Effect of Ionic Strength on Solvation Geometries in Aqueous Nitrate Ion

Mar 9, 2017 - Temperature-dependent infrared spectra of aqueous nitrate solutions with a range of concentrations and ionic strengths are used to deter...
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Effect of Ionic Strength on Solvation Geometries in Aqueous Nitrate Ion Solutions Konnor K. Jones, Logan H. Eckler, and Matthew J. Nee* Department of Chemistry, Western Kentucky University, 1906 College Heights Boulevard, Bowling Green, Kentucky 42101, United States S Supporting Information *

ABSTRACT: Temperature-dependent infrared spectra of aqueous nitrate solutions with a range of concentrations and ionic strengths are used to determine the effect of ionic strength on the relative stabilities of different solvation geometries in aqueous nitrate ion. The asymmetric stretching absorption band from 1250 to 1450 cm−1 changes line shape with temperature, allowing two distinct peaks to be fit for each spectrum. Because each peak is assigned based on electronic structure calculations as a proxy to a different solvation motif, van’t Hoff plots provide insight into the thermodynamics of exchange between different solvation geometries. A strong linear trend is seen between increased ionic strength and the magnitude of both the enthalpic and entropic contributions to the solvation geometry stabilities. Electronic structure computations of previously proposed structures in different ionic strengths are performed in the presence of external fields, roughly simulating the impact of ions in solution.

I. INTRODUCTION Solvation of polyatomic ions in water has been an area of intense study for decades, since the discovery that spectra of the solid, solution, and gas phase ions indicated differences not just in vibrational frequency but also in molecular symmetry. The advent of mass-selected ionic-cluster experiments allowed measurements of the spectra of progressively solvated ions, with the hope of bridging the gap between molecular-level and bulk structural depictions.1,2 These experiments provided substantial insight into possible solvation arrangements in solutions, but comprehensive searches for all possible arrangements, and the relative energetics of different solvation structures, have proven challenging in the gas phase. One of the most interesting features of aqueous solvation is the well-known symmetry breaking that occurs, a phenomenon which is documented thoroughly for nitrate ion (NO3−).1 The nitrate ion is ubiquitous in the natural environment, and has been shown to play vital roles environmentally, biologically, and in organic synthesis. It is a major component of sea-spray aerosols,3−5 which go on to form the highly concentrated, aqueous cores of secondary organic aerosols (SOA).6 At any wet surface, photolysis of nitrate ion is well-established to contribute to tropospheric levels of NO2 and NO, collectively known as NOx, and ozone (O3).7−9 Field observations have confirmed that an increase in NOx and O3 is correlated to nitrate content in snowpack in locations around the world.8−15 Laboratory experiments have shown that nitrate photolysis produces these same toxic gases.16−20 Numerous experiments in both snow and ice have demonstrated the importance of the © XXXX American Chemical Society

high concentration of electrolytes in the quasi-liquid layer as a facilitator of the kinetics,21−24 which is further complicated by nitrate’s increased concentration near, and different behavior at, surfaces.25−30 Kinetic models for the complex reaction networks which follow photocleavage of the N−O bond have been proposed;31−35 all rely to a certain extent on fitting a large number of variables to relatively small data sets. The reaction network is complicated immediately in part because photolysis under broadband ultraviolet (UV) radiation results in two product channels, one in which the additional electron associates with the NO2 moiety and the other in which it retains on the oxygen atom.36 Different solvation geometries could thus experience different kinetics, thereby producing different product ratios. Understanding the role of solvation on nitrate ion geometry (and, specifically, ionic strength effects, as in the work by Grassian37,38) will thus provide fundamental insight into the initial photochemical step in the process. The atmospheric and human-health hazards associated with these compounds make understanding the complete mechanism for photolysis a crucial problem. While several models have been proposed and incorporated into larger kinetic modeling packages, the impacts of ionic strength on the relative quantum yields of the photoproducts has drawn significant attention: studies by Grassian have recently shown the powerful role that ionic strength can play in reaction kinetics involving Received: December 1, 2016 Revised: March 8, 2017 Published: March 9, 2017 A

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The Journal of Physical Chemistry A nitrate ion.37,38 While this work has been critical in understanding the end products, a more complete understanding of the molecular reasons for the effect of ions lies, at least in part, in their influence on the solvation geometries of reactants in aqueous solution. The delocalized π-orbital extending over the entire nitrate ion results in a trigonal-planar molecular structure which is nominally D3h symmetry, and contributes significantly to the large Raman cross-section of nitrate ion by providing a highly polarizable electronic distribution. This same polarizability makes nitrate ion particularly sensitive to effects of electrostatic fields, including those generated by the presence of polar solvents and ions in solution. Although the gas-phase molecular structure of nitrate ion has been observed experimentally and calculated to be D3h (trigonal planar), interactions with solvent molecules break this symmetry.39,40 This symmetry breaking manifests as a split peak in the asymmetric-stretching region (1340−1390 cm−1) observed in the infrared (IR) spectrum, but has also been reported based on resonance-Raman studies by Kelley41,42 and Asher.25,26 In bulk solutions, the effect of anions on hydrogen-bonding and water structure remains an active discussion,43−49 with recent multidimensional spectra indicating that nitrate ion is actively engaged with no more than one water at a time.36 Allen and co-workers have also shown the effect of divalent cations on the generation of ion-contact pairs50 at high concentrations, which arise because of thermodynamic stability of the ion pairs in high electrolyte concentration solutions. The distortion of nitrate ion upon interaction with a water molecular results in the degenerate asymmetric stretch vibration splitting into two discernible peaks in bulk aqueous solutions. Because the splitting appears immediately upon the addition of a single water molecule in mass-selected multiphoton dissociation spectra, it has been suggested that the presence of a single water molecule may be a valid descriptor of the solvation geometry.39 This is consistent with several calculations performed over the past few decades, which suggest that a Cs-symmetry arrangement, where one water molecule is effectively hydrogen bonded to the water molecule serving as a single donor, beginning with Schaefer and coworkers, who added water molecules explicitly to confirm the symmetry breaking, finding two stable structures with a single water (singly- and doubly-bound).51,52 More exhaustive searches for minimum energy structures and other calculations in small aqueous clusters revealed that splitting is largely recovered by the addition of the first water molecule.53,54 More recently, simulations attempting to reproduce the infrared vibrational spectrum have focused on mixed quantum/classical calculations. Such molecular dynamics (MD) simulations study bulk behavior in nitrate ion solutions more fully.55−61 MD simulations of ions became possible only following the pioneering work of Jungwirth and Tobias62−67 cleared the path for studies of polarizable ions in solution.68−70 These calculations suggest that, in the bulk, more than one bonding motif may be responsible for the IR spectrum. For a given bonding motif, different oscillator strengths could be associated with each of the two asymmetric stretching motions, making spectral analysis somewhat complicated. Several questions remain unanswered. First, while UV absorption studies have suggested that there are two distinct nitrate solvation geometries present in aqueous solution,71 UV spectra offer little information about molecular structural differences between the two arrangements proposed. Fourier-

transform infrared (FTIR) studies will help resolve these matters because of the clearer structure-spectrum correlation. Second, the use of an isosbestic point (as in the UV spectra) has been shown insufficient in unequivocally identifying two chemically distinct species, particularly for aqueous solutions.72 More complete modeling could provide a more rigorous explanation of any temperature dependence to the equilibrium spectra of nitrate ion. Understanding the direct effects of ionic strength on the molecular structure of nitrate ion is crucial to understanding the high-osmolality environments in which so many environmentally relevant reactions occur. Here, we report temperature-dependent infrared spectra of the asymmetricstretching region of aqueous nitrate that are consistent with the presence of two solvation geometries. We comment on their relative thermodynamic stabilities, and identify a pronounced effect of ionic strength on those relative energies.

II. EXPERIMENTAL METHODS II.A. Temperature-Dependent Infrared Spectrometry Cell. Solutions were prepared in deionized water (18 MΩ) from KNO3 (Aldrich). The ionic strength of solutions was adjusted by the addition of NaCl (Aldrich). All spectra were collected using a PerkinElmer Spectrum One Fourier-transform infrared (FTIR) spectrometer. Samples were prepared in a custom-designed sample-cell holder. To generate a thin layer of sample for IR analysis, a few drops of aqueous solution were placed onto a CaF2 window, which has a 50-μm Teflon spacer ring on top. A second window is placed over the sample, sealing it between the two windows. The sample cell is warmed and cooled by a commercial temperature-controlled IR-sample-cell holder (Pike Technologies) with a range of 5 to 130 °C, but because of thermal expansion concerns, the cell was maintained between 10 and 50 °C for these experiments. For each solution, the infrared spectrum was collected at 5 °C intervals. The sample cell was exposed to a constant flow of N2 gas for temperatures below 30 °C to prevent condensation from forming on the windows. To ensure reproducibility, spectra were collected multiple times at each temperature. When sample evaporation did not occur and adequate time was allowed for thermalization, there was no significant difference observed between series of spectra collected from cold to hot compared to collecting from hot to cold. All data shown were collected beginning at 10 °C. For a given solution composition, two experimental campaigns are averaged in the final results. For each campaign, a fresh sample solution was prepared, and FTIR spectra were measured at each temperature three times; the final results presented are thus six averaged values for each composition. The variability between campaigns is typically slightly larger than the variability between individual measurements, but they are of similar magnitudes. II.B. Computational Methods. All calculations were performed on the WKU High-Performance Computing Center (HPCC) using the Gaussian 09 electronic structure package.73 Isolated nitrate ion was geometry-optimized with the B3LYP functional74 using Dunning’s augmented, correlation-consistent, double-ζ basis (aug-cc-PVDZ).75 Nitrate-water clusters were optimized similarly. The geometries suggested as lowest energy by previous calculations51,52 (one bidentate, C2v structure, and a monodentate Cs structure, shown in the Supporting Information, Figure S1) were then geometry optimized with the same functional at the same basis, and vibrational mode and frequency analysis was performed, including the calculation of infrared absorption intensities. To B

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but not constant, background arises from the tail end of the water bending feature near 1635 cm−1. As has been well documented,76,77 this feature of water is dependent on both the temperature and the ionic strength of the solution. Fortunately, the region of the spectrum of the nitrate asymmetric stretch absorption (1200−1500 cm−1) is far enough removed from the water feature that both of those effects amount to the addition of a linear offset to the spectrum. As shown in Figure S3, points at each end of the range are selected as the zero absorbance values, and a line connecting them is subtracted from the entire spectrum, resulting in consistent features that are easier to compare as a function of temperature. From Figure 1a, it is clear that as the temperature increases, the higher frequency peak grows in area relative to the lower frequency peak. This could suggest that some sort of energetic barrier is increasingly surmounted in solvated nitrate ion over this temperature range. To interpret this result, Figure 1b shows the B3LYP-calculated IR absorption spectrum (intensities and frequencies convolved with 30 cm−1-wide Gaussian peaks) for two different possible solvation geometries (with no added external electric field). Intensities are based on those calculated directly by the computational package. In the double-bound (C2v) geometry shown in the black line, the higher frequency peak has a much greater intensity relative to the lower-frequency peak. In a striking contrast, the Cs geometry shows the opposite trend. Thus, one possible explanation for the temperature-dependent spectrum in the asymmetric stretch in aqueous nitrate becomes clear: the peaks, despite arising from two different modes, report by proxy on the relative intensities of the two dominant solvation geometries. Such changes are consistent with earlier reports on the UV spectra of nitrate ion solutions, which showed an isosbestic point indicating a change from one solvation geometry to another.71 This surprising result would appear to imply that our experimental data, which shows a decrease in the high-frequency end of the spectrum with an increase in the temperature, are consistent with a C2v structure which is lower in energy than the Cs structure. We openly acknowledge that the assumption that nitrate ions in solution are in one of these two minima may not be fully representative of the chemical reality. Instead, we divide the solvation geometries broadly into symmetric and asymmetric motifs. Regardless, this analysis is useful to provide insight into the extent to which local electric fields influence vibrational spectra of ions subject to symmetry breaking. To explore the temperature-dependence of the FTIR spectra further, Figure 2 shows a van’t Hoff plot of the same data from Figure 1a. Error bars shown in the data are standard deviations of discrepancy from the linear fits. In this case, each asymmetric stretching feature is fit to two Gaussian peaks. Because the relative areas of each peak are assumed to be indicative of the abundance of a corresponding solvation geometry, we can use the ratio of the areas of the high-frequency and low-frequency peaks as indicative of the equilibrium constant, Keq (methods described in detail in the Supporting Information, Figure S3). Then, using the familiar van’t Hoff rearrangement of the relationship between Gibbs energy and equilibrium,

simulate the effect of increasing the ionic strength of the solution on the optimized geometry, total energy, and calculated vibrational spectrum, the calculations on both the bare nitrate and the water−nitrate clusters were then repeated in the presence of a range of external electric fields. In an attempt to keep our computational results as simple as possible, we limited our calculations to only linear field contributions, neglecting higher moments in the dipole expansion. On the basis of purely classical molecular dynamics simulations, we estimate a reasonable range of electric fields for 0.1−1.2 M solutions (the range of the experiments here) to be ±7.0 × 10−3 atomic units, where 1 atomic unit = 5.142206 × 1011 V m−1; the electric fields used in these calculations cover that range. Further details are included in the Supporting Information, including a histogram of field occurrence frequency (Figure S2).

III. RESULTS AND DISCUSSION III.A. Pure KNO3 Solutions. A set of spectra of 0.1 M KNO3 solutions collected in the N−O asymmetric-stretching range are shown in Figure 1a, displaying the well-known double

Figure 1. FTIR spectra (a) of the asymmetric-stretching region of 0.1 M aqueous nitrate solution at different temperatures. Arrows indicate relative changes in the two peaks in the spectrum with increasing temperature. Electronic structure calculations (b) show that proposed solvation geometries have different intensities for the two formally degenerate modes active in this region of the spectrum. The relative intensities of the two asymmetric stretching modes are different for the symmetric (black) and asymmetric (red) geometries.

peak owing to the breaking of symmetry in aqueous solution. The nominally-D3h nitrate ion has a degenerate asymmetric stretch which, in the presence of solvents, can become nondegenerate depending on the arrangement of the water molecules around the ion.39,40 As explained in the Supporting Information (Figure S3), each spectrum has a temperaturedependent, linear background subtracted from it. This linear,

ln Keq =

Δr H ° Δ S° + r RT R

(1)

the relative size of thermodynamic parameters associated with solvation for different samples can be estimated. It is important to note here that each value (e.g., ΔrHo) can be assumed to be C

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Figure 2. Van’t Hoff plot for pure KNO3 solutions, with Keq defined as the ratio of the low frequency to peak to the high frequency peak in Figure 1. The fitted line has a slope which is indicative of ΔH°/R, with an intercept related to ΔS°/R. At lower concentration (a), the enthalpic difference between geometries is less than that at higher concentration (b). Error bars are standard deviations of residuals from linear fits.

Figure 3. A comparison of fitted van’t Hoff parameters at different apparent ionic strengths. As the ionic strength increases, a linear increase in (a) the slope of the van’t Hoff plot emerges; a similar trend is observed in (b) the offset. Error bars are standard deviations of six independent measurements.

approximations only, because each peak naturally contains some contributions from both solvation geometries. Regardless, for the purposes of estimating the temperature dependence of solvation geometries and, in particular, for comparing the effect of ionic strength, the estimate should be sufficient. For 0.1 M KNO3 solutions, the slope of the van’t Hoff plot is quite different from those in 0.2 M KNO3 solutions, shown in Figure 2b. This could arise simply from a change in the electrostatics of the solutions themselves, or it could be due to some increasing competitive effect of nitrate ions for solvent molecules as the solute concentration increases. We consider the first possibility to be more likely based on the evidence provided by the addition of sodium chloride to the solutions, as described in the next section. III.B. Effect of Ionic Strength. Although the ratio of the dominant peaks in Figure 1 always shifts as a function of the temperature, the shift is more pronounced at higher electrolyte concentrations, resulting in a value for the effective enthalpy of conversion that is significantly higher in 0.2 M KNO3 solutions than for 0.1 M solutions. A series of experiments were performed in which the spectra were collected for a solution which contained both KNO3 and NaCl. This allows us to assess the effect of apparent ionic strength (that is, the ionic strength based on the amount of electrolyte added, rather than based on some phenomenological analysis of ionic strength) on the changes to the van’t Hoff parameters for nitrate ion solutions at different temperatures. The slopes and offsets of the van’t Hoff plots for these experiments as a function of ionic strength are shown in Figure 3. Here, error bars represent the standard deviation of six measurements collected over two different campaigns. The nitrate ion concentration was 0.1 M, as in

Figure 2a, but the total ionic strength (including concentrations from both KNO3 and NaCl) ranged from 0.1 to 1.2 M. It is clear from Figure 3 that apparent ionic strength, not concentration, is the major factor in the change of temperature dependence of nitrate ion infrared spectra. We interpret this change to result from an effect of average local electric fields in solution. As the ionic strength increases, the local electric fields at each nitrate ion become stronger. This manifests as a change in the nitrate geometry, and, thus, a change in the relative stabilities of nitrate ion solvation geometries. Given that the symmetry breaking which leads to the splitting of the asymmetric stretching peaks arises due to variations in local electric field, it is natural to expect that increasing that field by the addition of ions in solution will make it even more pronounced. However, it is less obvious that a change in ionic strength should result in favoring of one particular solvation geometry, as suggested by the temperature dependence here. Our interpretation is that this occurs because the different solvation geometries are affected differently by the changes to local electric field induced by the introduction of additional electrolytes in solution. The trend in energetic difference between the two peaks is well fit by a linear relationship, implying that increasing electric field further stabilizes the already lower-energy (symmetrical) structure. This preference could provide some support for the ionic-strength dependence of the quantum yields of photoproducts from nitrate ion: the less-symmetrical solvation arrangement predisposes the production of NO2 and OH D

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Figure 4. Effect of external electric field in the nitrate plane on the calculated vibrational frequencies of the asymmetric-stretching modes of nitrate ion. At zero field, the two modes are degenerate. As electric field increases, the expected frequency separation is recovered. Experimental splitting is accomplished within the field range expected for 1 M solutions.

Figure 5. Calculated (B3LYP) total energies of two nitrate-water structures, (a) C2v and (b) Cs, in linear fields within in the X−Y plane. All energies are in hartrees; each image is referenced to the energy of that cluster calculated at zero field. Although the trend as a function of electric field is less clear here than for the bare nitrate ion, the overall pattern suggests that, on average, the C2v structure should be more favored at higher electric fields.

ion. At a field of roughly 4 × 10−3 au magnitude (a value consistent with the maxima seen in the distributions of fields from MD simulations shown in Figure S2), the splitting between them is approximately 50 cm−1. Thus, the vibrational frequencies calculated are consistent with the experiments presented in Figure 1 and analyzed above, validating our computational approach. A broader series of calculations on pure nitrate ion indicates that, while the vibrational frequency changed drastically as the x- and y-components of the electric field ranged from 0 to 7.0 × 10−3 au, the change in asymmetricstretching frequency as a result of out-of-plane electric fields (shown in the Supporting Information Figure S4) was negligible, changing the frequency by approximately 3 cm−1 over that full range. Similarly, the nondegenerate symmetric stretch shifts by only approximately 8 cm−1 over this range. These results are also in good agreement with previous experimental data,50 and suggest that modeling solvated nitrate as an effect of electric fields reproduces the observed effects of solvation and the presence of electrolytes. Next, we can model the effect of local electric field on the relative energetics of two fundamental water-nitrate arrangements (the Cs and C2v geometry minima identified by Schaefer51,52) with similar calculations on nitrate-water clusters.

radical as long-term products.38 While full confirmation of this would require a more sophisticated modeling of the excited electronic states as a function of solvation geometry, the data reported here offer strong evidence that solvation geometry changes that are due to the presence of electrolytes in solution can have a nontrivial impact on chemical reactivity in aqueous polyatomic ions. C. Computational Modeling. To shed molecular insight on these somewhat surprising experimental results, we present some preliminary calculations that begin to model the effect of ionic strength on the vibrational structure of nitrate ion in aqueous solution. First, we show that calculations performed in external electric fields replicate the vibrational frequency splitting of aqueous nitrate ion. Taking the D3h-nitrate plane as the x−y plane, the effect of fields in the nitrate plane on vibrational frequency shows excellent agreement with the extent of symmetry breaking observed in solution (Figure 4). At zero field, the two asymmetric-stretching frequencies are degenerate at a value of 1390 cm−1, in good agreement with experimental data. Figure 4 shows that as the field magnitude increases, the frequency difference between the two asymmetric stretching modes increases. This is independent of the orientation of the field in the x−y plane relative to the nitrate E

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to favor a smaller set of solvation structures as electrolyte concentrations increase. This seemingly trivial effect could be critically important in many systems: small changes to molecular geometry and vibrational structure can have significant effects on the kinetics and dynamics of such ions, particularly their photolysis in the natural environment. All of these interpretations rely on the assumption that the changes in line shape analyzed here are due to equilibrium chemical exchange. Our experiments are not able to definitively prove the existence of multiple solvation geometries, as changes to line shape, even the creation of isosbestic points, can arise as a function of temperature. This is attributed largely to thermal access of higher rotational states, broadening and shifting the features slightly.72 However, in the case where two formally degenerate vibrational modes are analyzed, and the relative areas of their two peaks are considered, this effect should be minimized. First, both peaks should experience similar line shape changes as a function of temperature, whether they are intensity changes or red- or blue-shifting. Second, shifts should not be significant in our work: the total area of each peak is calculated for each temperature. Thus, even if there is some temperature dependence to the peaks in the absence of chemical exchange, we would expect that our analyses would not be significantly impacted by it. Similar arguments apply to motional narrowing, which can also change spectral lineshapes. Because of the structural similarities of the chromophore in the two solvation geometries, we would not expect a substantial enough disparity in their respective lineshapes to alter our analysis of the relative peak areas as a proxy for the relative concentrations of the two motifs used here. More sophisticated experimental approaches (such as multidimensional infrared methods)78 could confirm the importance of chemical exchange in this system, as well as the impact of ionic strength. More interestingly, they could provide the rates (forward and reverse) of that exchange and their ionic strength dependence, which would get more deeply at the fundamental dynamics of this system. Indeed, even if the temperature dependence of the nitrate ion peaks were determined by other experiments not to arise primarily from chemical exchange between solvation geometries, the ionic-strength dependence remains a feature of interest. Any alternative explanation would need to account for the linear increase in apparent enthalpic difference seen here.

The experimental data suggest a difference in energy between the symmetric and asymmetric bonding motifs that increases with increasing ionic strength. Thus, calculations on nitratewater clusters should show energetic differences between the Cs and C2v geometries which increase as electric field increases. Figure 5 shows the total energy of each complex as a function of external electric field for the two proposed solvation geometries. The energy scale shown is relative to the energy of that cluster at zero field. The energy of the C2v cluster at zero field is 0.0034 hartree (8.9 kJ/mol) lower than that of the Cs cluster. To determine the energy difference between the two geometries, it is tempting to calculate the difference between the values from the two images directly at each field, but this is inappropriate for two reasons. First, the energy does not fully represent the solvation stability, because that necessarily requires the inclusion of the additional solvent molecules. Second, it is not possible to align the fields to a consistent bond axis to make direct subtraction meaningful. However, by assessing the relative energies from the electronic structure calculations as a function of external electric field, we can gain some broad insight into the origin of the relative stabilization of the more-symmetric geometry by other electrolytes in solution. The ionic-strength dependence shown in Figure 5 implies that symmetric geometries are energetically altered as a function of field in ways that are different from the asymmetric geometries. Both structures are destabilized by positive fields oriented with components along the axis of the water location, and stabilized by corresponding negative fields. While the change (relative to zero field) is similar in magnitude for the stabilization region, as the electric fields increase (toward the positive edges of the plot), the values of the more symmetric (C2v) structure are changed much less severely than are those of the less symmetric (Cs) structure. This is consistent with our experimental results, particularly those shown in Figure 3: as ionic strength increases, the more symmetric structure becomes even more stable relative to the less symmetric structure than it is at infinite dilution. This manifests as an increasing slope to the van’t Hoff plots for the asymmetric stretching region of the FTIR spectrum. The calculations shown in Figure 5 suggest that this is a result of destabilization of the less stable structures, rather than stabilization of the more symmetric structures. This may be because the effect of the external electric field is a change in the rotation of the water molecule relative to the nitrate ion (compared to those in zero field, shown in Figure S1) in singly bound geometries. This optimized minimum comes at the expense of overall energy, whereas doubly bound geometries are less able to rotate in this way. Because the effect of electric field is so complex, a more complete analysis, which weights the vibrational intensities with the probability of a nitrate ion experiencing a particular electric field in solution, is underway to further investigate the impacts of electrolytes on solvation geometries and vibrational spectra. These results offer support to the existence of different solvent binding situations, each with a different population, dictated by the relative thermodynamic stabilities. However, they are not conclusive evidence that only two solvation geometries dominate in aqueous solutions: more complex simulations will incorporate a more complete solvation. The calculations presented here do, however, suggest that higher symmetry solvation geometries may have inherent thermodynamic advantages in high-osmolality solutions. Further, it raises a more important connection between solvation geometry and ionic strength, specifically, that solvation of small ions appears

IV. CONCLUSIONS We have shown based on temperature-dependent FTIR data that the familiar symmetry-breaking phenomenon of nitrate ion in aqueous solution varies as a function of the ionic strength of the solution. Mapping relative energies of symmetric and nonsymmetric solvation structures as a function of electric field (a method validated based on mapping vibrational frequencies) offers evidence to explain the ionic strength effects. While the simple analyses presented here are not definitive absolute evidence of a binary model for solvation of nitrate by water molecules, they raise some important points about the role played by ionic strength in the vibrational and molecular structures of small ions in solution. If, as our data suggest, ionic strength alters the relative thermodynamic stabilities of solvation geometries, it is natural to expect that it will also impact the branching ratios seen in photolysis experiments. This could happen both by adjusting the population of the different geometries, and by potentially changing the branching ratio of the initial photolysis step as a function of the solvation geometry. This represents a step toward a theoretical F

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Lee, T.; et al. Sea Spray Aerosol as a Unique Source of Ice Nucleating Particles. Proc. Natl. Acad. Sci. U. S. A. 2016, 113, 5797. (6) Ellison, G. B.; Tuck, A. F.; Vaida, V. Atmospheric Processing of Organic Aerosols. J. Geophys. Res.: Atmos. 1999, 104, 11633. (7) Jones, A. E.; Weller, R.; Anderson, P. S.; Jacobi, H. W.; Wolff, E. W.; Schrems, O.; Miller, H. Measurements of NOx Emissions from the Antarctic Snowpack. Geophys. Res. Lett. 2001, 28, 1499. (8) Gao, R. S.; Fahey, D. W.; Del Negro, L. A.; Donnelly, S. G.; Keim, E. R.; Neuman, J. A.; Teverovskaia, E.; Wennberg, P. O.; Hanisco, T. F.; Lanzendorf, E. J.; et al. A Comparison of Observations and Model Simulations of NOx/NOy in the Lower Stratosphere. Geophys. Res. Lett. 1999, 26, 1153. (9) Keim, E. R.; Fahey, D. W.; Del Negro, L. A.; Woodbridge, E. L.; Gao, R. S.; Wennberg, P. O.; Cohen, R. C.; Stimpfle, R. M.; Kelly, K. K.; Hintsa, E. J.; et al. Observations of Large Reductions in the NO/ NOy Ratio Near the Mid-Latitude Tropopause and the Role of Heterogeneous Chemistry. Geophys. Res. Lett. 1996, 23, 3223. (10) Morin, S.; Erbland, J.; Savarino, J.; Domine, F.; Bock, J.; Friess, U.; Jacobi, H. W.; Sihler, H.; Martins, J. M. F. An Isotopic View on the Connection between Photolytic Emissions of NOx from the Arctic Snowpack and its Oxidation by Reactive Halogens. J. Geophys. Res.: Atmos. 2012, 117, D00R08. (11) France, J. L.; Reay, H. J.; King, M. D.; Voisin, D.; Jacobi, H. W.; Domine, F.; Beine, H.; Anastasio, C.; MacArthur, A.; Lee-Taylor, J. Hydroxyl Radical and NOx Production Rates, Back Carbon Concentrations and Light-Absorbing Impurities in Snow from Field Measurements of Light Penetration and Nadir Reflectivity of Onshore and Offshore Coastal Alaskan Snow. J. Geophys. Res.: Atmos. 2012, 117, D00R12. (12) Jarvis, J. C.; Hastings, M. G.; Steig, E. J.; Kunasek, S. A. Isotopic Ratios in Gas-Phase HNO3 and Snow Nitrate at Summit, Greenland. J. Geophys. Res. 2009, 114, D17301. (13) Helmig, D.; Seok, B.; Williams, M. W.; Hueber, J.; Sanford, R., Jr. Fluxes and Chemistry of Nitrogen Oxides in the Niwot Ridge, Colorado, Snowpack. Biogeochemistry 2009, 95, 115. (14) Jarvis, J. C.; Steig, E. J.; Hastings, M. G.; Kunasek, S. A. Influence of Local Photochemistry on Isotopes of Nitrate in Greenland Snow. Geophys. Res. Lett. 2008, 35, L21804. (15) Thornton, J. A.; Wooldridge, P. J.; Cohen, R. C.; Martinez, M.; Harder, H.; Brune, W. H.; Williams, E. J.; Roberts, J. M.; Fehsenfeld, F. C.; Hall, S. R.; et al. Ozone Production Rates as a Function of NOx Abundances and HOx Production Rates in the Nashville Urban Plume. J. Geophys. Res. 2002, 107, ACH7. (16) Anastasio, C.; Chu, L. Photochemistry of Nitrous Acid (HONO) and Nitrous Acidium Ion (H2ONO+) in Aqueous Solution and Ice. Environ. Sci. Technol. 2009, 43, 1108. (17) Klanova, J.; Matykiewiczova, N.; Dolinova, J.; Klan, P. Bimolecular Photochemical Reactions in Ice. Organohalogen Compd. 2006, 68, 364. (18) Boxe, C. S.; Colussi, A. J.; Hoffmann, M. R.; Perez, I. M.; Murphy, J. G.; Cohen, R. C. Kinetics of NO and NO2 Evolution from Illuminated Frozen Nitrate Solutions. J. Phys. Chem. A 2006, 110, 3578. (19) King, M. D.; France, J. L.; Fisher, F. N.; Beine, H. J. Measurement and Modelling of UV Radiation Penetration and Photolysis Rates of Nitrate and Hydrogen Peroxide in Antarctic Sea Ice: An Estimate of the Production Rate of Hydroxyl Radicals in FirstYear Sea Ice. J. Photochem. Photobiol., A 2005, 176, 39. (20) Boxe, C. S.; Colussi, A. J.; Hoffmann, M. R.; Murphy, J. G.; Wooldridge, P. J.; Bertram, T. H.; Cohen, R. C. Photochemical Production and Release of Gaseous NO2 from Nitrate-Doped Water Ice. J. Phys. Chem. A 2005, 109, 8520. (21) Henson, B. F.; Robinson, J. M. Dependence of Quasiliquid Thickness on the Liquid Activity: A Bulk Thermodynamic Theory of the Interface. Phys. Rev. Lett. 2004, 92, 246107. (22) Henson, B. F.; Voss, L. F.; Wilson, K. R.; Robinson, J. M. Thermodynamic Model of Quasiliquid Formation on H2O Ice: Comparison with Experiment. J. Chem. Phys. 2005, 123, 144707.

explanation of the work by Grassian and co-workers, which found changes to the quantum yields of NO and NO2 as a function of ionic strength. More detailed experimental and computational work will be aimed at understanding the importance that changing solvation has on the reactivity of nitrate ion in solution. Specifically, the effect of counterion and investigations of more dilute solutions (using a long-pass cell) and very concentrated solutions (such as found in sea spray aerosols) remain to be studied. Indeed, the kinetic effect of ionic strength on nitrate photolysis is not monotonic outside the ranges studied here,37,38 so we might expect to find deviations from linearity over a wider range of ionic strengths. The computational efforts presented demonstrate the general principle that the presence of additional ions in solution has a measurable impact on the vibrational spectrum of symmetrybroken species. This area is relatively unexplored, but will demand a combination of experiments to evaluate the effect of charge and ion size, and simulations using mixed quantumclassical approaches, both of which are already underway in our laboratory.

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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.jpca.6b12102. Details of the orientations of nitrate and water in cluster calculations and on the molecular dynamics simulations used to estimate electric field magnitudes, further information on data work-up, and vibrational frequencies as a function of out-of-plane electric field (PDF)

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AUTHOR INFORMATION

Corresponding Author

*(M.J.N) E-mail: [email protected]. ORCID

Matthew J. Nee: 0000-0002-1715-3412 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported in part by the NSF through the Upper Green River Watershed REU (NSF 1004655) at WKU, by the Kentucky Space Grant Consortium (KSGC 3048107645-13-146), and by the Western Kentucky University Department of Chemistry and Office of Research. L.H.E. and K.K.J. were each supported separately by WKU FacultyUndergraduate Student Engagement (FUSE) grants.

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REFERENCES

(1) Lee, N.; Keesee, R. G.; Castleman, A. W., Jr. The Properties of Clusters in the Gas Phase IV: Complexes of Water and HNOx Clustering on NOx. J. Chem. Phys. 1980, 72, 1089. (2) Castleman, A. W.; Keesee, R. G. Ionic Clusters. Chem. Rev. 1986, 86, 589. (3) Grythe, H.; Ström, J.; Krejci, R.; Quinn, P.; Stohl, A. A Review of Sea-Spray Aerosol Source Functions Using a Large Global Set of Sea Salt Aerosol Concentration Measurements. Atmos. Chem. Phys. 2014, 14, 1277. (4) Quinn, P. K.; Collins, D. B.; Grassian, V. H.; Prather, K. A.; Bates, T. S. Chemistry and Related Properties of Freshly Emitted Sea Spray Aerosol. Chem. Rev. 2015, 115, 4383. (5) DeMott, P. J.; Hill, T. C.; McCluskey, C. S.; Prather, K. A.; Collins, D. B.; Sullivan, R. C.; Ruppel, M. J.; Mason, R. H.; Irish, V. E.; G

DOI: 10.1021/acs.jpca.6b12102 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A (23) Ryzhkin, I. A.; Petrenko, V. F. Violation of Ice Rules near the Surface: A Theory for the Quasiliquid Layer. Phys. Rev. B: Condens. Matter Mater. Phys. 2002, 65, 012205. (24) Nason, D.; Fletcher, N. H. Photoemission from Ice and Water Surfaces: Quasiliquid Layer Effect. J. Chem. Phys. 1975, 62, 4444. (25) Asher, S. A.; Tuschel, D. D.; Vargson, T. A.; Wang, L.; Geib, S. J. Solid State and Solution Nitrate Photochemistry: Photochemical Evolution of the Solid State Lattice. J. Phys. Chem. A 2011, 115, 4279. (26) Ghosh, M.; Wang, L.; Asher, S. A. Deep-Ultraviolet Resonance Raman Excitation Profiles of NH4NO3, PETN, TNT, HMX, and RDX. Appl. Spectrosc. 2012, 66, 1013. (27) Finlayson-Pitts, B. J.; Hemminger, J. C. Physical Chemistry of Airborne Sea Salt Particles and their Components. J. Phys. Chem. A 2000, 104, 11463. (28) Knipping, E. M.; Lakin, M. J.; Foster, K. L.; Jungwirth, P.; Tobias, D. J.; Gerber, R. B.; Dabdub, D.; Finlayson-Pitts, B. J. Experiments and Simulations of Ion-Enhanced Interfacial Chemistry on Aqueous NaCl Aerosols. Science 2000, 288, 301. (29) Miller, Y.; Thomas, J. L.; Kemp, D. D.; Finlayson-Pitts, B. J.; Gordon, M. S.; Tobias, D. J.; Gerber, R. B. Structure of Large NitrateWater Clusters at Ambient Temperatures: Simulations with Effective Fragment Potentials and Force Fields with Implications for Atmospheric Chemistry. J. Phys. Chem. A 2009, 113, 12805. (30) Xu, M.; Spinney, R.; Allen, H. C. Water Structure at the AirAqueous Interface of Divalent Cation and Nitrate Solutions. J. Phys. Chem. B 2009, 113, 4102. (31) Bock, J.; Jacobi, H.-W. Development of a Mechanism for Nitrate Photochemistry in Snow. J. Phys. Chem. A 2010, 114, 1790. (32) Boxe, C. S.; Saiz-Lopez, A. Multiphase Modeling of Nitrate Photochemistry in the Quasi-Liquid Layer (QLL): Implications for NOx Release from the Arctic and Coastal Antarctic Snowpack. Atmos. Chem. Phys. 2008, 8, 4855. (33) Jacobi, H.-W.; Hilker, B. A Mechanism for the Photochemical Transformation of Nitrate in Snow. J. Photochem. Photobiol., A 2007, 185, 371. (34) Wolff, E. W.; Jones, A. E.; Martin, T. J.; Grenfell, T. C. Modelling Photochemical NOx Production and Nitrate Loss in the Upper Snowpack of Antarctica. Geophys. Res. Lett. 2002, 29, 5-1. (35) Herrmann, H.; Ervens, B.; Jacobi, H. W.; Wolke, R.; Nowacki, P.; Zellner, R. CAPRAM2.3: A Chemical Aqueous Phase Radical Mechanism for Tropospheric Chemistry. J. Atmos. Chem. 2000, 36, 231. (36) Thogersen, J.; Gadegaard, A.; Nielsen, J.; Jensen, S. K.; Petersen, C.; Keiding, S. R. Primary Formation Dynamics of Peroxynitrite Following Photolysis of Nitrate. J. Phys. Chem. A 2009, 113, 10488. (37) Hudson, P. K.; Schwarz, J.; Baltrusaitis, J.; Gibson, E. R.; Grassian, V. H. A Spectroscopic Study of Atmospherically Relevant Concentrated Aqueous Nitrate Solutions. J. Phys. Chem. A 2007, 111, 544. (38) Roca, M.; Zahardis, J.; Bone, J.; El-Maazawi, M.; Grassian, V. H. 310 nm Irradiation of Atmospherically Relevant Concentrated Aqueous Nitrate Solutions: Nitrite Production and Quantum Yields. J. Phys. Chem. A 2008, 112, 13275. (39) Relph, R. A.; Bopp, J. C.; Johnson, M. A.; Viggiano, A. A. Argon Cluster-Mediated Isolation and Vibrational Spectra of Peroxy and Nominally D3h Isomers of CO3− and NO3−. J. Chem. Phys. 2008, 129, 064305. (40) Goebbert, D. J.; Garand, E.; Wende, T.; Bergmann, R.; Meijer, G.; Asmis, K. R.; Neumark, D. M. Infrared Spectroscopy of the Microhydrated Nitrate Ions NO3−(H2O)1−6. J. Phys. Chem. A 2009, 113, 7584. (41) Waterland, M. R.; Myers Kelley, A. Far-Ultraviolet Resonance Raman Spectroscopy of Nitrate Ion in Solution. J. Chem. Phys. 2000, 113, 6760. (42) Waterland, M. R.; Stockwell, D.; Kelley, A. M. Symmetry Breaking Effects in NO3−: Raman Spectra of Nitrate Salts and Ab Initio Resonance Raman Spectra of Nitrate-Water Complexes. J. Chem. Phys. 2001, 114, 6249.

(43) Gaffney, K. J.; Ji, M.; Odelius, M.; Park, S.; Sun, Z. H-bond Switching and Ligand Exchange Dynamics in Aqueous Ionic Solution. Chem. Phys. Lett. 2011, 504, 1. (44) Kropman, M. F.; Bakker, H. J. Femtosecond Mid-Infrared Spectroscopy of Aqueous Solvation Shells. J. Chem. Phys. 2001, 115, 8942. (45) Laage, D. Reinterpretation of the Liquid Water Quasi-Elastic Neutron Scattering Spectra Based on a Nondiffusive Jump Reorientation Mechanism. J. Phys. Chem. B 2009, 113, 2684. (46) Laage, D.; Stirnemann, G.; Sterpone, F.; Rey, R.; Hynes, J. T. Reorientation and Allied Dynamics in Water and Aqueous Solutions. Annu. Rev. Phys. Chem. 2011, 62, 395. (47) 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. (48) Park, S.; Odelius, M.; Gaffney, K. J. Ultrafast Dynamics of Hydrogen Bond Exchange in Aqueous Ionic Solutions. J. Phys. Chem. B 2009, 113, 7825. (49) Tielrooij, K. J.; Garcia-Araez, N.; Bonn, M.; Bakker, H. J. Cooperativity in Ion Hydration. Science 2010, 328, 1006. (50) Xu, M.; Larentzos, J. P.; Roshdy, M.; Criscenti, L. J.; Allen, H. C. Aqueous Divalent Metal-Nitrate Interactions: Hydration Versus Ion Pairing. Phys. Chem. Chem. Phys. 2008, 10, 4793. (51) Shen, M.; Xie, Y.; Schaefer, H. F., III; Deakyne, C. A. Hydrogen Bonding between the Nitrate Anion (Conventional and Peroxy Forms) and the Water Molecule. J. Chem. Phys. 1990, 93, 3379. (52) Shen, M.; Xie, Y.; Schaefer, H. F., III; Deakyne, C. A. The Hydrogen Peroxide-NO2− and H2NO2− Isomers of the Nitrate AnionWater Complex. Chem. Phys. 1991, 151, 187. (53) Gonzalez Lebrero, M. C.; Bikiel, D. E.; Elola, M. D.; Estrin, D. A.; Roitberg, A. E. Solvent-Induced Symmetry Breaking of Nitrate Ion in Aqueous Clusters: A Quantum-Classical Simulation Study. J. Chem. Phys. 2002, 117, 2718. (54) Merrill, G. N.; Webb, S. P. The Application of the Effective Fragment Potential Method to Molecular Anion Solvation: A Study of Ten Oxyanion-Water Clusters, A−(H2O)1−4. J. Phys. Chem. A 2004, 108, 833. (55) Pathak, A. K.; Mukherjee, T.; Maity, D. K. Microhydration of NO3−: A Theoretical Study on Structure, Stability and IR Spectra. J. Phys. Chem. A 2008, 112, 3399. (56) Bianco, R.; Wang, S.; Hynes, J. T. Infrared Signatures of HNO3 and NO3− at a Model Aqueous Surface: A theoretical Study. J. Phys. Chem. A 2008, 112, 9467. (57) Ramesh, S. G.; Re, S.; Hynes, J. T. Charge Transfer and OH Vibrational Frequency Red Shifts in Nitrate-Water Clusters. J. Phys. Chem. A 2008, 112, 3391. (58) Tongraar, A.; Tangkawanwanit, P.; Rode, B. M. A Combined QM/MM Molecular Dynamics Simulations Study of Nitrate Anion (NO3−) in Aqueous Solution. J. Phys. Chem. A 2006, 110, 12918. (59) Ramesh, S. G.; Re, S.; Boisson, J.; Hynes, J. T. Vibrational Symmetry Breaking of NO3− in Aqueous Solution: NO Asymmetric Stretch Frequency Distribution and Mean Splitting. J. Phys. Chem. A 2010, 114, 1255. (60) Zhang, H.; Feng, B.; Yu, J.-k.; Sun, C.-c. Ab-Initio Investigation on Ion-Associated Species and Association Process in NaNO 3 Solution. Chem. Res. Chin. Univ. 2010, 26, 656. (61) Vchirawongkwin, V.; Kritayakornupong, C.; Tongraar, A.; Rode, B. M. Symmetry Breaking and Hydration Structure of Carbonate and Nitrate in Aqueous Solutions: A Study by Ab Initio Quantum Mechanical Charge Field Molecular Dynamics. J. Phys. Chem. B 2011, 115, 12527. (62) Brown, M. A.; D’Auria, R.; Kuo, I. F. W.; Krisch, M. J.; Starr, D. E.; Bluhm, H.; Tobias, D. J.; Hemminger, J. C. Ion Spatial Distributions at the Liquid-Vapor Interface of Aqueous Potassium Fluoride Solutions. Phys. Chem. Chem. Phys. 2008, 10, 4778. (63) Dang, L. X.; Chang, T.-M. Molecular Mechanism of Ion Binding to the Liquid/Vapor Interface of Water. J. Phys. Chem. B 2002, 106, 235. H

DOI: 10.1021/acs.jpca.6b12102 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A (64) Jungwirth, P.; Tobias, D. J. Ions at the Air/Water Interface. J. Phys. Chem. B 2002, 106, 6361. (65) Jungwirth, P.; Tobias, D. J. Specific Ion Effects at the Air/Water Interface. Chem. Rev. 2006, 106, 1259. (66) Salvador, P.; Curtis, J. E.; Tobias, D. J.; Jungwirth, P. Polarizability of the Nitrate Anion and its Solvation at the Air/ Water Interface. Phys. Chem. Chem. Phys. 2003, 5, 3752. (67) Thomas, J. L.; Roeselova, M.; Dang, L. X.; Tobias, D. J. Molecular Dynamics Simulations of the Solution-Air Interface of Aqueous Sodium Nitrate. J. Phys. Chem. A 2007, 111, 3091. (68) Petersen, P. B.; Saykally, R. J.; Mucha, M.; Jungwirth, P. Enhanced Concentration of Polarizable Anions at the Liquid Water Surface: SHG Spectroscopy and MD Simulations of Sodium Thiocyanide. J. Phys. Chem. B 2005, 109, 10915. (69) Petersen, P. B.; Saykally, R. J. Confirmation of Enhanced Anion Concentration at the Liquid Water Surface. Chem. Phys. Lett. 2004, 397, 51. (70) Onorato, R. M.; Otten, D. E.; Saykally, R. J. Measurement of Bromide Ion Affinities for the Air/Water and Dodecanol/Water Interfaces at Molar Concentrations by UV Second Harmonic Generation Spectroscopy. J. Phys. Chem. C 2010, 114, 13746. (71) Simeon, V.; Butorac, V.; Tomišić, V.; Kallay, N. Existence of Two Forms of Nitrate Ion in Dilute Aqueous Solutions. Thermodynamic Parameters of Interconversion. Phys. Chem. Chem. Phys. 2003, 5, 2015. (72) Geissler, P. L. Temperature Dependence of Inhomogeneous Broadening: On the Meaning of Isosbestic Points. J. Am. Chem. Soc. 2005, 127, 14930. (73) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A., et al. Gaussian 09, Revision B.01, Gaussian: Wallingford CT, 2009. (74) Becke, A. D. Density-Functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648. (75) Dunning, T. H., Jr. Gaussian Basis Sets for Use in Correlated Molecular Calculations. I: The Atoms Boron through Neon and Hydrogen. J. Chem. Phys. 1989, 90, 1007. (76) Marechal, Y. IR Spectroscopy of an Exceptional H-Bonded Liquid: Water. J. Mol. Struct. 1994, 322, 105. (77) Bergonzi, I.; Mercury, L.; Brubach, J. B.; Roy, P. Gibbs Free Energy of Liquid Water Derived from Infrared Measurements. Phys. Chem. Chem. Phys. 2014, 16, 24830. (78) Anna, J. M.; King, J. T.; Kubarych, K. Multiple Structures and Dynamics of [CpRu(CO)2]2 and [CpRu(CO)2]2 in Solution Revealed with Two-Dimensional Infrared Spectroscopy. Inorg. Chem. 2011, 50, 9273.

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