Water is the most abundant component of a living cell, and it is usually thought to exist on earth as either ice, liquid, or vapor. Liquid water exhibits maximum density at T = 4°C. For this reason, a large mass of water is unable to freeze completely. With a large isochoric heat capacity minimizing temperature fluctuations, a minimum isobaric heat capacity at T = 37°C minimizing entropy fluctuations, a minimum isothermal compressibility around T = 46°C minimizing volume fluctuations, and the highest cohesive energy per molecular weight among all substances, liquid water is an ideal substance for sustaining life.
But that cannot be the whole story. Estimates indicate that for a globular protein, a nucleic acid, a collagen fiber, or a hyaluronate fiber, a monolayer of water molecules adsorbed on these biopolymers corresponds to a hydration state of 29 percent water (wt%), 33 wt%, 38 wt%, and 41 wt%, respectively. For an average hydration state of 70 wt%, typical of many cells, one could find at most four layers of water molecules around each biopolymer. Such interfacial water has quite different properties than water in its gaseous, liquid, or solid state, or water in dilute aqueous solutions. Whence the fourth state of water, a state that has often suggested a revolution in biology and medicine.
The revolution is still pending. Most spectroscopic techniques can be used as soon as analyzed species differ by at least one covalent bond, but the same molecule is found in both the liquid and morphogenic state. With no periodicity, both phases look very similar, no matter the X-ray, ultraviolet-visible, or infrared photons analysis. The revolution is pending for another reason. The fourth state of water is always found adsorbed on nanometer-sized surfaces. All colloids are unstable, and measuring them in order to track down the elusive fourth state of water may destabilize their fragile colloidal state.
The revolution is not only pending, but is itself in suspension, since there is a real challenge in characterizing the fourth state of water unambiguously. Whatever the analysis, it must use photons whose energies are less than the typical H-bond energy between water molecules—about 7–50 zeptojules (zJ), with 1 zJ = 10–21 J. Taking the lower limit of 7 zJ with Planck’s constant h = 663 zJ·fs, translates into a frequency fmax ≈ 1013 Hz = 10 THz ≈ 350 cm–1. This makes necessary the use of Raman and terahertz (THz) spectroscopy (1 THz ≤ f ≤ 10 THz with 1 THz = 33.356 cm–1). THz spectroscopy using wavenumbers 30–300 cm–1 has proven to be a unique tool to study the intermolecular vibrational modes of water, as well as hydration dynamics around solutes. From an examination of changes in the absolute absorption intensity between 2.1 THz and 2.8 THz (≈ 70–95 cm–1), it was found that the H-bond lifetime in bulk water was 1.5 picoseconds (ps), whereas for the first hydration layer, it was 1.9 ps for glucose and 2.1 ps for lactose and trehalose, with a significant retardation of H-bonds dynamics up to 6–7 Å.1
This view has been challenged by nuclear magnetic resonance (NMR) measurements showing that the dynamic perturbation factor ξ = 1.60 ± 0.02 for the first hydration layer of trehalose,2 where τ0 is the correlation time in bulk water and <τH> is the average correlation time for a number νH of perturbed water molecules. This has led to a controversy concerning the existence of an extended dynamical hydration shell (EDHS) around solutes exceeding the first hydration shell by ca. 3–4 Å.3 For proteins, the discrepancy between THz and NMR spectroscopy becomes thorny as the experimental data between 2.25 THz and 2.55 THz suggest that the EDHS extends beyond 20 Å, a distance much greater than the orientational correlation length of 3 Å that is usually observed.4 Finally, for anti-freeze proteins, measurements in the range 2.4–2.7 THz have revealed that the extent of the EDHS is 20 Å at T = 298K and 27 Å at T = 273K. This corresponds to roughly seven to nine hydration layers.5 For NMR spectroscopy, the perturbed layer of water molecules around proteins is limited to the first or second hydration layer, at most.6 A deeper understanding of the dynamical processes at work in bulk water is needed.
When dealing with interactions between solutes and water molecules, much effort has been directed toward understanding their underlying dynamics. From our everyday experience, we know that the timescales on which changes take place can vary depending on the size of the object. The slowest tools we have to follow such changes are based on radioactive decay. Following the motion of animals requires the use of fast mechanical devices, such as cameras with short exposure times. Electronic devices deal in microsecond and nanosecond timescales, giving rise to various techniques such as electrochemical impedance spectroscopy, NMR, electronic paramagnetic resonance, and nuclear quadrupolar resonance. Faster processes involving picosecond or femtosecond timescales require the use of the fastest tool available in nature, light itself. In the case of bulk water, a photon interacts in some way with the electronic clouds of water molecules by absorption or diffusion. The timescale being investigated is then directly linked to the frequency of the photon. Such is time-resolved or ultrafast spectroscopy.
Several time-domain techniques are available for understanding intermolecular motions in liquids: fluorescence up-conversion, optical Kerr effects, and THz spectroscopy. There are, as well, frequency-domain techniques, including Raman and infrared spectroscopies. In the time domain, water exhibits motion ranging from picoseconds down to a few femtoseconds. Timescales in liquid water at room temperature range from ≈ 10 femtoseconds (fs) for fast librational molecular motion to ≈ 100 fs for hydrogen-bond vibrations; and then from ≈ 1–10 ps for rearrangement dynamics in the hydrogen-bond network to ≈ 10 ps for the collective total dipole relaxation of water.7
In the visible and infrared portion of the electromagnetic spectrum, three kinds of intramolecular vibrations for water molecules can be identified. Made of three atoms each having three degrees of freedom, the fundamental modes of movement for a gas-phase water molecule may be regrouped under three categories: three modes of translation for the center of mass, three modes of rotation around the center of mass, and three modes of vibration leaving the center of mass unaffected. The three intramolecular vibration modes can be further decomposed into two stretching modes of the O-H bonds, a symmetric one leading to an absorption at a characteristic wavelength λ1 = 2.74 micrometers (μm) (f1 = 110 THz or 3,657 cm–1), and another at a shorter wavelength λ3 = 2.66 μm.8 In liquid water, the formation of hydrogen bonds between molecules leads to a redshift, thus broadening the two stretching modes. A single maximum of absorption around 3,400 cm–1 (102 THz) is then observed. The period associated to these changes in O-H distances within a disordered network of hydrogen bonds is on the order of 10 fs.
Intramolecular vibrations of water in its gas phase correspond to a symmetric bend in the H-O-H bond angle, which absorbs at a characteristic wavelength λ2 = 6.27 μm (f2 = 48 THz or 1,595 cm–1).9 Upon hydrogen bonding in the liquid, this bending mode is blue-shifted and is observed at around 1,640 cm–1. The period associated to these changes in H-O-H bond angles within a disordered network of hydrogen bonds is on the order of 20 fs.
The short wavelengths characteristic of asymmetric stretching mean that overtones are readily observable in the near infrared, at wavelengths from λ = 1470 nanometers (nm) to λ = 970 nm, but also in the visible part of the spectrum at λ = 604 nm and λ = 514 nm. Bending overtones may also be observed at λ = 1900 nm, λ = 1200 nm, λ = 836 nm, and λ = 660 nm. With four vibrational absorption bands in the red part of the spectrum, deep water exhibits a wonderful blue coloration. This tint does not depend upon electronic excitations. It is merely the observable effect of the molecular gymnastics performed by water molecules in response to sunlight.
Besides the broadening effect on the stretching and bending vibrations, hydrogen bonding impedes the three fundamental modes of rotation. Three libration modes can be observed using Raman spectroscopy: a twisting mode (L1) absorbing around λ = 25 μm or 435 cm–1, a rocking mode (L2) absorbing around λ =15 μm or 600 cm–1 (L2), and a wagging mode (L3) absorbing around λ = 12.5 μm or 770 cm–1. Within a disordered network of hydrogen bonds, the period associated with these librational motions is on the order of 40–80 fs. It is worth noting that low-frequency twisting corresponds to an impeded rotation around the C2-axis of the water molecule: it should not be infrared-active since it does not affect the dipole moment of the molecule.10 The facts seem to be otherwise. Infrared spectra display two absorption peaks at 380 and 665 cm–1, while dielectric spectra show two bands at 420 and 620 cm–1.11 A better guess is that the lowest frequency librational Raman L1 peak at 435 cm–1 corresponds to a transverse optical phonon-like mode, while the highest frequency L3 peak at 770 cm–1 corresponds to a longitudinal optical phonon-like mode.12 This explains why the highest frequency L3 Raman mode does not appear in infrared or dielectric experiments. The Raman L2 peak at 600 cm–1 belongs to the remnant of the single-molecule wagging response, involved in an (L2 + ν2) overtone with the bending mode observed around λ = 4.65 μm or 2,150 cm–1.13
Observations of water in the far infrared part of the electromagnetic spectrum led to the identification of another broad absorption band around λ = 55 μm. This band corresponds to collective vibrational modes involving intermolecular stretching of hydrogen bonds.14 The period associated to these changes is on the order of 200 fs. Such an absorption band can also be observed in dielectric and Raman spectra around f ≈ 170 cm–1.15 These motions may be further analyzed as symmetric stretching at ≈ 160 cm–1, or antisymmetric stretching at ≈ 290 cm–1, or even as degenerate antisymmetric stretching at ≈ 220 cm–1. The two modes at ≈ 220 cm–1 are estimated to contribute most to infrared activity. The highest antisymmetric mode at ≈ 290 cm–1 appears to be essentially silent.
Another vibrational absorbing mode at ≈ λ = 0.1–0.2 mm arises from intermolecular bending of hydrogen bonds, and can be observed only by dielectric or Raman spectroscopy.16 These hydrogen bond bending motions may be further analyzed as five different modes peaking significantly between 75 and 80 cm–1, but also featuring extended tails deep into the 200 cm–1 resonance.17
Finally, at 25°C, relaxation of the electric dipole of the water molecule is observed ≈ λ = 17 mm, yielding a relaxation time τ1 = 8.32 ps.18 It has been proposed that such a relaxation process corresponds to a water molecule hopping across a distance of 3.3 Å, the separation between occupied and unoccupied corners of a cube binding a pentawater tetrahedron.19 A shorter relaxation time τ2 = 0.31 ps has also been reported, and is associated to water molecules that are not engaged in hydrogen bonding.20 Still another interpretation of a fast relaxation mode occurring between 2 and 10 cm–1 in dielectric spectra is that it corresponds to intrawell rotational relaxation taking place during the waiting period between thermally activated large-angle jumps, which occur in the course of changing H-bond partners.21 Thus it was shown that the H-bond cleavage and the molecular reorientation of water molecules involve large-amplitude angular jumps, rather than small diffusive steps.22 Such jumps occur at a timescale of 1.60 ± 0.16 ps at room temperature and have been experimentally characterized using quasielastic incoherent neutron scattering.23
The trouble with such a conventional approach is just that observations are restricted to an inhomogeneous ensemble of similar molecules. The inevitable result is a picture of average dynamic response, together with a total absence of structural details, which are quickly smeared by fluctuations and the ensuing reorganization that they induce. Ultrafast time-resolved experiments offer the possibility of distinguishing the orientational dynamics of water molecules absorbing at different frequencies. The vibrational relaxation of O-H stretching induces a strong frequency dependence in water, both in the bulk and at its surface. This can be observed using time-resolved infrared spectroscopy.24 The intrinsic T1S lifetime of the relaxing stretch vibration varies continuously from ≈ 100 fs on the red edge of the band to ≈ 1.5 ps on the blue edge. The effect is strongly nonlinear. This longer vibrational lifetime for blue-shifted O-H oscillators results mainly from a reduced frequency overlap with the bending overtone of H2O. Such a result is evidence of the continuous intrinsic structural heterogeneity of liquid water, explaining the strong inhomogeneous broadening of O-H stretch absorption. Within the local H-bonding network, this indicates that faster relaxation occurs for more strongly or highly coordinated O-H groups, and slower relaxation, for more or less weakly coordinated water molecules. After energy transfer from the stretch excitation to the bend overtone, another very fast transfer occurs on a timescale of less than 50 fs toward two bending vibrations of neighboring molecules. The population of bending overtones remains close to zero.25
The lifetime of an excited bending mode is T1B = 176, 174, 200, and 250 ± 15 fs for temperatures T = 277, 295, 323, and 348K.26 Such lifetimes are consistent with a relaxation of the bend vibrational energy and the librational energy of the first hydration shell. The bending fundamental has about twice the frequency of the L2 librational band, while librational motion has the same symmetry as the bending vibration. The dominant energy transfer should be caused by Fermi resonance. The spectral density of the librational overtones at the O-H bending frequency decreases with increasing temperature, explaining the increased lifetime at higher temperature.
Further relaxation of the energy in excited librational motions toward low-frequency H-bond stretching or bending motions occurs with timescales T1L = 750 ± 30, 700 ± 30, 700 ± 30, and 670 ± 9 fs for temperatures T = 277, 295, 323, and 348K.27 Such energy transfers lead to the formation of a macroscopically hot ground state (HGS), corresponding to an overall weakening of the H-bond network. This is characterized by a blue shift in the stretching bands and a red shift in the bending absorption bands. Relaxation from the HGS leading to macroscopic heating of water involves breaking H-bonds, with a timescale of 1–10 ps depending on temperature. A cascading downhill energy relaxation presupposes a weak coupling regime, which effectively allows the contributions from stretching, bending, librational motions, and intermolecular modes to evolve independently.
There is, in fact, experimental evidence for the strongly mixed character of all intra- and intermolecular vibrations in liquid water.28 A better description would invoke delocalized vibrations involving coherent motion spanning several water molecules or vibrational excitons. Simulations suggest that owing to anharmonic interactions, the O-H stretching vibrations are expected to be delocalized over ≈ 5 water molecules. H-O-H bending vibrations should delocalize over ≈ 2–7 molecules, extending to the second solvation shell around a central water molecule.29 Librational modes have a collective character involving 10 to 100 water molecules over the majority of the librational spectrum, but are much more localized in the frequency range higher than 800 cm–1.30 From an experimental viewpoint, such a delocalization is observed as an ultrafast pump-probe anisotropy decay, showing that the initial excitation is quickly scrambled by librational oscillations. The timescale of HGS growth is ≈ 800 fs, regardless of the measurement method or the initial mode excited. This is incompatible with a cascading relaxation mechanism. Were such a mechanism in play, the HGS growth timescale would be longer for stretch excitation than for bend excitation.
How then to characterize the solvation of a newly created charge distribution? A molecular description of hydration dynamics represents a fundamental question in biology: water is the natural solvent of biological processes. The response of solvent molecules to electronic rearrangement should exert a critical influence on chemical reactions in liquids.31 Time-dependent fluorescence Stokes shift (TDFSS) experiments are a technique for measuring the instantaneous vibronic energy of a solute. Owing to their large change in the dipole moment upon optical excitation, large dye molecules are very efficient probes of solvation dynamics. Under the Franck–Condon principle, the equilibrium charge distribution of a solute is instantaneously altered, leaving the solvent molecules in their initial spatial and orientational configurations. Solvent molecules rearrange and reorient themselves in order to stabilize the new charge distribution in the excited state. The time dependence of this rearrangement is reflected in the continuous red shift of the emission spectrum on a timescale characterized by a solvation time τS (longitudinal relaxation).
This technique revealed that water was considered to be among the fastest solvents, with a Gaussian component for solvation of coumarin 343, and a subsequent slower bi-exponential decay.32 A complementary technique, the photon-echo peak shift, has shown that the dynamics for eosin Y in water are characterized by a fast component and two slower components, leading to an average solvation time of (17 × 0.73 + 400 × 0.15 + 2700 × 0.12) = 396 fs.33 The ultrafast solvation may be due to the high-frequency intermolecular vibrational and librational modes of water. It follows that the ultrafast component of the solvation dynamics in water is collective in nature, with a large number of participating water molecules.34 Even if these experiments measure the dynamics of the solvent around the solute, they do it from a solute perspective. Aqueous solvation has recently been studied from the water perspective by Saima Ahmed et al.35 A pulse-width-limited spike of increased THz absorption was observed. The remaining pedestal increases in two steps: the first with a time constant of 10 ± 3 ps corresponding to the Debye relaxation time of water, and the second corresponding to the electronic relaxation of the dye molecule from excited to ground state. Two crucial points emerge from these experiments. First, responses occur on the slowest timescale linked to Debye relaxation and not on the ultrafast timescale related to librational motions. Second, switching the dipole moment of a solute produces a transient THz signal from water, indicating that many water molecules have been affected.
The existence of a fourth state of water with a nanometric spatial range displaying coherent propagation of acoustic and optic modes is corroborated from a dynamical viewpoint. A revolution in biology may be anticipated by switching from a solute to a solvent perspective. The beautiful experiments reported by Ahmed et al. are a first step in such a direction and will pave the way for many other experiments in the field of low-frequency studies of water and aqueous solutions.
