Water structure and science


Hydrogen ion (H3O+) as a partially flattened pyramid


Hydrogen ion (H3O+) as a flattened pyramid with electrostatic potential

Hydrogen ions            H3O+

Hydrogen ions are molecular ions with the formula H3O+(H2O)n, formed by the addition of a proton to one or more water molecules.

link; The ionic product, Kw

link; pH
link; Hydroxide ions
link; Grotthuss mechanism

The structure and dynamics of the hydrogen ion in water have been reviewed [2628]. The bare hydrogen ion (a proton) has an extremely high charge density (≈ 2x1010 that of Na+), readily hydrates f and cannot exist freely in solution. Initial hydration forms the hydroxonium ion (H3O+) (commonly called the hydrogen ion and isoelectronic with ammonia, NH3). d This has a flattened trigonal pyramidal structure (with calculated gas phase values of O-H bond length 0.961 Å, H-O-H angle 114.7°; e this may be compared with the significantly different calculated liquid values of O-H bond length 1.002 Å, H-O-H angle 106.7° [709]) with C3v 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 energy of inversion for H3O+, from [2362]


Energy of inversion for H3O+ from [2362]

The structure can invert (like a wind-blown umbrella, see also aqueous ammonia) with an activation energy less than that of a hydrogen bond [2362], and this may occur as an alternative, or even preferred, pathway to rotation within a dynamic hydrogen-bonded cluster. This (hindered) umbrella motion of H3O+ has a broad absorption band centered at ~1337 cm-1 [3636].

H3O+ is also found in the monohydrates of HCl, H2SO4and HClO4, for example, [H3O+]2[SO42-]. b All the occupied molecular orbitals of H3O+are on another page. All hydrogen ions are formed from a 'core' H3O+. They are not fixed structures in aqueous solution but exist as 'flickering' clusters, as with other water clusters, with hydrogen-bonding water molecules continuously coming and going. The lifetimes of the clusters are independent of the lifetime of individual linkages. However, the energy differences between different types of the cluster in aqueous solution are small, and interconversions take place easily.

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]. A recent study of lone pairs shows the hydronium ion as not possessing the expected lone pair (see the 3a1 HOMO) as these electrons are spread out over the three protons and there is no minimum in the electrostatic potential in the expected place [2137]. This effectively means that the H3O+ cation can be considered as H9O4+ in solution. The polarization causes these first shell water molecules to 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].


H5O2+ showing the unequally spaced hydrogen bond (above)

and equally-spaced hydrogen bond in the C2 form (bottom)


Dihydronium ion (H5O2+)and hydrated hydroxide ion (H3O2-)

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


H5O2+ Energy diagram and the zero-point vibrational energies


Energy diagram from ab initio 6-31G** calculation) and the zero-point vibrational energies for H5O2+ dihydronium ions<


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].


H5O2+ in acetonitrile solution


H5O2+ in acetonitrile solution

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+][ClO4-]). 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).

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, that 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 broad range of O···H+···O distances and asymmetries associated with two water molecules [3674].


H+(H2O)4 [2136] with charges calculated using the 6-31G** basis set


H9O4+ with structure from [2136] and charges calculated using the 6-31G** basis set

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

H5O2+ may be hydrated by attachment of a water molecule on each end, so 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],


Symmetrical Zundel H+(H2O)6 ion


symmetrical H13O6+ ion


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 major 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 small movement of the proton gives rise to a much greater movement of the center of positive charge due to its asymmetric spread.


Ab initio H+(H2O)6 structure based on Eigen cation


ab initio H13O6+structure using the 6-31G** basis set


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.


Ab initio H+(H2O)6 structure, side on


ab initio H13O6+structure using the 6-31G** basis set. side on

Bond lengths in the H+(H2O)2 ion, from [3299]


Bond lengths in the H+(H2O)2 ion, from [3299]

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 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 key 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 a consideration of 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 H7O3+




Resonance structures of H9O4+; H+(H2O)4


resonance structures of H9O4+


H3O+.3(H2O) hydrated oxonium ion


H3O+.3(H2O) hydtated oxonium ion

However, the hydrated hydroxonium ion (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. Also, it can convert into, and revert from, both the H13O6+ ions (above) using any of the three 'arms'.

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] 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.

The central (positively charged) hydrated proton interacts very much more strongly with the oxygen of neighboring water molecules rather than any weakly forming hydrogen bonds; H2O···OH3+(H2O)3 being a very much stronger link than the hydrogen bond HO-H···OH3+(H2O)3 [1956]. This causes molecular rotations in the neighboring water molecules as a hydrogen ion moves through the solution so disrupting the hydrogen-bonded network. This O···O attraction even exists between H3O+ species as in more concentrated acid solutions (≈ 0.5 - ≈ 3 M) with the hydrated protons appearing to form contact ion-pairs, with the hydroxonium lone-pair sides pointing toward one another and the oxygen atoms only about 0.34 nm apart. This unusual “amphiphilic” behavior minimizes the disruption to the water's hydrogen bond network caused by the strong hydration of the protons [1837, 2042]. A similar effect may occur at the surface of concentrated acid solutions, causing the lone pairs to point towards the (hydrophobic) gas phase.

The excess protons at the air/water interface of water bridges (Explanation, [1361]) have a unique water arrangement that enables them to propagate without sinking into the bulk water and reduces the air/water interfacial tension from 80 to 32 N m-1 [3639].

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]) g falling to Earth. This leads to thunder and lightning and causes the surface of the Earth to be negatively charged. Air, being at the top of the triboelectric series is positively charged due to the easy stripping of charge from its water content [3631]. This charge separation is also responsible for the high viscosity of aqueous fogs [2241]. The Earth's surface is negatively charged. 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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a The hydration of 'Eigen' (H9O4+, or sometimes H3O+) and 'Zundel' (H5O2+) ions have been investigated [1372]. [Back]

b H2O accepts protons from stronger acids to form H3O+ and H3O+ donates protons to the bases of weaker acids. The acidity constant (Ka) of H3O+ is defined (as other acids) by the equation H3O+(+H2O)equilibrium arrowsH+(aq)+H2O. Therefore Ka= [H+][H2O]/[H3O+]. The definition of Ka is expressed in terms of activities rather than concentrations [1188], and the activity of pure H2O is defined as unity [2965] whereas that of solutes is defined relative to their standard state (1 mol kg-1). As [H+] is the same as [H3O+] and [H2O] is the activity of pure water, Ka = 1 (at 25 °C), and pKa = 0.00 (at 25 °C). [Back]

c Note that acid-base neutrality only occurs when the concentration of hydrogen ions equals the concentration of hydroxyl ions (whatever the pH). Neutrality is at pH 7 only in pure water when at 25 °C. A solution is acidic when the hydrogen ion concentration is greater than the hydroxide ion concentration, whatever the pH. [Back]

d The term 'hydroxonium ion' should be reserved for the H3O+ ion with the term 'hydronium ion' now obsolete. The term 'hydrogen ion' may refer to any of the group of protonated water clusters including H3O+. As many hydrated forms of hydrogen ion exist, it may be preferable to give its structure as H3O+(aq) or even H+(aq) [2132]. [Back]

e The hydroxonium ion and small hydrated hydrogen ion clusters as shown on this page were drawn using ab initio calculations using the 6-31G** basis set. Where not otherwise referenced, bond distances, angles, and atomic charges are derived from these calculations. [Back, 2, 3]

f H+ + H2O -> H3O+ (ΔG° = -651.4 kJ ˣ mol-1), this is followed by H3O+ + aq -> H3O+(aq) (ΔG° = 461.1 kJ ˣ mol-1; ≈ 260 nm) giving an overall H+ + aq -> H3O+(aq) (ΔG° = -1112.5 kJ ˣ mol-1). These calculations assume that the standard state of the solvent water is taken as 1.0 M. [1067]). A recent paper proposes slightly different values; a proton hydration free energy of -1106.2 kJ ˣ mol-1, a proton hydration enthalpy of -1137.1 kJ ˣ mol-1 and a proton hydration entropy of −102.6 J mol-1 K-1 [2256] and another paper presents a summary of estimates [2565]. [Back]

g Water drops can easily acquire a positive or negative charge in an electric field [2660]. 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 with the atmosphere being the major source and sink of water ions contributing to the electrostatic behavior of dielectric solids [3273]. [Back]

(c) Martin Chaplin 20 October, 2019
(printed 6 April 2020)