1 The water molecule and hydrogen bonds in water

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1 The Physics and Chemistry of Water 1 The water molecule and hydrogen bonds in water Stoichiometric composition H 2 O the average lifetime of a molecule is 1 ms due to proton exchange (catalysed by acids and bases). O-H bond R e (Å) θ e ( ) Isolated molecule Gaseous, experimental Liquid, ab initio Liquid, Neutron diffraction Hydrogen bonding weakens the covalent bonds (cf. bond angles in a tetrahedral structure: ) These structural parameters also apply (within the Born-Oppenheimer approximation) to isotopically substituted water, e.g. D 2 O, HDO and H 2 18 O.

2 Molecular size The van der Waals diameter is 2.8 Å, with about 5 % variation along different axes (similar to isoelectronic Ne). Molecular volume 18 Å 3. van der Waals diameters for water (Figure from Chaplin) Radial distribution of Ar and water Oxygen (From Franks)

3 What is so special with water... if anything at all? Water has precisely the properties one would expect from such a molecule. Water has unique properties, and is unsurpassed in complexity for a molecule of this size. Water is essential (necessary?) for life. Comparison with H 2 S e -binding R e (Å) θ e ( ) energy (ev) µ e (D) H 2 O (g) H 2 S (g) The bond angle difference is due to differences in electronic structure (greater separation between 3p and 3s atomic energies in S relative to the 2p-2s energies in O).

4 Electronic structure Contrary to common belief, the electron distribution does not show enhanced electron density where lone pairs in a sp 3 -hybrid orbital would occur. (From Chaplin) Although the lone pairs of electrons do not appear to give directed electron density in isolated molecules, there are minima in the electrostatic potentials in approximately the expected positions.

5 Molecular orbitals for water The occupied molecular orbitals (as electron probability distributions of the isolated molecule) with the lowest energy (most negative) molecular orbitals at the top. The calculated energies are -559 ev, -37 ev, -19 ev, -15 ev and -14 ev. It can be seen that the three highest energy orbitals are orthogonal around the oxygen atom, with two lowest energy orbitals (1s 2 and mostly 2s 2 ) approximately spherical (at the top). There are no obvious sp 3 hybridization characteristics. The highest energy orbital (1b 1 ) is predominantly p 2 z in character and mainly contributes to the lone pair effects. These orbitals are appreciably changed in ice and water, with the 3a 1 orbital being shown experimentally to contribute most to hydrogen bonding. (Figure from Chaplin).

6 Vibrational modes Symmetric Asymmetric stretch, ν 1 stretch, ν 2 Bend, ν 3 H 2 O (g) 3657 cm cm cm 1 H 2 O (l) 3490 cm cm cm 1 H 2 O (s) 3277 cm 1 D 2 O (g) 2727 cm 1 D 2 O (l) 2671 cm cm cm 1 Librational (rocking) modes restricted rotations due to H-bonds In liquids, IR and Raman spectra are complicated by coupling effects (vibrational overtones, combined vibrational and librational modes, intramolecular H-bond stretching or bending, cluster vibrations, oxygen-oxygen coupling modes... )

7 Uncoupled OD ν 1 bands, in 11 mol-% D 2 O in H 2 O, at various P and T A: 20 C/ MPa, B: 100 C/ MPa, C: 200 C/ MPa, D: 300 C/ MPa, E: 400 C/ MPa. A-D correspond to a constant density of 1000 kg/m 3. (From Franks) The bands are asymmetrical; the shoulders on the highfrequency sides have been attributed to different contributions from H-bonded and non-h-bonded O-H groups, the ratio of which varies with T and P. The bands shift to higher frequencies with both increasing T and/or P, indicating a reduced influence of H-bonds. In the high T /P limit, where H-bonds are broken, the peak is close to 2650 cm 1, still greater than the 2727 cm 1 found in D 2 O vapour, suggesting that the vibrations are still perturbed by surrounding molecules.

8 Uncoupled OH and OD stretch bands IR spectra of small amounts of HDO in CCl 4, liquid H 2 O or D 2 O, and crystalline H 2 O or D 2 O. (From Tanford)

9 Water s isotopic variations Nucleus Abundance (%) Nuclear spin 1 H /2 2 H O O /2 18 O Zero-point motion (RMS) Density maximum OH-stretch (Å) Bending T ( C) V m (cm 3 ) H 2 O D 2 O (At C V m for H 2 O is still less than for D 2 O!) The structural parameters R e and θ e apply also to isotopically substituted H 2 O (within the Born-Oppenheimer approximation). However, zero-point motion depends on the nuclear mass, and H 2 O is larger than D 2 O due to the differences in vibration amplitudes (but the molar volume of D 2 O is larger due to weakened H-bonding...!).

10 The hydrogen bond in water A hydrogen bond is formed when a H atom is attracted by rather strong forces to two atoms instead of only one (the convention is that an O-H hydrogen atom is being donated to the O- atom acceptor on another H 2 O molecule). Some bond strengths in water (kj/mol): O-H covalent bond 492 Hydrogen bond 23.3 van der Waals attraction 1.3 The H-bond has a partly covalent character, though the magnitude of this is disputed. Small deviations from linearity (up to about ± 20 ) have a minor effect, while the strength is exponentially decaying with separation. Since water molecules are well separated in most condensed phases, there is plenty of room for bending and stretching of the bonds. It is strong enough to result in about water dimers per cm 3 in the gas phase.

11 The misfit between tetrahedral angles and the water HOH bonds results in a non-linear H-bond. While the most favourable configuration of a dimer is a straight H-bond, these are average parameters in condensed water at 4 C: (Figures from Chaplin) H-bond patterns are random in water (and some ice phases) so that there is an equal probability for a particular site around a molecule to be occupied by a donor or an acceptor.

12 Hydrogen bonding is a cooperative process This cooperativity is a fundamental property of liquid water. A hydrogen bond in water can be 250 % stronger than in a water dimer! Cooperative H-bonding increases the O-H bond length while causing a 20-fold greater reduction in the H O and O O distances, compared to dimer H-bonds. In hydrogen-bonded chains (such as DNA), unzipping may occur as a result of breaking of a few hydrogen bonds in the chain. This supports formation of large clusters: in water at 0 C H-bonded clusters span over 400 molecules. Cations may induce strong cooperative hydrogen bonding due to polarization of water O-H bonds by cation-lone pair interactions: Cation + O-H O-H

13 Hydrogen bond kinetics The hydrogen bond network is essentially complete at ambient temperatures. H-bond lifetems are 1-20 ps. Broken bond lifetimes are about 0.1 ps. Dissociation of water is extremely rare, about once per times the hydrogen-bond breaks. Broken bonds are most likely to reform as the last hydrogen bond, so that the lifetimes of clusters are usually much longer than the H- bond lifetimes. The H-atoms may possess parallel (ortho-water) or antiparallel (para-water) nucelar spin. The equilibrium is allpara at 0 K, changing to about 3:1 ortho:para at higher temperatures. The equilibrium may take months to establish in ice, and about an hour in liquid water. This slow equilibration is a direct consequence of the preference for broken H-bonds to re-form rather than re-orient.

14 Structural implications of Hydrogen bonding in water Only 42 % of the volume of ice is filled with the van der Waals volume of the molecules, compared to 74 % in a close-packed structure. Each ice water molecule has only 4 nearestneighbours, compared to 12 in close-packing of spheres. The structuring of water carries information about solutes and surface over significant distances, up to distances of the order of nanometers.

15 General references F. Franks, Water: a matrix of life, 2nd ed., Cambridge: Royal Society of Chemistry Website by M. Chaplin, London South Bank University, An extensive site explaining many properties of water. C. Tanford, The hydrophobic effect: Formation of micelles and biological membranes, New York: Wiley 1973.