THz Spectra of Microsolvated Ions: Do they Reveal Bulk Solvation

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Clusters, Radicals, and Ions; Environmental Chemistry

THz Spectra of Microsolvated Ions: Do they Reveal Bulk Solvation Properties? Prashant Kumar Gupta, Philipp Schienbein, Janos Daru, and Dominik Marx J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b03188 • Publication Date (Web): 04 Jan 2019 Downloaded from http://pubs.acs.org on January 6, 2019

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The Journal of Physical Chemistry Letters

THz Spectra of Microsolvated Ions: Do they Reveal Bulk Solvation Properties? Prashant Kumar Gupta,∗,†,‡ Philipp Schienbein,∗,†,‡ Janos Daru,∗,† and Dominik Marx∗,† †Lehrstuhl für Theoretische Chemie, Ruhr–Universität Bochum, 44780 Bochum, Germany ‡Both authors contributed equally E-mail: [email protected]; [email protected]; [email protected]; [email protected]

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Abstract Complementing mid-IR spectroscopy mainly in the OH stretching region, liquidstate far-IR spectroscopy is successful in elucidating the properties of aqueous solutions by providing direct access to the hallmark of H-bonding at THz frequencies, namely the H–bond network peak of water at roughly 200 cm−1 and its modifications in the hydration shells around solutes. Here, the idea is scrutinized whether ion hydration can be understood by studying the THz regime of “small” ion-water clusters in the gas phase as a function of size with subsequent extrapolation to the bulk limit. Our ab initio simulations of Na+ (H2 O)n clusters followed by rigorous decomposition of their THz response demonstrate that the 200 cm−1 network peak is suppressed even at n = 20 in the gas phase, yet it emerges when transferring ion-water complexes as small as n = 7 out of the liquid into vacuum. The underlying physical reason is not missing electronic polarization or charge transfer effects in the gas phase, but rather the distinctly different structural dynamics of finite ion-water clusters in the gas phase compared to ion-water complexes of the same size in the liquid phase.

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Ion solvation is both, fundamental and ubiquitous in a wealth of chemical,technological,and physiological processes. The sodium ion, Na+ , in particular, plays important roles in ion transport across cell membranes, 1,2 in sodium-ion batteries, 3,4 in ion-induced nucleation, 5,6 and ion-specific interactions close to both, charged and neutral interfaces. 7–12 It is unambiguous that H-bonds get perturbed due to the presence of ions as manifest in the distinct dynamical and spectral properties of solvation water. 13–16 However, decades of intense research into ion solvation did not as yet converge to provide a fully coherent picture regarding the timescales and spatial extents of the perturbed H-bond networks close to ions in aqueous solutions. 17–25 Infrared (IR) spectroscopy has served since long as a key technique to probe the H-bond dynamics in bulk liquid water, 26–29 supercritical water 30 as well as water molecules near charged or neutral solutes and interfaces. 31–33 More recently, in particular far-IR or “terahertz” (THz) spectroscopy has played an outstanding role to directly probe the properties of solvation shells in aqueous solutions. 18,19,22,23,31,34–37 Liquid-state THz spectroscopy allows one to focus on the so-called H-bond network peak at about 200 cm−1 that stems from the hindered translational motion of H-bonded water pairs embedded in the three-dimensional network, i.e. H-bond stretching vibrations with distinct collective character. 36 Studying its modifications w.r.t. neat water upon hydration of solute species from simple to complex opens the door to extract solvation effects in the liquid phase. 18,19,22,23,31,34–37 Complementing such experimental and computational work carried out directly in the condensed phase, microsolvation clusters have been studied for a long time, which opens the door to using a broad range of gas phase, molecular beam, and cryogenic trap techniques. Apart from studying “small” clusters on their own right, they are often considered to serve as finite models for understanding H-bonding, proton transport or ion solvation with the idea to eventually describe the bulk limit. 38–47 Targeting neat water, the average oxygen-oxygen distance of water clusters (H2 O)n has been obtained as a function of n using low-temperature high-resolution far-IR vibration-rotation tunneling spectroscopy. 38,39 That intermolecular 3



distance was found to decrease steadily from n = 2 to 5 before increasing again for n = 6 (see Fig. 2 in Ref. 38 and Fig. 8 in Ref. 48, respectively), where the values for five and six water molecules are close to these distances in ice and liquid water, respectively. Yet, it has been mentioned that even (H2 O)6 may not be the best prototype for studying H-bonding in bulk water due to the lack of tetrahedral structure. 48 Moving to ion hydration, a wealth of insights has been obtained from mid-IR (action) spectroscopy by carefully analyzing mainly the OH stretching spectral region of ion-doped water clusters which provided deep insights into how their donor-acceptor patterns and thus H-bonding topologies change from small to large such clusters. 20,32,49–51 What remains yet unknown territory is to see the emergence of the very characteristic H-bond network THz peak at roughly 200 cm−1 , being the hallmark of bulk water and aqueous solutions, in case of ion-doped clusters of growing size despite pioneering insights in the limit of very small neat water clusters. 42 In what follows, we are starting to explore this territory using sodium cations embedded in water clusters of increasing size with reference to their bulk aqueous solution at ambient conditions. Recently, we have assigned the experimental THz difference spectra of aqueous ion solutions including Na+ (aq) using ab initio molecular dynamics (AIMD) 52 in conjunction with cross correlation analysis (CCA). 23 The key finding is that only three major dynamical contributions are necessary to describe the ion-induced far–IR spectral changes of these aqueous solutions compared to neat bulk water: 23 (i) additional spectral features as directly induced by the ion itself, i.e. its hindered translations as well as its coupling to first and second solvation shell water, (ii) spectral changes due to H-bonding between the first and second solvation shell of the ion w.r.t. the H-bonds in bulk water, and (iii) changes of hindered rotations (i.e. librational motion) of only the first shell water molecules referenced to the bulk. It immediately follows that all other contributions are not necessary to reproduce THz difference spectra of aqueous ion solutions in the bulk limit. Going a step further, this seems to support microsolvation approaches where gas phase clusters featuring second solvation shell water around the ion are used to address the solvation properties in the bulk limit. 4


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In the present Letter, we exemplarily investigate Na+ /water clusters of different sizes to scrutinize the microsolvation approach to address solvation shell properties at 300 K. In particular, can these microsolvation environments be utilized to deduce the solvation properties of the sodium cation in the bulk limit as seen by THz spectroscopy? If not, then to what extent and why does the THz spectral response of even quite large gas phase clusters differ from that of the bulk solution? To answer these questions, we have performed extensive AIMD simulations of Na+ (H2 O)n clusters with n = 4 – 8, 10, 12, 14, 17 and 20 H2 O molecules in vacuum at ambient conditions (300 K) using the dispersion-corrected so-called RPBE-D3? density functional; see Sec. S-1 of the Supporting Information (SI) for details on the simulations, the wavefunction-based benchmark calculations including the definition of D3? , and for the CCA tools. For each gas phase cluster we employ CCA to disentangle the total THz spectrum in full analogy to the bulk Na+ (aq) solution and thus the criteria to categorize individual water molecules into distinct topological groups (i.e. first versus second solvation shell and H-bonding criterion) are directly adopted from the Na+ (aq) study; 23 as a courtesy to the reader we reprint in Sec. S-1C of the SI the key ideas and formulae of our exact decomposition scheme as well as a summary of the employed classification parameters. The spectral contribution of the ion itself on the intensity scale of the total lineshape is rather small, i.e. the spectral response of the water molecules clearly dominates the total THz spectrum of the full cluster. Therefore, the spectral impact of the ion-induced term (i) is solely presented in Fig. S4 in the SI for completeness. In the following, we will discuss in detail the total and decomposed THz spectra of three representative gas phase clusters with 4, 7 and 20 water molecules in order to contrast them with the bulk solution Na+ (aq) at 300 K; the respective spectra for all the cluster sizes n are compiled in Fig. S3 in the SI. The decomposed contributions, namely, librations of water A A molecules in the first and second solvation shell (C11 (ω) and C22 (ω), respectively) as well HB as the spectral response due to H-bonds connecting the first and second shell (C12 (ω)) are

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depicted in Fig. 1b, c and d, respectively, whereas the total THz spectra are in panel a.

Figure 1: (a) Total THz vibrational spectra of representative finite Na+ (H2 O)n clusters (n = 4, 7 and 20) versus the aqueous Na+ (aq) bulk solution reported as extinction coefficients. A Decomposed THz responses due to (b) first solvation shell water molecules (C11 (ω)), (c) A second shell water molecules (C 22 (ω)) and (d) H-bonded water molecule pairs connecting HB (ω)). The circles mark the extrema and the black square in the first and second shell (C12 (d) highlights the H-bond network peak of the bulk solution. The decomposition of all other simulated clusters is shown in Fig. S3 in the SI and the bulk solution data are based on Ref. 23 A representative snapshot of the n = 7 cluster sampled from AIMD is depicted in (d) where the blue sphere highlights its first solvation shell. Inspecting Fig. 1, we notice at first glance that neither the total THz spectrum (solid black line) nor any of the three decomposed contributions matches the corresponding one of the bulk solution, which notably includes the n = 20 cluster as well. The librational bands of A A both, first (C11 (ω)) and second (C22 (ω)) solvation shell water molecules are significantly red-

shifted compared to the bulk solution. These red-shifts are directly caused by the incomplete H-bond network: In the case of gas phase clusters, rotational modes are much less hindered than in the bulk solution as the water molecules are not embedded within a proper H-bond 6


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network, even at n = 20, and thus they do not form as many H-bonds as in the bulk (Fig. 2b). Furthermore, as water molecules in the first solvation shell are surrounded by the second A (ω) is solvation shell, whereas the second solvation shell forms an interface with vacuum, C22 A generally more red-shifted than C11 (ω). Importantly, even in case of Na+ (H2 O)20 , where the

second solvation shell only lacks about 30 % of water molecules compared to bulk (Fig. 2b), a systematic red-shift w.r.t. Na+ (aq) is imprinted on the THz response of the first solvation A shell, C11 (ω).

N1 HB N12

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0.4 4

A C11

0.2

A C22

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0.0

2 5 8 11 14 17 20

n

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0

n

A HB Figure 2: (a) Frequency at maximum absorption of the C11 (ω), C A 22 (ω) and C12 (ω) finite cluster spectra (obtained from Fig. 1 and Fig. S3) as a function of cluster size n divided by the corresponding value in the bulk limit. (b) Average number of water molecules in the first (N1 ) and second (N2 ) solvation shell and of H-bonded water molecules connecting first and second solvation shell (NHB 12 ); the corresponding bulk limiting values are marked using horizontal lines of the same color. The the bulk solution data are based on Ref. 23

The prominent negative THz response due to H-bonds connecting the first and second HB solvation shell (C12 (ω), Fig. 1d) coincides for all n with the positive contributions caused

by librations of first and second shell water molecules. This indicates that the librational modes of the respective individual water molecules are strongly coupled via H-bonds and are, therefore, not independent but involved in collective intermolecular dynamics also in finite clusters akin to the bulk solution. 23 Most importantly, we notice that the H-bond HB contribution, C12 (ω), does not feature any other resonance, i.e. the famous “THz network

mode” of tetrahedrally coordinated water molecules 36 at ≈ 200 cm−1 remains unseen for 7



all gas phase clusters! This is in stark contrast to the bulk solution, Na+ (aq), where this resonance is clearly visible in Fig. 1d as a peak close to 200 cm−1 marked by a square. We conclude, therefore, that the THz spectra of these gas phase clusters are dominated by significantly red-shifted hindered rotations. Having deciphered the THz lineshape of Na+ (H2 O)n clusters, we now quantitatively investigate the system-size dependency of their THz spectra in terms of the frequency at A A HB maximal absorption of C11 (ω) and C22 (ω) and of minimal absorption of C12 (ω) in Fig. 2a as

a function of the microsolvation level, n, in comparison to the bulk solvation limit, Na+ (aq). Surprisingly, we observe that the center frequencies of these three contributions all red-shift as a function of cluster size until about n = 7 − 8. This behavior is counterintuitive, because one would expect that librational modes become more hindered by adding more molecules and thus the spectral response would blue-shift. Interestingly, having added about 7−8 water molecules we observe a trend reversal after which the absorbed central frequencies strongly blue-shift according to Fig. 2a. The molecular underpinnings are that around n = 7 − 8 the probability to find water molecules having just a single H-bond in the second shell peaks (see Fig. S7 and associated discussion in Sec. S-4D), and that these waters feature a red-shifted signal compared to water molecules in the first solvation shell to be shown below. In an effort to understand the trend reversal around n = 7 − 8 that is critical when extrapolating spectral properties toward the bulk limit, we employ CCA again to even further disentangle the librational spectra of the first and second solvation shells depending on the number of H-bonds that each individual molecule forms; see Sec. S-4A in the SI for details. The resulting librational responses as a function of H-bond neighbors are exemplarily shown for Na+ (H2 O)7 and Na+ (H2 O)20 in Fig. 3. We observe that the librational modes of a single water molecule strongly depend on the number of H-bonded neighbors. In case of Na+ (H2 O)7 , water molecules in the first shell (see Fig. 3a) without any H-bonded neighbors show a dominant feature around 300 cm−1 , whereas those in the second shell (see Fig. 3b) subject to a single H-bond show a pronounced maximum around 200 cm−1 . This analysis, 8


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a) 500

e A (ω) C 0i,0i e A (ω) C 1i,1i

c)

e A (ω) C 2i,2i

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e A (ω) C 2,2

A C11 (ω)

e A (ω) C 3i,3i

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e A (ω) C 0,0 e A (ω) C 1,1 A C22 (ω)

e A (ω) C 3,3

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Na+ (H2 O)7

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beyond first shell

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200 400 600 800 Frequency(cm−1 )

Figure 3: THz response due to the librational motion of water molecules depending on the number of H-bonded neighbors (X = 0 − 3) in the upper panels (a) and (c) in the first eA (ω)) around Na+ and in the lower panels (b) and (d) beyond the first solvation shell (C Xi,Xi A A e (ω)) and second solvation (ω)). The total contributions of the first (C11 solvation shell (CX,X A eA (ω) contributions are shell (C22 (ω)) are included for reference; note that only dominant C shown and thus the individual contributions do not necessarily add up to the total libration band of the respective shell. The left and right columns correspond to the n = 7 and 20 cluster, respectively. therefore, unveils that the Na+ ion itself hinders the rotation of adjacent water molecules stronger than a single H-bond. Yet, multiple H-bonds formed by a single water molecule in the first solvation shell hinder the rotation stronger than the ion-water interaction. Turning now from n = 7 to Na+ (H2 O)20 in Fig. 3c and d, we realize that water molecules forming more than one H-bond become important: Water molecules in the first shell with two or three H-bonds contribute resonances at 400 and 600 cm−1 and in the second shell at 300 and 400 cm−1 . This behavior is physically intuitive because librational motion becomes more hindered the more H-bonds are formed resulting in a systematic stiffening and thus blue-shift. Based on this full decomposition, the evolution of the total THz spectra with respect to the cluster size n depicted in Fig. 1a can be fully assigned. In case of Na+ (H2 O)4 , all water molecules are adjacent to the ion and do not form any H-bonds resulting in a single dominant resonance around 300 cm−1 (see Fig. 1b). By adding more water molecules, either no or a

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single H-bond per molecule is formed and the second shell becomes populated, and thus contributions at 200 and 500 cm−1 gain importance, whereas the aforementioned resonance at 300 cm−1 is weakened in turn. Around n = 8, however, the water molecules start to form more than one H-bond on average, i.e. the probability to find a water molecule with a single H-bond flattens as a function of cluster size and decreases again for n > 10 (see Fig. S7 and associated discussion in Sec. S-4D). It follows that for n > 8, librational contributions around 200 cm−1 weaken again, in favor of librations at 400 and 600 cm−1 resulting in a blue-shift of the total spectrum as seen in Fig. 1a. Moreover, this decomposition unveils that the total spectrum experiences the observed inhomogeneous broadening with increasing cluster size because of the very many distinct solvatomer conformations, and thus different H-bonding topologies, which all show different librational responses.

α(ω)(Lmol−1 cm−1 )

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2 1 0 −5 −10 −15 −20 −25 −30

n = 20 n = 7 (VD) n = 20 (VD) Na+ (aq)

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Frequency(cm−1 ) Figure 4: THz response due to those water molecule pairs that form a H-bond between the first and the second solvation shell around the Na+ ion for the n = 20 cluster in the gas phase and for n = 7, 20 “vertically desolvated” (VD, see text) clusters compared to the bulk Na+ (aq) solution; the intensity is normalized per H-bond and the bulk solution data are based on Ref. 23 Note the different intensity scales in the upper and lower parts of the figure as a courtesy to the reader. It still remains in the dark why microsolvated gas phase clusters containing as many as n = 20 water molecules do not provide even a glimpse of the much celebrated H-bond network peak at 200 cm−1 , in stark contrast to the THz difference response of the same ion in bulk 10


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solution. Our electronic structure based simulation approach can provide the quantitative answer based on (i) extracting the closest n = 7 and 20 water molecules around Na+ at each step of our bulk Na+ (aq) AIMD simulations, (ii) recomputing the dipole moments of these finite clusters in vacuum while keeping nuclear positions and velocities unchanged, and (iii) computing the THz spectral response from these dipolar fluctuations as usual. Using this “vertical desolvation” (VD) approach, we are able to generate finite gas phase clusters whose structural dynamics is identical to that determined by bulk solvation, whereas any electronic polarization and charge transfer effects due to the bulk environment (i.e. beyond the n nearest solvent molecules) are completely switched off. This enables us to explicitly compare the THz spectral contribution of H-bonded water pairs that connect the first to the second solvation shell around Na+ in the bulk solution to that of the gas phase and VD clusters in Fig. 4. It is immediately evident that the THz lineshapes of the VD clusters are qualitatively similar to the one of the bulk solution, whereas they are completely different compared to the gas phase clusters – even when using n = 20 water molecules to microsolvate Na+ . Most surprisingly, also the small n = 7 VD cluster, which is so different in its THz response in the gas phase compared to bulk according to all previous analyses, does now feature the THz network mode around 200 cm−1 found for bulk solvation! Moreover, the peak intensity of the H-bond network resonance increases when vertically desolvating the 20 closest water molecules together with Na+ , which is readily explained by enhanced electronic polarization and charge transfer contributions upon increasing system size and thus H-bond cooperativity. All this provides conclusive evidence that it is stark differences in structural dynamics, and not at all missing polarization effects in microsolvation versus bulk environment, that fully suppress the prominent H-bond network peak of aqueous bulk solutions around 200 cm−1 that is so characteristic in the THz frequency regime. In conclusion, we demonstrate that the THz spectra of small to medium-size microsolvated cations in the gas phase are fundamentally different compared to the bulk solution at ambient conditions. This is based on rigorous spectral dissection of the THz response of a 11



generic system, namely Na+ (H2 O)n at 300 K with n = 4 up to 20. First of all, we find that the THz contributions from H-bonds in the solvation shell of the ion are qualitatively different in gas phase clusters compared to the bulk environment. Secondly, the spectral peak shifts are found to be non-monotonic with respect to increasing cluster size, featuring a switch at about n = 7 − 8. Thirdly, even beyond that turning point, mimicking bulk solvation cannot be achieved when using as many as 20 microsolvating water molecules since the prominent H-bond network THz peak at roughly 200 cm−1 , being a hallmark of solvation in aqueous systems, is completely absent. This is traced back to the vastly different structural dynamics in the gas phase, whereas missing electronic polarization and charge transfer effects are found to play no role. Putting these three facts together, we conclude that gaining insights into bulk solvation properties from directly probing the H-bond network of small cationic gas phase clusters is a daunting task since it requires the size-selected spectroscopy of fairly large water clusters – twenty being by far not sufficient. Given the generic nature of the disclosed molecular underpinnings, it is expected that this fundamental finding is not at all restricted to microsolvated sodium cations. Indeed, these insights provide the detailed explanation why small neat water clusters, 38,39 despite featuring oxygen-oxygen distances and H-bond angles that are astonishingly close to the respective bulk values (in particular for some isomers of the water hexamer), are by far not large enough to mimic H-bonding and thus solvation in liquid water. 48 Moreover, ion-specific interactions with the second hydration shell including its structural fluctuations have been demonstrated recently to greatly impact on the solvation thermodynamics of aqueous electrolyte solutions. 53 In particular, considering only small ion-water cluster energies and only first hydration shell water molecules is found to limit the accuracy of computed single ion solvation free energies. 53 When it comes to spectroscopy, we are confident that our predictions at ambient temperatures will stimulate experimental work in view of the increasing availability of tunable IR light sources in large-scale facilities, such as free electron lasers, which provide high intensities down to the THz frequency regime.

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Acknowledgment This work was partially supported by Grant MA 1547/11 to D.M. and is also part of the Cluster of Excellence “RESOLV” (EXC 2033) both funded by Deutsche Forschungsgemeinschaft. The computational resources were provided by HPC@ZEMOS, HPC-RESOLV, BOVILAB@RUB, and RV-NRW.

Supporting Information Available Computational details, a brief derivation of our cross-correlation analysis, detailed discussion of THz spectrum of all the studied systems.

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THz Spectra of Microsolvated Ions: Do they Reveal Bulk Solvation

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