Correlations in the SoluteâSolvent Dynamics Reach Beyond the First

Letter pubs.acs.org/JPCL

Correlations in the Solute−Solvent Dynamics Reach Beyond the First Hydration Shell of Ions Philipp Schienbein,† Gerhard Schwaab,‡ Harald Forbert,§ Martina Havenith,*,‡ and Dominik Marx*,† †

Lehrstuhl für Theoretische Chemie, ‡Lehrstuhl für Physikalische Chemie II, and §Center for Solvation Science ZEMOS, Ruhr-Universität Bochum, 44780 Bochum, Germany S Supporting Information *

ABSTRACT: While the real-space structure of solvation shells has been explored for decades, a dynamical perspective that directly relies on changes in the H-bond network became accessible more recently mainly via far-infrared (THz) spectroscopies. A remaining key question is how many hydration shells are affected by ion-induced network perturbations. We disclose that theoretical THz difference spectra of aqueous salt solutions can be deciphered in terms of only a handful of dipolar auto- and crosscorrelations, including the second solvation shell. This emphasizes the importance of cross-correlations being often neglected in multicomponent models. Analogously, experimental THz responses of simple ions can be deciphered in a similar way. Dramatic intensity cancellations due to large positive and negative contributions are found to effectively shift intensity maxima. Thus, THz spectroscopy provides an unprecedented view on the details of hydration dynamics, which can be understood by a combination of experiment and theory.

U

the various vibrational spectroscopies in terms of correlation functions. This problem, in its turn, is immediately linked to the issue of nonlinear effects due to aggregation phenomena of solute species, which is ion-pairing in the present context,26 depending on the activities and other thermodynamic variables. In order to contribute to this debate both fundamentally and quantitatively, aqueous salt solutions of monovalent monatomic cations and anions appear to be the ideal test bed to convincingly answer these questions for charged species upon combining ab initio simulations and THz experiments. To this end, the coupled solute−solvent dynamics obtained from computer simulations is decomposed here into 21 distinct contributions that rigorously add up to the total theoretical THz spectrum. This enables the systematic reconstruction of different partial THz spectra depending on which physical coupling mechanisms are included as embodied in self- and cross-terms stemming from different classes of solvent species. It is important to recall that experimental THz absorption spectra are difference spectra, which are always referenced to pure bulk water in some way that depends on the analysis machinery. The straightforward approach would be to employ exactly the same procedure in analyzing the simulated spectra. This approach, however, falls short in the sense that it cannot answer the key question, namely, which ones out of the myriad of physical coupling mechanisms contribute to the observed THz spectra in terms of the difference to the corresponding couplings in the pure liquid.

nderstanding the solvation of ions and molecules in water as part of the emerging cross-disciplinary field “Solvation Science”1,2 is fundamental to a myriad of processes of key relevance from chemistry to biology, such as chemical reactions or enzymatic catalysis. Yet, the sometimes controversial discussion in the literature showed that the extent of what is loosely called “the solvation shell” around a solute in a liquid depends on the specific probe used to determine it. Dielectric relaxation spectroscopy, for instance, reveals information on rotationally and translationally slowed-down hydration shell water molecules and thus relates to dynamics.2,3 By contrast, diffraction of X-rays or scattering of neutrons provide orientationally averaged coordination numbers that are exclusively based on radial structure.2,4 In simulations, solvation shells determined from Voronoi tesselation or spatial distribution functions provide yet different perspectives, whereas those obtained from partial radial distribution functions are close in spirit to X-ray and neutron experiments.5 More recently, THz spectroscopy has been used to experimentally disclose properties of solvation shells in aqueous solutions.6−12 It provides complementary information on their extent in space as detected by solute-induced changes of the picosecond dynamics of H-bond fluctuations close to the solute as referenced to bulk water.13 Still, controversies continue to revolve around the question of how far away from a solute, in terms of distance or number of solvation shells, the interfacial H-bond network is dynamically affected. Even for the expectedly simple case of ions in water, astonishingly different viewpoints can be found in the extant literature as to how many hydration shells are structurally and dynamically affected by such charged impurities,5,7,12,14−25 which is essentially what is detected by © XXXX American Chemical Society

Received: March 24, 2017 Accepted: May 10, 2017 Published: May 10, 2017 2373

DOI: 10.1021/acs.jpclett.7b00713 J. Phys. Chem. Lett. 2017, 8, 2373−2380

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The Journal of Physical Chemistry Letters

contribution, αeff ∼ cS ϵeff lin, contains the spectral signatures of solvated anions and cations as well as hydration water at the given salt concentration cS. In the absence of ion pairing the eff experimentally determined ϵlin can therefore be directly compared to simulated THz spectra obtained from adding up the respective single ion spectra, vide infra. To this end, the following decomposition of the effective ionic extinction is introduced here (see Section S-2B in the Supporting Information (SI) for full details):

An alternative ansatz, introduced herein, is to directly compute the required difference of the ionic solutions versus the pure solvent already at the level of the distinct correlation functions. This allows us to suitably group together various terms with the aim to synthesize the theoretical THz difference spectra of simple electrolyte solutions, XY(aq), by following Occam’s principle of trying to use the minimum amount of distinct mechanistic contributions that is required to reproduce the key features of the experimental THz difference spectra. Our so-called “cross-correlation analysis” (CCA) strategy is introduced and used to compute the THz difference spectra of four aqueous solutions, specifically NaCl(aq), NaBr(aq), LiCl(aq), and LiBr(aq), which can be confronted one-to-one with their experimental counterparts. Moreover, as we will explicitly demonstrate for Li+(aq), Na+(aq), Cl−(aq), and Br−(aq), this sort of theoretical analysis, in its turn, enables much deeper decomposition of the experimental data toward extracting separately the individual contributions of the cationic and anionic species to the total difference spectra. Last but not least, even those significant mechanistic contributions that in the end largely compensate at the level of the experimental THz difference line shape function can be separated for both cationic and anionic species once a common reference is introduced. As a result of using this synergy of theoretical and experimental linear THz absorption spectroscopy, we unveil that the difference spectra of aqueous electrolyte solutions can be fully understood qualitatively in terms of a few key contributions, namely auto- and cross-correlations involving the ion, the local H-bond network, and librational modes. However, it is found that these dipolar response spectra are not additive in terms of distinct shell-wise fluctuations or in the spirit of simple multicomponent models, but that much less intuitive cross-correlations are vital in order to rationalize the THz response in terms of physical mechanisms. In addition, significant compensation effects involving large individual components are disclosed, which not only reduce the intensity, but also shift intensity maxima along the frequency axis. Together, this implies that the observed peaks in the THz difference spectra of ion solutions emerge as a result of a complex interplay of auto- and cross-correlations up to the second hydration shell in case of the investigated ions. The introduced quantitative approach in general will allow one to decipher the THz spectra of more complex molecules such as amino acids or even proteins, which feature significant hydrophobic regions in addition to charged functional groups. Moreover, the approach is not restricted to water as solvent molecules but can systematically be applied to completely different solvents. Experimental THz Spectroscopy. A series of experiments6,8,10,11 demonstrated that the concentration-dependent absorption of aqueous electrolyte solutions is to a large extent additive in the THz regime. In an effort to separate ion- and hydration water-related contributions the effective ionic absorption αeff ion = αsol − cwat ϵbulk is obtained from the total absorption of the solution αsol, the water concentration cwat in the solution as obtained from density measurements, and the molar extinction ϵbulk of pure bulk water at the given temperature. Principal component analysis of the spectra at different concentrations allows one to separate spectral and concentration-dependent information.10 Typically, only one or two spectral components are sufficient to reproduce the experimentally observed absorption changes. The leading linear

N

ϵeff lin = − nhydr ϵbulk + nlow ϵ low + nhigh ϵhigh +

∑ 3n n=1

(1)

where ϵbulk denotes the bulk water, and nhydr is the effective number of water molecules with an absorption different from bulk water. Thus, −nhydrϵbulk compensates the fact that all water in the solution was assumed to absorb like bulk water when calculating αeff. Increased absorption at the low (300 cm−1) frequency ends of the observed spectral range is taken into account using the terms nlow ϵlow and nhighϵhigh, where ϵlow and ϵhigh are the low-frequency Debye mode and the two librational modes of the bulk water spectrum, respectively (see SI for details). Positive contributions arise from a small number of resonances with damped harmonic oscillator line shapes of the form 3 n(ν)̃ =

anwn2ν 2̃

⎡ ν 2̃ w 2 4π 3⎢ 2n + νn2̃ + ⎣ π

(

wn2 4π

2

2⎤ − ν 2̃ ⎥ ⎦

)

(2)

where an, wn and ν̃n are amplitude, width, and center frequency of the nth damped harmonic oscillator mode. Since anion, cation and hydration water modes overlap, we choose a combination of ϵeff lin and difference spectra of solutions containing the same anion or cation. This allows us to classify the different contributions either as anion- or cation-specific resonances or as contributions that are independent of the ion charge. Evidently, spectral features present in both anionic and cationic hydration shells cannot be separated without the help from theoretical THz spectroscopy. Theoretical THz Spectroscopy. (1) Systematic Decomposition of Dipole Correlations. The key idea in what follows is the mathematically complete decomposition of all dynamical dipole correlations of all species in the aqueous solution, as obtained from ab initio molecular dynamics27 trajectories, in terms of suitably defined solute/solvent classes. Our “cross-correlation analysis” (CCA) strategy builds upon pioneering simulation work on IR spectroscopy of aqueous solutions28−32 (where the total solute/solvent correlations have been split in three terms due to the total solute-only, solvent-only, and solute−solvent coupling contributions; see also Section 7.2.6.2 in ref 27). Yet, CCA significantly transcends previous such methods in several respects as will become obvious in the following. At this point, we only concisely summarize CCA, mainly to introduce the contributions into which we are going to decompose the computed total absorption cross section, α(ω), together with our terminology and nomenclature; background and full details are deferred to the SI (Section S-1B). Guided by experiment, we aim at decomposing the total spectrum in terms of four key groups of particles, namely • solute species (S) being an ion when considering the solution or being a water molecule in case of the pure solvent reference, 2374


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correction”33 and accounts for the ω−2 prefactor that results from Fourier-transforming the product of dipole moment derivatives instead of using dipole moment autocorrelations.27 All theoretical spectra are thereafter normalized to a concentration of 1 mol/L. When computing the theoretical THz difference spectra, ΔαXY(ω), only three distinct mechanistic contributions based on only five specific correlations, in addition to two due to the pure water reference, turned out to be crucial for all considered ions X(aq). The first contribution

• first solvation shell (1) containing all water molecules in the first solvation shell of the ion (see SI, Section S-1B, for definitions), • second solvation shell (2) containing all water molecules that are H-bonded to any water molecule in the first shell, and • rest (R) collecting all remaining water molecules. For each group of such particles ζ(t), we define so-called group selectors, Gζ,i(t), which are unity if the particle i belongs to group ζ at time t and 0 otherwise; note that the term “particle” denotes here either individual atoms (such as monatomic ions) or molecules depending on the context. In full analogy, we also introduce relations γ(t) between particles and the corresponding relation selectors, Rγ,i,j(t), where three different group relations are defined, namely, • autocorrelation relations (A): RA,i,j(t) = δij(t), • cross-correlation relations (C): RC,i,j(t) = 1−δij(t), and • H-bonding relations (HB): RHB,i,j(t), which further decompose cross-correlations and equal unity if two H2O molecules are H-bonded at time t and 0 otherwise. Using the defined groups and relations we denote Cγζξ(t) to be a correlation function between the two groups ζ(t) and ξ(t) employing the relation γ(t) . For the specific case of the aqueous solutions of Li+, Na+, Cl−, and Br−, we found after careful assessments that the following rigorous decomposition of the exact total dipole (velocity) correlation function of the system, i.e., ⎯→̇ ⎯→̇ C(t ) = ⟨M (0)M (t )⟩, in terms of particle groups and their relations,

A C C ΔC Ion(ω) = CSS (ω) + CS1 (ω) + CS2 (ω)

includes the self-term of the ion and its cross-correlations with water molecules in the first and second shell, respectively. Physically, this spectral contribution describes exclusively those changes that are due to the solvated ion complex itself, in particular its hindered translational motion (which implies that it excludes any changes due to both auto- and cross-correlations of water molecules within either the first or second solvation A/C shell, i.e., CA/C 11 (ω) and C22 (ω)). The second term HB C ΔC HB(ω) = C12 (ω) − N1IonCS1 − ref (ω)

(3)

is both necessary and sufficient to qualitatively reproduce and thus to decipher the experimental THz spectra, vide inf ra; note that dipole velocities instead of the dipole moments themselves are used for technical reasons (see SI, Section S-1C) All other fluctuation mechanisms, in particular both the auto- and crosscorrelations within the second hydration shell CA/C 22 (t) as well as the cross-correlations within the first shell CC11(t), turned out to be not relevant and are thus lumped together in the rest term CRest(t) that rigorously contains all remaining correlations that render C(t) exact after summation (see SI, Section S-1B) In other words, based on the five key structural-dynamical contributions according to eq 3, we are able to synthesize the total THz difference spectra of the four aqueous solutions LiCl, LiBr, NaCl, and NaBr completely. (2) Synthesizing THz Difference Spectra f rom Key Contributions. As a second step, the total absorption cross section difference of an aqueous salt solution XY(aq) compared to pure water, i.e., ΔαXY(ω), can be synthesized based on computing the partial spectrum γ Cζξ (ω) =

β 6ϵ0Vc

A ΔC1(ω) = C11A(ω) − N1IonCSS − ref (ω)

(7)

quantitatively captures the difference between the hindered rotational (i.e., librational) motion of water molecules in the first solvation shell compared to these librations in the pure bulk water reference system (normalized with the first shell hydration number of the ion). It turns out that this term ΔC1(ω) stays fairly constant up to about 300 cm−1 but becomes very important thereafter. Last but not least, concerning the contributions of librational modes of water molecules beyond the second shell, analysis shows (see Section S-1G in the SI) that already those within the second shell behave almost like bulk water molecules in terms of their own dipolar responses, CA22(ω), thus not contributing much to the difference spectra as also will be shown by Figure 4 for H-bonds. Based on these changes of the solutions with regard to the pure liquid, the total contribution of an ion X to the THz difference spectrum of an X(aq) solution,

∞

∫−∞ e−iωt Cζξγ(t ) dt

(6)

quantifies the spectral difference due to H-bonding between the first and second solvation shell around the ion in the solution w.r.t. standard H-bonds in the pure solvent reference (-ref) system being pure bulk water in the present case (thus, again, excluding changes due to auto- and cross-correlations of water molecules within the first and second shell as supported by Figure 4, vide infra). Hence CCS1−ref(ω) is computed from the pure bulk water reference simulations, whereas CHB 12 (ω) is obtained from the ion solution; NIon 1 is the average number of water molecules in the first solvation shell of the ion (see Table S1 in the SI). The third and last term,

A C C HB C(t ) = CSS (t ) + CS1 (t ) + CS2 (t ) + C11A(t ) + C12 (t )

+ C Rest(t )

(5)

(4)

ΔC X(ω) = ΔC Ion(ω) + ΔC HB(ω) + ΔC1(ω)

for each and every of the above decomposed correlation functions individually, where β = 1/kBT, kB is the Boltzmann constant, T is the temperature of the system, ϵ0 is the vacuum permittivity, V is the volume of the simulation box and c is the speed of light in vacuum. Note that this classical expression includes what is commonly called the “harmonic quantum

(8)

is obtained as the sum of all three above-described contributions and, correspondingly, the total THz difference spectrum of the salt solution, XY(aq), is given by ΔC XY(ω) = ΔC X(ω) + ΔC Y(ω) 2375

(9)


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The Journal of Physical Chemistry Letters As detailed in the SI (Section S-1D), Δα(ω) n(ω) = ΔC(ω) where the refractive index n(ω) is obtained from the Kramers− Kronig relation9,29 applied to an effective C(ω) for solutions of the single ions and the salts. This is our basis for computing the linear THz absorption cross section differences, ΔαX(ν̃) and ΔαXY (ν̃), that enables the one-to-one comparisons to experiment. THz Spectra of Salt Solutions: Theory versus Experiment. Before starting to decipher the experimentally determined THz lineshapes in terms of the underlying physical mechanisms we challenge our simulations by comparing the computed total THz difference spectra ΔαXY(ν̃) of aqueous LiCl, LiBr, NaCl, and NaBr solutions directly to the corresponding experimental data in Figure 1. The qualitative agreement in terms of both

Figure 2. Theoretical linear THz absorption cross section differences, ΔαX (ν̃) reported on the right y-axis, of aqueous Li+, Na+, Cl− and Br− solutions using blue, pink, green, and brown solid lines, respectively, and their decomposition in terms of ΔCIon(ω), ΔCHB(ω), and ΔC1(ω) (as defined in the text and corresponding to α(ν̃) n(ν̃) for these distinct contributions according to eq S22 in the SI, see the left y-axis) using light blue, red, and orange dashed lines, respectively. The inset in the upper left corner displays the pronounced THz peak of Li+(aq) at about 450 cm−1 where the corresponding intensity scale of ΔαLi+(ν̃) is reported on its right y-axis.

the Li+ cation, we computationally detect a prominent peak at ≈450 cm−1 (inset Figure 2) that overlaps with librational contributions, which is unfortunately outside of the frequency range accessible to our THz spectrometer. Thus, only a single peak is experimentally observed in this case, yet an additional resonance at ν̃n = 400 cm−1 is considered via eq 2. Decomposition into Molecular Contributions: Theory. At this stage, we can faithfully analyze how the three key physical contributions, i.e., the specific structural-dynamical dipole correlations that underly the ΔCIon(ω), ΔCHB(ω), and ΔC1(ω) terms, do shape the THz spectra of the different ions, X(aq), and thus the resulting aqueous solution spectra of the corresponding salts, XY(aq). Inspecting Figure 2, we observe that the overwhelming contribution to the THz frequency modulation is caused by ΔCIon(ω) (dashed light blue lines) and thus stems from the autocorrelation of the ion and its cross-correlations with water molecules not only in the first, but also in the second solvation shell. Importantly, a strongly negative signal centered around 200 cm−1 is caused by the second term, ΔCHB(ω) (dashed red), i.e., by the change of the H-bond network dynamics that couples water molecules in the first solvation shell to those in the second shell compared to H-bonding in pure bulk water. The contribution ΔC1(ω) (dashed orange), i.e., the autocorrelation of first shell water molecules, is essentially THz silent up to about 300 cm−1 but increases steeply in intensity thereafter, thus being the molecular origin of the pronounced high-frequency wing of the experimental THz line shape functions. The specific behavior of the anions can be qualitatively understood as follows. In Cl−(aq), we find for ΔCIon(ω) a very intense positive feature around 200 cm−1. However, this unimodal peak is strongly compensated by the negative contributions due to ΔCHB(ω), thus resulting in a considerably weakened but still significant peak that is blue-shifted to ≈220 cm−1 in accord with experimental data. Similarly, Br−(aq) is characterized by a prominent peak at 150 cm−1 due to

Figure 1. Comparison of the theoretical linear THz absorption cross section differences (ΔαXY (ν̃): red solid lines) of aqueous LiCl, LiBr, NaCl, and NaBr solutions to the experimental difference spectra (αeff XY (ν̃) = cS ϵeff lin: black crosses). The computed single ion contributions ΔαX are plotted as dashed lines in blue, pink, green and brown for Li+, Na+, Cl−, and Br−, respectively.

intensity and frequency modulations is overall satisfactory, considering in particular that we report absolute intensity differences according to the statistical-mechanical formulas given without any a posterori adjustments and moreover refrain from scaling the frequency axis as often done to increase agreement. It is noted in passing that nuclear quantum effects are unlikely to play a significant role given the striking similarity of the THz spectra of heavy and light liquid water13 and the “modest differences” observed for ion solvation dynamics in aqueous solutions,34 thus leaving us with deficiencies in the description of the electronic structure as the most likely reason for quantitative differences. In the case of LiCl(aq), we find one positive feature and for LiBr one negative feature, both located around 200 cm−1. From the single ion contributions, X(aq), to be discussed below based on Figure 2, it can be deduced that these two features can be grossly attributed to Cl− and Br− solvation, respectively. These gross findings agree with the measured spectra in both cases. In contrast to LiX(aq), we find two features in the spectra of the NaCl and NaBr solutions. Here, next to the anion-specific absorption an additional maximum at about 100 cm−1 is observed for NaCl(aq) as well as for NaBr(aq), which therefore can be attributed to Na+(aq). Also the two aqueous NaX solutions are in accord with the experimental ones. Regarding 2376


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The Journal of Physical Chemistry Letters ΔCIon(ω), whereas an additional weak signal is located at 50 cm −1 . For this anion, adding the negative ΔC HB (ω) contribution leaves only a pretty weak and broad peak that is red-shifted to about 140 cm−1. In stark contrast to Cl−(aq), we find moreover after summing up all three terms that an overall negative contribution around 250 cm−1 is generated for the ion spectrum of Br−(aq), which indeed is observed in the experimentally decomposed spectrum of Br−(aq) close to 200 cm−1, vide infra. In summary, it is significant positive and negative spectral contributions that shape the THz responses of these individual anions in water as a result of a subtle intensity compensation mechanism of distinct dipole correlations. For the two cations, the ΔCIon(ω) terms contribute richer modulations since they feature two significant peaks at 100 and 150 cm−1 for Na+(aq) and around 200 and 450 cm−1 in case of Li+(aq). Note that, experimentally, two features are also found for Na+(aq) at similar frequencies, whereas the high-frequency peak seen for Li+(aq) is outside the accessible range but clearly is present via its pronounced low-frequency wing. Akin to the anionic cases, significant negative intensities due to ΔCHB(ω) again greatly smoothen out the peak modulations of these line shape functions, whereas ΔC1(ω) is responsible for correctly contributing the steeply increasing intensity at the highfrequency edge of the THz window. Decomposition into Molecular Contributions: Experiment. Guided by these insights from simulations, we were able to regroup our experimentally determined spectral components into physically meaningful contributions in Figure 3 in order to greatly transcend what has been possible experimentally so far; the details of the decomposition of the experimental data are described in the SI, Section S-2B. Shortly, we simultaneously analyzed the ϵeff lin spectra of six XY(aq) solutions (LiCl, LiBr, LiI, NaCl, NaBr, NaI) and recent data on Ni2+ and Mn2+ halide solutions.10 Based upon a global fit of these absorption spectra

and their respective difference spectra we are able to obtain separate estimates for the spectral changes due to ion hydration resulting from the first and second shell, ΔCHB(ω) + ΔC1(ω), and the spectral changes due to the individual ions, ΔCIon(ω) . To this end, eq 1 was rearranged for each ion in the following way: ϵeff lin = [ − nhydr (ϵbulk − ϵ low ) + nhigh ϵhigh ] N eff + [nlow ϵlow +

∑ 3 n] n=1

(10)

such that the first bracket contains the best experimental estimate of ΔCHB(ω) + ΔC1(ω) together and the second one yields the effect due to ΔCIon(ω) . We separate nlow = nhydr + nefflow, thereby dissecting the hindered translational and librational modes at frequencies >200 cm−1 that are attributed to dynamics in the hydration shells from the low frequency parts which describe correlated water ion motions and are approximated by the low frequency part of the pure water spectrum. Based on the simulation results in Figure 2, we neglected the effect of the Li+ ion on the hydration water and incorporated that ΔCHB(ω) affects mainly the absorption in the 200 cm−1 band. In order to extract ΔC1(ω) + ΔCHB(ω) from the experiment we had to set that very contribution to zero using Li+ as the reference. This assumption is in accordance with the simulation results showing that the hydration number is smallest for Li+ among all discussed ions (see Table S1 in the SI). Based on this analysis, it is first of all intriguing to see that the contributions due to the individual ions with regard to pure bulk water, ΔCIon(ω) and ΔCHB(ω) + ΔC1(ω), can be obtained separately from the experimental spectra; recall that the ion is directly involved only in the first term, whereas it is exclusively correlated to water molecules and their H-bonds in the combined second and third term. Remarkably, it is possible to extract the THz response of a given individual solvated ion exclusively from an experimental database! Based on this analysis, we can experimentally confirm the compensation of large positive and negative THz responses attributed to the ΔCIon(ω) and ΔCHB(ω) + ΔC1(ω) terms. This implies that the observed THz spectral line shape of solvated salts is a result of the superposition of the solvated ions plus a negative correlated hydration water spectral response. Importantly, the previously postulated assumption in the literature when analyzing the THz response of aqueous electrolyte solutions, namely, to only consider those correlations where the ions are directly involved as encoded in ΔCIon(ω), is shown here to fail. Instead, indirect ion-induced changes that significantly involve cross-correlations between water molecules in the first and second solvation shell as well as autocorrelations of just the first shell (but not the second shell) are required! This unifying picture is able to describe all experimentally observed THz spectra: those that apparently do not show resonances due to their hindered translations as well as those that do show such pronounced ion signals, called “rattling modes” (compare, for instance, the THz difference spectra of Br−(aq) to Na+(aq), respectively). Deciphering Solute−Solvent Correlations: Hindered Ion Translation. Let us now describe those effects that are directly induced by the presence of the ion, i.e., all effects collected in ΔCIon(ω) . This term contains the autocorrelation of the ion with itself CASS(ω) as well as the cross-correlations between the ion and water molecules in the first and second solvation shell,

Figure 3. Experimental THz difference spectra stemming from the individual ionic contributions of Li+, Na+, Cl−, and Br− using blue, pink, green, and brown solid lines, respectively, based on the measured aqueous salt solutions and their decomposition (see text) into the contributions due to the ion itself (corresponding to ΔCIon(ω): light blue dashed lines) and due to hydration water (corresponding to ΔCHB(ω) + ΔC1(ω): red dashed lines). Note that for Li+ the experimental ΔCHB(ω) + ΔC1(ω) was set to zero. Consequently, ΔCIon(ω) is equivalent to the total THz contribution of Li+. The corresponding computed contributions are illustrated for comparison using dotted lines and the same color code. 2377


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The Journal of Physical Chemistry Letters i.e., CCS1(ω) and CCS2(ω); see Figure S7 in the SI for all four simulated ions. Therefore, neither water autocorrelations nor water−water cross-correlations within either the first or second solvation shell contribute to ΔCIon(ω) . For both anions, we observe two major peaks in CASS(ω) itself, whereas only one prominent signal remains in the total single ion contribution ΔCIon(ω) of X(aq); note that the main feature in the Br−(aq) spectrum around 140 cm−1 is very weak and is only visible in the total experimental difference spectrum when considering iodides in the data evaluation procedure (see the SI, Section S2C for details). One of these features gets compensated by CCS1(ω), whereas, at the same time, the other signal is intensified by CCS2(ω) . This means that one of the genuine ion resonances in the ion self-term is counteracted by its own crosscorrelations with the first solvation shell and therefore remains invisible, whereas the other one is promoted by ion−water cross-correlations, but by those with the second solvation shell! This is the structural-dynamical reason why the ion contribution cannot be understood solely in terms of the pure autocorrelated ion motion CASS(ω) given that the crosscorrelations with regard to solvation water up to the second shell are fundamentally required to describe all effects that are directly induced by the presence of the ion (ΔCIon(ω)). The importance of the cross-correlations in shaping the THz spectra is even more pronounced when analyzing ΔCIon(ω) of the two investigated cations. In the case of Na+(aq), our analysis discloses that the main Na+ signal at 100 cm−1 in ΔCIon(ω) is even not contained as a proper resonance or mode in any one of the three underlying terms, in particular not in the ion self-term CASS(ω), but emerges only due to the interplay of all its three mechanistic contributions! In stark contrast to the appealing but wrong picture that rests exclusively on the ion self-term, the total ion contribution ΔCIon(ω) fundamentally results from the combined effect due to auto- and both crosscorrelations, whereas none of these contributions on its own suffices to generate the observed peak ascribed to Na+(aq). For Li+(aq), we see that the main signal located at 450 cm−1 is very broad and it therefore affects the line shape in the entire accessible frequency range. This is in full harmony with experiment where, on one hand, no Li+-specific resonances are found in the accessible frequency window up to 370 cm−1, but, on the other hand, a resonance at 400 cm−1 was required in order to fit the high-frequency wing of the THz difference spectra involving Li+(aq), vide supra, keeping in mind that all computed peaks are systematically blue-shifted with regard to the experimental spectra. H-Bond Network Dynamics. We already worked out that the H-bond network modes, which are described by the crosscorrelation CHB 12 (ω) between all H-bonded water pairs where one partner is in the first solvation shell and the other molecule belongs to the second shell as embodied in the definition of ΔCHB(ω), also turned out to be crucial to describe the X(aq) THz difference spectra. However, what are the THz contributions due to all other H-bonds in the solvation spheres around ions in water? Inspecting Figure 4, we observe that the absolute THz response due to the H-bonds within the second HB solvation shell, i.e., C22 (ω), is already almost bulk-like. Consequently, the effect of these H-bonds plays a negligible role in the THz difference spectrum where pure bulk water is the reference system. Moreover, the absolute THz response of the H-bonds within the first solvation shell (CHB 11 (ω)) almost vanishes, which is consistent with the fact that there are essentially no intact H-bonds within the first shell (see Table S1

Figure 4. Theoretical spectra exclusively caused by the H-bonds within the first solvation shell (CHB 11 (ω), blue), within the second solvation shell (CHB 22 (ω), red), and in between the first and the second shell (CHB 12 (ω), green) around an ion compared to the corresponding THz signal of H-bonds in pure bulk water (CHB S1−ref(ω), dashed black).

in the SI). Finally, which one is the contribution that does make the difference? It is precisely those H-bonds that connect the first to the second solvation shell as embodied in the CHB 12 (ω) term that produce a large difference compared to the pure water reference! These particular H-bond cross-correlations are, therefore, the most important contribution to THz difference spectra among all(!) H-bonds around ions in water. The famous network mode of pure bulk water is essentially an intermolecular stretching mode that involves the H-bonds of mostly tetrahedrally coordinated water molecules13 and is found close to 200 cm−1 in the present ab initio simulation approach. Indeed, the CHB S1−ref(ω) term nicely captures this very mode in the pure liquid as revealed by the dashed line in Figure 5. When analyzing the identical cross-correlations due to Hbonding between two water molecules, but involving instead water molecules in the first and second solvation shell around an ion, X(aq), we find that this peak is not shifted in frequency with regard to the bulk reference (maybe with the exception of the 4-fold coordinating Li+ cation, where there is a blue-shift on the order of 20 cm−1). This observation is consistent with the finding that the respective H-bonds connecting the first to the second solvation shell around these ions are also structurally nearly identical to those in the pure liquid, as demonstrated in Figure S2 in the SI. Thus, the H-bond stretching motion of only those water pairs in the first and second solvation shell around an ion that are connected via H-bonds contribute a THz response that is essentially identical in its line shape to that stemming from the H-bond stretching modes in pure bulk water. In stark contrast to these properties, there is a systematic difference observed in terms of peak intensities that an individual H-bond contributes to the THz reponse (which is why CHB 12 (ω) reported in Figure 5 has been normalized per Hbond using the average number of water molecules in the first solvation shell of the respective ion, 1/NIon 1 ). Their THz activity is found to be significantly suppressed compared to bulk if the H-bonded water pairs are those that connect the first to the second solvation shell of ions. Therefore, in terms of the THz difference of X(aq) versus pure bulk water defined via 2378


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supports our mechanistic interpretation that the aforementioned negative contribution qualitatively scales with the number of overall broken H-bonded water pairs once they move from the bulk into an ionic solvation shell! Librational Dynamics. The librational modes encoded by ΔC1(ω) do not play any role in understanding the prominent modulations of the THz difference spectra up to about 350 cm−1; the corresponding spectra can be found in Figure S5 in the SI for inspection. However, these contributions are required in order to mechanistically capture the increase of relative absorption toward the librational modes, which sets in as a foot at about 300 cm−1. Among all investigated ions, Br− shows the most intense librational band compared to the other investigated ions, which results in a quite early increase in intensity. This finding is also supported by the experimental data where a spectral intensity increase can be seen between 300 and 350 cm−1. Overall, the detailed mechanistic analyses based on our crosscorrelation analysis (CCA) technique demonstrate that it is significant positive and negative spectral contributions due to very distinct intermolecular (auto- and cross-) correlations that shape the total THz responses of anions and cations in water on the basis of a subtle intensity compensation mechanism. These molecular underpinnings of the THz line shape of aqueous salt solutions cannot be unveiled by directly subtracting the spectra of either the solutions or of the individual ions from the pure bulk water reference spectrum− neither experimentally nor computationally. Based on this rigorous analysis, we provide clear evidence that the second solvation shell cannot be neglected to describe the THz response of cations and anions in water. The generality of these findings allows us to transfer the concepts to experimental data of similar systems without having to repeat the (very demanding) ab initio calculations of THz spectra. Beyond aqueous electrolyte solutions, combining quantitative experimental with predictive theoretical THz spectroscopy paves the way to qualitatively understand at the molecular level the THz response of both more complex solutes in homogeneous environments and heterogeneous solvation at liquid/solid interfaces.

Figure 5. Theoretical spectra stemming from those H-bonds that connect the first to the second solvation shell of an ion in water Ion normalized with its respective hydration number, i.e., CHB 12 (ω)/N1 , for + + − − Li , Na , Cl , and Br solutions in water using blue, pink, green, and brown, respectively, compared to the THz contribution due to the Hbonds between a water molecule and all its H-bonded neighbors in the reference liquid (CHB S1−ref(ω), black dashed line). The inset shows the respective difference spectra, ΔCHB(ω), using the same color code.

ΔCHB(ω), it becomes clear that the H-bond network mode contributes strongly negative intensities centered essentially around the same frequency as the network mode of pure water, i.e., close to 200 cm−1 in our simulations (again, Li+(aq) is the exception where ΔCHB(ω) is shifted toward roughly 160 cm−1). Importantly, this mechanism is operational for cations as well as for anions and is, thus, independent of the solvation pattern of the first shell, being greatly different around positively and negatively charged solutes. How can this intensity decrease of CHB 12 (ω) and thus the negative contribution of ΔCHB(ω) to the total THz difference spectra of all ions be understood? It cannot be a dramatically different THz response of individual H-bonds in the solvation shell versus the pure liquid as already shown in detail; moreover, it is demonstrated in the SI that they behave rather similarly concerning both their structure (Section S-1E) and electrostatics (Section S-1F). However, a single water molecule has, on average, less H-bonded partners in the first solvation shell of an ion compared to bulk water due to steric blocking, which implies that there are less H-bonds on average per water molecule in the first shell simply due to excluded volume effects around the ionic core. Yet, it is exactly those H-bonds that connect the first to the second solvation shells, which greatly affect the THz response as we have seen. This can be quantified with the help of NHB 12 compiled in Table S1, which is the average number of H-bonds formed between first-shell water molecules and those in the second shell. Clearly, this number of roughly 2.7−2.8 is much lower than the average H-bond number in pure bulk water, about 3.88. Taking into account the different first-shell hydration numbers, NIon 1 , a total of approximately 6.2 and 4.7 H-bonds is lost in the case of Br− and Li+, respectively, which is consistent with the observation that the resulting negative peak is most prominent for Br− and much less pronounced for Li+ according to the inset in Figure 5. This

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.7b00713. Computational details, a comprehensive derivation of our cross correlation analysis, structural properties of solvation shells and H-bonding, dipole moment distributions, librational effects beyond the first solvation shell, ion self-terms, experimental setup and measurements, detailed experimental decomposition scheme, and fit parameters (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Philipp Schienbein: 0000-0003-2417-1472 Notes

The authors declare no competing financial interest. 2379


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ACKNOWLEDGMENTS

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REFERENCES

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We are grateful to Matthias Krack for having provided the TZV2P basis set for Br, and to Fabian Böhm, Dominique Decka and Christian Schneider for experimental support. This work was partially supported by Grant MA 1547/11 to D.M. and is also part of the Cluster of Excellence “RESOLV” (EXC 1069) both funded by Deutsche Forschungsgemeinschaft. The computational resources were provided by Leibniz-Rechenzentrum München (SuperMUC) as well as by HPC-RESOLV, HPC@ZEMOS, BOVILAB@RUB, and RV-NRW.

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