1 – The water molecule and hydrogen bonds in water
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The Physics and Chemistry of Water
1 The water molecule andhydrogen bonds in water
Stoichiometric composition H2O the average
lifetime of a molecule is 1 ms due to protonexchange (catalysed by acids and bases).
O-H bond Re (A) e ()
Isolated molecule 0.9584 104.45
Gaseous, experimental 0.9572 104.47
Liquid, ab initio 0.991 105.5
Liquid, Neutron diffraction 0.970 106
Hydrogen bonding weakens the covalent bonds
(cf. bond angles in a tetrahedral structure: 109.47.)
These structural parameters also apply (within
the Born-Oppenheimer approximation) to isotopi-
cally substituted water, e.g. D2O, HDO and H218O.
The van der Waals diameter is 2.8 A, withabout 5 % variation along different axes (similar
to isoelectronic Ne). Molecular volume 18 A3.van der Waals diameters for water
(Figure from Chaplin)
Radial distribution of Ar and water Oxygen
What is so special with water . . .if anything at all?
Water has precisely the properties one wouldexpect from such a molecule.
Water has unique properties, and is unsur-passed in complexity for a molecule of this
Water is essential (necessary?) for life.
Comparison with H2S
e-bindingRe (A) e (
) energy (eV) e (D)H2O (g) 0.9572 104.52 10.085 1.85
H2S (g) 1.328 92.2 7.43 0.97
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).
Contrary to common belief, the electron distri-
bution does not show enhanced electron density
where lone pairs in a sp3-hybrid orbital would
Although the lone pairs of electrons do not ap-
pear to give directed electron density in isolated
molecules, there are minima in the electrostatic
potentials in approximately the expected posi-
Molecular orbitals for water
The occupied molecular orbitals(as electron probability distri-butions of the isolated molecule)with the lowest energy (mostnegative) molecular orbitals atthe top. The calculated energiesare -559 eV, -37 eV, -19 eV,-15 eV and -14 eV. It can beseen that the three highestenergy orbitals are orthogonalaround the oxygen atom, withtwo lowest energy orbitals (1s2
and mostly 2s2) approximatelyspherical (at the top). Thereare no obvious sp3 hybridizationcharacteristics. The highestenergy orbital (1b1) is predom-inantly p2z in character andmainly contributes to the lonepair effects. These orbitalsare appreciably changed in iceand water, with the 3a1 orbitalbeing shown experimentally tocontribute most to hydrogenbonding.
(Figure from Chaplin).
stretch, 1 stretch, 2 Bend, 3H2O (g) 3657 cm
1 3756 cm1 1595 cm1
H2O (l) 3490 cm1 3450 cm1 1645 cm1
H2O (s) 3277 cm1
D2O (g) 2727 cm1
D2O (l) 2671 cm1 2788 cm1 1178 cm1
Librational (rocking) modes restrictedrotations due to H-bonds
In liquids, IR and Raman spectra are compli-
cated by coupling effects (vibrational overtones,
combined vibrational and librational modes, in-
tramolecular H-bond stretching or bending, clus-
ter vibrations, oxygen-oxygen coupling modes . . . )
Uncoupled OD 1 bands, in 11 mol-%D2O in H2O, at various P and T
A: 20C/0.1 108 MPa, B: 100C/1 108 MPa, C: 200C/2.8 108 MPa, D: 300C/4.7 108 MPa, E: 400C/3.9 108 MPa. A-Dcorrespond to a constant density of 1000 kg/m3. (From Franks)
The bands are asymmetrical; the shoulders on the high-frequency sides have been attributed to different contribu-tions from H-bonded and non-H-bonded O-H groups, the ra-tio of which varies with T and P .
The bands shift to higher frequencies with both increasing Tand/or P , indicating a reduced influence of H-bonds.
In the high T/P limit, where H-bonds are broken, the peak isclose to 2650 cm1, still greater than the 2727 cm1 found inD2O vapour, suggesting that the vibrations are still perturbedby surrounding molecules.
Uncoupled OH and OD stretch bands
IR spectra of small amounts of HDO in CCl4,
liquid H2O or D2O, and crystalline H2O or D2O.
Waters isotopic variations
Nucleus Abundance (%) Nuclear spin1H 99.985 1/22H 0.015 116O 99.759 017O 0.037 5/218O 0.204 0
Zero-point motion (RMS) Density maximum
OH-stretch (A) Bending T (C) Vm (cm3)H2O 0.067 8.7
3.984 18.011D2O 0.056 7.4
(At 11.185 C Vm for H2O is still less than for D2O!)
The structural parameters Re and e applyalso to isotopically substituted H2O (within
the Born-Oppenheimer approximation).
However, zero-point motion depends on thenuclear mass, and H2O is larger than D2O due
to the differences in vibration amplitudes (but
the molar volume of D2O is larger due to weak-
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 H2O 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 strengthis exponentially decaying with separation.
Since water molecules are well separated inmost condensed phases, there is plenty of room
for bending and stretching of the bonds.
It is strong enough to result in about 1016 wa-ter dimers per cm3 in the gas phase.
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 parame-
ters in condensed water at 4C:
(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 oc-
cupied by a donor or an acceptor.
Hydrogen bonding is acooperative 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 bondlength while causing a 20-fold greater reduc-
tion in the H O and O O distances, com-pared 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: inwater at 0C H-bonded clusters span over 400molecules.
Cations may induce strong cooperative hydro-gen bonding due to polarization of water O-H
bonds by cation-lone pair interactions:
Cation+ O-H O-H
Hydrogen bond kinetics
The hydrogen bond network is essentially com-plete 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 1016 times the hydrogen-bond breaks.
Broken bonds are most likely to reform as thelast hydrogen bond, so that the lifetimes of
clusters are usually much longer than the H-
The H-atoms may possess parallel (ortho-water) or anti-
parallel (para-water) nucelar spin. The equilibrium is all-
para at 0 K, changing to about 3:1 ortho:para at higher
temperatures. The equilibrium may take months to estab-
lish 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.
Structural implications of Hydrogenbonding in water
Only 42 % of the volume of ice is filled withthe van der Waals volume of the molecules,
compared to 74 % in a close-packed structure.
Each ice water molecule has only 4 nearest-neighbours, compared to 12 in close-packing
The structuring of water carries informationabout solutes and surface over significant dis-
tances, up to distances of the order of nanome-
F. Franks, Water: a matrix of life, 2nd ed., Cambridge:Royal Society of Chemistry 2000.
Website by M. Chaplin, London South Bank Univer-sity, http://www.lsbu.ac.uk/water/index.html. An ex-tensive site explaining many properties of water.
C. Tanford, The hydrophobic effect: Formation of mi-celles and biological membranes, New York: Wiley 1973.