Dynamics of confined water molecules

Abstract

We present femtosecond midinfrared pump–probe measurements of the molecular motion and energy-transfer dynamics of a water molecule that is enclosed by acetone molecules. These confined water molecules show hydrogen-bond and orientational dynamics that are much slower than in bulk liquid water. This behavior is surprising because the hydrogen bonds to the C=O groups of the acetone molecules are weaker than the hydrogen bonds in bulk water. The energy transfer between the O—H groups of the confined water molecules has a time constant of 1.3 ± 0.2 ps, which is >20 times slower than in bulk water. We find that this energy transfer is governed completely by the rate at which hydrogen bonds are broken and reformed, and we identify the short-lived molecular complex that forms the transition state of this process.

Water plays an essential role in many chemical and biological processes. Over the last decades, this notion has motivated a lot of work on the dynamical properties of bulk liquid water (1–7). However, the role of water in (bio)chemical processes is often played by a limited number of water molecules in a strongly restricted molecular environment. For example, the stability, structure, and biological function of proteins are largely determined by only a few surrounding layers of water molecules (8). When the water molecules participate directly in a reaction, the number of involved water molecules is even smaller. For example, the proton-pumping function of bacteriorhodopsin involves changes of the hydrogen network that is formed by particular amino acids of the protein and only a few confined water molecules (9–12).

Recently, the dynamics of water in restricted environments was studied by comparing the spectral dynamics of an optically excited probe molecule embedded in a hydrated (bio)molecule with the spectral dynamics of the same probe molecule in bulk water (13). The spectral dynamics reflect the collective rearrangement of the solvating water, and were found to be much slower within the hydrated (bio)molecule than in bulk water. In this article, we present a study of the hydrogen-bond and energy-transfer dynamics of individual H₂O and ¹H²HO molecules in a confined environment. In this study, we probed the dynamics of the water molecules directly with femtosecond midinfrared laser pulses that are resonant with the O—H stretch vibrations.

Experimental Methods

The system of confined water molecules is prepared by dissolving water (0.4 mol/liter) in a mixture of acetone (4.0 mol/liter) and CCl₄. The structures that are formed in this mixture have a polar internal part consisting of an enclosed water molecule forming hydrogen bonds to the C=O groups of a few surrounding acetone molecules, and an apolar external part formed by the methyl groups of the acetone molecules. The favorable interaction between the methyl groups and the CCl₄ molecules allows these structures to enter the apolar CCl₄ matrix. The molecular ratio of H₂O/acetone/CCl₄ is 1:10:40. The system of confined ¹H²HO molecules is prepared by using a mixture of H₂O and D₂O instead of pure H₂O. The molecular ratio of the resulting system of ¹H²HO/D₂O/acetone/CCl₄ is 1:4:50:200.

In the pump–probe experiments, an intense femtosecond midinfrared pulse (pump) is used to excite a fraction of the water molecules to the first excited vibrational state of the O—H stretch vibration. The absorption changes that result from this excitation are probed with a second, much weaker pulse (probe). The probe pulse is sent through a variable delay to measure the time-dependence of these absorption changes. In the experiments on vibrational relaxation, the probe polarization is at the magic angle (54.7°) with respect to the polarization of the pump. In the experiments on the orientational relaxation, the probe is polarized at 45° with respect to the direction of polarization of the pump, and it is split after the sample in a parallel and a perpendicular part. The transmitted probe beams are dispersed in a monochromator and detected by a 3 × 32 MCT (mercury–cadmium–telluride) array detector. The frequency resolution is 16 cm^-1 per pixel of the array. The midinfrared pump and probe pulses are generated by means of nonlinear frequency conversion processes that are pumped by the pulses of a commercial system of a Ti:Sapphire oscillator, a regenerative amplifier, and a multipass amplifier. These pulses have a central wavelength of 800 nm, a pulse energy of 2.6 mJ, and a pulse duration of 100 fs. The midinfrared pump pulses are generated by means of parametric generation and amplification in β barium borate (BBO) and KTiOPO₄ (KTP) crystals. The midinfrared probe pulses are generated by means of parametric generation and amplification in a BBO crystal, followed by difference frequency generation in a AgGaS₂ crystal. The pump and probe pulses are independently tunable between 2.6 and 3.3 μm (3,000–3,800 cm^-1), and they have a pulse duration of 170 fs, spectral widths of 60 and 300 cm^-1 (full width at half maximum), and energies of 10 and 0.1 μJ, respectively. Frequency-resolved cross-correlation measurements show that the large bandwidth of the probe does not result from a linear chirp.

Results

In Fig. 1a, absorption spectra of the confined water molecules are shown for both H₂O (solid curve) and ¹H²HO (dashed curve). The spectra of H₂O and ¹H²HO show great similarity, both showing a broad band at 3,530 cm^-1 and a narrow band at 3,690 cm^-1. These frequencies are obtained from a decomposition of the spectrum into Gaussian bands. The bands at 3,530 and 3,690 cm^-1 cannot represent the symmetric and asymmetric O—H stretching modes of H₂O, because then they would not have been observed for ¹H²HO. Instead, these bands represent the vibration of a hydrogen-bonded O—H group (ν_b = 3,530 cm^-1) and a non-hydrogen-bonded O—H group (ν_f = 3,690 cm^-1) (14, 15). The absorption of the band at ν_b is much stronger than the band at ν_f, because the cross section of the O—H stretch vibration increases (by a factor of ≈10) upon hydrogen-bond formation. The similarity of the spectra of H₂O and ¹H²HO shows that the two O—H vibrations of H₂O are decoupled in a similar fashion as the O—H vibration and O—D vibration of ¹H²HO. Hence, in the dominant conformation formed by H₂O/¹H²HO with acetone (structure S in Fig. 1a) only one of the two groups of the H₂O/¹H²HO molecule is hydrogen bonded to anacetone molecule.

Fig. 1.

Linear and nonlinear spectral response. (a) Spectra of H₂O (blue curve) and ¹H²HO (green curve) molecules in acetone/CCl₄. (Inset) The two different structures of the water–acetone complex with the corresponding O—H vibrational modes are shown. The labels ν_b and ν_f denote the stretch vibrations of the hydrogen-bonded and non-hydrogen-bonded O—H group of structure S, respectively. ν_s and ν_a denote the symmetric and asymmetric stretch vibrations of the two hydrogen-bonded O—H groups of structure T. The peak at 3,400 cm^-1 represents the absorption of the overtone of the C=O stretch vibration of acetone. (b) Transient spectra of H₂O molecules confined in acetone/CCl₄ at three different delays after excitation with an intense femtosecond pump pulse with a central frequency of 3,690 cm^-1.

The H₂O spectrum shows a weak additional band at 3,635 cm^-1 that is not observed for ¹H²HO. This band represents the asymmetric O—H stretching mode of the H₂O molecule. This band indicates the presence of a less abundant second conformation (structure T in Fig. 1a), in which the water molecule forms two hydrogen bonds of approximately equal strength with two acetone molecules. As a result, the O—H stretch vibrations of H₂O in structure T form delocalized symmetric and antisymmetric vibrations. The anti-symmetric O—H stretch vibration is observed as a small peak at 3,635 cm^-1 (ν_a). The symmetric O—H stretch vibration has a weaker absorption than the antisymmetric O—H stretch vibration and absorbs at a lower frequency. The absorption of this vibration cannot be distinguished in the spectrum, because it is completely dominated by the strong ν_b band of structure S.

The dominance of the S structure over the T structure can be explained from the steric interactions of the acetone molecules. The formation of a T structure requires the proximity of two acetone molecules. Because of the repulsion of the methyl groups, the hydrogen bonds of the T structure are relatively long and weak, thus making the T structure less stable than the singly bonded S structure.

In Fig. 1b, the changes in the absorption spectrum of confined H₂O induced by a strong pump pulse with a central frequency of 3,690 cm^-1 are shown at three different delays after the excitation. This pump pulse is resonant with the 0→1 transition of the ν_f band. In all spectra, a decrease in absorption of the three bands ν_b, ν_a, and ν_f is observed. This absorption decrease results from the bleaching of the fundamental 0→1 transition of the O—H stretch vibrations. In addition, new absorptions are observed at 3,180 and 3,350 cm^-1. The band at 3,350 cm^-1 mainly represents the 1→2 excited state absorption of ν_b, but also contains the 1→2 absorption of ν_a. These bands are red shifted compared with the fundamental transitions because of the anharmonicity of the O—H stretch vibrations. The band at 3,180 cm^-1 is not observed for the ¹H²HO system, which implies that this band cannot result from acetone or CCl₄. This band likely results from the transition from the ν = 1 state of the ν_f mode to the ν = 2 state of the ν_b mode of the H₂O molecule, which is a transition that involves a change of three vibrational quanta. The presence of this transition indicates that the two O—H groups of confined H₂O are anharmonically coupled. The transient spectra show a strong dependence on delay. The bleaching signal of the ν_b band at 3,520 cm^-1 increases in the delay time interval of 0.5–2 ps, which indicates that the original excitation of ν_f is partially transferred to ν_b. For delays of >3 ps, the shape of the transient spectrum no longer changes, and only the amplitude of the spectrum decreases, because of the relaxation of the ν = 1 state of the O—H stretch vibrations.

To study the dynamics of the energy transfer between ν_f and ν_b, we measured delay time scans for both confined H₂O and ¹H²HO (Fig. 2). These curves are measured by using an angle of 54.7° (magic angle) (16) between the pump and the probe polarization. As a result, the measurements only reflect the population relaxation dynamics and the energy transfer between different vibrational bands. All curves shown in Fig. 2 are nonmonoexponential, and they show a strong dependence on the frequencies of pump and are probed for delays of <3 ps. When the ν_b band is both pumped and probed (upper curve of Fig. 2a), a fast initial decay with a time constant of 1.3 ± 0.2 ps is observed. If instead ν_f is pumped and ν_b is probed (lower curve), an ingrowth with the same time constant is observed. These results show that there is an equilibration of the excitation of the ν_b and ν_f bands with a time constant of 1.3 ± 0.2 ps. As a result of this equilibration, both bands show the same exponential decay at delays of >3 ps. The time constant of this decay is 6.3 ± 0.5 ps and represents the averaged lifetime T₁ of the O—H stretch vibrations. For bulk liquid water, the vibrational lifetime was observed to be 260 fs (17), which implies that the confined water molecules retain the excitation of the O—H stretch vibration >20 times as long. In Fig. 2b, measurements for ¹H²HO obtained with the same pump and probe frequencies are shown. Interestingly, the observed dynamics are the same as in Fig. 2a, which implies that the equilibration of the excitation between ν_b and ν_f cannot result from a direct transfer of vibrational energy between the two O—H groups. The similarity of the data measured for H₂O and ¹H²HO shows that the transfer between the ν_b and the ν_f bands in the spectrum must result from hydrogen-bond dynamics. When a hydrogen bond is formed at an excited nonbonded O—H group, the frequency of the excitation changes from ν_f to ν_b. Vice versa, when a hydrogen bond is broken at a hydrogen-bonded, excited O—H group, the frequency changes from ν_b to ν_f.

Fig. 2.

Delay time scans of H₂O molecules confined in acetone/CCl₄ (a and c) and ¹H²HO molecules confined in acetone/CCl₄ (b) measured with different pump and probe frequencies.

The absence of direct energy transfer between the two O—H groups of H₂O in structure S is surprising, because the presence of the relatively strong band at 3,180 cm^-1 shows that the two O—H groups of H₂O are strongly anharmonically coupled. However, energy transfer requires not only the presence of a strong (anharmonic) coupling, but also that the interacting (combinations of) states are in resonance. Apparently, the energy difference of ≈160 cm^-1 of the ν = 1 states of the ν_b and ν_f modes is too large for energy transfer to be possible. Clearly, energy matching is not an issue in exciting the ν = 1 state of the ν_f mode with a 3,180 cm^-1 photon to the ν = 2 state of the ν_b mode, so that anharmonic coupling can be effective in enabling this transition.

In Fig. 2c, the ν_a band of H₂O is pumped. If the ν_a band is also probed (upper curve), the signal contains a rapid decay component with a time constant of 150 ± 50 fs. If the ν_b band is probed (lower curve), a rapid ingrowth with the same time constant is observed. These results show that structure T is short-lived and rapidly converted into structure S. At delays of >1 ps, the signal decays with the same time constant of 6.3 ± 0.5 ps that was observed at delays >3 ps (Fig. 2 a and b).

To get additional information on the hydrogen-bond dynamics and the mechanism of energy transfer of the confined water molecules, we measured the dynamics of the anisotropy of the excitation. In our experiments, the excitation is anisotropic, because predominantly O—H groups are excited that are oriented parallel to the pump polarization. The anisotropy is defined as follows:

where Δα_∥ and Δα_⊥ are the absorption changes measured with probe pulses that are polarized parallel and perpendicular to the polarization of the pump, respectively. For an ensemble of randomly oriented dipolar oscillators, Δα_∥ = 3Δα_⊥ at zero delay, so that R = 0.4. At later delays, R decays because of the reorientation of the water molecule and/or because of resonant energy transfer between the two O—H groups. In Fig. 3a, the ν band of ¹H²HO was pumped and probed and R is observed to show a monoexponential decay with a time constant of 6 ± 1 ps. Clearly, for ¹H²HO there can be no energy transfer between two differently oriented O—H groups, so that the dynamics of R represents only the molecular reorientation. In Fig. 3b,the ν_b band of H₂O was pumped and probed. At delays of >3 ps, the signal shows the same decay with a time constant of 6 ± 1 ps that was observed for ¹H²HO in Fig. 3a. However at shorter delays, the anisotropy shows an additional rapid decay with a time constant of 1.1 ± 0.3 ps to a value of ≈0.1. This time constant is similar to the time constant of the hydrogen-bond dynamics of 1.3 ± 0.2 ps. This similarity and the absence of the fast component for ¹H²HO indicate that the hydrogen-bond dynamics not only lead to a change of the vibrational frequency of the excited O—H group (Figs. 2 a and b) but also mediate a transfer of energy to the other O—H within the H₂O molecule. When this process is complete, the two O—H groups of the H₂O molecule have equal probability of being excited, and the anisotropy should have a value of (18), where P₂ is the second-order Legendre polynomial and δ is the angle between the two transition dipoles. For δ = 104°, which is the angle between the two OH-groups of the water molecule, this expression gives R(0) = 0.12, which is in good agreement with the experimental observation. In Fig. 3c, the ν_a band was pumped and the ν_b band was probed. In this experiment, R is observed to have a starting value of 0.12. This result implies that structure T is converted to structure S with equal probability for the two O—H groups to become the hydrogen-bonded O—H group. Note that the dynamics of Fig. 3c do not give information on the dynamics of this conversion, because the anisotropy parameter reflects only the orientation of the probed excitation and not its amplitude.

Fig. 3.

Anisotropy decay of ¹H²HO molecules confined in acetone/CCl₄ (a) and H₂O molecules confined in acetone/CCl₄ (b and c) measured with a probe frequency of 3,350 cm^-1 (resonant with the 1→2 transition of the ν_b mode). The pump frequencies are 3,520 cm^-1 (a and b) (resonant with the 0→1 transition of the ν_b mode), and 3,620 cm^-1 (c) (resonant with the 0→1 transition of the ν_a mode).

Based on the findings described above, we can identify the mechanism of energy transfer of the confined water molecules, as shown in Fig. 4. The four structures S_I–IV differ in which O—H group is hydrogen bonded and in which local O—H vibration (ν_b or ν_f) is excited. The mechanism by which energy is transferred from one O—H group the other is as follows. The strong hydrogen bond to one of the O—H groups of an S structure weakens, while simultaneously at the other O—H group, a new hydrogen bond is formed. The time scale of this process is 1.3 ± 0.2 ps. When the hydrogen bonds are approximately equal in strength, the uncoupled O—H stretch vibrations are in near resonance, with the result that the coupling between the two O—H groups leads to a strong delocalization of the vibrational excitation over the molecule. This delocalized state constitutes the transition state T. T rapidly evolves with a time constant of 150 ± 50 fs to one of the four different structures S_I–IV by strengthening one of the hydrogen bonds and breaking the other and by transferring the delocalized O—H stretch excitation into a local excitation of one of the O—H groups. Hence, the original excited structure S is equilibrated over all four structures S by going through the T structure. This process leads to an equilibration of the excitation over the ν_b and ν_f modes and over the two O—H groups. The confined ¹H²HO molecule shows exactly the same hydrogen-bond dynamics and molecular reorientation as the confined H₂O molecule. However, an important difference is that for ¹H²HO there are only two S structures because the excitation of the O—H stretch vibration can only reside at one side of the molecule. Therefore, for ¹H²HO the S structures are either S_I and S_II (O—H at the right side of the molecule), or S_III and S_IV (O—H at the left side of the molecule). This notion means that for ¹H²HO the interconversion of the S and T structures will leave the excitation at the same side of the molecule. Hence, for ¹H²HO the interconversion of the S and T structures only leads to an equilibration of the excitation over the ν_b and ν_f modes.

Fig. 4.

Schematic representation of the mechanism of energy transfer for water molecules confined in acetone/CCl₄. Arrows next to O—H groups indicate that the vibration is excited.

The mechanism of Fig. 4 implies that the ν_a band observed in the spectrum constitutes the absorption spectrum of the transition state T for the transition between different S states. For this state, the hydrogen bonds are expected to be weaker than those of the reactant/product structures S_I–IV. The energy splitting between the delocalized ν_s and ν_a modes of the H₂O molecule is ≈100 cm^-1 (19). Hence, the uncoupled O—H vibrations of the T structure are expected to have frequencies of ≈3,580 cm^-1, which is less red shifted with respect to the gas phase O—H stretch frequency than the frequency of the ν_b band. This smaller red shift shows that the hydrogen bonds of T are indeed weaker.

Discussion

The observed hydrogen-bond and orientational dynamics of the confined water molecules strongly differ from the corresponding dynamics of bulk liquid water. The hydrogen-bond dynamics of bulk liquid water have been extensively studied with femtosecond midinfrared techniques. In the older studies (1–3), the hydrogen-bond length correlation function was observed to show a single-exponential decay, with a time constant of ≈500 fs. More recently, evidence was found that the decay of this correlation function is nonmonoexponential, with time scales of ≈100 fs and ≈1 ps (5–7). The reorientation of bulk water was observed to have a characteristic time scale of 2.6 ps (20), which is approximately three times shorter than the reorientation time of 6 ± 1 ps observed here for confined water molecules.

Note that the difference between bulk and confined water cannot be explained from the strength of the hydrogen-bond interactions. From the frequencies of the O—H stretch vibrations, it follows that the hydrogen bonds between water and the C=O groups are weaker than those between the molecules in bulk liquid water, from which it could be expected that the dynamics of confined water would be faster instead of slower than the dynamics of bulk water. However, for bulk liquid water, the energy cost of locally breaking a hydrogen bond can be largely compensated by a simultaneous strengthening and/or formation of bonds at nearby molecules, so that the energy barriers in changing the molecular orientation and hydrogen-bond structure can be relatively low.

An interesting finding is the complete absence of direct energy transfer between the two O—H groups of the confined water molecule in structure S, as evidenced by the strong similarity of the spectral dynamics of confined H₂O and confined ¹H²HO (Fig. 2 a and b). Apparently, the energy mismatch of the ν = 1 states of the ν_b mode and the ν mode of ≈160 cm^-1 cannot be compensated easily by the participation of a low-frequency intermolecular mode in the energy transfer. This finding may seem surprising, because in the relaxation of the O—H stretch vibration of ¹H²HO dissolved in D₂O, the energy gaps to the accepting modes are much larger than 160 cm^-1, whereas the relaxation time constant T is only 740 fs. However, ¹H²HO dissolved in D₂O and the present system of confined water molecules strongly differ in their mode density of strongly coupled intermolecular low-frequency modes. For ¹H²HO dissolved in D₂O, there exists a high density of intermolecular hydrogen-bond stretching and bending vibrations that have relatively high frequencies and that are strongly coupled to the O—H stretch vibration. Therefore, an energy mismatch of a few hundred wavenumbers can be compensated easily, leading to relatively fast vibrational relaxation. In the H₂O/acetone/CCl₄ system, there are not that many high-frequency intermolecular modes as in bulk water, and these fewer modes will only be weakly coupled to the O—H stretch vibrations of the confined H₂O molecule. Therefore, the energy mismatch of ≈160 cm^-1 between the ν = 1 states of the ν_b and the ν_f modes cannot easily be compensated by the solvent, thus making the direct energy transfer between these states very slow. The weak coupling with low-frequency intermolecular modes also explains the relatively long vibrational lifetime T₁ of 6.3 ± 0.5 ps of confined H₂O and ¹H²HO in comparison with ¹H²HO/D₂O and bulk H₂O.

Because the energy mismatch of the ν_b and the ν_f modes cannot be compensated, the energy transfer has to wait for the two O—H oscillators to become shifted into resonance. This aspect makes the mechanism of energy transfer of confined water essentially different from that of bulk liquid water. In bulk liquid water, there exists a high concentration of near-resonant O—H oscillators. As a result, these oscillators show a dipolar (Förster) energy-transfer process that is completely independent of the structural (hydrogen-bond) dynamics of the liquid (4). In contrast, for confined water, the energy flow within the molecule is governed completely by the rate at which hydrogen bonds are being broken and reformed, which slows down the energy transfer by a factor >20 in comparison with bulk water.

Conclusions

We studied the ultrafast dynamics of confined water molecules by using femtosecond midinfrared pump–probe spectroscopy. In the studied system of a water molecule enclosed by acetone, the hydrogen-bond and orientational dynamics have time constants of 1.3 ± 0.2 ps and 6 ± 1 ps, respectively, which implies that these processes are much slower than in bulk liquid water. This result is surprising, because the hydrogen bonds of the confined water molecules are weaker than the hydrogen bonds in the bulk liquid. The vibrational relaxation time T₁ of the confined water molecules is 6.3 ± 0.5 ps, which means that the O—H stretch vibrations of these molecules retain the excitation energy >20 times as long as the O—H stretch vibrations in bulk liquid water.

The two O—H groups of the confined water molecules show energy transfer with a time constant of 1.3 ± 0.2 ps. This energy transfer involves a mechanism that is essentially different from the mechanism of resonant energy transfer in bulk liquid water. For confined water molecules, energy transfer occurs only after the two O—H oscillators are shifted into resonance. As a result, the energy transfer in confined water is governed completely by the breaking and reformation of hydrogen bonds, which slows down the energy transfer by a factor of >20 in comparison with bulk water.

These results show that the dynamics of confined water molecules strongly differ from those of bulk liquid water. This finding means that water molecules participating in (bio)chemical processes cannot be viewed as small amounts of water having bulk water properties. To understand the role of these water molecules in the (bio)chemistry, a specific study of their structure and dynamics would be indispensable.