Myths about the Proton. The Nature of H⁺ in Condensed Media

CONSPECTUS

Recent research has taught us that most protonated species are decidedly not well represented by a simple proton addition. What is the actual nature of the hydrogen ion (the “proton”) when H⁺, HA, H₂A⁺ etc. are written in formulae, chemical equations and acid catalyzed reactions? In condensed media, H⁺ must be solvated and is nearly always di-coordinate – as illustrated by isolable bisdiethyletherate salts having H(OEt₂)₂⁺ cations and weakly coordinating anions. Even carbocations such as protonated alkenes have significant C-H---anion hydrogen bonding that gives the active protons two-coordinate character.

Hydrogen bonding is everywhere, particularly when acids are involved. In contrast to the normal, asymmetric O-H---O hydrogen bonding found in water, ice and proteins, short, strong, low-barrier (SSLB) H-bonding commonly appears when strong acids are present. Unusually low frequency IR νOHO bands are a good indicator of SSLB H-bonds and curiously, bands associated with group vibrations near H⁺ in low-barrier H-bonding often disappear from the IR spectrum.

Writing H₃O⁺ (the Eigen ion), as often appears in textbooks, might seem more realistic than H⁺ for an ionized acid in water. However, this, too, is an unrealistic description of H_(aq)⁺. The dihydrated H⁺ in the H₅O₂⁺ cation (the Zundel ion) gets somewhat closer but still fails to rationalize all the experimental and computational data on H_(aq)⁺. Researchers do not understand the broad swath of IR absorption from H_(aq)⁺, known as the “continuous broad absorption” (cba). Theory has not reproduced the cba, but it appears to be the signature of delocalized protons whose motion is faster than the IR timescale. What does this mean for reaction mechanisms involving H_(aq)⁺?

For the past decade, the carborane acid H(CHB₁₁Cl₁₁) has been the strongest known Brøsted acid. (It is now surpassed by the fluorinated analogue H(CHB₁₁F₁₁).) Carborane acids are strong enough to protonate alkanes at room temperature, giving H₂ and carbocations. They protonate chloroalkanes to give dialkylchloronium ions, which decay to carbocations. By partially protonating an oxonium cation, they get as close to the fabled H₄O²⁺ ion as can be achieved outside of a computer.

1. Introduction

Writing H⁺ for the proton covers a multitude of sins. The problem begins with nomenclature. We are wedded to calling H⁺ a proton when we really mean a hydrogen ion or hydron.¹ A proton is an electron-free elementary particle of physics or the ¹H isotope. It would be quixotic to try and change our habits in this regard. The use of “the proton” is far too useful. But to put this into perspective, an electron-free proton has an estimated acidity 10⁵⁶(!) times greater than 100% H₂SO₄, the threshold of superacidity.² Adding a bare proton to a molecule is a real event in the gas phase but only a solvated hydrogen ion can be transferred in condensed phases.

Semantics aside, what is the real identity of a protonated species in condensed media? The size and mobility of the actual proton carrier is important throughout biology, particularly where proton pumping³ and accessibility to a reaction center is important.⁴ The prevalence of water molecules over amino acid residues as H⁺ carriers has been noted,⁵ giving importance to the structure and proton mobility of H(H₂O)_n⁺ species in proteins and protein-like environments (i.e. organic solvents). The degree of water solvation of H⁺ markedly affects the rates of protonation chemistry,⁶ particularly in proton relay (shuttle) mechanisms^7–9 and coupled proton/electron transfer.¹⁰

Most protonation reactions are misrepresented by a simple proton addition. A self-ionizing acid HA is very unlikely to form a mono-protonated H₂A⁺ cation, as is commonly written (Eq. 1)

$$2\mathrm{H}\mathrm{A}={\mathrm{H}}_2{\mathrm{A}}^{+}+{\mathrm{A}}^{-}$$ (1)

More likely is a two-coordinate core cation, [HA⋯H⁺⋯AH], with positive charge delocalization extended through additional H-bonded HA molecules.¹¹ It is better represented by Eq. 2.

$$3\mathrm{H}\mathrm{A}=[\mathrm{H}\mathrm{A}\cdots {\mathrm{H}}^{+}\cdots \mathrm{A}\mathrm{H}]+{\mathrm{A}}^{-}$$ (2)

Correctly and widely recognized is the di-solvated salt of the H(OEt₂)₂⁺ cation formed when strong acids dissolve in diethyl ether (Fig. 1).¹² Indeed, a major lesson learned from the past decade of research on H⁺ in condensed phases is that the hydrogen ion is almost invariably two-coordinate. Even the seemingly mono-coordinate H⁺ of the benzenium ion, derived from protonating benzene, has substantial C-H⋯anion hydrogen bonding at the protonated carbon atom (Fig. 2).¹³ Similarly, t-butyl cation (i.e. protonated iso-butene) salts are significantly stabilized by C-H⋯anion H-bonding¹³ (possibly trumping hyperconjugation¹⁴), again illustrating the propensity of acidic H atoms to become two-coordinate (or higher, when bifurcated CH hydrogen bonding is involved). See Fig. 3.¹⁴

FIGURE 1.

The historic early X-ray structure of the H(OEt₂)₂⁺ cation¹² that showed two-coordination of H⁺ and captured the essence of the delocalized or averaged location of H⁺ involved in short, strong, low-barrier (SSLB) H-bonding.

FIGURE 2.

X-ray structure of the benzenium ion salt [C₆H₇⁺][CHB₁₁Me₅Br₆⁻]³³ showing CH⋯·Br hydrogen bonding of the acidic CH₂ group at the protonated C atom.

FIGURE 3.

X-ray structure of the t-butyl cation salt [C₄H₉⁺][CHB₁₁Cl₁₁⁻] showing CH⋯·Cl hydrogen bonding, some of which is bi-furcated (e.g. to H3A, H3B and H3C).¹⁴

Writing H₃O⁺ (the Eigen ion)¹⁵ might seem more realistic than H⁺ for an ionized acid in water but this too is a highly inaccurate description of H_(aq)⁺ that still appears regularly in textbooks. The two-coordinate hydrogen ion in the H₅O₂⁺ cation (the Zundel ion)¹⁶ gets closer but still fails to fully rationalize the IR spectrum of H_(aq)⁺.^17,18 In contrast to the typical asymmetric H-bond found in proteins (N-H⋯O) or ice (O-H⋯O), the short, strong, low-barrier (SSLB) H-bonds found in proton disolvates, such as H(OEt₂)₂⁺ and H₅O₂⁺, deserve much wider recognition.

The tendency to think of protonation in terms of a simple H⁺ addition is not just due to the ease of writing it that way. For the past four decades, experimental studies on protonation have been largely confined to the gas phase where, because of low pressure, the shared-proton H⁺ species found in condensed phases are rarely encountered. Moreover, the accompanying emphasis on theoretical descriptions of protonation frequently involved computations that omitted anions and treated solvents in an abstract manner. Earlier still, in the pioneering experimental work of Gillespie¹⁹ and Olah²⁰ in liquid superacids, protonation targets were typically at low concentration compared to acid. So mono-protonation was also the expected result. However, such superacidic media are rarely used in everyday acid/base chemistry and, in the important areas of acid catalysis and biological acidity, low concentrations of H⁺ are the rule. And with that comes proton di-solvation.

This Account highlights recent insights into the nature of H⁺ in condensed media from our labs. Particular interests have been (a) making the strongest acid, (b) approaching the dicationic H₄O²⁺ ion, (c) the prevalence of di-solvation of H⁺, (d) IR criteria for short, strong, low barrier (SSLB) H-bonding, (e) the nature of H(H₂O)_n⁺ cations in wet (i.e., typical) organic solvents, and (f) the unique nature of H⁺ in water, one of the oldest unsolved problems in chemistry.

2. The Strongest H⁺ Acid

For the last decade, the strongest pure acid has been the carborane acid H(CHB₁₁Cl₁₁)^21,22 or possibly the comparable isoelectronic, diprotic H₂(B₁₂Cl₁₂).²³ This has been established in all phases: in solution using the Fărcaşiu²⁴ mesityl oxide Δδ¹³C NMR method in liquid SO₂ and by the fact that these acids protonate benzene, in the solid state as trioctylammonium salts using the νNH IR anion basicity scale,²⁵ and in the gas phase by calculating²⁶ and measuring²⁷ record-low deprotonation enthalpies. High solution acidity can of course be obtained with traditional mixed Brøsted/Lewis acids e.g., Magic Acid (HFSO₃/SbF₅) but the presence of redox-active Lewis acids such as SbF₅ introduces significant disadvantages: corrosiveness and basicity suppression.²⁸

Carborane acids are said to be “strong yet gentle” because, despite their great acid strength, they do not engage in the corrosive redox chemistry of traditional mixed superacids. This is because of the extraordinary inertness of carborane anions²⁹ compared to the oxyanions and haloantimonates of traditional superacids. As a consequence, protonation chemistry via carborane acids is frequently cleaner than with traditional superacids, and this has led to the easier isolation of fragile species such as protonated C₆₀,³⁰ phosphabenzenes, phosphazenes, etc. and imparted remarkable stability to classic cationic intermediates of organic chemistry: t-butyl⁺ (Fig 3), the C₆H₇⁺ benzenium ion (Fig. 2), etc.²⁸

With the potential exception of acids based on perfluoroalkylsulfonamide analogues of triflic acid³¹ or by using cooperative strategies,³² the prospects for synthesizing a class of acids stronger than carborane acids appear slim. Quite simply, there does not appear to be any other class of anion that fits the duel requirements of lower basicity than a carborane anion and, critically, chemical stability towards H⁺. Anions such as perfluorinated tetraarylborates are weaker bases than carboranes²⁵ but they decompose when attempts are made to prepare their conjugate acids.³³

Perfluorinated CB₁₁ carborane or B₁₂ boron cluster anions³⁴ are less basic than their perchlorinated counterparts^25,26 so the conjugate acid H(CHB₁₁F₁₁) is expected to be stronger than the currently published strongest acid, H(CHB₁₁Cl₁₁). The preparation of H(CHB₁₁F₁₁) has very recently been achieved in our lab³⁵ and a demonstration of its superior acidity is seen in the protonation of alkanes. Remarkably, H(CHB₁₁F₁₁) protonates butane to form t-butyl cation at room temperature whereas H(CHB₁₁Cl₁₁) requires elevated temperatures to carry out the same reaction (Eq. 3).

$${\mathrm{C}}_4{\mathrm{H}}_{10}+\mathrm{H}(\mathrm{C}\mathrm{H}{\mathrm{B}}_{11}{\mathrm{F}}_{11})\to [t-\mathrm{B}{\mathrm{u}}^{+}][\mathrm{C}\mathrm{H}{\mathrm{B}}_{11}{\mathrm{F}}_{11}]+{\mathrm{H}}_2$$ (3)

Thus, H(CHB₁₁F₁₁) is now the strongest pure acid known. Unfortunately, it is a lot of work to synthesize even small amounts and its ultra-high acidity is easily lost via hydration by adventitious water when [H(H₂O)_n⁺][CHB₁₁F₁₁⁻] salts are formed.

One recent intriguing application of the strength of H(CHB₁₁Cl₁₁) is the demonstration by IR of H-bonding to the lone pair of an oxatriquinane cation.³⁶ Oxatriquinanes are tricyclic analogues of the H₃O⁺ ion (Scheme 1). H-bonding to the remaining lone pair of the O atom octet (Fig. 4) is as close as one can get, outside of a computer, to the formation of a tetravalent oxygen species with a formal 2+ charge, i.e. an analogue of the H₄O²⁺ ion.

SCHEME 1.

Analogy of an oxatriquinane oxonium cation (left) to the H₃O⁺ ion (right).

FIGURE 4.

Graphical representation of the H-bond between the oxatriquinane cation and H(CHB₁₁Cl₁₁).³⁶

Another illustration of the acid strength of H(CHB₁₁Cl₁₁) is the ready protonation of chlorocarbons. For example, chloroethane is protonated with loss of HCl (Eq. 4) to give isolable diethyl chloronium ion salts³⁷ which decay to previously unrecognized oligomeric carbocations.³⁸

$$2\mathrm{E}\mathrm{t}\mathrm{C}\mathrm{l}+\mathrm{H}(\mathrm{C}\mathrm{H}{\mathrm{B}}_{11}\mathrm{C}{\mathrm{l}}_{11})\to [\mathrm{E}\mathrm{t}\mathrm{C}\mathrm{l}{\mathrm{H}}^{+}][\mathrm{C}\mathrm{H}{\mathrm{B}}_{11}\mathrm{C}{{\mathrm{l}}_{11}}^{-}]+\mathrm{E}\mathrm{t}\mathrm{C}\mathrm{l}\to [\mathrm{E}{\mathrm{t}}_2\mathrm{C}{\mathrm{l}}^{+}][\mathrm{C}\mathrm{H}{\mathrm{B}}_{11}\mathrm{C}{{\mathrm{l}}_{11}}^{-}]+\mathrm{H}\mathrm{C}\mathrm{l}$$ (4)

The linear polymeric structure of H(CHB₁₁Cl₁₁)³⁹ nicely illustrates the propensity of strongly acidic protons to be two-coordinate (Fig. 5). Although the bridging acidic protons cannot be located with certainty in the X-ray structure, the IR spectrum is notable for the lack of bands in the range 2000–2500 cm⁻¹, the normal region for νHCl bands. Only broad bands at low frequency are visible, indicating that H⁺ is located more symmetrically between Cl atoms on carborane anions. The IR is indicative of short, strong, low-barrier (SSLB) H-bonding^40,41 which has been studied more fully in proton disolvates with O-atom donors, described in the following section.

FIGURE 5.

The X-ray structure of the carborane acid H(CHB₁₁Cl₁₁)³⁹ showing bridging, di-coordinate H⁺ (white); green = Cl, orange = B, gray = C.

3. Two-coordination and SSLB Hydrogen Bonding

There is a high level of awareness of proton di-solvation in salts of the H(OEt₂)₂⁺ cation because of the wide utility of this oxonium salt in organometallic chemistry.^42,43 More recently, the generality of HL₂⁺ proton disolvates has been established with a variety of O-atom and N-atom donor solvents (L = ethers, ketones, amines, etc.) using weakly coordinating counterions (carboranes, oxyanions such as ClO₄⁻, complex haloanions such as SbX₆⁻).⁴⁴ Acetonitrile is a more complicated solvent giving rise to many byproducts from protonation.⁴⁵ More coordinating anions such as Cl⁻ can of course replace a solvent molecule but two-coordinated H⁺ is usually .

When subjected to X-ray crystal analysis, most proton disolvates of O-atom solvents show characteristically short O⋯·O separations in the range 2.37–2.43 Å.⁴⁴ These can be compared to the longer average distance of ca. 2.56 Å found in ice or in protonated water clusters where normal, unsymmetrical O-H⋯O hydrogen bonding is present.^46,47 Short O⋯·O distances are an indicator of low-barrier H-bonding.^40,41 The proton potential energy diagrams for these two types of H-bonding are illustrated qualitatively in Fig. 6. The barrier for H⁺ motion within an interval between the O atoms (see gray box around H in Fig. 6, right) is so low that the location of H⁺ becomes indeterminate, with unusual consequences for the IR spectrum. Conceptually, a completely flat-bottomed potential may exist but evidence is found only in certain neutron diffraction studies of carboxylate dimers.⁴⁸ The use of the word “strong” in “short, strong, low-barrier” (SSLB) does not imply that the low barrier imparts any particular additional bond strength to the H-bond.⁴⁸ It simply means that low-barrier H-bonds occur in the general realm of relatively strong H-bonding.

FIGURE 6.

Proton potential energy diagrams illustrating (left) normal, unsymmetrical H-bonding and (right) short, strong, low-barrier (SSLB) H-bonding.

A convenient indicator of short, strong, low-barrier (SSLB) H-bonding is the very low frequency of νOHO. Instead of νOH in the familiar range near 3000 cm⁻¹, a diagnostic band appears near 1000 cm⁻¹.⁴⁴ It is found not only in salts of the H(OEt₂)₂⁺ ion, but also in proton disolvates of dimethylsulfoxide, nitrobenzene and tetrahydrofuran.⁴⁴ Its migration from 3296 cm⁻¹ in Et₂OH⁺(Xe) to 840 cm⁻¹ in H(OEt₂)₂⁺ as a function of di-solvate symmetry, has been detailed in the gas phase.⁴⁹

A poorly understood feature of the IR spectra of proton disolvates in condensed phases is that IR bands associated with groups adjacent to H⁺, such as νCO in H(Et₂O)₂⁺ or νCO and δCOH in H(CH₃OH)₈⁺,⁵⁰ lose much of their intensity or disappear entirely.⁵¹ This has been discussed in terms of delocalization of the proton along the flat bottom of its potential well and is consistent with an indeterminate position of H⁺ within an interval between the two O atoms. In a static description, this is equivalent to an extreme case of inhomogeneous broadening where neighboring chromophores are subject to a highly varied charge distribution and their absorption bands lose their definition. In a kinetic description, motion of the proton in the L-H⁺-L moiety is fast on the vibrational time scale and produces rapid modulation of the force constants in neighboring vibrations. This issue becomes even more important in the IR spectrum of H_(aq)⁺, discussed in section 5, where a continuous broad absorption (cba) appears across the entire IR spectrum.

4. Nature of H(H₂O)_n⁺ in Organic Solvents

Most acid catalysis is carried out in polar organic solvents. What is the nature of an acid under these conditions? If the solvent is relatively polar and is rigorously dry, then the likely species is a disolvated cation, H(solv)₂⁺, as described above. However, it is difficult to maintain solvents much drier than 10⁻⁴ M water during normal lab usage and, since water is more basic than most organic solvents, dissolved acids are likely to be hydrated. This does not necessarily mean they are ionized to H(H₂O)_n⁺ cations. In wet dichloroethane, the strong NH-type acid bis(trifluoromethylsulfonyl) imide simply forms an H-bonded complex with water, (CF₃SO₃)₂N-H ⋯OH₂, rather than ionizing.⁵² This contrasts with triflic acid which, although of similar acid strength, ionizes to CF₃SO₃⁻⋯H₃O⁺ ion pairs. The difference can be understood in terms of anion polarizability and the specific geometry of the anion donor atoms. Ion pairing is the rule rather than the exception when considering ionized acids in organic solvents. This can be deduced from the sensitivity of the IR spectra of solutions of H(H₂O)_n⁺ salts to anion variation in the following.

H₃O⁺ (Eigen ion)

Conditions for the existence of the C_3v H₃O⁺ ion are much more exacting than previously appreciated and the IR criteria used for three decades for its identification have been shown to be incorrect.⁵³ For H₃O⁺ to be present, there must be a linear dependence between the frequencies of ν_max(OH) and δ(OH₃) within the ranges 3010-2536 cm⁻¹ for ν_max(OH) and 1597–1710 cm⁻¹ for δ(OH₃). H₃O⁺ is always tri-solvated with solvent molecules or weakly basic anions via three H-bonds. One novel structure of the H₃O⁺ ion is that in [H₃O·3C₆H₆][CHB₁₁Cl₁₁] whose X-ray structure shows three O-H⋯π hydrogen bonds (Fig. 7).⁵⁴ The O-H bonds are directed towards π electron density just inside of the C₆ ring, not at its center. This interaction explains why low n H(H₂O)_n⁺ carborane salts have a useful degree of solubility in arene solvents, despite low solvent permittivity. Outside of the range of solvent basicity bound at the lower end by chloroalkanes and the upper end by water or tributyl phosphate, and with anions that do not meet the stringent requirements of weak basicity, low polarizability and high chemical stability, lower symmetry species are formed. One H-bond from H₃O⁺ to the surrounding bases becomes stronger than the other two and for bases (B) stronger than tributyl phosphate, H₂O-H⁺-B type species are formed that are more closely related to the H₅O₂⁺ ion than to H₃O⁺.

FIGURE 7.

Perspective view O-H⋯·π H-bonding in the X-ray structure of the cation in [H₃O·3C₆H₆][CHB₁₁Cl₁₁].⁵⁴

H₅O₂⁺ (Zundel ion)

Like the H₃O⁺ ion, the H₅O₂⁺ ion is only formed under selected conditions of water concentration and particular strong acids, such as carborane acids. It is the favored ion for a number of strong acids in wet acetonitrile.⁵⁵ In our experience, this ion is always tetra-solvated with traditional H-bonds from the four terminal OH groups, i.e., H₅O₂⁺·4Solv. One early structure, trapped in a cryptand, has four solvating water molecules, making a H₁₃O₆⁺ ion that is best formulated as H₅O₂⁺·4H₂O.⁵⁶ In most solid state structures, however, H-bonds to the counterion replace most or all of the solvent molecules. For example, [H₅O₂⁺·C₆H₆][CHB₁₁Cl₁₁⁻] has one O-H⋯π interaction with benzene and three O-H⋯Cl interactions with the carborane anion.⁵⁷

As with the HL₂⁺ proton disolvates discussed in section 3 above, the most distinctive feature of the IR spectrum of the H₅O₂⁺ ion is the broad, low-frequency νOHO band at ca. 1000 cm⁻¹ arising from the central, short, strong, low-barrier (SSLB) H-bond.⁵³ Its quantum nature has been studied in the gas phase.⁴⁹ The other distinctive feature of the IR spectrum of the H₅O₂⁺ ion, in condensed phases, is the disappearance of the δH₂O band. As discussed above, the broadening or disappearance of bands in all HL₂⁺ species having SSLB H-bonds can be understood in terms of the motion and indeterminate position (i.e., distribution) of the bridging proton in its flat-bottomed potential well.

H₇O₃⁺ ions

Contrary to general expectation and data from gas phase experiments, neither the trihydrated Eigen ion, H₃O⁺·(H₂O)₃, nor the tetrahydrated Zundel ion, H₅O₂⁺·(H₂O)₄, are good representations of H⁺ when acids ionize in wet organic solvents, i.e., the common condition of solvents in most acid-catalyzed chemistry, where the water concentration produces H(H₂O)_n⁺ ions for n >3. Rather, the core ion structure is H₇O₃⁺ (Fig. 8).⁵⁷ This finding reflects the unfortunate fact that perceptions regarding the nature of the aquated proton in solution have, over the past three decades, become too biased by calculations and by experiments in the gas phase, where counterions are absent. 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. Prevalent ion pairing drives the structure away from the higher symmetry Eigen- and Zundel-type ions, i.e., with H⁺ delocalized over one or two water molecules, towards the H₇O₃⁺ ion where H⁺ is delocalized over three water molecules. The overall positive charge can influence up to five additional solvating molecules via H-bonding.

FIGURE 8.

The H₇O₃⁺ ion core typical of H(H₂O)_n⁺ in organic solvents⁵⁸ plus additional H-bonding to as many as five solvent molecules (or anion donor atoms).

The H₇O₃⁺ ion has its own unique and distinctive IR spectrum that allows it to be distinguished from alternate formulations of the same stoichiometry, namely H₃O⁺·2H₂O and H₅O₂⁺·H₂O.⁵⁸ It has its own particular brand of low-barrier H-bonding involving the 5-atom OH-O-H-O core and it has somewhat longer O⋯·O separations than in the H₅O₂⁺ ion. Because of its core symmetry, the five peripheral O-H bonds offer three distinct sites for H-bonding to solvents, water and counterions. The central OH site of the C_2v O-H-O-H-O framework (labeled 1 in Fig. 8) has the highest affinity for H-bonding, a consequence of being closest to the center of positive charge.

5. The Unique Structure of H⁺ in water

The first question to be answered about the “excess proton” in water is the extent of influence of positive charge, i.e., how many water molecules solvate H⁺? Because the subtraction of background water solvent from the IR spectrum of H(H₂O)_n⁺ is difficult, this fundamental question had not been seriously addressed before. From exacting difference IR spectroscopy,¹⁷ the answer is six. This means that H_(aq)⁺ is an H₁₃O₆⁺ ion. This immediately rules out an Eigen ion formulation where symmetry requires H₉O₄⁺ or H₁₅O₇⁺ stoichiometries. A tetrahydrated Zundel ion of formula H₅O₂⁺·4H₂O begins to look more viable but IR spectroscopy and X-ray crystallography indicate something unique and different.

The IR spectrum of H_(aq)⁺ is shown in Fig. 9 (red).¹⁷ The five band spectrum (green deconvolution) is notably simple, consistent with a highly symmetrical species. It is distinctly different from that of Eigen-type species.¹⁸ One band is missing, the δH₂O band, indicating low barrier H-bonding is present. There is some resemblance to Zundel-type species but the so-called “Zundel marker band”, associated with the central νOHO band, has an anomalous frequency that suggests a longer central O⋯·O separation than those in typical SSLB H₅O₂⁺ tetrasolvates (2.39–2.45 Å). The X-ray crystal structure of H(CHB₁₁I₁₁)·8H₂O, which is made up of nanotubes of H_(aq)⁺ enclosed by cylindrical walls of CHB₁₁I₁₁⁻ anions,⁵⁹ provides the only existing model for the structure of the H₁₃O₆⁺ ion in liquid water. It shows an H₁₃O₆⁺ ion with a central O⋯·O separation of 2.57 Å. Such a long distance is unprecedented in a symmetrical species. It appears to be a function of the high degree of hydration of H⁺ in this particularly crystal, making it more like liquid water than in any previous X-ray structure.

FIGURE 9.

The IR spectrum of H(aq)⁺ (red) and its deconvolution into five bands (green) plus an underlying continuous broad absorption (blue). The points of inflexion in the red spectrum near 1630 and 1050 cm⁻¹ are artifacts.

Thus, IR and X-ray data indicate that the structure of H_(aq)⁺ is the unique H₁₃O₆⁺ ion shown in Fig. 10. It should be named the Stoyanov ion after my collaborator who carried out all the meticulous IR work to establish its nature experimentally. It differs from the structure favored by theory that treats H_(aq)⁺ as a charge defect⁶⁰ and which, in adopting a distorted Eigen ion structure, reproduces neither the present IR spectrum nor the long O⋯·O distance.

FIGURE 10.

The structure of the H₁₃O₆⁺ ion with a long central O··H⁺··O distance representative of H(aq)⁺. Typical ion-pairing is also shown. The dashed blue circle indicates the extent of positive charge delocalization.

A particularly interesting and unique part of the IR spectrum of H_(aq)⁺ is the continuous broad absorption (cba) shown in Fig. 9 (blue).¹⁸ This distinctive featureless plateau spreads across nearly the entire IR frequency range and is not to the same as the broad so-called ABC features⁶¹ seen in other H-bonded systems.⁶² The cba is clearly a manifestation of unique, low-barrier H-bonding within the unique five-H-atom core of the H₁₃O₆⁺ Stoyanov ion whose proton dynamics are faster than the IR timescale. We estimate that the cba accounts for ca. 70% of the IR absorption of H_(aq)⁺ at room temperature, the remaining 30% being manifest in the normal line spectrum (green in Fig. 9). As expected, the ratio of the intensity of the cba to that of the line spectrum appears to get smaller with decreasing temperature.⁶³ The reproduction of these features creates an exacting test for theory.

What does it mean for reaction mechanisms when the proton dynamics in the H₅O₂⁺ core of 70% of H_(aq)⁺ ions are faster than the IR timescale? According to the Jencks principle,⁶⁴ eloquently enunciated by Cox,⁶⁵ a species cannot be an intermediate in a reaction if it does not exist on the IR timescale under the conditions of the reaction. For the purposes of the H₁₃O₆⁺ ion, this means that H⁺ is available instantaneously from its H₅O₂⁺ core and the rate of H⁺ transfer to any substrate will be dependent only on the timescale of Grotthuss proton hopping⁶⁶ through the outer solvation shell of the H₅O₂⁺ core, i.e., through one or two water molecules. Thus, mechanisms of proton transfer in aqueous solution should be written in terms of H₁₃O₆⁺ or H_(aq)⁺ but only one or two water molecules solvation of H⁺ will appear in the rate equation. Ironically, this gives an accidental reality to mechanisms written in terms of Eigen (H₃O⁺) or Zundel (H₅O₂⁺) ions but the H₁₃O₆⁺ description is the accurate identity of H_(aq)⁺.

A final word on ion pairing. The dependence of the IR spectrum of H_(aq)⁺ on the nature of the counterion, even with large, weakly-coordinating anions such as carboranes, indicates that most fully ionized acids exist in aqueous solution as solvent-separated ion pairs.¹⁸ This will come as a surprise to many since the high electrical conductivity of aqueous acids is typically equated with ideal (i.e., fully ionized) electrolyte behavior. It must be a consequence of the electrostatic fields of the ions and the ability of water to delocalize their charge via H-bonding.

This is the sine qua non of our findings. Liquid water provides a unique environment for H⁺ that leads to greater mobility and delocalization of charge than previously suspected. Results from the solid state and the gas phase have been quite misleading with respect to the liquid phase.

6. Conclusion

Hydrogen bonding is everywhere and acid/base concepts lie at the heart of many chemical reactions. As the lightest element, hydrogen shows more non-classical, i.e., quantum behavior than any other element. It is no wonder that H⁺ shows such complex chemistry. This Account has summarized recent advances in the chemistry of acids and H-bonding in condensed media with the goal of providing realism to the descriptions of chemistry hidden under the often simplistic designations H⁺, HA, H₂A⁺, H₃O⁺ and H₅O²⁺. For such a seemingly mature area of chemistry, our adventures have been more than interesting. They have changed the way we think about the proton and suggest some ways that myths can be removed from textbooks.

Biography

Christopher A. Reed is Distinguished Professor of Chemistry at the University of California, Riverside. He was born in New Zealand and educated at The University of Auckland. After postdoctoral studies at Stanford University in1971–1973, he joined the faculty at the University of Southern California and spent 25 years there. In 1998, he moved to University of California, Riverside, to create the Center for s and p Block Chemistry. His current research focuses on reactive cations across the periodic table. Earlier research interests included the bioinorganic chemistry of iron porphyrins and copper proteins, spin-spin coupling phenomena, fullerene redox chemistry and supramolecular assembly.