Classical Description of the Vibrational Spectroscopy, Structure, and

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Classical Description of the Vibrational Spectroscopy, Structure and Electrostatics of the Halide Solvation Shell With the POLIR Potential Gungor Ozer, and Tom Keyes J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/jp509907v • Publication Date (Web): 30 Jan 2015 Downloaded from http://pubs.acs.org on February 18, 2015

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The Journal of Physical Chemistry

Classical Description of the Vibrational Spectroscopy, Structure and Electrostatics of the Halide Solvation Shell with the POLIR Potential Gungor Ozer and Tom Keyes∗ Department of Chemistry, Boston University, Boston, MA 02215 E-mail: [email protected]

Abstract POLIR (POLarizable for IR) [J. Chem. Phys. 129, 034504 (2008)] is a polarizable, flexible, and transferable water potential which describes the IR spectrum in the O—H stretch region via the classical dipole correlation function with simple quantum corrections. POLIR also reproduces experimental spectral shifts in solutions of Ca2+ , Mg2+ and Cu2+ [J. Am. Chem. Soc. 133 (2011)]. Here we present an extended investigation of POLIR water in the solvation shell of the halides F− , Cl− , Br− , and I− using various interaction potentials, polarizabilities and short-range electrostatic damping parameters. Our results indicate that the correlation of the first solvation shell dipoles produces IR spectra that are in agreement with experiment: that is, vibrational spectral shifts may be obtained with classical mechanics and simple corrections. Calculated ion induced dipoles agree with quantum simulations. Further analysis shows that ion-dependent shifts in the spectra may be attributed to the hydrogen bond O · · · O—H angle distribution within the first solvation shell, decomposed into ion-water and water-water contributions. ∗ To

whom correspondence should be addressed

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Keywords: Water, ionic solutions, polarization, IR spectra, O—H vibrations, hydrogen bond angles.

Introduction Polarization is the creation of induced dipoles by local electric fields. It is well established that intermolecular polarization is important for the physical properties of liquids, and for their response to experimental probes, e.g. light scattering, 1–6 optical Kerr effect, 7–9 dielectric relaxation, etc. The theoretical and computational methods for polarizable calculations are available. The situation is less clear for intramolecular polarization on the length scale of chemical bonds, and the related probe of vibrational spectroscopy.

A quantal approach is naturally suggested for such short

distances; however, we aim to show that polarizable classical mechanics remains applicable. 10 Water has been aptly called 11 “a responsive small molecule”. Condensation of the vapor produces an increase of ≈ 18× in the IR absorption/molecule and a vibrational redshift of ≈ 300cm−1 , which are enormous changes compared to other molecules. The former was shown to arise from polarization, 12,13 and the latter from hydrogen bonding (H-bonding), in which the polarization energy plays an important role. Thus it seems that polarization is a crucial element of the responsiveness of the intramolecular vibrations of a water molecule to its environment, as is the case for intermolecular properties. With the O—H vibration strongly quantized, it is surely not obvious 14 that a quantitative classical polarizable description is possible. We have argued that it is. To describe such short distances, damped electrostatics, taking the finite extent of atomic charge distributions as formulated by Thole, 15 must be carefully implemented. The polarization-centric POLIR potential 16 yields good absolute IR spectra of water liquid, clusters, and ice via the classical dipole correlation. Only the simplest quantum corrections are required, a harmonic intensity correction and a Berens-Wilson anharmonic peak frequency correction. 17 The latter corrects for the difference between the harmonic frequency at the bottom of the potential well, seen in classical dynamics, and


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the 0→1 transition frequency. Our approach would not be so useful if this quantity varied strongly from case to case, but we have found that it is remarkably constant 18 among diverse environments. A spectroscopic theory based upon the dipole correlation is extremely convenient, as the dipole may be decomposed in any relevant fashion, isolating the contributions of specific groups of molecules, permanent vs induced dipoles, etc. Collective, many-body induced dipoles are seamlessly described, while quantum mechanically they require inclusion of “non-Condon effects.” There is no need to choose the size of the entity, e.g. a cluster, to be used as in the quantum calculations. “Force field development” optimizes the parameters in empirical potentials, typically for structure, e.g. pair distribution functions, and energetics. Since polarization is so important for aqueous spectroscopy, we consider that optimizing POLIR for spectroscopy has broader implications: it is a novel and very good way to optimize the treatment of polarization, which influences almost all aqueous behavior. In fact, the only bulk liquid property built into POLIR is the absolute IR spectrum. This paper provides a test of whether a POLIR-based model is therefore readily extended to non-bulk solvation spectra. The local electric field at a molecule that creates the induced dipole is the vector sum of the contributions from all the neighbors. The field from a roughly symmetric arrangement of neighbors in bulk is quite different from that with, e.g., an ion in one direction and water elsewhere. Corresponding changes of aqueous vibrational spectra from the bulk liquid are sensitive probes of heterogeneous environments, notably interfaces and the solvation shell. Non-polarizable water potentials incorporate polarization for the bulk environment in a mean-field fashion, but cannot adapt to heterogeneous environments: they are not “transferable”. The responses of the spectra, dipole, and local energetics and structure, are captured by a polarizable potential, and the question is, how well? POLIR plus compatible polarizable water-solute potentials was shown 18–20 to yield the spectra, dynamics, energetics and structure of the solvation shells of doubly charged cations and “synthetic” solutes designed to be tunable between hydrophilic and hydrophobic. Here we consider solvation of the halides. While the approach is generally unchanged, now,



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in contrast to the cation case, halide· · ·H–O hydrogen bonds, as well as O· · ·H–O hydrogen bonds modified by the presence of the solute, directly influence the OH frequencies, making the results more sensitive to the choice of ion-water potential. Several potentials will be evaluated. The results for the spectra will be seen to be robust, and it will be shown that our classical approach correctly reproduces spectral blue shifts from bulk, the structure and distributions of dipole moments of the the solvation shell, and the trends among the different halides. In particular, we obtain and interpret the singular nature of fluoride. Aqueous spectra are broad and the effect of a solute cannot be simply summarized by a peak shift, and the blue shifts will be discussed accordingly. The relation of the spectra to the distribution of H-bond angles 20 will be demonstrated.

Polarizable classical methods for solvation spectra Ion-water potentials Ions were assigned point charges and polarizabilities, leading to Coulomb and polarization energies 16 14 in the presence of POLIR water molecules. An ion-O van der Waals potential of form ( Ar16 + + Ar14 iO

A12 12 riO

+

A6 6 ), riO

iO

was included, where riO is the ion-(water oxygen) distance.

Condensed-phase potentials can invoke “effective” atomic properties, e.g .charge, different from the monomer values. However, our approach is to keep the monomer properties unchanged, and have the environment exert its influence via polarization. Accordingly, the F− , Cl− , Br− and I− ions were assigned charges of -1 and isotropic monomer polarizabilities, α , taken from the literature. There is no definitive set of polarizabilities, so we have considered both “high” and “low” values. Most of the earlier studies used the low polarizabilities (LP) estimated from static crystal polarizabilities by Coker 21 in 1976. For F− , Cl− , Br− and I− these values are 1.38, 3.94, 5.22, and 7.81 Å3 , respectively. High level quantum calculations produced relatively higher polarizabilities (HP) of 2.47, 5.48, 7.27, and 10.27 Å3 for F− , Cl− , Br− and I− , respectively. 22 For the details of our application of damped polarizable electrostatics, see our earlier pa4 ACS Paragon Plus Environment

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pers. 18–20 The Thole 15 parameters must also be chosen. As in POLIR, the power of riO in the exponentials, expressing the short-range damping, was 4, following Burnham. 23 The parameters “a”, setting the length scale for damping, were chosen either to resemble pure POLIR, or, for Cl− only, from Masia’s recent work. 24 Masia’s Thole damping scheme is slightly different from that employed in POLIR, making an exact correspondence of parameters impossible. He expresses damping as a function of (r/a)3 , while in POLIR a function of a(r/A)4 is used, where A is the natural length, A = (αi α j )1/6 . Thus a is the characteristic length in the former case, and adjusts the natural length in the latter. Moreover, Masia damps only the charge-charge (CC) interaction between O and Cl− and charge-dipole (CD) and dipole-dipole (DD) interactions between H and Cl− . In POLIR, all three types of interaction are damped in the short-ranged interactions between both O-Cl− and H-Cl− . So, in order to project Masia’s damping parameters into POLIR, we assume that charge-charge and charge-dipole damping for O-Cl− are identical to those for H-Cl− and similarly dipole-dipole damping for H-Cl− identical as that for O-Cl− . We then note that damping is most significant at short range, choosing 1Å as representative, and make the necessary conversion by equating (1/aM )3 to aP /A4 (“M” denotes Masia, “P” POLIR). Recall that a is the adjustable electrostatic damping parameter Electronic structure calculations on the ion-water dimers were performed to obtain the global minima. We then scanned the minimum ab initio energy, with respect to the water orientation, as a function of riO and the van der Waals parameters were adjusted to reproduce the results. The potential is underdetermined with this information, so equally good fits were obtained for all polarizabilities and “a” parameters. The potentials under consideration are summarized in Tables I, II in the Supporting Information (SI). By testing different potentials, we will obtain an evaluation of the optimal paramaterization of damped electrostatics for halide solvation and spectra.



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Classical computation of the IR spectrum The classical IR spectrum is proportional to the Fourier transform, denoted C(ω ), of the time auto-correlation function (TCF), C(t), of the total dipole moment of the simulation box, M (t). The charges, permanent dipoles, and induced dipoles on the water molecules, plus the induced dipole on the ions, all contribute to M . The classical TCF is corrected using the harmonic quantum intensity correction, Q(ω ). The final expression for the absolute intensity is

I(ω ) =

4π 2 ω (1 − e−β h¯ ω ) · Q(ω ) ·C(ω ), 3cV h¯

(1)

where V is the volume of the box and Q(ω ) = h¯ ω /(1 − exp(−β h¯ ω )). We employ the Berens-Wilson anharmonic quantum frequency correction, 17 expressing the difference between the frequency at the bottom of the potential well, seen in classical simulations, and the quantal 0 → 1 transition frequency. The Partridge-Schwenke monomer potential 25 used in POLIR acquires a 184 cm−1 red-shift of the O—H stretching band, and a 187 cm−1 shift was previously found 16 with an effective bulk liquid potential, indicating that the shift is quite constant upon condensation. More recently 18 we found a negligible change in the shift for the very strongly bound Mg2+ -water dimer. Thus we can proceed under the assumption that the shift is independent of the environment, an important element of our approach. In order to examine the contributions to the spectra from water molecules in different environments, we calculated the spectra resulting from waters in different solvation shells around the ion. For example, the spectrum arising from the first solvation shell was calculated as follows. On each MD time step, waters were defined as belonging to the first shell if the ion-O distance was inside the first minimum of the ion-O radial distribution function; the members of the shell can vary during the simulation. The autocorrelation function of the total dipole moment of the first-shell waters, permanent plus induced, plus the induced dipole on the ion, is used to determine the spectrum. In a non-polarizable theory, of course, the ion would not have an oscillating dipole at a vibra-


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tional frequency. The contribution of the ion to the IR spectrum is entirely due to polarization, and it would be very interesting if it had a unique experimental signature. Similarly, a range of ion-O distances defines the second shell, etc. Since the induced dipoles are created by local fields from all the species in the box, the result is not a property of the indicated shell only. Nonetheless, these spectra are very useful in identifying the species that give rise to different signatures in the IR spectra, and for comparing with experimental “ion correlated spectra”.

Computational details Mankoo and Keyes used Gaussian03 26 to calculate the minimum potential energy for a pair of water molecules as a function of rOO using the aug-cc-pVTZ basis set at the MP2 level of theory. The POLIR potential was fit to the results by optimizing the corresponding damping and van der Waals parameters. Kumar and Keyes used the same level of theory and basis set to calculate the pairwise interaction potential between a chloride ion and a POLIR water molecule. 19,20 We have used the same procedure in creating fluoride-water and chloride-water potentials. However, for larger ions—bromide and iodide—we have used the less detailed basis set LANL2DZ at the MP2 level. For consistent comparisons and identifying trends, we have also made potentials for fluoride and chloride with this basis set, recognizing that it is not the best choice. Thus, we will present data from the LANL2DZ potential for all four ions and from the aug-cc-pVTZ potential for F− and Cl− . The results obtained below indicate that, despite its limitations, use of the LANL2DZ potential does yield correct trends in the halide spectra. Figure Figure 1 shows the dimer minimum energy potentials between POLIR water and all four halides from quantum calculations. (solid lines from LANL2DZ; dashed lines from aug-cc-pVTZ level of theory) and the corresponding POLIR fits (discrete symbols). Circles and squares represent the fit for low and high polarizabilities, respectively. For Cl− , there are two additional symbols, diamonds and triangles representing Masia’s damping at high and low polarizibilities, respectively. The fit parameters (van der Waals) were employed with the POLIR code for various polarizability 7 ACS Paragon Plus Environment


0

Energy (kcal/mol)

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-10

-20

F- (A) Cl- (A) F- (L) Cl- (L) Br- (L) I- (L)

-30

1.5

2

2.5

3

3.5

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X-O Distance (Å) Figure 1: The ab initio scans of the halide-water dimer minimum energies and corresponding fits to the POLIR model as a function of the ion-oxygen distance. Solid and dashed lines represent the ab initio energies calculated using LANL2DZ (L) and aug-cc-pVTZ (A) level of theory. Symbols represent the pairwise ion-POLIR water interaction energies fitted to the ab initio energies. Circles and squares are for low and high polarizability, respectively. Diamonds represent the original Thole damping term and triangles are for Masia’s method.


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and damping values as discussed in Section IIA. These parameters are listed in Tables I, II in the SI. Molecular dynamics simulations are then carried out in the NVE ensemble using our in-house code with a cubic simulation box of length 15.64 Å with periodic boundary conditions. Each cell contains 127 water molecules and a single ion, corresponding to 0.43 M or 0.78 mol%, which is within the experimental range. The long-range electrostatic interactions were treated using Ewald sums that introduce uniformly distributed background charge to neutralize the simulation box. 27 While more waters would be better, we consider that, based on the results of our prior work and those to be demonstrated below, 127 waters are adequate to demonstrate physically significant trends in solvation spectra. The system was initially equilibrated in the NVT ensemble at 300 K. The time step is set to 0.2 fs to accommodate our aim of calculating accurate vibrational spectra. We have not tested nor benchmarked the effect of the length of time steps and elected to use shortest computationally feasible to us. We have generated 12 independent trajectories of 250,000 steps for each ion and potential model. So for any given ion, polarizability, choice of basis set and damping (Cl− only) we collected 600 ps of time-evolved data which includes coordinates, velocities, dipoles and energetics.

Results and Discussion We have analyzed the simulation data with various measures and metrics. These include structural properties such as the radial distribution function Figure 1 in the SI) and H-bond β -angle distribution, polarizable electrostatic properties such as the ion dipole distribution, and, most significantly, the IR spectrum.



Ion dipoles We first consider the distribution, and average, of the magnitude of the dipole moment of the ion. Note that there is no ion dipole without polarization. In general in a classical simulation, these quantities depend on the water model and the ion-water interaction and in particular are strongly correlated to the polarizability (LP vs HP) and damping parameters. As seen in Figure Figure 2, unsurprisingly, the average ion dipole of all halides shifts to significantly higher values in HP compared to LP. For Cl− , use of different damping, namely aM and aP , leads to a slight difference in LP and a dramatic difference in HP. With aM and HP, the dipole distribution of Cl− is shifted to even beyond that of Br− .

Normalized Distribution

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(D)

0

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Dipole (D)

4

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-

FCl (P) Cl (M) Br I

2

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4

5

Figure 2: The distribution of the ion dipole. Data from aug-cc-PVTZ potential with low (A) and high (B) polarizability and from LANL2DZ with low (C) and high (D) polarizability are shown. P and M indicate POLIR and Masia damping. Carr-Parinello quantum simulations are available for the chloride dipole, 24 and our low-polarizability results are in excellent agreement. One of our goals is illuminating why F− is an “outlier” among the halides, and Figure Figure 2 does so, in terms of the dipole distribution. The low mean dipole magnitude is primarily due to the low polarizability, which is not terribly interesting, but the narrow width indicates small local field fluctuations arising from the uniquely rigid F− solvation shell. Below we will demonstrate the corresponding unique distribution of F− hydrogen bond angles. 10 ACS Paragon Plus Environment

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Solvation spectra Ionic solutions of halides are well studied using Raman and IR spectra. Compared to bulk water, halides exhibit a higher frequency (blue shift) 28 of the O—H stretch. The question of which water molecules, in terms of distance from the ion, produce these shifts, is a subject of debate. Some studies show that the hydrogen bond arrangements of the bulk water even beyond the first salvation shell are affected by ionization. 29,30 On the other hand, recent ultrafast IR pump-probe measurements suggest that ionization only affects the vibrational relaxation times of water molecules in the first solvation shell. 31 Our prior work, 18–20 and that of Sharp, Madan et al., 28 is based upon the assumption that waters in the first solvation shell are primarily responsible for the shifts, and, within our approach, it is justified. Adding the second shell, or considering the whole box, primarily makes the ion-specific trends more difficult to analyze. We will continue with first-shell spectra below. We calculated vibrational spectra of water influenced by halides from the classical dipole correlation, with trivial quantum corrections. The results indicate that this method, remarkably, can reproduce the IR spectra of a strongly quantized O—H stretch. Our dataset includes both low polarizability (LP) and high polarizability (HP). Even though the ion dipole changes from LP to HP (Figure Figure 2), the IR spectra are similar for LP and HP. Thus, in view of the good agreement with Ref. 24 with LP, we will only show data from our LP simulations in the following. In discussing the shifts in aqueous spectra due to ionic solvation, experimentalists must isolate the “ion correlated” spectra. 32 We do the same by using the dipole of the ion plus first solvation shell waters. Being able to easily examine any physically significant part of the dipole is a powerful advantage. Classical simulations yield the blue shift of halide solutions relative to neat water. In Figure 2 in the SI, the vibrational spectra of all water molecules is compared to neat water. These spectra contain contributions from unperturbed water and thus are not the most sensitive reporters of our topics of interest, but the blue shifts are evident. However, shifts appear to exhibit little discrimination among halides, even with the aug-cc-pVTZ potential (Figures 2A,B in the SI), and 11 ACS Paragon Plus Environment


3 2.5 2 1.5 1 0.5 0 3 2.5 2 1.5 1 0.5 0

3

Normalized Intensity (x10 )

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(A)

Neat FCl (P) Cl (M) Br I

3000

(B)

3250

3500

3750

ω (cm-1) Figure 3: IR spectra of the first solvation shell in the O—H stretching region. Total dipole of the first shell water molecules and induced dipole of the corresponding ion are used to calculate the vibrational spectra. Top (A) and bottom (B) panels represent data from aug-cc-pVTZ and LANL2DZ potentials, respectively.


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this suggests that the strong first-shell effects are being diluted by less strongly influenced waters. To examine the full extent of halide effect on the O—H vibrations, we calculate the spectra using only the first shell water molecules (Figure Figure 3). First-shell spectra obtained from the aug-cc-pVTZ potentials shows that Cl− spectrum has a peak at 3474 cm−1 and 3462 cm−1 using POLIR damping (P) and Masia’s damping (M), which translates into a blue shift of 130 cm−1 and 118−1 , respectively (Figure. Figure 3, A and B). For F−1 , the blue shift of the peak at 3414 cm−1 is a much smaller 70 cm−1 . The unique character of the F− spectrum is evident in the strong enhancement on the red side of the peak; this spectrum is not described by peak position and width only. For the potentials based upon LANL2DZ (Figure. Figure 3, C and D), however, the blue shifts are smaller and more similar, which makes it harder to visually differentiate halide specific spectra. Nevertheless, since they are available for all four halides, we will focus upon them to identify trends. They are considerably more attractive than the aug-cc-pVTZ potentials but, for Cl−1 and F−1 , show similar trends. LANL2DZ spectra will be treated with a physically motivated 2-Gaussian fit analysis which quantitatively characterizes the halide spectra and allows their interpretation in terms of hydrogen bonding in the solvation shell. In discussing the shifts in aqueous spectra due to ionic solvation, experimentalists must isolate the “ion correlated” spectra. 32 We do the same by using the dipole of the ion plus first solvation shell waters. Being able to easily examine any physically significant part of the dipole is a powerful advantage. Figure Figure 4 shows representative solvation spectra for Cl− , Br− , and l− ; the vertical line indicates the peak position of neat water. The most obvious conclusion is that the classical approach does indeed reproduce the blue shifts found experimentally. 32 The spectra are not simple enough to describe with a width and peak position alone, but we may also say that the blue side of the peak correctly becomes bluer with increasing ion size and polarizability. Now consider fluoride, the “outlier”. Figure Figure 5 compares F− , l− and neat water; recall that the red side of the other halides is identical to l− . With decreasing frequency from 3200 cm−1 ,


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2

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0 3000

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ω (cm-1) Figure 4: Smoothed IR spectra in the O—H stretching region obtained from the correlation of dipoles of the first shell water molecules plus the induced dipole on the ion. P indicates that original POLIR damping. For comparison between the POLIR (P) and Masia’s (M) damping see Figure Figure 3.


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the F− spectrum is seen to first exceed that of the other halides, and eventually neat water; there is a red tail, in agreement with Ben-Amotz’ Raman spectra. 32 What causes the blue shifts, and the singular behavior of fluoride? The interpretation of the spectra is complicated by uncertainty about the normal modes. In a water monomer, the two O—H stretches are resonantly coupled into the antisymmetric and symmetric stretches, with the former and the latter split about 50 cm−1 above and below the average frequency of ≈ 3700 cm−1 , respectively. In the liquid, the peak is red shifted by about 300 cm−1 to ≈ 3400 cm−1 , primarily due to softening of the O—H potential by H-bonding. It is not clear if the local modes are correspondingly restored, or if the symmetric and antisymmetric stretches persist. Space, Moore et al. 12,13 performed instantaneous normal mode (INM) analysis and found that the modes in the band center were O—H stretches, while antisymmetric and symmetric stretches were found at the blue and red edges, respectively. 3


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0 3000

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3750

ω (cm-1) Figure 5: Smoothed IR spectra in the O—H stretching region obtained from the correlation of dipoles of the first shell water molecules plus the induced dipole on the ion.

Ben-Amotz et al. have clearly demonstrated 32 the presence of resonance in the neat liquid,



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with the prominent red shoulder on the vibrational Raman spectrum strongly suppressed by isotopic substitution and by the presence of a halide ion. The coupling being weakened could be intramolecular O—H, intermolecular O—H, or intramolecular stretch-bend overtone.

Hydrogen bonding in the first solvation shell The O—H bond networks in the first coordination shell explain the spectral shifts. It is a plausible simplification to describe neat water spectra as an inhomogeneous superposition of local O—H modes, with different frequencies due to their different hydrogen bonding, and there is a stronger argument for so treating solvation spectra, which are inherently inhomogeneous and experience the above-mentioned suppression of resonance. A stronger H-bond gives a lower, redder frequency. We interpret our spectra from that viewpoint, incorporating the ideas of Sharp, Madan et al. 28 They computed the distribution of H-bond angles, β , defined as as the smallest of the four possible O · · · O—H angles (Figure. Figure 6), for neat water and for the solvation shell, and found it to be bimodal, with distinct peaks for straight, strong (≈ 10◦ , more red) and bent, weak (≈ 55◦ , more blue) bonds. The neat water IR was fit to two Gaussians corresponding to the straight and bent H-bonds. Using the same Gaussians with variable amplitudes, frequency shifts caused by several solutes were interpreted in terms of changes in the straight vs. bent populations. Previously we applied the approach to more solutes. 18 The distributions of first-shell waterwater β angles are well represented by varying the amplitudes of the neat water peaks. The spectral shifts follow the amplitudes: more bent is bluer, more straight, redder. However, the most strongly interacting Mg2+ and Cu2+ are quite different. Now most of the angles are around 85◦ , unlike anything in pure water and perhaps too bent to really be H-bonds at all, and the spectrum has a large red shift. These ions do not act like their more weakly interacting brethren. It is as if there is a transition in the solvation shell above a critical interaction strength. Unlike those solutes, halides H-bond to a water H in the solvation shell, replacing a waterwater H-bond. Blue shifts are usually explained by a water-halide H-bond being weaker than a water-water H-bond. As F− is smallest with the strongest interaction it is certainly a candidate for 16 ACS Paragon Plus Environment

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anomalous behavior. Here we propose an extended picture with four kinds of H-bond for waters in the solvation shell, straight and bent versions of ion-water and water-water bonds, suggesting a four-Gaussian fit. However, the resulting large number of parameters is undesirable. We proceed with two Gaussians, arguing as follows: The red sides of the Cl− , Br− and I− spectra are undistinguishable, Figure Figure 4. We concluded that the red-side vibrations are identical to those of the straight water-water H-bonds. Our fit to neat POLIR water gives peak positions and widths in cm−1 of (3310, 114) and (3408, 109) in reasonable agreement with Sharp et. al. Thus we fixed the low-frequency Gaussian as (3310, 114) for the indicated ions, and fit the “blue” Gaussian and the intensities of each. Figure Figure 5 clearly shows the unique behavior of fluoride: it alone has a red-side tail. Thus we originally considered fixing the high-frequency Gaussian as that of neat water, saying that the blue side for F− was the bent water-water H-bonds, and fitting the low-frequency peak. However, surprisingly, the resulting peak frequency was 3310, i.e., the fit is telling us to use the straight water-water H-bonds at low frequency for all four ions, regardless of the red tail on F− , and that is our procedure. In agreement with experiment, Cl− , Br− and I− give a blue shift that increases with ion size. The blue Gaussians are shifted by 71, 77 and 86 cm−1 with respect to neat water. Taking the fixed red Gaussian into account, average shifts would be smaller. Widths also increase with ion size, 118, 124 and 135, vs 114 for the bent H-bonds in neat water. The blue Gaussian is forced to represent the bent water-water H-bonds and all the ion-water Hbonds. We have calculated the β angle distributions. Figure Figure 6 shows that for Cl− , Br− and I− , the first-shell water-water H-bonds are primarily straight and the ion-water bonds primarily bent, so, roughly, the blue side of these spectra arises from bent ion-water H-bonds and the red side, as already described, from straight water-water H-bonds. Fluoride is quite different. Most strikingly, the fluoride-water H-bonds are almost entirely straight. This is consistent with the findings of Xantheas and Dang, 33 who studied F− (H2 O)n 17 ACS Paragon Plus Environment

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Normalized Distribution (x10 )


-

(A)

4

FCl (P) Cl (M) Br I

2 0

(B)

4 2 0 0

30

60

90

120

150

180

Angle Figure 6: The distribution of β -angles for first-shell water - ion hydrogen bonds and first-shell water-water hydrogen bonds in top (A) and bottom (B) panels, respectively. P and M indicate POLIR and Masia damping. Definition of α and β , two possible hydrogen bond angles, between two water molecules is illustrated in the inset.


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clusters and found that the angle approached zero for the shortest F− -O distances. The waterwater bonds are primarily bent reversing the trend of the other ions. Thus the second Gaussian represents both straight ion-water bonds and bent water-water bonds, explaining its large width, 154 cm−1 , and relative intensity, 5 vs ≈1 for the other ions. The peak frequency of 3402 cm−1 is slightly, and uniquely, red shifted, by 6 cm−1 , with respect to neat water. The 2-Gaussian picture does not describe the red tail on F− , which we suggest comes from the strongest straight water-F− bonds. Solvation spectra are often described in terms of the relative strength of ion-water and waterwater H-bonds. We hope this discussion makes it clear that invoking a single type of bond is inadequate. The distinction between straight and bent is important, corresponding to 100 cm−1 in neat water. Bent ion-water bonds are weaker than bent (and straight) water-water bonds for Cl− , Br− and I− , while straight water-F− bonds are stronger than bent water-water bonds and weaker than straight water-water bonds. The β angle distributions are extremely helpful in this analysis, in particular in uncovering the anomalous behavior of fluoride. In sum, Cl− , Br− and I− cause a blue shift with respect to neat water due to the presence of weak bent ion-water H-bonds on the blue side, while F− causes a slight red shift because straight ion-water H-bonds on the blue side are stronger than bent water-water bonds in neat water. A remarkable description of the solvation spectra is obtained from the classical dipole correlation, which may be understood in terms of the strengths of the four types of H-bonds and the bond angle distributions.

Summary The large-scale goal of this research is to demonstrate that a careful treatment of polarization at short range, including intramolecular effects, can enable a classical theory of nominally quantal phenomena. Polarization is a many-body interaction that promotes “transferability”, allowing the effective pair interaction to depend upon the environment. Here we specifically studied the halide



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solvation shell. Our methods give a remarkable description of the its structure, the ion dipole, and the vibrational spectra of the solvating waters. The central result of this paper is that the vibrational shifts from bulk caused by halides are captured by our methods, via the classical dipole correlation of (ion + first shell waters). To explain our findings an extension of the usual inhomogeneous broadening picture was presented, with the spectra arising from O—H vibrations perturbed by straight and bent ion-water and first-shell waterwater hydrogen bonds. Correspondingly, the distributions of H-bond angles, β , were calculated. The unique character of strongly-interacting F− was crystal clear from the distributions. As we previously found with divalent small cations, the solvation shell appears to undergo a transition at a critical interaction strength.

Acknowledgement Acknowledgment is made to the National Science Foundation (grant CHE 0848427) for support of this research. The computing resources necessary for this research were provided in part by the National Science Foundation through XSEDE resources provided by the NICS (National Institute for Computational Infrastructure) XT5 Cray Linux Cluster (Kraken) at the University of Tennessee under grant number TG-CHE120001. The authors thank Prof. Revati Kumar for discussions.

References [1] Ladanyi, B. M.; Keyes, T. The role of local fields and interparticle pair correlations in light scattering by dense fluids. Mol. Phys. 1977, 33, 1063–1097. [2] Keyes, T.; Ladanyi, B. M. The role of local fields and interparticle pair correlations in light scattering by dense fluids. Mol. Phys. 1977, 33, 1099–1107. [3] Ladanyi, B. M.; Keyes, T. The role of local fields and interparticle pair correlations in light scattering by dense fluids. Mol. Phys. 1977, 33, 1247–1269.


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[4] Keyes, T.; Ladanyi, B. M. The role of local fields and interparticle pair correlations in light scattering by dense fluids. Mol. Phys. 1977, 33, 1271–1285. [5] Ladanyi, B. M.; Keyes, T. Effect of internal fields on depolarized light scattering from nalkane gases. Mol. Phys. 1979, 37, 1809–1821. ˘ ˇ [6] Ladanyi, B. M.; Keyes, T. Effective polarizabilities of nâAŽÃ DÃłalkanes: Intramolecular interactions in solution and in the gas phase. J. Chem. Phys. 1982, 76, 2047–2055. [7] Ladanyi, B. M.; Keyes, T. Theory of the static Kerr effect in dense fluids. Mol. Phys. 1977, 34, 1643–1659. [8] Keyes, T.; Ladanyi, B. M. The relation of the Kerr effect to depolarized Rayleigh scattering. Mol. Phys. 1979, 37, 1643–1647. [9] Ladanyi, B. M.; Keyes, T. The influence of intermolecular interactions on the Kerr constant of simple liquids. Can. J. Phys. 1981, 59, 1421–1429. [10] Keyes, T.; Napoleon, R. L. Extending Classical Molecular Theory with Polarization. The Journal of Physical Chemistry B 2011, 115, 522–531. [11] Shultz, M. J.; Vu, T. H.; Meyer, B.; Bisson, P. Water: A Responsive Small Molecule. Acc. Chem. Res. 2012, 45, 15–22. [12] Ahlborn, H.; Ji, X.; Space, B.; Moore, P. B. A combined instantaneous normal mode and time correlation function description of the infrared vibrational spectrum of ambient water. J. Chem. Phys. 1999, 111, 10622–10632. [13] Ahlborn, H.; Space, B.; Moore, P. B. The effect of isotopic substitution and detailed balance on the infrared spectroscopy of water: A combined time correlation function and instantaneous normal mode analysis. J. Chem. Phys. 2000, 112, 8083–8088.



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[14] Li, S.; Schmidt, J. R.; Corcelli, S. A.; Lawrence, C. P.; Skinner, J. L. Approaches for the calculation of vibrational frequencies in liquids: Comparison to benchmarks for azide/water clusters. J. Chem. Phys. 2006, 124, –. [15] Thole, B. Molecular polarizabilities calculated with a modified dipole interaction. Chem. Phys. 1981, 59, 341–350. [16] Mankoo, P. K.; Keyes, T. POLIR: Polarizable, flexible, transferable water potential optimized for IR spectroscopy. J. Chem. Phys. 2008, 129, –. [17] Berens, P. H.; Wilson, K. R. Molecular dynamics and spectra. I. Diatomic rotation and vibration. J. Chem. Phys. 1981, 74, 4872–4882. [18] Kumar, R.; Keyes, T. Classical Simulations with the POLIR Potential Describe the Vibrational Spectroscopy and Energetics of Hydration: Divalent Cations, from Solvation to Coordination Complex. J. Am. Chem. Soc. 2011, 133, 9441–9450. [19] Kumar, R.; Keyes, T. The polarizing forces of water. Theo. Chem. Accts. 2012, 131. [20] Kumar, R.; Keyes, T. The relation between the structure of the first solvation shell and the IR spectra of aqueous solutions. J. Biol. Phys. 2012, 38, 75–83. [21] Coker, H. Empirical free-ion polarizabilities of the alkali metal, alkaline earth metal, and halide ions. J. Phys. Chem. 1976, 80, 2078–2084. [22] Hâ´LŽÂ˘gttig, C.; Heâ´LŽÃij, B. A. TDMP2 calculation of dynamic multipole polarizabilities ˘ ˘ ˘ and dispersion coefficients for the halogen anions FâAŽÃ˘ aÃ ,ClâAŽÃ˘ aÃ ,BrâAŽÃ˘ aÃ and ˘ IâAŽÃ˘ aÃ . J. Chem. Phys. 1998, 108, 3863–3870. [23] Burnham, C. J.; Anick, D. J.; Mankoo, P. K.; Reiter, G. F. The vibrational proton potential in bulk liquid water and ice. J. Chem. Phys. 2008, 128, –. ˘ ardia, E.; Masia, M. The polarizable point dipoles method with electro[24] Sala, J.; Guâ´LŽâA˘ static damping: Implementation on a model system. J. Chem. Phys. 2010, 133, –. 22 ACS Paragon Plus Environment

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[25] Partridge, H.; Schwenke, D. W. The determination of an accurate isotope dependent potential energy surface for water from extensive ab initio calculations and experimental data. J. Chem. Phys. 1997, 106, 4618–4639. [26] Frisch, M. J. et al. Gaussian 03, Revision C.02. Gaussian, Inc., Wallingford, CT, 2004. [27] Smith, W. Point Multipoles in the Ewald Summation (Revisited). CCP5 Newsletter 1998, 46, 18–30. [28] Sharp, K. A.; Madan, B.; Manas, E.; Vanderkooi, J. M. Water structure changes induced by hydrophobic and polar solutes revealed by simulations and infrared spectroscopy. J. Chem. Phys. 2001, 114, 1791–1796. [29] Leberman, R.; Soper, A. Effect of high salt concentrations on water structure. Nature 1995, 378, 364–366. [30] Dillon, S. R.; Dougherty, R. C. Raman Studies of the Solution Structure of Univalent Electrolytes in Water. The Journal of Physical Chemistry A 2002, 106, 7647–7650. [31] Omta, A. W.; Kropman, M. F.; Woutersen, S.; Bakker, H. J. Negligible Effect of Ions on the Hydrogen-Bond Structure in Liquid Water. Science 2003, 301, 347–349. [32] Perera, P. N.; Browder, B.; Ben-Amotz, D. Perturbations of Water by Alkali Halide Ions Measured using Multivariate Raman Curve Resolution. J. Phys. Chem. B 2009, 113, 1805– 1809. [33] Xantheas, S. S.; Dang, L. X. Critical Study of Fluoride-Water Interactions. J. Phys. Chem. 1996, 100, 3989–3995.

Supporting Information Available POLIR fit parameters and ion—O radial distribution functions are shown in the Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org/. 23 ACS Paragon Plus Environment


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Graphical TOC Entry

Simulation snapshot illustrating the hydrogen bond network formed by water molecules around a Cl− ion.


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Classical Description of the Vibrational Spectroscopy, Structure, and

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