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

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 has 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 isolelectronic 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 compare 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.

Energy of inversion for H3O+ from [2362] The structure can invert (like a wind-blown umbrella) 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 clusters.


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 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].

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

Energy diagram (rom 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 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 ˣ mol-1 [118]. In this symmetric form (the 'Zundel' cation, shown bottom opposite, 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 mid way 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 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.


H9O4+ with structure from [2136] and charges calculated using the 6-31G** basis set The occupied molecular orbitals, found using the 6-31G** basis set, of H5O2+ 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 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 surely the major reason for the ease of transfer of protons between water molecules; the proton moving 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 H13O6+structure using the 6-31G** basis set

There are two forms of H13O6+ 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 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 H13O6+structure using the 6-31G** basis set. side on

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


The ab initio computed H13O6+structure based on the Zundel cation (see right) is less symmetrical but slightly more stable (~1 kJ ˣ mol-1) . It has almost identical charge distribution and bond lengths to the Eigen based structure above and can be formed from it by a 60° anticlockwise rotation around the central hydrogen bond. However it should be noted that the relative stability of these structures is easily washed out by interactions with further outer shell water molecules which may hydrogen bond both by weaker donor and stronger acceptor to the outer four H2O molecules. Preference for the Zundel cation structure 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 given in the current ab initio calculation) or the lone H5O2+ Zundel ion [1633].


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 half way between those in (H2O)2 and H5O2+ (the calculated minimum energy structure is shown [815]),


resonance structures of H7O3+

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].

resonance structures of H9O4+

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 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.


As unaccompanied hydrogen ions can be readily stripped from aqueous surfaces [1883] as constituents of small positively charged clusters or as aerosol, there may be a build-up of positive charge within clouds and negative charged droplets (~-16 pC ˣ g-1; ~108 e-ˣ g-1 [2703]) g falling to Earth that leads to thunder and lightning. This charge separation is also responsible for the high viscosity of aqueous fogs [2241].

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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 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 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 (so-called) triboelectric series. Triboelectric charging occurs when certain materials become electrically charged after they come into frictional contact with a different material. Everyday examples 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. [Back]




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This page was established in 2001 and last updated by Martin Chaplin on 5 August, 2017

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