Ultrafast hydrogen bond dynamics of liquid water revealed by terahertz-induced transient birefringence

The fundamental properties of water molecules, such as their molecular polarizability, have not yet been clarified. The hydrogen bond network is generally considered to play an important role in the thermodynamic properties of water. The terahertz (THz) Kerr effect technique, as a novel tool, is expected to be useful in exploring the low-frequency molecular dynamics of liquid water. Here, we use an intense and ultrabroadband THz pulse (peak electric field strength of 14.9 MV/cm, centre frequency of 3.9 THz, and bandwidth of 1–10 THz) to resonantly excite intermolecular modes of liquid water. Bipolar THz field-induced transient birefringence signals are observed in a free-flowing water film. We propose a hydrogen bond harmonic oscillator model associated with the dielectric susceptibility and combine it with the Lorentz dynamic equation to investigate the intermolecular structure and dynamics of liquid water. We mainly decompose the bipolar signals into a positive signal caused by hydrogen bond stretching vibration and a negative signal caused by hydrogen bond bending vibration, indicating that the polarizability perturbation of water presents competing contributions under bending and stretching conditions. A Kerr coefficient equation related to the intermolecular modes of water is established. The ultrafast intermolecular hydrogen bond dynamics of water revealed by an ultrabroadband THz pump pulse can provide further insights into the transient structure of liquid water corresponding to the pertinent modes.


Supplementary information SI. Experimental setup and correction of the THz signal detected from GaP
The experimental setup is schematically depicted in Fig. S1. Regarding the acquisition of the THz electric field waveform, we use electro-optical sampling with 100 μm GaP. Because the intense THz pulse saturates the GaP response, we use the THz Kerr signal of diamond to calibrate the THz electric field strength [1][2][3] . For an ultrabroadband THz pulse, it is additionally distorted by frequency-dependent phase matching, reflection, dispersive propagation, and absorption in the electro-optic detection crystal. Therefore, we use the full complex response function of GaP detector to reconstruct all the spectra presented in this work [4][5][6][7] , and the obtained data are shown in Fig. S2. As a result, we obtain an intense (with peak electric field E=14.9 MV cm -1 ) and ultrabroadband (over the range of 1-10 THz with a center frequency of 3.9 THz) THz pulse. The full complex response function ) ( R of the detector is given by： where () G  is a complex function for correcting the mismatch between the THz phase velocity and the group velocity of the optical pulse.
r  is the electro-optic coefficient of the sensor material affected by dispersion and resonant enhancement.
represent the group refractive index of the optical pulse and the complex refractive index of the THz radiation, respectively. According to the full complex response function () R  of the GaP crystal, the THz time and frequency domain signals are reconstructed, and the results are depicted in Fig. S2.

SIV. The Gouy-phase shift has no effect in our experiment
For THz pump pulses of different frequencies, the spot sizes, Rayleigh lengths, and the positions of the beam waist will change slightly. The potential Gouy-phase shift may affect the actual THz electric field waveform. However, in our experiments, the effect of the Gouy-phase shift is negligible 8 .
We define the collinear propagation direction of the THz wave and 800 nm beam as the Z-axis. The independent variable z is the position of the detector (GaP crystal or water film) in the experimental system, and z0 represents the center of the THz beam waist. The positions of GaP crystal or water film are scanned along Z-axis, and the peak points of time-domain waveforms corresponding to the detector positions are plotted in Fig. S5.  ) is less than 0.0605π, the Gouy phase shift caused by switching the LPFs can be ignored.
In the experiment, the system was continuously purged with dry nitrogen gas to eliminate the absorption of water vapor and the gas pressure in the box is constant. In addition, we improved the experimental device to minimize the influence of water vapor on the measurement signal. We adopted the method commonly used by previous researchers to effectively reduce water vapor diffusion 9 . In this method, the water is transported to the reservoir through a funnel and a silicone tube, and the reservoir is placed outside the inflatable box to reduce the absorption of THz wave caused by water evaporation. The method can ensure that water vapor does not accumulate around the water film, which effectively suppresses the interaction between water vapor and the THz electric field. The previous THz spectroscopic results have demonstrated the effectiveness of this method 9 .
However, the nitrogen gas has a small TKE response in our experimental condition. Fig. S7a shows the TKE background responses of nitrogen gas with different THz filters (remove the water film). From the figure, we can observe N2 revivals 10 . These results show that nitrogen gas is likely to affect the TKE response of water. In fact, we observed the revival characteristics of nitrogen gas from the raw data of the TKE response of water (Fig. S7b). We believe that the fluctuations of the TKE signal at about 2 ps, 4 ps come from the N2 revivals. In addition, we did not observe the TKE response characteristics of water vapor (positive response with a relaxation curve extending over hundreds of picoseconds) 11 , which is mainly due to the weak water vapor density and high THz driving frequency in our experiment. Since the water film occupies the focal position of THz wave and water has a strong absorption coefficient in the THz band, the TKE response of nitrogen gas will be reduced due to the presence of water film. We reduced the TKE response of nitrogen gas by a factor of about 1.5 to obtain the red line shown in Fig. S8a. This red line is consistent with the nitrogen gas portion of the raw data for the TKE response of liquid water (blue line shown in Fig. S8a). Therefore, the actual TKE response of water (Fig. S8b) is the result of the difference between the two lines (blue and red lines in Fig. S8a). With the above method, the data shown in our manuscript have all been subtracted the contribution of nitrogen gas to TKE signal.

SVI. Analysis of heating effects
In this work, the pulse fluence at the center of the beam waist is about 30 mJ/cm 2 . Considering the factors such as the heat capacity of liquid water, the reflectivity of the front surface of water, the THz wave absorption of water (We estimate the effective medium length of THz wave in water is about 25 µm in our experiment. At this distance, 90% of THz energy is absorbed by water.), and assuming that all the heat is transferred to the excited volume of water instantaneously without dissipation, each THz pulse can increase the water temperature by approximately 2.6 °C. However, this heating process requires a certain time 2 / rD   [12][13][14] , where r is the characteristic length and D is the thermal diffusivity ( . In our experiment, the THz pulse duration is far less than the thermalization time, thus we believe that the heating effect within extremely short pulse duration is negligible.
In addition, the stable gravity-driven, free-flowing water film used in our experiment has the flow rate of 10 mL min -1 . Within the time interval of 1 ms between two adjacent pulses, the distance that the gravity-driven water film will fall is about ~ 370 µm, which is much larger than the pump spot size of 160 µm. Therefore, there is no heat accumulation between two adjacent pulses.
Moreover, it is challenging to analyze the time-dependent temperature disturbance in the sample excited by an ultrashort pulse until now. In general, this thermal disturbance has a decay time of more than 20 ps in liquid water [14][15][16] . However, in our work, the measured TKE signal of water decreases to the noise level after ~ 1.5 ps upon THz pulse excitation. The experimental results do not reflect the signal characteristics caused by the non-diffusive thermalization effects.
In summary, we believe that the contribution of heating effects to the TKE signal in the experiment is negligible.