Hydrogen ions

The bare hydrogen ion (a proton) readily hydrates^f and cannot exist freely in solution. Initial hydration forms the oxonium ion (H₃O⁺) (sometimes called the hydrogen ion).^d This has a flattened trigonal pyramidal structure (calculated gas phase values O-H bond length 0.961 Å, H-O-H angle 114.7°;^e compare with the significantly different calculated liquid values of O-H bond length 1.002 Å, H-O-H angle 106.7° [709]) with C_3v symmetry and equivalent protons. H₃O⁺ has an effective ionic radius of 0.100 nm [1946], somewhat less than that of the H₂O molecular radius (0.138 nm). Its molar volume is -5.4 cm³ mol^-1 due to electrostriction [1946]. It forms the core of the 'Eigen' cation,^a described later. The structure can invert (like a wind-blown umbrella) with an activation energy less than that of a hydrogen bond and this may occur as an alternative, or even preferred, pathway to rotation within a dynamic hydrogen bonded clusters. H₃O⁺ is also found in the monohydrates of HCl, H₂SO₄and HClO₄, for example, [H₃O⁺]₂[SO₄^2-].^b All the occupied molecular orbitals of H₃O⁺are on another page.

It has been shown that H₃O⁺ can donate three hydrogen bonds (but accepts almost none); the strength of these donated hydrogen bonds being over twice as strong as those between H₂O molecules in bulk water [1198]. This effectively means that the H₃O⁺ cation can be considered as H₉O₄⁺ in solution. The polarization causes these first shell water molecules to also each donate two further hydrogen bonds (but also accept little) with strengths still somewhat higher than bulk water [1198]. Second shell water molecules also donate two hydrogen bonds (but also accept only one with a rather weak hydrogen bond) with strengths still fractionally higher than bulk water [1198]. The bias towards donated hydrogen bonds, within the two-shell H₂₁O₁₀⁺ ion cluster, requires that it must be surrounded by a zone of broken hydrogen bonds. This is confirmed by infrared spectra that show that the presence of an H₃O⁺ ion extends to affect the hydrogen bonding of at least 100 surrounding water molecules [1246].

The oxonium ion binds strongly to another water molecule in two possible manners. 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 asymmetric structure (top) of H₅O₂⁺ is found to be more stable using the 6-31G** basis set. However, other more thorough ab initio treatments have found the symmetric hydrogen-bonded structure (bottom), with a slightly shorter hydrogen bond, to be the global minimum of by about 0.6 kJ mol^-1 [118].

In this symmetric form (the 'Zundel' cation, shown bottom opposite), 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 mid way 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.

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

H₅O₂⁺ may be fully hydrated, also with an equally spaced central hydrogen bond, with one water molecule hydrogen bonded to the four free hydrogen atoms as H₁₃O₆⁺. The presence of these three similar energy minima for the proton lying so close between the two oxygen atoms is surely the major reason for the ease of transfer of protons between water molecules; the proton moving very quickly (< 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 small movement of the proton gives rise to a much greater movement of the center of positive charge. Preference for the Zundel cation structure occurs when its outer hydrogen bonding is approximately symmetrical as in H₁₃O₆⁺ (right) [815], although the O····O separation may be greater than expected for the lone H₅O₂⁺ Zundel ion [1633].

When the extra proton is shared equally between more than one water molecule the approximate structure can be deduced from a consideration of the resonance structures; for example, the two shared protons in H₇O₃⁺ give rise to bond lengths half way 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⁺ (below; the calculated minimum energy structure is shown [815]). Once correctly oriented, the potential energy barrier to proton transfer is believed to be very small [161].

However, the hydrated oxonium ion (opposite; the 'Eigen' cation)^e may be the most stable 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.

In acid^c solutions, there will be many contributing structures giving rise to particularly broad stretching vibrations associated with the excess protons (for example, magic number ions). 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]. H₇O₃⁺ and H₉O₄⁺ are both also found in HBr.4H₂O, i.e. [H₉O₄⁺][H₇O₃⁺][Br^-]₂.H₂O.

As hydrogen ions can be readily stripped from aqueous surfaces [1883], by themselves, as constituents of small clusters or as aerosol, there may be a build -up of positive charge within clouds and negative charge on Earth that leads to thunder and lightning.

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