The Structure of the Hydrogen Ion (H_aq⁺) in Water

Abstract

The H_aq⁺ ion in water is a unique H₁₃O₆⁺ entity that defines the boundary of positive charge delocalization. Its central unit is neither a C_3v H₃O⁺ Eigen-type ion nor a typical H₅O₂⁺ Zundel-type ion. IR spectroscopy indicates that the H₁₃O₆⁺ ion has an unexpectedly long central O⋯O separation (≫2.43 Å) showing that, compared to gas and solid phases, the environment of liquid water is uniquely proficient in delocalizing positive charge. The will change the description of H_aq⁺ in textbooks of chemistry and a more extensive delocalization of positive charge may need to be incorporated into descriptions of mechanisms of aqueous proton transport.

One of the oldest problems in chemistry is obtaining an accurate molecular description of H_aq⁺ when an acid ionizes in water.¹ The value of n in H(H₂O)_n⁺ is poorly defined and there has been a long debate over the relative importance of Eigen-type² H₃O⁺·3H₂O (I) versus Zundel-type³ H₅O₂⁺ (II) structures:^4-19

The Eigen ion I has three classical, unsymmetrical H-bonds (O⋯O ∼2.51 Å)²⁰ while the Zundel ion II has a short, symmetrical H-bond (O⋯O = 2.39-2.43 Å)^21-25 and a low barrier to proton movement within the double-well potential region of classical H-bonding. Recent theory favors a kinetic description that blurs the distinction between these static structures. A distorted Eigen-type ion with one short O⋯O bond (the “special pair”) is the calculated energy minimum at short timescales.^18,19 We now present experimental evidence that an adequate description of H_aq⁺ requires formulation as an H(H₂O)₆⁺ ion. The IR spectrum of this ion matches neither Eigen- nor Zundel-type ions.

The problem of developing an accurate molecular description of H_(aq)⁺ from experimental data lies in the difficulty of establishing n in H(H₂O)_n⁺, isolating its IR spectrum from that of bulk water, and interpreting its dauntingly broad features.^3,26 IR spectroscopy is the method of choice because of its fast timescale and high sensitivity to hydrogen bond formation. Mainly carborane acids²⁷ were chosen for this study because their large molecular weights allow quantitative measurements to be extended to low molarities where strong acids are fully ionized. To optimize quantification, IR spectra were run in ATR mode, placing a drop of solution on a diamond window.

The IR spectrum of a strong aqueous acid consists of overlapping spectra from three types of water molecules: bulk water, water associated with H_aq⁺, and water perturbed by the anion. As shown in detail in the Supp. Info., the spectrum of water perturbed by the anion is readily subtracted using the spectrum of its equimolar alkali metal salt because the spectrum of a hydrated alkali metal cation, M(H₂O)_n⁺, happens to coincide with that of bulk water.²⁸ The spectrum of bulk water can also be subtracted but will be over-subtracted by an amount equal to the number of water molecules included in the H(H₂O)_n⁺ cation. This gives rise to a spectrum of H(H₂O)_n⁺ that is distorted by negative peaks from bulk water at ∼3400 and at ∼1630 cm^-1. Using the +S/-S method,²⁹ the spectrum of bulk water is then added with a scaling factor that provides optimal removal of the spectral distortions. This leads not only to the true spectrum of the H(H₂O)_n⁺ cation but also to the value of n (Table 1). For aqueous solutions of three different carborane acids, and for perchloric acid, the average value of n is 6.0 ± 0.3. The apparent contradiction between this H(H₂O)₆⁺ formulation and the distorted Eigen-type H(H₂O)₄⁺ structure favored by theory^18,19 can be reconciled by recognizing that shortening of one O-H⋯O bond in I to create the “special pair” attracts two outer sphere water molecules closer to the Eigen core, converting it into an H(H₂O)₆⁺ ion.

Table 1.

The stoichiometry of H⁺(H₂O)_n in water solutions of carborane and perchloric acids.

Anion	Molarity	n in H+(H2O)n
CHB11Cl11-	0.46	5.97
CHB11Cl11-	0.330	5.7
CCD-	0.427	6.06
CHB11I11-	0.259	6.10
CHB11I11-	0.22	6.15
CHB11I11-	0.176	5.86; 6.10
ClO4-	0.5	5.98
ClO4-	0.75	5.95

Deconvolution of the IR spectrum (Fig. 1 red) gives the often noted but poorly understood continuous broad absorption (cba, blue) overlaid with Guassian bands (green) with frequency variances for the four different acids of 3134 ± 12, 2816 ± 40, 1746 ± 11, 1202 ± 4 and 654 ± 12 cm^-1. This spectrum for these 0.2-0.75 M acids refines those reported earlier for more concentrated acids^3,4,26 where only bands at ∼1740 and ∼1200 cm^-1 could be identified with H_aq⁺. The small variation with anion is ascribed to weak outer-sphere ion-pairing effects on the H(H₂O)₆⁺ ion.

Figure 1.

Isolated IR spectrum of H(H₂O)_n⁺ from 0.330 M aqueous H(CHB₁₁Cl₁₁) (red) showing deconvolution into 5 bands (green), a continuous broad absorption (blue) and their summation (black). The points of inflection in the red spectrum near 1630 and 1050 cm^-1 arise from the +S/-S subtraction process.

We conclude from these experiments that in aqueous solutions of strong acids, the H_aq⁺ cation has six spectroscopically distinct water molecules that define the boundary of influence of the positive charge. Positive charge will extend out onto the O atoms of an outer hydration shell but not significantly enough to make their O-H stretching vibrations distinguishable from those of bulk water.

What is the structure of the H(H₂O)₆⁺ ion giving rise to the red spectrum in Fig. 1? A static Eigen-type structure based on the C_3v symmetric H₃O⁺ ion is easily ruled out since this would require an n value of 4 or 10 to preserve symmetry. Moreover, the IR spectrum of the H₃O⁺·3H₂O cation in the X-ray structurally characterized carborane salt has no cba and bands associated with the O–H⋯O groups occur at ca. 2575, 2290 and 1865 cm^-1,³⁰ quite different from those of H(H₂O)₆⁺. There is a closer, but still poor match to the spectra of symmetric H₅O₂⁺·4L Zundel-type ions.²² In particular, the ∼1200 cm^-1 band occurs at anomalously high frequency. This Zundel ion marker band, associated with proton oscillation along the O⋯O trajectory of the central symmetrical O-H⁺-O group,^22,31,32 occurs in the 840-1085 cm^-1 range for gas phase ions^31,32 and 1000-1160 cm^-1 for the condensed phase²² where its frequency increases with basicity of L. It is lowest (1084 cm^-1) for L = benzene which is a weaker base than water,²² reaches 1140 cm^-1 for tributylphosphate whose basicity coincides with that of liquid water,³³ and increases to 1160 cm^-1 for L = phosphine oxides whose basicities exceed that of water.³⁴ The ∼1200 cm^-1 frequency in H(H₂O)₆⁺ is out of line with this spectroscopic regularity. Since the O⋯O distance in the central OHO group increases as a function increasing basicity of L because of positive charge removal, an unexpected elongation of the O⋯O separation would rationalize the 1200 cm^-1 band for H(H₂O)₆⁺. Thus, we propose structure III for this cation. The dotted circle passing through the O atoms of the outer sphere hydration shell defines the extent of positive charge delocalization:

This possibility was recently discovered in the X-ray structure of H(CHB₁₁I₁₁)·8H₂O where, unlike all other Zundel-type structures which have central O⋯O separations in the range 2.39-2.42 Å,^21-25 that in a centrosymmetric H₁₃O₆⁺ ion is anomalously long (2.57 Å).³⁵ The difference between this H₁₃O₆⁺ ion and those in all previously known Zundel ion-type structures appears to lie in their outer sphere environments. Zundel ion structures have typically been characterized in relative rigid, discrete cation/anion structures whereas the H₁₃O₆⁺ ion in H(CHB₁₁I₁₁)·8H₂O is located in a nanotube of protonated water, much closer to the environment of liquid water. Positive charge is more delocalized and the O⋯O separation increases accordingly.

The simplicity of the 4-band spectrum of the aquated H₁₃O₆⁺ ion and the relatively narrow bandwidth of νOH at ∼3140 cm^-1 is indicative of a high symmetry structure. Distorted Eigen-type structures such as the hydrated H₇O₃⁺ ion,³⁰ various HCl hydrates³⁶ etc., have more complex IR spectra. The distorted Eigen-type structures favored by current theory^18,19 have lifetimes that are shorter than the IR timescale and therefore cannot be detected by the present experiments.

In summary, H_aq⁺ is a unique entity requiring formulation as a hydrated H₁₃O₆⁺ ion. This defines the boundary of delocalization of the positive charge and should become an essential part of mechanistic discussions involving H_aq⁺. Its IR spectrum matches neither a C_3v Eigen ion nor a typical Zundel ion with a short central O⋯O distance. Delocalization of the positive charge is more extensive. The IR spectrum is consistent with a centrosymmetric structure and the high frequency of the ∼1200 cm^-1 band indicates an unexpectedly long O⋯O separation. With its delocalized proton in the central OHO group, the H₁₃O₆⁺ ion in water is quite distinct from the tetrahydrated Zundel ion H₅O₂⁺·4H₂O in the solid state or gas phase. They bear only topological similarity. Liquid water is a unique environment for the hydrated proton.