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Hydrogen-Bonding in Liquid Water at Multi-Kilobar Pressures Hendrik Vondracek, Sho Imoto, Lukas Knake, Gerhard Schwaab, Dominik Marx, and Martina Havenith J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.9b06821 • Publication Date (Web): 16 Aug 2019 Downloaded from pubs.acs.org on August 16, 2019

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The Journal of Physical Chemistry

Hydrogen-bonding in Liquid Water at Multi-kilobar Pressures Hendrik Vondracek,†,¶ Sho Imoto,‡,¶ Lukas Knake,† Gerhard Schwaab,∗,† Dominik Marx,∗,‡ and Martina Havenith∗,† †Lehrstuhl für Physikalische Chemie II, Ruhr-Universität Bochum, 44780 Bochum, Germany ‡Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, 44780 Bochum, Germany ¶These authors contributed equally E-mail: [email protected]; [email protected]; [email protected]

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Abstract High-precision THz (30 to 360 cm−1 ) spectra of bulk liquid water are presented from ambient conditions up to hydrostatic pressures of 10 kbar. In concert with ab initio simulations, this allows us to characterize the molecular-level changes of the H– bond network under solvent stress conditions. Both, the experimental and theoretical THz spectra reveal a blue shift in the intermolecular translational mode at 180 cm−1 by 40 cm−1 at 10 kbar and a blue shift together with an intensity increase in the relaxation mode. These changes can be traced back to a pressure-induced increase of the population of so-called short H–bond double donor configurations at the expense of those with longer such intermolecular bonds. Distinct electronic polarization effects are critical to capture the characteristic intensity changes of the THz lineshape function. These advances in high-pressure THz spectroscopy open the door to investigate the pressure response of solvation shells and solute–solvent couplings.

Introduction The bulk thermodynamic properties of water in its different phases can now be described within their experimental uncertainty by accurately parameterized models. 1 Nevertheless, the underlying microscopic picture is strongly debated even today. 2–5 A variety of methods focused on temperature dependent studies under ambient pressure conditions giving access to enthalpic changes. In contrast, pressure perturbation techniques probe activation volume changes and provide complementary information in the multi-kilobar regime. 6 In what follows, we focus on water at high hydrostatic pressure (HHP) conditions. Structural changes in HHP water have been investigated by X-ray diffraction 7–14 and neutron scattering. 15–17 The most recent X-ray scattering studies 10,11,14 report that the position of the first peak at ≈ 2.8 Å in the radial distribution functions gmol and gO-O remains nearly unaffected by HHP conditions while a gradual inward shift of the second and subsequent peaks is observed. The recent study 14 in the pressure range up to 3.6 kbar revealed significant deviations of g(r) 2


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in the range between 3 and 5 Å, indicating that a non-H–bonded fifth water molecule, the so-called interstitial water, is penetrating into the voids of the tetrahedral network. The increasing importance of interstitial water upon hydrostatic compression was confirmed by simulation studies based on the SPC/E 18 and TIP4P 19,20 water models. They find that the distances of the central water oxygen to its first shell neighbors as well as the tetrahedral water structure are hardly affected up to pressures of 10 kbar. However, the entering of the interstitial molecules into the space between first and second shell leads to a

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reduction of the second shell water distances and a broadening of the angular distributions 20 OI1−4 –O– OII 5−8 between the central water oxygen and first shell and second shell oxygens.

Simulations using the TIP5P water model 21 found that the orientational order as a measure of the degree of tetrahedrality is affected in both shells while the translational order as a measure of density variations is mainly changed in the second shell. Recent ab initio molecular dynamics (AIMD) simulations of neat water at 10 kbar versus 1 bar, 22 reveal that the interstitial molecules are so-called topological second to fourth H–bonded neighbors that are squeezed into the tetrahedral voids formed in the first shell by the H–bonded water molecules. In Raman studies, 23–25 no major impact of pressure on the H–bond network in the pressure range up to 10 kbar is observed. While for the OH stretch at 3530 cm−1 , a small redshift of only 5 cm−1 /kbar was found, the center frequency of the water bending mode did not change within error bars. At low frequencies up to 400 cm−1 , two bands centered at 60 and 175 cm−1 were observed at room temperature and assigned to the transverse acoustical (TA) and longitudinal acoustical (LA) phonon modes, respectively. However, they show only a mild pressure dependence whereas they are strongly affected by temperature changes. 25 More recently, the OD stretching mode of HDO in water has been investigated 26 as function of pressure (up to 8 kbar) and temperature, showing that the linewidth changes nonlinearly with water density at room temperature with a turning point at around 1.2 kbar. In a follow-up 2D IR study, 27 the same group showed that the spectral diffusion is nearly 3



pressure-independent while the rotational reorientation times decrease from 2.4 to 1.2 ps. Here, we set out to scrutinize the pressure response of the H–bond network of bulk liquid water at ambient temperature up to its thermodynamic equilibrium freezing point at roughly 10 kbar (i.e. 1 GPa) by combining THz absorption spectroscopy and ab initio molecular dynamics. We focus exclusively on the low frequency (30–360 cm−1 ) IR spectrum of water which includes the hindered translation band at 180 cm−1 and the onset of the librational region at ambient conditions. 28,29 During the last years, we have shown that especially the 30–400 cm−1 THz/FIR spectral range allows one to probe solvent-solute interactions for a large variety of solutes from simple ions 30,31 to hydrophobic hydration of alcohols 32 to complex proteins. 33 Experimentally, detailed analyses of observed center frequencies and line widths of the collective H–bond network modes yield information on structural changes in the hydration layer 34 as well as dynamical processes occurring on femtosecond timescales. 31 Moreover, using AIMD simulations, 35 we were able to fully dissect the THz absorption spectrum of bulk water at ambient conditions 28 and to relate it to the concerted water dynamics in the first and second solvation shells. Here, upon combining experimental and theoretical THz spectroscopy at HHP conditions, we are able to unravel the pressure-induced changes of the H–bond network of liquid bulk water from 1 bar up to its hydrostatic compression limit of about 10 kbar.

Experimental Methods We have measured the low frequency spectrum (30-360 cm−1 ) of water in the pressure range up to 10 kbar using a diamond anvil cell in a FT spectrometer as described earlier 36 using a Almax Easylab VivoDAC Diamond Anvil Cell (DAC). Brass rings (LMB Automation) with an outer diameter of 3.95 mm, an inner diameter of 0.5 mm and a thickness of 40 µm were used without any pre-indentation. Ultra pure (Milli-Q) water was filled into the hole of the gasket, using a syringe with a dental cannula. The DAC was closed with a

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torque of 3.5 N m, applied by a torque wrench. The spectrometer was evacuated to increase signal intensity and restrict absorption by water vapor. After pressurization of the DAC using an automated pressurizing system and a waiting time of three minutes, spectra were recorded with a resolution of 1 cm−1 , averaging over 64 datasets. The changes in the thickness of the sample cell as a function of gas membrane pressure were measured ex-situ using two confocal distance sensors (Micro-Epsilon IFS 2403, Micro-Epsilon, Ortenburg, Germany). All our experimental analyses have been performed using Mathematica 11 (Wolfram Research, Champaign, IL, USA). A full description of the data analysis and the experimental setup is given in the Suppl. Information.

Results and Discussion 35

A

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Figure 1: Experimental absorption (A) and extinction (B) coefficients of bulk water as function of sample pressure. The left and right insets provide the same observables as obtained from AIMD simulations (without any intensity or frequency adjustment or scaling) at pressures of 1 bar (blue line) and 10 kbar (red line) adapted from Ref. 37. Absorption and extinction coefficients of liquid water at a room temperature (T ≈ 296 K) as obtained from our experimental data are shown in Figures 1A and 1B, respectively, for selected hydrostatic sample pressures p. The absorption coefficient is found to increase with pressure over the full accessible frequency range. The H–bond stretch mode is significantly blue-shifting upon increasing p leading to the disappearance of the pronounced intensity min5



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imum at 260 cm−1 of water at ambient conditions. All these pressure-induced changes of the absorption and extinction coefficients are captured by our AIMD simulations 37 at 10 kbar compared to the 1 bar reference (see insets of Figure 1). In order to separate molecular properties and density changes, we determined the molar extinction coefficient (p) = α(p)/cw (p) using the pressure dependent water concentration cw (p). After density correction, the part of the corresponding spectrum below 180 cm−1 is nearly pressure independent while the high frequency part shows still an increase indicating a change in the H–bond network. For further analysis, a spectral decomposition of the experimental data has been performed. At each sample pressure, the extinction (˜ ν ) is dissected into a sum of three damped harmonic oscillator functions of the form

f (ν, ν0 , I0 , w) = 4π 3

I0 ν 2 w2 2 w 2 ν02 + 2π − ν2 + 4

w 2 2π

(1)

ν2

with ν0 , I0 , and w as center frequency, amplitude and width, respectively. For the lowfrequency part, the center frequency was fixed to ν0 = 0 based on work by Shiraga et al. 29 Since the center frequency of the librational band lies outside our accessible spectral range, we have fixed it to νlib = 450 cm−1 for the purpose of fitting the data, so that the total number of varied parameters per spectrum is seven. To exclude systematic effects of the center frequency of the librational band on other line parameters we reanalyzed the data using νlib = 480 cm−1 . We found no significant influence of νlib on the line parameters of the hindered translational and the low frequency bands. Figure 2 shows the results of the fit as a function of sample pressure. The amplitude and width of the librational band experience only small changes when the pressure is increased from 1 bar to 10 kbar. The low frequency band displays an apparent blue-shift of the band maximum and an increase in intensity upon increasing p. We attribute the observed low frequency band to a superposition of unresolved overdamped and nearly overdamped low frequency phonon-like water network motions that involve water molecules beyond the first 6


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30 ϵ in cm-1dm3mol-1

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20 Hind. Transl. 10

Libr.

Relax.

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-1

Figure 2: Lineshape variation of the three contributions to the bulk water spectrum as function of pressure, see text. hydration shell. 28 Each of the modes is coupled to a thermal bath providing fast statistical frequency perturbations (see Schwaab et al. 31 and Shiraga et al. 29 for more details). This corresponds to the Lorentzian (i.e. homogenoeus) limit in the linear response theory of an oscillator coupled to a thermodynamic bath. Since the absorption coefficient is proportional to α ∝ ν˜2 , the highest frequency contribution and the corresponding damping factor will dominate this spectral convolution. We find that we can approximate the low frequency band by a damped harmonic oscillator with zero center frequency and an effective damping factor wrel which is related to the effective relaxation time τrel of the high frequency modes in the low frequency band via τrel = 1/(c wrel ), where as usual, c is the speed of light. The shift of the absorption maximum of the low frequency band can be attributed to a decrease of the fast relaxational time constant, as demonstrated by the red data in the inset of Figure 2. τrel 7



remains constant for pressures below 2 kbar and then decreases nearly linearly. This is in line with viscosity measurements 38 at 20◦ C as well as self diffusion measurements, 39 where the viscosity (self diffusion) remains constant up to 2–3 kbar and then increases (decreases). Interestingly, an opposite effect has been observed for anisotropy decay times that change rapidly for pressures below 2 kbar and remain constant afterwards. 26,27 For the hindered translational (HT) band (ν0 = 180 cm−1 ), the most pronounced pressure effect is a strong blueshift upon increasing pressure. If we use the damped harmonic oscillator model described by Equation 1 we find that the exponential decay time τHT = 1/(c wHT ) first decreases by about 20% and then increases for pressures exceeding p ≈ 5 kbar. That timescale τHT is known to be correlated to the distribution of thermal bath states and their coupling to the oscillator under observation. 40 Therefore, we propose that with increasing pressure the weakening of the H–bond network observed by scattering techniques 14 leads to a broader distribution of thermal bath states and therefore to a reduction of the time constant. At pressures beyond 5–6 kbar, where the compressibility enters a linear regime, 1 increasing pressure results in a stiffening of the H–bond network which causes an effective reduction of the number of accessible thermal bath states either due to a narrower distribution or a reduced coupling strength. To provide the underlying molecular picture, accompanying AIMD simulations 35 at 300 K have been carried out 37 at 1 bar and 10 kbar (see SI for computational details). The theoretical THz spectra (Figure 1, insets) reproduce the experimentally observed changes at 10 kbar compared to 1 bar, namely (i) the blue–shift of the H-bond network peak, (ii) the filling of the local minimum at 260 cm−1 and (iii) the gross intensity increase at frequencies of the network peak and above. To separate the contributions of molecular hindered translations, hindered rotations (librations) and intramolecular vibrations to the low-frequency spectra, we use the instantaneous normal mode (INM) approach; 37,41–45 we refer the interested reader to Ref. 37 for a detailed assessment of the INM approximation applied to the THz spectra of liquid water at ambient and high pressure conditions in direct comparison to the time–correlation 8


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220 Experimental 210 νT in cm-1

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200 Blue shift and intensity increase

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Density scaling

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4 6 p in kbar

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Figure 3: Left: Pressure-induced blue shift of the experimental center frequency of the translational stretching band with error bars. The inset shows that pressure dependence computed from AIMD simulations without any adjustment based on two different analysis protocols (where “ambient” and “10 kbar” refers to using the 2–ds and 2–dl partial THz spectra computed at ambient and 10 kbar conditions which are depicted in the right bottom panels, respectively, as explained in the text) which provides information on the systematic error. Right, top panels: Relative populations of water molecules in bulk liquid water at 1 bar (left) and 10 kbar (right) categorized by the number n of H–bond donor molecules as well as the average H–bond distance being either short or long, n–ds and n–dl , respectively. Right, bottom panels: Partial THz spectra of bulk liquid water at 1 bar (left) and 10 kbar (right) originating from the hindered translation–translation self–correlations, see text. Red circles, blue triangles, and green squares represent the 1–d, 2–d, and 3–d pair classes, respectively, whereas solid and dashed lines with filled and open symbols distinguish furthermore short and long H–bonds for each n–d class, respectively. The thick solid blue lines without symbols are the sums of the 2–ds and 2–dl partial THz spectra at both pressures, whereas the thick dashed–dotted blue line at 10 kbar represents the same data but normalized using the water density at 1 bar. All AIMD data are adapted from Ref. 37. function formalism based on the same trajectories. The pronounced librational band peaked at roughly 700 cm−1 (not visible in Figure 1, inset) mainly arises from rotation–rotation (r–r) self–correlations. It still contributes significant intensity in the frequency range of the H– bond network peak at ≈ 200 cm−1 in perfect agreement with the experimental decomposition in Figure 2. The H–bond network peak originates mainly from translation–translation (t–t) self–correlations as well as contributions due to translation–rotation (t–r) cross–correlations and emerges only as a result of dynamical many–body electronic polarization and intermolec9



ular charge transfer effects. 46–49 The t–t self–correlations are furthermore decomposed within the INM framework in terms of the number n of H–bond donor molecules in the solvation shell. 37 H–bond donors interact strongly with the lone pairs of the reference water molecule. This leads to pronounced electronic polarization and charge transfer effects. Moreover, the different THz responses of H–bonded water pairs subject to H–bond distances shorter and longer than 2.9 Å are computed separately (the cutoff criterion used has been assessed in detail in Ref. 37). Altogether, this yields the six distinct partial THz spectra, labeled n–ds and n–dl with n = 1, 2, 3 (Figure 3, right top panels). Both, at ambient and high pressure conditions, it is found that the n = 2 double donor species contribute most of the intensity to the H–bond network peak (thick solid blue lines). The right bottom panels in Figure 3 reveal that the 2–d species subject to short H–bonds (2–ds , solid blue lines with filled triangles) have their peak maxima systematically blue–shifted by 100 cm−1 compared to those with long H–bonds (2–dl , dashed blue lines with open triangles). This blue–shift exclusively depends on the H–bond length, which implies that it is pressure independent. Upon compression (Figure 3, top right panels) the fraction of 2–ds water significantly increases at the expense of a decreasing population of 2–dl water (whereas the fractions of 1–d and 3–d species subject to short/long H–bonds barely change upon compression from 1 bar to 10 kbar). This is a purely structural effect. To quantify the effect of the increased number density when compressing water from 1 to 10 kbar, the partial THz spectra at 10 kbar have been normalized by concentration (Figure 3, bottom right: thick dashed–dotted blue line). The rescaled maximum peak intensity at 10 kbar is close to that at 1 bar (while not affecting the pressure–induced blue–shift). Thus, experiment and theory agree that mostly the density change is responsible for the absorption increase of the total THz spectrum in the frequency regime of the network mode (Figure 1). Finally, we estimate the pressure dependent blue-shift of the H–bond network mode from the hindered t–t self–correlation contributions of the 2–ds and 2–dl configurations, 10


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that together dominate the H–bond network peak 37 at 1 bar and 10 kbar. Populations of these configurations were computed from AIMD at intermediate pressures (from 1, 2, . . . , 9 kbar). This allows us to approximately synthesize the corresponding total resonance by a weighted pressure-dependent superposition. Since the partial 2–ds and 2–dl spectra at 1 bar and 10 kbar are approximately similar, yet quantitatively different according to Figure 3, we took both sets of reference partial spectra in order to estimate the center frequency of the resulting synthetic total peak (blue and red peak shifts in the inset to the left panel in Figure 3). The shift varies between 20 and 35 cm−1 within our approximations upon compressing liquid water at 300 K from 1 bar to 10 kbar compared to ≈ 40 cm−1 experimentally. As also experimentally observed, the blue–shift of the network mode is most pronounced at lower kbar pressures, whereas it flattens at around 10 kbar.

Conclusions In summary, we developed an experimental procedure for precise, quantitative, and reproducible THz absorption measurements of liquids for pressures up to about 10 kbar and applied it to bulk water. The most prominent peak in the accessible spectral range is the hindered translational (i.e. H–bond network) mode centered around 180 cm−1 . It shows a monotonically increasing blue shift of 40 cm−1 and an intensity increase upon compressing liquid water from 1 bar to 10 kbar. Accompanying ab initio molecular dynamics simulations at 1 bar and 10 kbar in combination with instantaneous normal mode analysis provide the underlying physical picture on the molecular level. The observed blue shift and part of the intensity increase can be traced back to a conversion of long H–bond double donor configurations to configurations with short such H–bonds, the latter showing a larger molar extinction coefficient and a blue-shifted center frequency. Upon compression into the multi– kbar regime, the absorption coefficient is further increased due to density changes. Thus, our analysis traces back the key experimental observations to molecular and electronic struc-

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ture changes in combination with density effects. Beyond pure water, our experimental and computational advances pave the way to quantitatively investigate the H–bond network of pressurized aqueous solutions.

Supporting Information Available Description of the experimental setup; Details to improved pressure calibration, reproducibility of pressure transducer function and thickness measurements; Details to spectral analysis and global fit of spectral, thickness and pressure changes; reconstruction of pressure dependent spectrum of bulk liquid water; Computational methods and details.

Acknowledgement The authors thank Inga Kolling and Katja Mauelshagen for assistance in the lab and Claudius Hoberg for fruitful scientific discussions. This work is supported by the Forschergruppe (FOR 1979 “Exploring the Dynamical Landscape of Biomolecular Systems by Pressure Perturbation”) and is also part of the Cluster of Excellence RESOLV (EXC 1069 and EXC 2033), both funded by the Deutsche Forschungsgemeinschaft.

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Hydrogen-Bonding in Liquid Water at Multi-Kilobar Pressures | The

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