Energy flow in the hydrogen bonding network of water is traced by resonant terahertz excitation and off-resonant optical probing.
Energy dissipation in water is very fast and more efficient than in many other liquids. This behavior is commonly attributed to the intermolecular interactions associated with hydrogen bonding. Here, we investigate the dynamic energy flow in the hydrogen bond network of liquid water by a pump-probe experiment. We resonantly excite intermolecular degrees of freedom with ultrashort single-cycle terahertz pulses and monitor its Raman response. By using ultrathin sample cell windows, a background-free bipolar signal whose tail relaxes monoexponentially is obtained. The relaxation is attributed to the molecular translational motions, using complementary experiments, force field, and ab initio molecular dynamics simulations. They reveal an initial coupling of the terahertz electric field to the molecular rotational degrees of freedom whose energy is rapidly transferred, within the excitation pulse duration, to the restricted translational motion of neighboring molecules. This rapid energy transfer may be rationalized by the strong anharmonicity of the intermolecular interactions.
Water is a major substance on the earth surface. Its diverse anomalous properties make life on our planet viable. Notably, its large heat capacity turns oceans and seas into giant heat reservoirs for regulating the earth climate. In living organisms, the same property makes water a superb thermal buffer for the function of biochemical reactions (
The molecular dynamics (MD) associated with this network, including the restricted translations and rotations as well as the diffusive motions, cover an exceptionally broad frequency range, with a bandwidth of more than 1000 cm−1. These spectrally broad intermolecular degrees of freedom may then serve as a heat sink with abundant pathways for the accommodation/dissipation of deposited excess energy in water (
While linear-type spectroscopic methods, such as dielectric relaxation, determine the polarization decay of the infrared (IR)–active modes of liquids, nonlinear IR spectroscopy has extensively been used to provide complementary microscopic insights into the accompanying energy dissipation processes. For example, the O─H stretch vibration has been used as a local probe to interrogate the dynamics of its surrounding (
However, despite these efforts, there are still various open questions regarding the energy flow in the H-bond network. For example, to what extent do intermolecular modes and processes contribute to the energy transfer within the H-bond network of water? What is the time scale for the energy transfer between these motions, and how strongly they are coupled? We believe that a more accurate understanding of the energy dissipation process in water will emerge by direct interrogation of the low-frequency intermolecular degrees of freedom. Because the spectral fingerprint of the intermolecular H-bonding dynamics lies in the terahertz (THz) frequency range, it is promising to resonantly pump the low-frequency collective modes/processes of water with a THz pulse and watch the response of the system in real time.
This method has already provided insights into intramolecular mode coupling in halogenated liquids (
Here, we resonantly excite the collective rotational degrees of freedom of water with intense THz pulses and probe the resulting optical anisotropy in a THz Kerr effect (TKE) configuration (
A schematic of the TKE experiment is shown in
(
In a first set of experiments, water is excited in a top-open bucket to directly compare its TKE signals in the vapor and the liquid states. In this experiment, the sample is excited with the THz pump pulse centered at 0.7 THz, and its temperature is raised from 283 to 340 K. The density of the vapor on top of the bucket is changed with temperature.
To precisely obtain the TKE response of liquid water with no vapor contribution, a liquid water film (thickness of 100 μm) is held between a rear glass window and a 150-nm-thick silicon nitride (SiN) membrane as the entrance window (
We also compare the THz field–induced optical birefringence of liquid water and that induced by an optical pump pulse. Both optical and THz excitations are conducted in the same setup under otherwise identical conditions.
In the TKE process of polar liquids, the THz pulse resonantly drives the IR-active intermolecular degrees of freedom, and the optical probe pulse interrogates the dynamics of the Raman-active modes/processes. To facilitate the interpretation of our observed signals, the dielectric loss (Im ε) and the incoherent Raman spectrum of liquid water are provided in
The lowest-frequency THz pulse at ~0.7 THz (cyan area) is generated by optical rectification of laser pulses (center wavelength, 800 nm; pulse duration, 350 fs; pulse energy, 4 mJ; repetition rate, 1 kHz) from an amplified laser system in a 1.3 mole percent MgO-doped stoichiometric LiNbO3 crystal (LN) with the tilted pulse front technique (
We start with the TKE signal in the top-open bucket of water after its excitation with the pulse at ~0.7 THz. As shown in
In a vertical configuration, the THz pump and optical probe pulses propagate into a top-open bucket of water. The ratio of vapor to liquid in the path of the two beams varies by temperature. The vapor (liquid) signal is dominant at higher (lower) temperatures. The strong oscillations indicate single-molecule coherent rotational motion of water vapor. A remarkable effect, pertinent to the current study, is the bipolar TKE signal of liquid water.
The measured TKE signal of water (pumped at ~1 THz) in the cell and at room temperature is shown in
(
1)Bipolarity: The TKE response of liquid water excited at about 1 THz is bipolar, in stark contrast to the TKE signal of water vapor, the OKE signal, and the TKE signals of water pumped at ~3 and ~19 THz. The bipolar TKE signals of liquids have so far been observed only in water and n-alcohols (
2)Relaxation: The tail of the TKE signal relaxes with a time constant of ~0.5 ps. To determine this time constant, we phenomenologically modeled the TKE signal of water by convoluting two exponential functions with the assumed instantaneous electronic response of water, estimated by the TKE signal of a thin diamond plate. As illustrated in fig. S2, two exponential components with opposite signs and decay times of ~0.12 (green line) and ~0.5 ps (red line) can fit the experimental result reasonably well (magenta line). The discrepancy at the leading edge of the THz pulse most likely arises from the dispersion of water, which was neglected in the modeling. As the faster 0.12-ps component overlaps with the instantaneous electronic response, we focus in the current study on the 0.5-ps component. Note also that, as we use an ultrathin cell window (150-nm-thick SiN membrane), the measured TKE signal can be uniquely assigned to the liquid response. For thick windows, subtraction of the window response from the liquid response is essential and often a technical challenge, which may easily lead to the extraction of different relaxation time constants from the measured signal (
3)Enhancement: Relative to the amplitude of the feature around time zero, which resembles the THz electric field square, the bipolar TKE signal of water has an enhanced amplitude. In both the off-resonant optical excitation and the resonant excitations at ~19 and ~3 THz, the nuclear part of the dynamic Kerr signals has relatively small amplitudes.
As shown in
At lower frequencies at about 6 THz, there is a relatively strong contribution of the H-bond stretch vibration. With a resonance frequency of ΩO − O/2π ≈ 200 cm−1 and a damping rate of γO − O ≈ 180 cm−1, the stretch vibration is believed to be the result of the charge delocalization along the H-bonds (
The very low frequency region of water dynamics is typically fit by two Debye processes. The slowest Debye process D1 with the relaxation time τD1 ≈ 9 ps has a pronounced presence in the dielectric spectrum of water, while its Raman contribution is negligible (
Because of the action of the pump field, polarized along
ΔΠM characterizes the degree of anisotropy of the unperturbed Π and is usually labeled Δα for single gas-phase molecules (
Although the purpose of this work is to understand the collective dynamics of liquid water, it is useful to discuss the TKE signal of single water molecules in the gas phase. In the TKE process of polar molecules, the molecular alignment is achieved by the coupling of the THz electric field and the molecular permanent dipoles (
Although the gas-like rotation of single water molecules is fully damped in the liquid, it exists as the hindered rotation at frequencies above ~10 THz. Thereby, the unipolar TKE signal of water from the THz pump at ~19 THz (
The latter discussion declares that the single-molecule rotational dynamics cannot explain the bipolar shape the TKE signal of liquid water, in contrast to the conclusion drawn in (
We first calculate the degree of molecular orientation as an ensemble average of the angle between the THz electric field (at ~1 THz) and the molecular bisector. The results of our AIMD and FFMD simulations are given in
The orientational dynamics of water molecules after THz excitation obtained from both AIMD and FFMD simulations. The θ in
Likewise, we simulate the degree of molecular alignment 〈cos2θ(
To shed some light on the origin of the bipolar TKE response of water, we directly calculate the THz electric field–induced polarizability anisotropy evolution from the MD. As detailed in the Supplementary Materials, our calculation is based on a dipole-induced dipole (DID) model for the FFMD (
The main outcome of our MD simulations, shown in
To shed light on the nature of the underlying motion, we refer again to our MD simulations and calculate the kinetic energy (KE) evolution of water molecules after their excitation with the THz pulse at ~1 THz. In the AIMD simulations, we partition the total KE of the system into three contributions from molecular rotational KErot, translational KEtrans, and intramolecular vibrational contributions. The latter component remains almost constant within the noise level, thereby is not shown. In the FFMD simulations, molecules are rigid and their KE has only rotational and translational contributions.
The FFMD simulations results, namely, KErot(
(
With the higher noise level in AIMD, the step-like rise in temperature cannot be seen. So here, we alternatively monitor the deviation from equipartitioning by plotting the ratio of the translational (rotational) KE to the instantaneous total KE. A deviation of this ratio from one-third gives a nonequilibrium distribution of KE. Here, we also observe the transient nonequilibrium partitioning of KE between the molecular translational and rotational dynamics, with KEtrans gaining more KE at the expense of KErot. Note that the calculated ratio of the translational and rotational KEs to the instantaneous total KE from the FFMD approach (fig. S4) gives similar results as in the AIMD method, indicating the consistency of the MD results. The MD simulation results also show that the relaxation dynamics of the excess KEtrans match nicely with the relaxation tail of the TKE signal of water. In the FFMD, KEtrans relaxes exponentially with time constant τ ≈ 0.5 ps, and in AIMD, it relaxes to its equilibrium value also exponentially with a time constant of τ ≈ 0.75 ps.
Although the KE plot in
The situation with AIMD is more subtle. Here, not only rotations but also translations are IR active. Previous AIMD simulations have shown that the H-bond stretching peak at ~200 cm−1 is IR active, while the H-bond bending peak at 50 cm−1 does not seem to be so (
The latter notion is also endorsed by our TKE experiment at ~3 THz. As shown in
One remaining aspect that needs explanation is the nature of the collective motions that gives rise to the collision-induced polarizability and, consequently, the bipolar TKE response of water. One important hint is provided by the many-body expansion of water’s polarizability by Medders and Paesani (
We also believe that the TKE signal of water and its peculiar bipolar shape have unique capacity to provide new microscopic insight on the collective dynamics associated with H-bonding network of water. A suggestive path would be the comparison between the measured TKE signal of water and the calculated Δ
The agreement between AIMD and FFMD results, shown in our study, suggests that the dynamics of water around 1 THz can be well reproduced with a rigid and nonpolarizable water potential. Moreover, the dynamic TKE of water can be simulated by the subsequent retracing of the force field trajectory using the DID model. However, the extension of this conclusion to the dynamics at higher frequencies, such as the O─O stretch vibration at ~5 THz, in which the intermolecular charge fluctuations are crucial (
In summary, upon resonant excitation of the low-frequency rotational motion of water molecules, a Raman response is observed, which is consistently ascribed to the restricted translational motion of water molecules. This response, which arises from the coupling of the intermolecular degrees of freedom of water, declares a pathway for the dissipation of external THz energy into the network of H-bonds. Our MD simulations corroborate this conclusion and show the increase of the KE of the molecular translational motion after the initial coupling of the THz electric field to the rotational motions. The ultrafast flow of energy in the H-bonding network of water may be explained by the strong anharmonicity of the interaction energy of the intermolecular degrees of freedom. Thereby, the TKE may be implemented to measure the efficiency of the rotational-translational energy transfer in aqueous solutions and open a new avenue to explore the impact of ions and biological macromolecules on the H-bonding structure of water (
In the experiment, the linearly polarized THz pump pulse is focused onto the sample cell. The induced transient birefringence is measured by a temporally delayed and collinearly propagating probe pulse whose incident linear polarization is set to an angle of 45° relative to the THz electric field. Because of the pump-induced birefringence, the probe field components polarized parallel (∥) and perpendicularl (⊥) to the pump field acquire a phase difference Δϕ when propagating through the sample, thereby resulting in elliptical polarization. Δϕ is detected with a combination of a quarter-wave plate and a Wollaston prism, which splits the incoming beam in two perpendicularly polarized beams with power
For the temperature-dependent TKE measurements, the static cell is attached to a Peltier element and the temperature of the liquid is calibrated in advance. The stability and accuracy of the liquid’s temperature is determined to be ±0.5 K.
To ensure that the accumulation of pump heat does not influence the results, we performed the TKE experiments also in a flow cell with the same SiN windows. We found no difference between static and flow cells in terms of both dynamics and amplitudes of the signals. Note that the simple calculations based on ∆
The AIMD results also confirm that the temperature rise and the change in the H-bond density along the AIMD trajectory are negligible (see fig. S6). The H-bond survival probability (fig. S7) also shows no effect of the THz excitation on the lifetime of an H-bond. Therefore, the THz excitation in the experiment can be regarded as a small perturbation, which minimally distorts the H-bonded structure of water. After the pulse, we find a slight increase in the probability of H-bond being broken due to the translational diffusion of an initially H-bonded partner, and a slight decrease in the probability that an H-bond is broken because of rotational diffusion of an H-bond donor relative to the acceptor, with the effects cancelling each other so that the probability of survival of the H-bonds remains unaffected by the pulse.
We thank the Paderborn Center for Parallel Computing (PC2) for the generous allocation of supercomputer time.
Supplementary material for this article is available at