Hydrophilic Solvation Dominates the Terahertz Fingerprint of Amino

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Hydrophilic Solvation Dominates the THz Fingerprint of Amino Acids in Water Alexander Esser, Harald Forbert, Federico Sebastiani, Gerhard Schwaab, Martina Havenith, and Dominik Marx J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b08563 • Publication Date (Web): 27 Dec 2017 Downloaded from http://pubs.acs.org on December 30, 2017

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The Journal of Physical Chemistry

Hydrophilic Solvation Dominates the THz Fingerprint of Amino Acids in Water Alexander Esser,† Harald Forbert,‡ Federico Sebastiani,¶ Gerhard Schwaab,¶ Martina Havenith,∗,¶ and Dominik Marx∗,† Lehrstuhl für Theoretische Chemie, Ruhr–Universität Bochum,44780 Bochum, Germany, Center for Solvation Science ZEMOS, Ruhr-Universität Bochum, 44780 Bochum, Germany, and Lehrstuhl für Physikalische Chemie II, Ruhr-Universität Bochum, 44780 Bochum, Germany E-mail: [email protected]; [email protected]

Abstract

charged functional groups that form strong Hbonds with their hydration shells. Thus, the hydrophilic groups and their solvation shells dominate the THz absorption difference while on the same intensity scale the influence of hydrophobic water can be neglected.

Spectroscopy in the THz frequency regime is a sensitive tool to probe solvation-induced effects in aqueous solutions. Yet, a systematic understanding of spectral lineshapes as a result of distinct solvation contributions remains terra incognita. We demonstrate that modularization of amino acids in terms of functional groups allows us to compute their distinct contributions to the total THz response. Introducing the molecular cross-correlation analysis method provides unique access to these sitespecific contributions. Equivalent groups in different amino acids lead to look-alike spectral contributions, whereas side chains cause characteristic but additive complexities. Specifically, hydrophilic solvation of the zwitterionic groups in valine and glycine leads to similar THz responses which are fully decoupled from the side chain. The THz response due to Hbonding within the large hydrophobic solvation shell of valine turns out to be nearly indistinguishable from that in bulk water in direct comparison to the changes imposed by the

Introduction Solvation of molecules including biomolecules in particular is a key topic in cross-disciplinary molecular science since long. Fundamental issues are the understanding of the structural and also dynamical properties of the hydrogen bond (HB) network spanned by water molecules, as well as its distinct interactions with solute structure and dynamics. In the case of biomacromolecules, be it lipids, proteins or DNA, it is the subtle balance between the solvation of hydrophilic and hydrophobic groups by water molecules versus self-solvation of water in the homogeneous bulk limit that determines their structural dynamics – and thus also their biological function 1–6 . Water is known to actively participate in molecular recognition by mediating the interactions with the substrate 7 , it affects functional groups of membrane proteins which extend deep into the solvent where they regulate processes 8 possibly by shaping hydration water dynamics 9 , it dis-

∗

To whom correspondence should be addressed Lehrstuhl für Theoretische Chemie, Ruhr– Universität Bochum,44780 Bochum, Germany ‡ Center for Solvation Science ZEMOS, RuhrUniversität Bochum, 44780 Bochum, Germany ¶ Lehrstuhl für Physikalische Chemie II, RuhrUniversität Bochum, 44780 Bochum, Germany †

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ular dynamics (AIMD) 34 with fully quantitative THz measurements. Importantly, the required dipole moment (to be autocorrelated and Fourier-transformed to yield the linear THz absorption cross section α(ω)) is directly obtained from the concurrent electronic structure calculations 34 . This includes the all-important polarization effects as well as charge-transfer contributions due to solute-solvent interactions without which, for instance, the famous HB network peak in bulk water at roughly 180 cm−1 would be absent. Moreover, the total dipole moment can be rigorously split into effective molecular contributions which allows one to disentangle solute and solvent contributions to IR spectra 34–37 . Our THz study of glycine in water revealed the fundamental interactions of the hydrophilic sites with their solvation shells which determine the characteristic lineshape modulations of the THz spectrum of Gly(aq) as obtained from so-called “supermolecular solvation complex” (SSC) analysis 25 . Two key questions arise at this stage when addressing more complex situations: (i) are THz spectra roughly additive in terms of distinct classes of modes and, more importantly, (ii) what is the additional contribution of hydrophobic groups to the total THz response. A first experimental study of solvated alcohols using THz light revealed that the changes are small 38 . This is challenging for theoretical intensity predictions since the solvation shells of hydrophobic sites lack the explicit solutesolvent H-bonding interactions that are so characteristic to hydrophilic solvation. This also implies that the SSC method 25 is no longer suitable to disclose the effects of hydrophobic water in the realm of THz spectra. In this study, we address the above points by introducing a novel technique, dubbed “molecular cross-correlation analysis” (mCCA), to aqueous solutions of glycine and valine, the latter carrying a bulky hydrophobic side chain. In conjunction with SSC analysis of the strongly H-bonding functional groups, theoretical THz spectra of these solutions can be fully synthesized in nearly quantitative agreement with our experimental data based on only a handful of well-defined distinct physical-mechanistic

plays enormous spatial and temporal heterogeneities in DNA hydration which might impact on DNA-ligand interactions and on the intercalation of anti-cancer drugs 10 , it might be involved in drug-induced blocking of protonconducting channels depending on channel hydration 11 , and it plays a decisive role by increasing solvent entropy being the main driving force for assembly of β-amyloid aggregates 12 to name but a few examples. Therefore, a vast amount of research is aimed at understanding biomolecules in their native solvation environment at the molecular level 1–6 . Among a multitude of spectroscopic approaches, liquid-state THz spectroscopy 13,14 has proven itself in the last decade as a vital tool for studying solute/solvent couplings in particular via H-bonding interactions in aqueous solutions. The low frequency motions take place on a femto- to picosecond time scale which makes THz spectroscopy a perfect tool for their detection and observation. Indeed, THz spectroscopy has been applied to a wide range of aqueous solutions from simple ions to small molecules to real enzymes at work 15–27 in order to elucidate the interactions and the dynamics of the solvating HB network. In case of large solutes species, ”an extended dynamical solvation shell around proteins” 17 has been discovered, whereas for simple ions 20 or small solutes with strongly H-bonding functional groups such as zwitterionic amino acids 25 dissolved in water, significant THz-spectral changes are largely restricted to the first or second solvation shell as quantitatively revealed by theoretical THz spectrocopy 25,28–30 . Despite impressive progress, understanding and quantifying the THz response due to hydrophobic versus hydrophilic solvation remains largely unexplored. In particular, experimental techniques by themselves are limited toward unfolding the full molecular picture, whereas their intimate combination with tailor-made theory turns out to be fruitful by providing detailed molecular insights 25,28,29,31,32 . Here, we tackle the hydrophobic versus hydrophilic solvation issue for representative amino acids in aqueous solution by combining theoretical THz spectroscopy 33 based on ab initio molec-


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contributions. Our decomposition approach is modular and, therefore, can be generalized to assign the THz spectra of more complex molecular solutes in water.

plete set of topological groups within a given molecule are computed in the mCCA approach which yield the total spectrum due to the sum rule. As will turn out later in the detailed analysis, all non-local cross-correlations are small compared to the signal in the present case, which provides both a physical basis and justification of this decomposition approach based on chemically motivated groups (such as functional groups or fragments within a solute molecule). It is expected that the same holds true for other molecules, which provides the basis for applying mCCA beyond the specific case of amino acids in water. These “user defined” topological groups provide a complete basis to expand all correlations. Relevant subsets can be selected guided by chemical intuition. For instance distinct functional groups or different backbone sites of the solute, but also selected sets of water molecules such as those that are, or are not, Hbonded to specific sites or second-nearest neighbors etc. can be used to define the groups whose correlations must yield the total spectrum by construction. Therefore, the mCCA method is rather an “inductive” (or bottom-up) technique compared to SSC which works in a “deductive” (top-down) manner. Another key difference of mCCA w.r.t. SSC is that the group contributions can be properly normalized with respect to the same sort of contribution that would be provided in homogeneous bulk solvent. Thus, the mCCA approach can directly provide theoretical THz difference spectra of solutions with reference to the bulk solvent at the same thermodynamic conditions, akin to what is done experimentally. In order to use mCCA, the solvent molecules must be classified concerning their relationship to the molecular solute. Here we distinguish between first (‘1’) and second (‘2’) solvation shell water molecules as well as the remaining waters (‘Rw’). Furthermore, we classify the water molecules as hydrophilic or hydrophobic depending on whether they are within the solvation shell of hydrophilic (‘COO’, ‘NH3’) or hydrophobic (‘CHR’) sites within the molecule; see SI for details.

Methods Accessing Hydrophobic Solvation: Molecular Cross-correlation Analysis Infrared spectra down to the THz frequency range can be computed from AIMD 34 via the well-established dipole autocorrelelation function formalism 33 which provides direct access to the linear absorption cross section α(ω), see Eq. 1 in the SI. Note that we are utilizing dipole time-derivatives to obtain the charge-current (or dipole velocity) autocorrelation function which is required to describe charged (sub-) systems. Moreover, using these currents also covers cases were the dipole correlation function itself diverges when ω approaches zero. Earlier, we have devised the “supermolecular solvation complex” (SSC) method 25 as a systematic approach for quantifying the individual contributions of strongly H-bonding functional groups and thus of hydrophilic water to THz spectra. In the case of amino acids, the SSCs are constructed separately for the two zwitterionic − groups, –NH+ 3 and –COO , and are denoted by SSC(+) and SSC(−), respectively; more details can be found in the SI. In stark contrast to glycine 25 , valine is characterized by a bulky hydrophobic side chain R being –CH(CH3 )2 , which is unable to accept or donate H-bonds. Here, the so-called crosscorrelation analysis (CCA) method for simple monoatomic ions in aqueous solution 30 is generalized to arbitrarily complex polyatomic molecules. The key idea of this molecular CCA (mCCA) is complementary to SSC: instead of fully decomposing a total spectrum in terms of mode-specific absorption cross sections αk (ω) (which subsequently allows one to re-synthesize partial spectra mode-by-mode 25 ) and an ill-defined “rest”, all possible self- and cross-correlations of a suitably defined com-


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HB ters that are H-bonded to each other CX,Y , and the correlation between water molecules that N X N nHB X are not H-bonded to each other CX,Y . γ =h (Gζ,i (0)Gξ,j (t)Rγ,i,j (0)µ˙ i (0)µ˙ j (t))i, Cζ,ξ A key ingredient of mCCA is to split also the i j solute autocorrelation into site-specific contri(1) butions coming from the individual functional where i and j are elements of the groups ζ groups, and ξ, respectively. The dipole velocity µ˙ i (0) is a member of group Gζ,i (0) and the relaCS,S =CNH3,NH3 + CCOO,COO + CCHR,CHR + tionship between the pairs i and j is deter2CNH3,COO + 2CNH3,CHR + 2CCOO,CHR , mined by the relationship selector Rγ,i,j . For (4) the present systems, we can split the total (M) correlation function into contribution from the where CA,A with A = NH3, COO, CHR is the solute (S) and solvent (L). Furthermore, we disself-correlation of the respective group (prototinguish groups within the amino acids called nated amino, carboxylate or hydrophobic side NH3, COO, and CHR and within the solvent by chain groups), and CA,B is the cross-correlation NH3-1, NH3-2, COO-1, COO-2, CHR-1, CHRbetween these groups. This relation implies, 2, Rw. For example, water molecules within chemically speaking, that the self contribution the first solvation shell of the protonated amino of only the solute molecule is split furthermore group are part of the NH3-1 group. The total within mCCA into the invididual self contribucorrelation is recovered by summing the solute tions of all functional groups that have been self-correlation, the solvent self-correlation, and “defined by the user” to make up the entire sothe solute-solvent cross-correlation, i.e. CM,M = lute species, and again all cross-correlations as CS,S + CL,L + 2CS,L , respectively, a solutea result of this specific choice. solvent splitting which has been used since long Within our hierarchical mCCA decompositime 36,37 . Here, the solvent self-correlation CL,L tion approach, the finally remaining soluteis split further, solvent cross-correlation C can be split (in

Next, cross-correlations are defined as

S,L

CL,L =C1,1 + C2,2 + CRw,Rw + 2C1,2 + 2C1,Rw + 2C2,Rw ,

the very same spirit as in case of the complete splitting of the solvent-solvent and solute-solute self-correlations as just explained) into terms involving the individual groups of the solute as well as the H-bonded and non-H-bonded water molecules within the respective solvation shells. For example, the cross-correlation of a water molecule in the first solvation shell of the amino group with an H-bonded water molecule in the second solvation shell of the amino group is deHB noted by CNH3−1,NH3−2 . Here γ = HB requires the relationship of i and j being H-bonded to each other, thus the relationship selector Rγ,i,j will be unity in case i and j form a HB and 0 otherwise. Computing the cross-correlation of the functional groups in valine with their first solvation shells is therefore readily accessible via

(2)

where CX,Y is the self-/cross-correlation contribution to the total solvent self-correlation from each solvation shell (X,Y=1, 2, Rw). Chemically speaking, the self contribution stemming from all water molecules is thereby split into contributions originating exclusively from the self terms of the individual solvation shells (and that of all remaining water molecules that have been lumped together in the Rw term), which contributes the first three terms in the sum, and the three (considering symmetry) resulting cross-correlation signals. At the next level, these correlations are furthermore disentangled self HB nHB CX,Y = CX,Y + CX,Y + CX,Y ,

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0 self Cval,1 =Cval,val + HB HB HB 2CNH3,NH3−1 + 2CCOO,COO−1 + 2CCHR,CHR−1 . (5)

by describing separately the water molecule self self-motion CX,Y , the correlated motion of wa-


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Results and Discussion

Another advantage of the mCCA approach is that we can readily compute the difference spectrum of water molecules within the first solvation shell of valine and water molecules in the first solvation shell of water molecules in bulk water, thus providing direct access to experimental THz difference spectra without the need to subtract large (noisy) numbers. Moreover, this also provides a direct measure of the change of the spectrum of a single HB when it moves out of a homogeneous bulk environment into a specified solvation shell. In order to compute the difference, we need to scale all correlations to the same concentration, thus all differences we compute are based on absorptions that are scaled to a concentration of 1 M whereas differences are computed for a single HB based on ∆A,B HBXY

HB HB CWat−X,Wat−Y CA−X,B−Y ; − = nHB nHBWat

Molecular Solute Spectra of Valine versus Glycine The pure solute THz spectrum, dubbed Valonly, displays a significantly increased complexity compared to glycine according to Fig.1 (a). The Gly-only response is characterized by only two distinct features at around 300 cm−1 and 80 cm−1 , which have been traced back to purely intramolecular (‘backbone’) motion and quasirigid-body dynamics, respectively 25 . In the case of Val-only, the 300 cm−1 signal is a double peak, while at around 200 cm−1 , i.e. right where the overriding bulk water network mode is located, a hitherto unknown but pronounced signal arises. Moreover, the quasi-rigid-body modes of Val-only below 80 cm−1 feature a much lower intensity compared to glycine. In the subsequent SSC mode decomposition, it will be unveiled how all these changes are imprinted by the dipolar dynamics of the bulky valine side chain.

(6)

here Wat denotes the corresponding reference group from a pure bulk water simulation, A and B stands for the NH3, COO or CHR groups, whereas X and Y can be first shell, second shell and remaining water molecules, that is 1, 2, or Rw. This molecular CCA approach can be applied straightforwardly to any solute in any solvent. For the present purpose, we compute THz spectra that are directly comparable to experimental difference spectra by

Hydrophilic Solvation of Valine versus Glycine

Although the decompositions of the Val(aq) and Gly(aq) THz spectra in terms of modespecific absorption cross sections αk (ω) from their SSC analyses look vastly different at first sight, see Fig. 1(b)-(c), they are charself HB + 2CNH3,NH3−1 + CVal(aq) = Cval,val acterized by significant inherent similarities. HB HB 2CCOO,COO−1 + 2CCHR,CHR−1 + cage modes (dashed lines) The quasi-rigid-body X −1 A,A A,A A of valine (68 cm , 54 cm−1 , 56 cm−1 and nA HB11 ∆HB11 + nHB12 ∆HB12 , 50 cm−1 ) are systematically red-shifted relaA=NH3,COO,CHR tive to glycine (82 cm−1 , 62 cm−1 , 73 cm−1 (7) and 64 cm−1 ). Additionally, they are of a where we include explicitly the changes of the roughly comparable maximum intensity which, HB network w.r.t. bulk water as well as all however, is unexpectedly small compared to all correlations of the solute with the solvent, with other THz modes of Val(aq). The bulky side nA being the number of HBs in the respecchain introduces additional motions that distort HBXY tive solvation shell. the rigid-body-motions compared to glycine, resulting in lower intensities of these modes. This is born out by the energy decomposition (see SI) where a higher contribution of rotational motion is revealed, thus reducing the overall change of the dipole moment from these modes. ACS Paragon Plus Environment

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These features explain the rather low absolute intensity of the THz lineshape below about 100 cm−1 in the case of Val(aq). When it comes to intramolecular modes at higher frequencies, the double peak structure, observed from roughly 300 to 350 cm−1 , originates from several intramolecular valine modes. The same sort of backbone mode as in glycine underlies the resonance at ≈ 350 cm−1 , while the main contribution to the lower-frequency part of the double peak signal comes from a novel opening/closing motion of the side chain, namely the NCCC I (317 cm−1 ) and NCCC II (280 cm−1 ) modes involving the two methyl groups of the side chain. The pronounced valine peak which sticks out at 200 cm−1 in Fig.1 (a) originates as well from an intramolecular side chain mode. Concerning solute-solvent couplings in terms of distinct intermolecular modes, the prominent contribution in Gly(aq) at ≈ 250 cm−1 is mainly due to HB stretching involving the hydrophilic group (Fig. 1 (c), solid black lines with symbols). The very same mode also exists for Val(aq), albeit as an unusually broad feature shifted to lower frequencies, ≈ 150 cm−1 . These assignments based on SSC(+) analysis are supported by those of the SSC complex that involves H-bonding to the carboxylate group, SSC(−), which is therefore presented only in the SI. At this stage, we conclude that all modes observed in glycine are also found in valine, albeit frequency-shifted, while valine’s side chain introduces distinct new modes, including some of them in the frequency window of the bulk water network peak at ≈ 200 cm−1 . This underlies the increased complexity of the THz spectrum of Val(aq) in terms of its frequency-dependent modulations. Yet, it can again be fully assigned in terms of quasi-rigid-body hindered translation and rotation, proper intramolecular modes, as well as additional intermolecular modes due to specific solute-solvent couplings.

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Cα out-of-plane HB bend I cage libration I cage Rattling I cage Rattling II cage Rattling III

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Figure 1: (a) Intramolecular solute THz spectra of the valine and glycine molecules in the Val(aq) and Gly(aq) solutions corresponding to the Val-only and Gly-only absorption cross sections. Panels (b) and (c) display the mode-specific THz absorption cross sections αk (ω) of Val(aq) and Gly(aq), respectively, obtained from the supermolecular solvation complex involving the protonated amino group, i.e. SSC(+). The displacement vectors corresponding to each mode k are visualized in the supporting figures S9– S34 for Val(aq). whereas the SSC(−) spectra and their mode decompositions are presented as supporting figures S35– S53. All spectra in this figure are scaled to a concentration of 1 M.


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Complementary Analysis of Hydrophilic Solvation

of their intensity- and frequency-dependence turns out to be similar for Val(aq) and Gly(aq). This indicates that the bulky hydrophobic side chain of valine does not lead to any significant steric perturbations of the hydrophilic interactions of the charged nearby groups at the level of dipolar correlations in Val(aq) as probed by THz spectroscopy. These observations strongly suggest that the THz contributions of distinct functional groups are roughly additive even in so-called “Chemical Space”, and thus of an essentially modular nature! The dipolar correlations due to solvation of the hydrophobic group of valine by water molecules, abbreviated by CHR, are referenced with respect to the carbon sites of the two methyl groups of the side chain, R = CH(CH3 )2 , whereas R = H for glycine so that the Cα carbon serves as the reference site. For Gly(aq), it turns out that the THz response due to these CHR dipolar correlations contributes a weakly modulated but essentially flat line with an amplitude on the order of only ±1 cm−1 that merely adds a constant background to the total spectrum. Surprisingly, the picture for valine in water is not that different! Looking at the corresponding CHR term obtained from the mCCA method reveals an essentially constant baseline in the THz regime.

After having successfully decomposed and assigned the THz contributions of the hydrophilic groups of Val(aq) based on SSC analysis, we now explore to what extent the novel molecular CCA method can provide insights into hydrophilic solvation – before applying it to hydrophobic solvation where the SSC approach fails. We therefore set out to synthesize the THz spectrum of Gly(aq) obtained from the SSC(±) methods by computing and adding up individual self- and cross-correlation contributions as defined in the mCCA framework according to Eqs. 3, 4 and 5, where we only take into account, as explained below, the solute-self term, the cross-correlations of the corresponding hydrophilic site with its first solvation shell and the first solvation shell self term. We find that mCCA is, indeed, able to quantitatively recover the Gly(aq) low-frequency spectrum as demonstrated in detail in the SI, see in particular Fig. S7 in Sec. 2.4, thus proving the fundamental consistency of the two very distinct approaches to the dissection of THz spectra of molecular solutions. In particular, the mCCA approach is able to rigorously split the total THz spectrum into arbitrarily selected site-specific contributions à la carte, and therefore can be applied to hydrophobic sites as well.

Deciphering the Experimental Spectrum: Hydrophilic versus Hydrophobic Solvation

Quantifying the Contribution of Hydrophobic Water to THz Spectra

Having all separate contributions at hand – hydrophilic and hydrophobic – we are now able to compare the decomposed and re-synthesized spectrum to the THz difference spectrum of Val(aq) that has been measured at several concentrations, see Fig. 3 (top). The experimental spectrum at the lowest concentration is characterized by rather weak yet significant modulations of the THz lineshape, which only grow in intensity upon increasing the concentration. Thus, the pronounced peak structure, which is grossly different from that of the Gly(aq) spectrum 25 , comes out most clearly at the highest concentration. There is no low-frequency

Having proven that the mCCA approach can quantitatively account for site-specific hydrophilic solvation, we are prepared to apply it to disclose the THz contributions around hydrophobic sites, which remains terra incognita up to this point. The relative intensity scale for the hydrophobic contributions is set by the strongly modulated THz responses of the charged groups, see Fig. 2. The latter hydrophilic contributions due to both anionic and cationic zwitterionic sites are rather similar for Val(aq), which confirms what has been found for Gly(aq). More interestingly, the gross trend


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Figure 2: Molecular cross-correlation analysis, mCCA, of the functional groups (–NH+ 3: − squares, –COO : triangles, side chain: circles) in aqueous valine (a) and glycine (b) soHB HB lutions. Shown are the CNH3,NH3−1 CCOO,COO−1 HB and CCHR,CHR−1 contributions.

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Figure 3: Comparison of the experimental THz difference spectra of Val(aq) at the indicated concentrations in (a) to computed mCCA difference spectra of Val(aq) (violet line with crosses) in panel (b) being synthesized term by term. The bottom panel (b) shows the consecutive sums of the distinct contributions to the mCCA difference spectrum as follows (see also text): Starting from valine’s self term (solid black line with squares) the cross-terms of the molecular sites (dashed red and dashed blue lines) are added resulting in the orange spectrum (with circles). Adding further the sum of the ∆A,A HB11 terms (dashed green line) the solid green line (with triangles) is obtained. Finally, upon adding the sum of the ∆A,A HB12 terms (dashed purple line) we obtain the total mCCA difference spectrum (solid purple line with crosses). Note: all computated spectra are scaled to the highest experimental concentration for one-to-one comparison.

resonance around 80 cm−1 or below, the most prominent peak is now close to 200 cm−1 and unexpectedly narrow with a shoulder extending down to 100 cm−1 which originates from the HB stretching mode as seen in Fig. 1 (b), while the high-frequency feature is split in terms of a double peak structure with maxima at about 320 and 350 cm−1 . It is found that the effective solute absorption increases linearly with concentration and shows no evidence of peak shifts. The computed spectrum of the valine molecule itself (black line with squares) is already qualitatively similar to the experimental one but also subject to unacceptable stark differences concerning the intensity modulations along the frequency axis, see Fig. 3 (b). Not only is the total intensity significantly lower than the experimental one, recalling that our intensities as obtained from AIMD are reported on an absolute scale, but also the peak at approximately 80 cm−1 is much less pronounced in the experimental spectrum. Upon adding further contributions obtained from the mCCA approach namely the dipolar response due to HB the hydrophilic solvation shells (CNH3,NH3−1


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How Different is Hydrophobic Water from Bulk Water?

HB and CCOO,COO−1 the sum of which is plotted as the dashed blue line in Fig. 3 (b)), it is seen that the agreement with experiment is substantially improved (orange line with circles). In particular, the overall total intensity increases appropriately and the low-frequency feature around 50 to 100 cm−1 is considerably suppressed as a result, all in accord with the measured spectrum. The systematic intensity increase toward the high-frequency end of the frequency window is traced back to a long tail due to the dipolar response as a result of usual librational water motion. Apart from these observations, it is interesting to see that the cationic and anionic functional groups of the zwitterionic solute contribute rather similarly to the total THz lineshape, but that they are both required in order to establish the correct absolute intensity scale. But what about the THz contribution due to hydrophobic solvation? There is not much visible on the relevant scale of the gross intensity modulations, which is about 10 cm−1 , as it is imprinted by the major contributors being the purely intramolecular solute correlations as well as the dipolar fluctuations as a result of hydrophilic solvation of the charged zwitterionic groups. The hydrophobic solvation shell, albeit it is much larger (consisting of ≈ 17 water molecules on average) than the cationic (≈ 3) and anionic (≈ 4) shells together, leads to an essentially structureless background as nicely exposed in Fig. 3 (b), see dashed red line. We therefore conclude that the hydrophobic solvation shell in Val(aq) appears to be barely distinguishable from bulk water in the THz regime. This provokes the question if such a contribution that is negligible compared to the peak intensities, is due to a number effect or due to a slightly perturbed THz response of those water molecules which are direct neighbors of bulky groups that are unable to be engaged in direct HB interactions with solvation water (but are rather “straddled” by these hydrophobic water molecules instead, as shown for the methyl groups in aqueous TMAO solutions 39 ).

Let us finally address this question given the findings from the previous section concerning the bulk-like appearance of hydrophobic water. Molecular CCA cannot only be applied to solvated solutes, but also to the pure solvent in the absence of any heterogeneities in the sense that a (specific but arbitary) solvent molecule serves as the “solute group”, which in turn gets solvated by first, second etc. shell H-bonded water neighbors being the ”solvent groups”. This idea opens the door to quantify in terms of THz response how H-bonds between water molecules within a specific solvation shell do change relative to the analogous H-bonds in bulk water. In order to address this issue quantitatively, Fig. S6 in the SI displays the difference of a water-water H-bond within the three different solvation shell environments compared to the corresponding H-bond in bulk water as defined by Eq. 6. Clearly, H-bonds within the hydrophilic solvation shells, both around –NH+ 3 and –COO− , are significantly altered compared to the respective H-bonds in pure water (top panel). H-bonds between water molecules in the hydrophobic shell, however, are hardly affected, the THz response changes being on the order of ∆α ≈ ±1 cm−1 only. In contrast, the change of the HB spectrum due to H-bonding between the first and the second solvation shell is similar but of opposite sign for hydrophobic and hydrophilic water, albeit very small. This implies that the influence of a solute as small as valine is limited to affecting the THz response of the first solvation shell and does not extend further at the level of intensity modulations that significantly exceed ±1 cm−1 .

Conclusions and Outlook The THz spectra of aqueous solutions are characterized by distinct lineshape modulations which encode the underlying solvation structural dynamics which strongly hinges on the three-dimensional H-bonding properties of water. The molecular cross-correlation analysis


9


(mCCA) method has been introduced and applied in order to site-specifically decompose the THz response of aqueous solutions in terms of distinct contributions stemming from hydrophilic and hydrophobic functional groups. Studying aqueous valine versus glycine solutions, Val(aq) and Gly(aq), the hydrophilic sites in the two cases are found to lead to almost identical contributions to the THz difference spectra and are essentially decoupled from other factors. In the case of Val(aq), additional complexities are introduced in the THz regime, which are however of purely intramolecular origin and add features to the contribution due to the so-called ‘backbone’ mode that is already present in Gly(aq). These additional signals include a prominent sharp peak at about 200 cm−1 that sits on top of the broad feature stemming from intermolecular H-bonding modes that involve the strongly hydrophilic, charged groups. Valine is characterized by a voluminous hydrophobic side chain that is merely straddled by the closeby water molecules in the absence of any capability to form H-bonds. The mCCA approach allows us to compare the THz response of those water molecules that form the hydrophobic solvation shell versus the corresponding response in the homogeneous bulk limit. It is found that the change of the spectral response upon moving from bulk into the hydrophobic hydration sphere is on the order of one wavenumber only in the THz frequency regime and does not add additional structure to the computed total spectrum. Even considering the large number of hydrophobic water molecules, compared to the few that form Hbonds with the hydrophilic groups, they do not contribute much on the intensity scale of the total modulations of about 20 cm−1 . Overall, we conclude that the THz contributions of distinct functional groups are essentially additive and thus modular in Chemical Space. The mCCA approach is able to split the total THz spectrum into site-specific individual contributions à la carte. Moreover, considering all site-specific contributions of a solute is shown to yield the total THz difference spectrum of the corresponding aqueous solution in

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close accord with experimental spectra. Together, this offers the opportunity to access THz spectra of more complex solutions by a “divide and conquer” approach.

Associated Content Supporting Information. The Supporting Information containes detailed information on the theoretical methodology, experimental setup and shows detailed mode-specific absorptions and mode-displacements patterns.

Acknowledgements It gives us great pleasure to thank Philipp Schienbein for fruitful discussions. This work was partially supported by Deutsche Forschungsgemeinschaft via MA 1547/11 and is also part of the Cluster of Excellence RESOLV (EXC 1069). The computational resources were provided by SuperMUC@LRZ, HPC–RESOLV, HPC@ZEMOS, BOVILAB@RUB, and RV– NRW.

Supporting Information Available The supporting information includes computational and experimental details, modespecific absorption spectra and detailed mode displacement patterns. This information is available free of charge via the Internet at http://pubs.acs.org

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Graphical TOC Entry


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Hydrophilic Solvation Dominates the Terahertz Fingerprint of Amino

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