Water's Quantum Jazz

Other reports in this series

• Cooperative and Coherent Water
• Dancing with Ions
• Dancing with Macromolecules
• The Rainbow Ensemble

---

Dancing with Ions

Water has a special dynamic relationship with ions dissolved in it that will determine their chemistry in the cell Dr. Mae-Wan Ho

Bonding with ions or not

The interaction of water with ions has been studied for over a century, but much remains to be understood.  In general, ions are classified into two groups - ‘kosmostopes’ or ‘chaotropes’ - according as to whether they induce order or disorder in water [1].

Thus, Li⁺ (lithium) dissolving in water results in a large negative entropy change, as typical of a kosmotrope, while Cs⁺ (caesium) dissolving is accompanied by a positive entropy change, as appropriate for a chaotrope. Another measure is viscosity, which increases with lithium and decreases with caesium.

Both types of ions are generally surrounded by water molecules forming a ‘solvation shell’ that shield their charges from other ions. The strength with which the ions bind to their solvation shell is expressed in terms of activation energy, the energy needed to strip a water molecule away from the ion relative to that needed to strip a water molecule from another water molecule. Kosmotropes are strongly bound to their neighbouring water, and therefore have large positive activation energies, as distinct from chaotropes that are more weakly bound.

In general, the solvation shell consists of a single layer of water molecules hydrogen-bonded to the ion. A strong kosmotrope could have up to 5 or 6 water molecules in its solvation shell. A strong chaotrope, on the other hand, could bind a single water molecule, or none at all, as it approaches the limit of a nonpolar solute, where the surrounding water molecules only form hydrogen bonds with one another, enclosing the solute in a cage-like clathrate structure (see [2] Cooperative and Coherent Water, SiS 48).

The jumping bond

How rigid is the solvation shell around the solute, and does the hydrogen bond - which breaks and reforms within a picosecond (10^-12s) - readily change partners or orientate?

Molecular dynamic simulations carried out on NaCl solutions by researchers at Ecole Normale Superieure Paris, France, and University of Colorado, Boulder, Colorado, USA, showed that the hydration sphere around chloride ions is labile, consistent with previous assessment of chloride as a weak chaotrope [3]. A molecule in the first solvation shell can  switch partners by a large reorientation - an ‘angular jump’ of some 60 to 70˚ - after which the water molecule involved leaves the anion’s solvation shell and moves to the second shell (see Fig. 1).

Figure 1  A water molecule switching partners in hydrogen-bonding between the ion and another water molecule

This will, no doubt, contribute to the challenging study of water dynamics in the hydration shells of biomolecules such as proteins and nucleic acids, where both experiments and simulations have already pointed to a dynamical regime quite different from bulk water. In particular, it suggests that the first hydration shell is very labile, exchanging rapidly with the second shell and not rigid as has been previously suggested

Researchers led by KJ Gaffney at Stanford University California in the USA and Stockholm University in Sweden decided to put the simulation result to experimental test. They devised a variant of two-dimensional infrared spectroscopy to investigate this jump in orientation that occurs on switching partners in hydrogen bonding. The results confirmed that a water molecule can shift its donated hydrogen bond between water and perchlorate acceptors by large angular jumps of 49 + 4˚ on average.

Actually, changing partners involves the water molecule doing a swivel dance in two steps: a really fast swivel of 40˚ in about 50 fs (femtosecond, 10^-15s), followed by a slower rotation of 27˚ in 1 about ps.

Dissolving sodium chlorate NaClO₄ in water mixed with heavy isotope deuterium tracer (D₂O) makes it possible to distinguish two kinds of OD bonds by the way they stretch when excited by infrared light. The OD group acting as donor to another water molecule (ODw) absorbs at 2 534 cm-1, whereas the OD group donating to a perchlorate anion (ODp) absorbs at 2 633 cm-1. Thus, one can track hydrogen-bond exchange in two-dimensional infrared spectroscopy. In addition, the orientation jump angle can be measured using polarized probes that make the signal from the exchanged hydrogen bond highly dependent on the polarization direction. That was how the researchers managed to catch this exotic dance step in water’s quantum jazz

Dancing with multiple partners at the same time

What happens when more than one kind of ions exist in solution as is usually the case in real life?

Researchers at the Institute for Atomic and Molecular Physics in Amsterdam, Netherlands, used a combination of Terahertz dielectric spectroscopy and femtosecond infrared (fs-IR) spectroscopy to study water dynamics around different ions: magnesium, lithium, sodium and caesium cations, as well as sulphate, chloride, iodide and perchlorate anions. They found that the effect of ions and counterions on water can be strongly interdependent and nonadditive, and in certain cases, extends well beyond the first solvation shell, the layer of water immediately surrounding the ion.

Terahertz dielectric spectroscopy involves characterizing the propagation of a Terahertz (10¹² Hz) pulse lasting ~1ps through the salt solution. The pulses are delayed by refraction (bending of electromagnetic waves) and diminished by absorption. In water, a marked frequency dependence of refraction and absorption arises when the dipoles of water molecules fail to keep up reorienting with the externally applied oscillating field. This leads to a large absorption peak at GHz (10⁹ Hz) and a smaller one around 0.6 THz for pure water at room temperature. These peaks are attributed respectively to the collective reorientation of water molecules (relaxation time t_D ~8ps), and the reorientation of partly hydrogen-bonded individual water molecules (relaxation time t₂ ~250 fs). As the result of interaction with solvated ions, the reorientation of water molecules around ions slows down, shifting the absorption peak to lower frequencies and reducing the absorption at THz frequencies. This is referred to as depolarization.

. The hydration number Np is the number of moles of slow water dipole per mole of dissolved salt and is directly proportional to the slopes of the lines plotting depolarization against concentration (Fig 2 left). Generally, ions with a high charge density (small, multivalent ions with more than one charge) affect the dynamics of a large number of water molecules (high hydration number); these correspond to the kosmotropes described earlier. Ions with a lower charge density (large monovalent ions with only a single charge) tend to affect a small number of water molecules and have a small hydrations number; these correspond to the chaotropes.

Figure 2  Dielectric relaxation (left) vs femtosecond infrared spectroscopy (right)

The results for MgCl₂, LiCl and CsCl are in good agreement with this general rule. For Mg(ClO₄)₂, Np = 6 because ClO₄ is a very weakly hydrated anion, the observed slowly reorientating water molecules are likely located in the first solvation shell of the Mg²⁺ ion. In contrast, for Cs₂SO₄, Np is only 1. Apparently, the water molecules in the solvation shell of Cs⁺ show reorienting dynamics similar to those of the bulk water, probably because the positive charge of the Cs⁺ ion is distributed over a large volume. The slowly reorienting water can be attributed to a water molecule located within the solvation shell of strongly hydrated SO₄²⁺ ion, probably forming hydrogen bonds, with both OH groups, to two oxygen atoms of the SO₄²⁺ ion. The low values of Np found for Cs₂SO₄ indicates that the effect of anions on water reorientation is either negligible or not measurable by dielectric spectroscopy.

Fs-IR spectroscopy probes the reorientation dynamics of individual water molecules with high time resolution. In these experiments, water is doped with 4 percent of D₂O. The OD-stretch vibration is excited, and molecules with their OD group preferentially aligned along the polarization axis of the excitation pulse are most efficiently tagged. By using a second laser probe pulse to interrogate the number of tagged molecules parallel and perpendicular to the excitation axis, the rotation of tagged molecules can be tracked.

Remarkably, MgSO₄ shows a very slow reorientation component, whereas Mg²⁺ and SO₄^2- individually, in combination with other ions do not. This demonstrates that the effect of ions on water dynamics can be non-additive, which needs to be explained.

Also in need of an explanation is an apparent discrepancy between the dielectric measurements and the fs-IR measurements. For hydrated cations, the two methods give different results: Mg²⁺ and Li⁺ show large immobilized fractions when measured with dielectric spectroscopy (Fig. 1, left), but the fs-IR measurements of Mg(ClO₄)₂ and LiI show almost complete reorientation, with a negligible slow fraction (see Fig. 1, right).

The differences between the results of dielectric relaxation and fs-IR spectroscopies can be understood by noting the different vectors that the two techniques probe: the permanent dipole moment of water p in the case of dielectric relaxation and the OD-stretch transition dipole moment m in the case of fs-IR spectroscopy (Fig. 3).

Figure 3  Cooperative dynamics of water induced by ions

The local electric field around the ions causes the dipole vector p of water molecules in the solvation shell of a cation to point  away from the cation (Fig. 3A), whereas for an anion, one of the OH groups of a hydrogen-bonded water molecule points linearly towards the anion (Fig. 3B). For cations, the rotational motion of water molecules that changes the dipole vector m  in the solvation does not lead to reorientation of the vector p. In the case of anions, the reverse effect occurs. the motion of p is unrestricted within a cone with fixed axis m, This explains the insensitivity of dielectric spectroscopy towards anionic hydration, and fs-IR spectroscopy towards cationic hydration. For both cations and anions, these observations lead to a molecular picture of semi-rigid hydration, i.e., water molecules in ionic solvation shells that reorient in a propeller-like manner, giving rise to partial reorientation along a distinct axis. This picture holds for salts for which one of the counterion is weakly hydrated. However, when both ion and counterion are strongly hydrated, the effect on water dynamics can be much stronger and nonadditive.

The dielectric spectroscopy data show that Mg(ClO₄)₂ has a hydration number Np=6 and that Cs₂SO₄ has a hydration number Np=1; these values are associated with water molecules directly adjacent to the Mg²⁺ ion and a water molecule hydrating the SO₄^2- ion respectively. For MgSO₄, Np=18, much larger than the sum of the hydration numbers of Mg(ClO₄)₂  and  Cs₂SO₄; and this is because of a cooperative effect between the cation and the anion. The size of most ions allows them to be structurally surrounded by four to six water molecules. Hence a value of Np>6 and Nm>12 implies that the effect of the ion on the orientational dynamics of water extends well beyond the first hydration shell of water molecules.

The same cooperativity is observed in the fs-IR measurements where MgSO₄ has a much larger fraction of slowly reorienting water molecules, corresponding to a hydration number Nm = 32; whereas Mg(ClO₄)₂  and  Cs₂SO₄ have hydration numbers Nm of 4 and 9 respectively. For MgSO₄, there are about twice as many slowly rotating OH groups as slowly rotating dipoles, which indicates that the same collection of slow water molecules is observed by fsIR and THz DR spectroscopies. Even the combination of moderately strongly hydrated cation Na⁺ with the strong anion SO₄^2-  is observed to affect the dynamics of a large number of water molecules.

The cooperativity in ion hydration can be explained by the fact that the cation and anion lock different degrees of freedom of the water molecules. The nearby presence of both ions can thus lead to a locking in both directions of the hydrogen-bond structure of several intervening water layers, giving rise to slowed water molecules well beyond the first salvation shell (see Fig.2 C). The solvation structure is expected to be quite directional between the ions. This interpretation also means that the slowly reorienting water molecules are not arranged in a spherically symmetric way around the ions.

These findings have large implications on water dynamics within the living cell that contains a huge variety of molecular and ionic species all participating in water’s quantum jazz. We can get an inkling of that from the effect of inorganic ions on proteins in solution [5] (The Rainbow Ensemble, SiS 48). 

Article first published 28/09/10

---

References

1. Dill KA, Truskett TM, Vlachy V and Hribar-Lee B. Modelling water, the hydrophobic effect and ion solvation. Ann Rev Biophy Biomed Struct 2005, 34, 173-99.
2. Ho MW. Cooperative and coherent water. Science in Society 48.
3. Laage D and Hynes JT. Reorientational dynamics of water molecules in anionic hydration shells. PNAS 2007, 104, 11167-72
4. Tielrooij KJ, Garcia-Araez N, Bonn M and Bakker HJ. Cooperativity in ion hydration. Science 2010, 328, 1006.
5. Ho MW. The rainbow ensemble. Science in Society 48.