Hydrogen ions            

The hydroxonium ion binds strongly to another water molecule in two possible manners (in a vacuum). Opposite are shown the two H₅O₂⁺ dihydronium ions with closely matched energies, where the proton is asymmetrically (top) or symmetrically (bottom) centered between the O-atoms. ^e

The potential energy barrier (≈ 2 kJ ˣ mol⁻¹) for the proton switching from asymmetrically positioned water molecules (see above right) is very low compared with the vibrational energy of the proton (shown blue). The asymmetric structure (top left) of H₅O₂⁺ is found to be more stable using the 6-31G** basis set. It has a strong hydrogen bond (159 kJ ˣ mol⁻¹) that reduces to -69 kJ ˣ mol⁻¹ when stretched to 0.244 nm and -20 kJ ˣ mol⁻¹ at 0.431 nm [2957].

However, other more thorough ab initio treatments have found the symmetric hydrogen-bonded structure (above bottom), with a slightly shorter hydrogen bond, to be the global minimum of by about 0.6 kJ ˣ mol⁻¹ [118]. In this symmetric form (the 'Zundel' cation, shown right, lifetime ≈ 0.5 ps [2440]), all O-H bonds are the same length (0.95 Å) except the two involved in the hydrogen bond, which are covalent and equally-spaced (1.18 Å; similar to that in ice-ten, and as found by neutron diffraction in some crystals midway between the oxygen atoms [118a], such as the dihydrates of HCl and HClO₄, for example, [H₅O₂⁺][ClO_4⁻]). There is localized but low electron density around the central hydrogen atom. The vibrational spectrum of H₅O₂⁺ shows a strong, sharp peak (at 1090 cm⁻¹) for its shared proton similar to H₃O₂⁻. As expected, these spectra are much broadened, shifted, and poorly resolved in bulk liquid water (see spectrum). This broadened proton stretching vibration of Zundel-like configurations has a similar frequency to the umbrella motion of Eigen-like configurations, with both resonant at ∼1200 cm⁻¹. Decoding the 2D IR spectrum around 1200 cm⁻¹ has shown it is dominated by the proton stretch vibrations of Zundel-like and intermediate geometries, broadened by the heterogeneity of aqueous configurations [4239]. Using the vibrational sum frequency spectroscopy technique, it has been shown that the antisymmetric O-H stretch of the Eigen H₃O⁺ core can be readily identified at ~2540 cm⁻¹ on negatively charged substrates [2218]. The band shifts to ~1875 cm⁻¹  for D₃O⁺.

Isolated H₅O₂⁺ units (Zundel cations) have been studied in moderately concentrated (0.26 M HClO₄/ 0.88 M H₂O) deuterated acetonitrile solution [2989] (see above right). The proton fluctuates along the line of the hydrogen bond, which shows a low barrier double minimum potential energy well. The proton in an idealized centrosymmetric Zundel structure (H₅O₂⁺) should be Raman vibration forbidden and infrared vibration allowed, while the symmetric stretch vibration of an idealized Eigen structure (H₃O⁺) should be Raman allowed and IR forbidden. Thermal fluctuations in liquid water give rise to a broad continuum of hydrated proton configurations resulting in a broad range of O···H⁺···O distances and asymmetries associated with two water molecules [3674].

The occupied molecular orbitals of H₅O₂⁺, found using the 6-31G** basis set, are on another page.

H₅O₂⁺ may be hydrated by attaching a water molecule on each end, forming a short 'water wire ' H₉O₄⁺ allowing the shuttling of protons between the four water molecules. This structure has been (surprisingly) found in the vapor phase by IR spectroscopy [2136],

H₅O₂⁺ may be fully hydrated, with an equally spaced or unequally spaced central hydrogen bond, with one water molecule hydrogen-bonded to the four free hydrogen atoms as H₁₃O₆⁺ (the Stoyanov ion [2134, 2135]). The unit positive excess charge is thus spread out over at least 13 hydrogen atoms. The presence of these energy minima for the proton lying so close between the two oxygen atoms (left and right plus a possible very shallow central minimum) is undoubtedly the primary reason for the ease of transfer of protons between water molecules. The proton moves very quickly (faster than the infrared vibrational timescale [2134], < 100 fs, [1032]) between the extremes of triply-hydrogen bonded H₃O⁺ (H₉O₄⁺, 'Eigen cation') ions through symmetrical H₅O₂⁺ ions ('Zundel cation') ^a [161], with the low potential energy barriers washed out by the zero-point motion of the proton [1032]. Note that the slight movement of the proton gives rise to a much greater movement of the center of the positive charge due to its asymmetric spread.

There are two forms of H₁₃O₆⁺ {H⁺(H₂O)₆} with very similar energy, based on Eigen or Zundel ions; neither are planar, although often depicted as such. The one with slightly higher energy (≈ 1 kJ ˣ mol⁻¹ using the 6-31G** basis set ) is based on merging two Eigen H₃O⁺ ions (only one excess proton) twisted 180° and joined through the excess proton (H₅O₂⁺). This ab initio computed H₁₃O₆⁺ structure (left and below) shows a puckered structure with an unsymmetrically placed central hydrogen atom with the greatest positive charge spread on the side with this hydrogen atom. The hydrogen bonds and peripheral water molecules are also more affected on this side.

Preference for the Zundel cation structure, where the central hydrogen ion is symmetrically placed (see above), occurs when its outer hydrogen-bonding is approximately symmetrical [815], although the O····O separation may be greater than expected (≈ 2.57 Å [2134]) or the lone H₅O₂⁺ Zundel ion [1633]. 2D infrared spectroscopy indicates the movement of the central H⁺ between the left-hand position (Eigen), the central position (Zundel, lifetime 480 fs), and the right-hand position (Eigen) [3292].

The H₁₃O₆⁺ ion is a crucial player in the Grotthuss mechanism. When the extra proton is shared equally between more than one water molecule, the approximate structure can be deduced from the resonance structures. For example, the two shared protons in H₇O₃⁺ give rise to bond lengths halfway between those in (H₂O)₂ and H₅O₂⁺ (the calculated minimum energy structure is shown [815]), and the three shared protons in H₉O₄⁺ giving rise to bond lengths a third of the way between those in (H₂O)₂ and H₅O₂⁺. The calculated minimum energy structure is shown below [815]). Once correctly oriented, the potential energy barrier to proton transfer is believed to be very small [161]. The structure varies between the symmetrical structure shown in the middle and three identical structures based around the Zundel H₅O₂⁺ cation [3053].

Resonance structures of H₇O₃⁺; H⁺(H₂O)₃

Resonance structures of the Eigen cation, H₉O₄⁺; H⁺(H₂O)₄

However, the hydrated hydroxonium ion, with its central hydronium ion tightly hydrogen-bonded to
three equivalent water molecules (opposite; the 'Eigen' cation), ^e may be the most prevalent hydrated proton species in liquid water, being slightly more stable than the symmetrical dihydronium ion, due to electronic delocalization over several water molecules being preferred over the nuclear delocalization. Simulations have shown that the dominant 'Eigen' cation is distorted as it continuously switches its closest hydrogen bond to one of the three surrounding water molecules. On average, a distorted Eigen cation results in three equivalent, but dynamically exchanging, distortions [4377]. Also, it can convert into, and revert from, both the H₁₃O₆⁺ ions (above) using any of the three 'arms'.

In acid ^c solutions, many contributing structures will give rise to particularly broad stretching vibrations associated with the excess protons (for example, magic number ions). 76 Ionized water clusters (H₂O)_n⁺, n = 2 to 6 have been described [4002]. It has been determined from studies of freezing point depression that H₃O⁺(H₂O)₆ (that is, H₁₅O₇⁺) is the mean structural ion in cold water [250] whereas H₁₃O₆⁺ is indicated by vibrational spectroscopy [2135]. H₇O₃⁺ and H₉O₄⁺ are both also found in HBr.4H₂O, i.e., [H₉O₄⁺][H₇O₃⁺][Br⁻]₂.H₂O.

Water drops can easily acquire a positive or negative charge in an electric field [2660, 3967]. Water flowing through tubes of different materials (such as glass, copper, or PTFE) picks up a positive charge. [2703]. The magnitude of this positive charge is correlated with the materials' position in the triboelectric series. Triboelectric charging occurs when certain materials become electrically charged after they come into frictional contact with a different material [3631]. It usually involves surface water molecules. Everyday examples of such charging are rubbing glass with fur and combing hair, both of which can build up triboelectricity, often known as static electricity. The triboelectric series gives the order that materials can gain electrons (by friction) from other materials. Water lies at the top of the triboelectric series except for air. This charging involves the adsorption of ions formed by dissociation of water vapor or adsorbed water molecules. The atmosphere is the primary source and sink of water ions contributing to the electrostatic behavior of dielectric solids [3273].

Because unaccompanied hydrogen ions can be readily stripped from aqueous surfaces [1883], as constituents of small positively charged clusters or as an aerosol, there may be a build-up of positive charge within clouds and negatively charged droplets (≈ -16 pC ˣ g⁻¹; ≈ 10⁸ e⁻ ˣ g⁻¹ [2703]) falling to Earth. This charge separation leads to thunder and lightning and causes the surface of the Earth to be negatively charged. At the top of the triboelectric series, the air is positively charged due to the easy stripping of charge from its water content [3631]. It is also responsible for the high viscosity of aqueous fogs [2241]. Although the average electric field at the Earth surface is ≈ 100 V ˣ m⁻¹, electrical currents are usually insignificant due to the low electric conductivity of the air.

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