added water molecule. The ν_asH₂O band appears at 3650 cm⁻¹, the lower frequency ν_sH₂O band is masked by other νOH vibrations, and the νOH band from the OH group of the H₇O₃⁺ cation to which the fifth H₂O molecule is H-bonded (type (ii), marked blue in IV) appears at 3350 cm⁻¹. A small shift in the cba to higher frequency (in the range of the A band) results in a broad band at 2980 cm⁻¹. With the exception of a weak δ_H2O band from fifth H₂O molecule, there are no changes below 2500 cm⁻¹. Similar difference spectra of cations are obtained with n = 6 (counterion {CCD⁻}, DCE) and n = 5.2 (counterion {H₅Br₆⁻}, DCE), except that the relative intensity of the band at 2980 cm⁻¹ is weaker. So all changes in the spectra are in accordance with structures III, IV and V. In the difference spectra of cations with n = 6.5 and 5.5 (DCE, CCD⁻ as counterion) the intensities of the bands at 3655, 3400 and 1608 cm⁻¹ increase in accordance with additional water molecules of type (i) or (ii). The cba is not changed. However, for the first time, a δ_H2O band appears at ∼1630 cm⁻¹ (Figure 17 inset). This is assigned to water molecules of type (iii) having both OH groups H-bonded to solvating H₂O molecules. A similar band with higher intensity appears in the difference spectrum of cations with n = 8–9 and n = 5.5. Thus, attachment of the seventh and eight water molecules to H(H₂O)₆⁺ cation leads to cation VI.

Figure 18.

Deconvolution of the difference spectrum between cations with n = 4.52 and n = 4 for benzene solution (counterion {Cl₁₁⁻}).

The structure of the H(H₂O)₇⁺ cation has been determined by X-ray in the crystalline hydrate H₂SiF₆·9.5H₂O.⁵⁷ It comprises the H₇O₃⁺ building block surrounded with five H₂O molecules and one F atom from a SiF₆²⁻ anion as shown in (v).

This is very similar to structure VI proposed for H(H₂O)₈⁺ in solution. The O⋯O distances in the O⋯H−O−H⋯O group of (v) are lengthened to 2.505(2) Å compared with the average of 2.481(x) Å in [H₇O₃⁺][H₉O₄⁺]Br⁻₂ ·H₂O (iv) where the H₇O₃⁺ ion is bonded with only two water molecules. It is evident that increasing the number of H-bonded water molecules solvating the H₇O₃⁺ cation delocalizes the positive charge and weakens H-bonding in the core O⋯H−O−H⋯O unit. The 2.505 Å O⋯O distance is close to that in dimers of dialkylphosphinic acids (2.51–2.52 Å) which is why their cba are quite similar. Structure v reflects the weak H-bonding between the H₇O₃⁺ cation and three solvating water molecules (R_O⋯O = 2.77–2.81 Å). They are comparable to those in neutral liquid water (R_O⋯O = 2.78 Å).⁵⁸ The OH* group forms a somewhat stronger H-bond with R_O⋯O = 2.62 Å, which nevertheless is insufficient to contribute to the cba below 2600 cm⁻¹.

Comparison with gas and solid phases

The structures of H(H₂O)_n⁺ cations in acidified organic solutions are similar to those in the gas phase only when n = 1, 2^7,9 and 3. For n ≥ 4 they can be quite different. In the gas phase, the Gibbs energy dependence of the addition of the n-th molecule of H₂O to the H(H₂O)_n−1⁺ hydrate indicates extra stability of the H(H₂O)₄⁺ and H(H₂O)₆⁺ cations.¹³ Indeed, the stability of H(H₂O)₄⁺ is higher than that of H₇O₃⁺. In organic solvents, the situation is different. The stability of H₃O⁺, H₅O₂⁺ and H₇O₃⁺ is high but starting with the H(H₂O)₄⁺ cation, stability sharply decreases without any particular stability of cations with further increasing n.

In accordance with quantum mechanical calculations^10,19,59 and confirmed by IR spectroscopy,^10,19 the most stable structures for the H(H₂O)₄⁺ and H(H₂O)₆⁺ cations in vacuo are symmetrical structures VII and VIII respectively. However, some calculations (G3B3 and CBS-QB3²² or DFT²¹) predict a slightly higher stability for structure V compared to VIII for H(H₂O)₆⁺ cation. There energy difference is so small that both V and VIII may coexist. In any case, cations H₃O⁺·3H₂O (VII) and H₅O₂⁺·4H₂O (VIII) have also been characterized in the solid phase by X-ray diffraction.^60,61

The gas phase spectrum of VII develops two bands ν_sH₂O = 3644 and ν_asH₂O = 3730 cm⁻¹ from the three equivalent H₂O molecules surrounding the H₃O⁺ ion and a broad band of ν_as and ν_s at 2665 cm⁻¹ for the central H₃O⁺.¹⁰ In the crystalline state of [H₃O⁺·3H₂O]{Cl₁₁}⁻ the OH stretch frequencies from H₃O⁺ occur as a coalesced broad band at lower frequency, 2576 cm⁻¹ (Figure 19), because the three H-bonded water molecules are made more basic by the anion environment. A combination band appears at 2291 cm⁻¹. The frequencies of the three terminal water molecules of H₃O⁺·3H₂O appear at ν_as 3637, ν_s 3578 and δ_H2O 1605 cm⁻¹ bands. In the low frequency region, a weak band appears ∼1200 cm⁻¹, possibly ν₂H₃O, overlapped with strong bands from counterion. The spectrum is also very similar to that of the C_3v symmetric H₃O⁺·3TBP cation, an analogue of VII.²⁷ The slightly higher basicity of TBP compared to H₂O results in a small red shift νOH to 2530 cm⁻¹ and the combination band to 2206 cm⁻¹.

Figure 19.

IR spectra of H(H₂O)₄⁺{Cl₁₁⁻} (N = 3.91) in benzene (red), crystalline [H₃O⁺·3H₂O] {Cl₁₁⁻} (blue) and [H₃O⁺·3TBP] FeCl₄⁻ in CCl₄ (black dashed). Red and blue are normalized to unit intensity of anion.

Comparing the spectrum of the symmetrical H(H₂O)₄⁺ cation in [H₃O⁺·3H₂O]{Cl₁₁}⁻ with that in solution reveals differences ascribable to different structures: the symmetrical Eigen-type H₃O⁺·3H₂O cation in the crystal and the less symmetrical H₇O₃⁺·H₂O cation in benzene or DCE solution (Figure 19). They show some similarities in the cba region, originating from conjugated O−H⋯O group vibrations, but nevertheless there are important distinctions in the distribution of the cba intensity that defines the νOH frequencies. For the H₇O₃⁺·H₂O cation in benzene solution, νOH is about 120 cm⁻¹ lower than in the H₃O⁺·3H₂O cation (Table 3). This reflects shorter O⋯O distances in the O⋯H−O−H⋯O core of the H₇O₃⁺·H₂O cation compared to O−H⋯O in H₃O⁺·3H₂O. In the X-ray structure of [H₇O₃⁺][H₉O₄⁺]Br⁻₂·H₂O⁵⁶ where both cations appear in the same crystal this difference is 2.48(1) versus 2.56(1) Å (averaged over equivalent bonds). The average O⋯O distance in the H₃O⁺·3H₂O cation is 2.51(2) Å⁶⁰ with {H₅Br₆}⁻ as counterion and 2.530(2) Å with {Cl₁₁}⁻.

Similarly, a comparison of the H(H₂O)₆⁺ cation in solution versus the gas phase or a symmetrical crystal environment reveals considerable structural differences. For the gas phase, the measured and calculated IR spectra provide evidence that the H(H₂O)₆⁺ cation has a H₅O₂⁺ core.^10,19 However, other calculations based on different levels of theory predict that the lowest energy state in vacuo of the tetrahydrated H₅O₂⁺ ion, namely H₅O₂⁺·4H₂O cation VIII, is insignificantly lower (or even higher) than that for the H₇O₃⁺·3H₂O ion (V).^21,22 For the crystal state, only one example of a type VIII cation is known. It is found in the strictly symmetric Cl⁻ anion environment of a cage compound [(C₉H₁₈)₃(NH₂)₂Cl]⁺Cl⁻ crystallized from HCl solution.⁶¹ In the solutions of the present study, the IR data on H(H₂O)₆⁺ retain the characteristics of the H₇O₃⁺ core, indicating formulation as the H₇O₃⁺·3H₂O ion, structure V. Since the vibrations of the O⋯H−O−H⋯O core of H₇O₃⁺·nH₂O cations in solution with n ≥ 6 are very similar to those from the O−H⋯O group of phosphinic acid dimers, the O⋯O distances should be similar. They are ∼2.49–2.53 Å for phosphinic acid dimers.^46,47,62 The average O⋯O distance in the core of the H₇O₃⁺·4H₂O cation in the SiF₆²⁻ salt is 2.505 Å.⁵⁷ Therefore, in H(H₂O)_n⁺ cations with n ≥ 6 in solution the O⋯O distances should be ca. 2.51 Å. By comparison, the central O⋯O distance in H₅O₂⁺·4H₂O should be ca. 2.39(2) Å as in crystal state.⁶¹ This distance is typical for L−H⁺−L proton disolvates with strong L bases, such as diethylether.^54,63 These cations, including H₅O₂⁺, develop intense bands in the 800–1000 cm⁻¹ region from O−H⁺−O group vibrations^7,54,63. In accordance with DFT/B3LYP and MP2 calculations,⁶⁴ complexation of the H₅O₂⁺ cation with four H₂O molecules only marginally influences the frequency and strong intensity of these bands. However, they are absent in the spectra of H₇O₃⁺·3H₂O in solution.

Thus, the Eigen and Zundel-type symmetrical cations H₃O⁺·3H₂O VII and H₅O₂⁺·4H₂O VIII exist in gas phase where counterions are absent. Rare cases also exist in the solid phase where the cation happens to be nearly symmetrically surrounded by anions or other ligands. In solutions with aprotic solvents such as benzene and chlorinated hydrocarbons, the one-dimensional electrostatic influence of the anion in solvent-separated ion pairs results in higher stability of the H₇O₃⁺·H₂O cation with structure III and H₇O₃⁺·3H₂O with structure V.

The present results better allow us to appreciate the similarities and differences of the excess proton in water versus methanol.³³ In benzene solution with carborane counterions, the H(H₂O)_n⁺ and H(CH₃OH)_n⁺ cations have similar spectra and structures for n = 2 and 3. At n = 4, however, different core structures become the building blocks for higher solvation. This occurs because the O-H* group in H₇O₃⁺ is replaced by an O-CH₃ group in H(CH₃OH)₃⁺ and is therefore unavailable for H-bonding. Water clusters can grow in dendritic fashion whereas methanol clusters are forced to grow as linear chains. As a result, methanol clusters grow linearly as unique cations up to n = 4, each with individual spectral properties. Solvation continues up to n = 8 chains retaining the properties of the H(CH₃OH)₄⁺ core.³³ On the other hand, water clusters cease to develop unique cations after n = 3, retaining the H₇O₃⁺ core.

Conclusions

Study of the stepwise bonding of water molecules to H⁺ in weakly basic solvents with weakly basic anions shows that the first three hydrates, namely H₃O⁺, H₅O₂⁺ and H₇O₃⁺, behave as individual ions with unique and distinctive structures and IR spectra. Additional water molecules are H-bonded to the H₇O₃⁺ cation via stepwise replacement of organic solvent molecules from its first coordination sphere via Eq. 1 and Figure 20.

$$[{\mathrm{H}}_7{{\mathrm{O}}_3}^{+}·{(\text{Solv})}_5]+m{\mathrm{H}}_2\mathrm{O}\to [{\mathrm{H}}_7{{\mathrm{O}}_3}^{+}·{(\text{Solv})}_{5-\mathrm{m}}{({\mathrm{H}}_2\mathrm{O})}_{\mathrm{m}}]+m\text{Solv}$$ (1)

Figure 20.

The H₇O₃⁺·(Solv)₅ cation showing the structurally distinct sites of the first solvation shell. Site 1 is hydrated first, then sites 2 and 3, and finally sites 4 and 5.

Hydration of the H₇O₃⁺·(Solv)₅ ion occurs first at the strongest coordination position, site 1. The second and third H₂O molecules replace solvent molecules at positions 2 and 3 forming the H⁺(H₂O)₆ cation which is stable with all studied counterions in both benzene and DCE. Finally, with some of the studied counterions in DCE solvent, two further H₂O molecules can be introduced in positions 4 and 5 to form the less stable H⁺(H₂O)₈ cluster, completing the first coordination sphere of H₇O₃⁺ cation. There are detectable changes in the spectrum of the H₇O₃⁺ ion as it is solvated by 1–3 water molecules but the core structure is retained for all m. Comparisons of IR data and X-ray data lead to the conclusion that in H(H₂O)_n⁺ cations with n > 4 the two O⋯O distances in conjugated O⋯H−O−H⋯O group, where the excess proton resides, are ca. 2.51 Å.

Notably, neither Eigen-type structures with the H₃O⁺ core nor Zundel-type structures with the H₅O₂⁺ core are present. This finding is contrary to popular expectation and contrary to calculation and experiment in the gas phase. It reflects the unfortunate fact that perceptions regarding the nature of the aquated proton in solution have become too biased by calculations and experiments in the gas phase, where counterions are absent. The present work suggests that the obligatory presence of a counterion in solution, no matter how weakly coordinating, exerts an anisotropic electrostatic influence on H(H₂O)_n⁺ cations that has been largely ignored. The presence of the conjugate base of the acidic H(H₂O)_n⁺ cations is the principal reason that different structures exist in the condensed phase vis à vis the gas phase. The question about where the positive charge is localized has been typically been phrased in terms of Eigen and/or Zundel type ions, i.e. on one water molecule, or shared between two. For the presently studied H(H₂O)_n⁺ clusters the excess proton is localized between three oxygen atoms and the positive charge influences up to six water molecules. Additional water molecules above n = 6 are essentially indistinguishable from bulk water.

The next challenge will be to determine experimentally the nature of H(H₂O)_n⁺ in liquid water. Most theory focuses on Eigen versus Zundel ions,¹¹.¹² or a continuum of structures in between,⁶⁵ although one study favors H₇O₃⁺ as the major ion present.⁶⁶ The present work provides an excellent experimental fingerprint for this ion.