Short-Range Cooperative Slow-down of Water Solvation Dynamics Around SO₄^2––Mg²⁺ Ion Pairs

Abstract

The presence of ions affects the structure and dynamics of water on a multitude of length and time scales. In this context, pairs of Mg²⁺ and SO₄^2– ions in water constitute a prototypical system for which conflicting pictures of hydration geometries and dynamics have been reported. Key issues are the molecular pair and solvation shell geometries, the spatial range of electric interactions, and their impact on solvation dynamics. Here, we introduce asymmetric SO₄^2– stretching vibrations as new and most specific local probes of solvation dynamics that allow to access ion hydration dynamics at the dilute concentration (0.2 M) of a native electrolyte environment. Highly sensitive heterodyne 2D-IR spectroscopy in the fingerprint region of the SO₄^2– ions around 1100 cm^–1 reveals a specific slow-down of solvation dynamics for hydrated MgSO₄ and for Na₂SO₄ in the presence of Mg²⁺ ions, which manifests as a retardation of spectral diffusion compared to aqueous Na₂SO₄ solutions in the absence of Mg²⁺ ions. Extensive molecular dynamics and density functional theory QM/MM simulations provide a microscopic view of the observed ultrafast dephasing and hydration dynamics. They suggest a molecular picture where the slow-down of hydration dynamics arises from the structural peculiarities of solvent-shared SO₄^2––Mg²⁺ ion pairs.

Introduction

Interactions of molecules with their environment have a direct impact on their structure and on chemical reactions in the condensed phase. Liquid water, the native medium of biochemical and cellular processes, consists of a complex network of polar molecules and responds to the presence of a solute, both by modification of its local hydrogen-bond structure as well as by modifying the long-range electric force by dielectric screening. Such properties are particularly relevant for accommodating charged species, that is, electrons, protons, and/or molecular ions. The inherent many-body character of the interactions, together with thermally activated ultrafast fluctuations of the water structure, makes studies of the solvation of charged species in water a challenge for both theory and experiment.

Ions in water are embedded in local hydration shells with a structure and dynamics different from the bulk of the liquid. In bulk water, the ultrafast thermal motions of H₂O molecules induce picosecond breaking and formation of hydrogen bonds. Insertion of ions generates local water shells with a different molecular arrangement, hydrogen bond strength, and dynamics.^1,2 In particular, the electrostatic energy is minimized by reorienting the polar water molecules in the first and, to lesser extent, next few solvation shells around the ion site, thus introducing steric constraints and affecting the hydrogen bond structure.

A broad range of experimental methods of structure research and spectroscopy have been applied to unravel equilibrium geometries, dielectric properties, and nonequilibrium elementary excitations of hydrated ions and their impact on water dynamics.³⁻¹⁴ Regarding the latter, both retarding and accelerating mechanisms have been introduced, including concepts of cooperativity between cations and anions in their impact on the solvent. A large body of molecular dynamics (MD) simulations based on empirical force fields and ab initio simulations has addressed the underlying molecular interactions and provided insight into dynamic hydration geometries.¹⁵⁻²⁴ Different, in most cases very high ion concentrations in the experiments have led to partly conflicting results, while the complex many-body character of ion solvation in a polarizable liquid represents a major challenge for theoretical and simulation work.

Hydrated sulfate ions are prototypical in this context, given their broad abundance in minerals and their relevance in physiology and biochemistry, for example, of heparin-protein interactions.^25,26 A prominent example is the solvation structures of the SO₄^2– ion and (counter)ions such as NH₄⁺, Na⁺, Ca²⁺, or Mg²⁺ which have frequently been categorized as spatially uncorrelated free ion pairs (FIP), ion pairs with separate first water layers around a SO₄^2– and a cation in the neighborhood (solvent separated ion pairs, SSIP), ion pairs sharing water molecules in their first solvent shell (solvent shared ion pairs, SIP), and directly interacting contact ion pairs (CIP).^27,28 The relative abundance of the different species and, in particular, the occurrence of CIP has remained highly controversial. For MgSO₄, early results from dielectric relaxation and Raman spectroscopy have been interpreted in terms of a simultaneous presence of all species.^8,29 A component of the dielectric spectrum around 10 GHz, changes in the shape of the SO₄^2– Raman band at 980 cm^–1 (ν₁ mode) and a Raman band around 350 cm^–1 [ν₁ mode of Mg(OH₂)₆²⁺] have been attributed to CIP formation. This view has been challenged by other Raman³⁰ and THz¹¹ measurements and, in particular, the comparison of experimental dielectric spectra with those calculated from MD simulations of MgSO₄ and Na₂SO₄ in water.¹⁰ A slowing down of the orientational dynamics of water molecules in hydration shells with a cooperative impact of SO₄^2– and Mg²⁺ ions has been inferred from polarization-resolved femtosecond pump–probe studies of the water OH stretching vibration in highly concentrated ionic solutions together with THz dielectric relaxation spectroscopy.¹²

The work reported in refs (8), (10)–¹² and (29) has been performed at ion concentrations of up to several moles/liter (M). Under such conditions, ions are found at an average distance of less than 1 nm and can only accommodate a few water molecules in between.¹ Thus, the space available for water molecules in an undistorted bulk arrangement is substantially diminished and ion–ion interactions as well as the overlap of ion hydration shells become relevant. From a conceptual point of view, SO₄^2– vibrations probe local interactions at solvation sites, whereas the water OH stretching response is spatially unspecific and averaged over all water geometries in the ionic solution.

Understanding sulfate hydration at the molecular level requires experimental probes of local dynamics and in-depth theoretical analysis of interactions and MD. Here, we introduce the infrared-active asymmetric stretching vibration of the SO₄^2– ion (ν₃ mode) as a local probe of solvation sites and interactions between the ions and their surrounding. Nonlinear two-dimensional infrared (2D-IR) spectroscopy is applied to identify the character and time scale of structural fluctuations and determine their impact on the vibrational line shapes at a moderate 0.2 M concentration of SO₄^2– ions in water. To get specific insight into the interactions between SO₄^2– and cations in water, MgSO₄ and Na₂SO₄ are studied in direct comparison, including samples of Na₂SO₄ with additional Mg²⁺ ions present. In the Na₂SO₄ solution, librational fluctuations of the water shell result in spectral diffusion on a sub-100 fs time scale, followed by slower kinetics. Spectral diffusion is slowed down significantly in the presence of Mg²⁺ ions, both for MgSO₄ and Na₂SO₄ with excess Mg²⁺ ions added. This behavior demonstrates a direct impact of Mg²⁺ ions on the water shell of a nearby SO₄^2– ion.

The experimental results are complemented by MD simulations and quantum mechanical/molecular mechanical (QM/MM) simulations, which give a quantitative understanding of the vibrational line shape of SO₄^2– stretching vibrations, the observed ultrafast dephasing and reorientational water dynamics, as well as the spatial range of water molecules and ions impacting the fingerprint vibrational probe of the SO₄^2– tetrahedron. Our results suggest that the slow-down of the water reorientational dynamics observed for MgSO₄ arises from water molecules structurally associated with Mg²⁺–SO₄^2– SIP, while there is no evidence for CIP geometries. The two ions of the SIP species induce cooperativity of hydration dynamics in the first two solvation shells already at dilute ion concentrations.

Results

Figure 1a shows the linear absorption spectra of Na₂SO₄ and MgSO₄ dissolved in water in the frequency range of the asymmetric SO₄^2– stretching vibration (ν₃ mode) for an ion concentration of 0.2 M after subtraction of the water background (see the Supporting Information). The isolated sulfate ion SO₄^2– has tetrahedral symmetry T_d with three degenerate asymmetric stretching modes and the sulfur atom found in an ideal tetrahedral environment of oxygen atoms. Hydration breaks this molecular symmetry and lifts the degeneracy,³¹⁻³³ giving rise to a broad unstructured line shape. The two spectra display a different maximum absorption strength and slightly different line shapes, as is evident from the difference spectrum ΔA = A(MgSO₄)–A(Na₂SO₄) shown as a dashed line in Figure 1c (absorbance A = −log(T); sample transmission T). The presence of Mg²⁺ ions causes a decrease of maximum absorption and an absorption shoulder around 1150 cm^–1.

Figure 1.

(a) Experimental linear absorption spectra of Na₂SO₄ (black) and MgSO₄ (red) in the frequency range of the asymmetric SO₄^2– stretching vibration (ν₃ mode, concentrations 0.2 M in water). (b) Linear absorption spectra of Na₂SO₄ (concentration 0.2 M, sample thickness 25 μm) for various added concentrations of MgCl₂. (c) Differential linear absorption spectra of Na₂SO₄ and Na₂SO₄ with added MgCl₂ as indicated (Na₂SO₄ concentration 0.2 M). The dashed line represents the difference of the MgSO₄ and Na₂SO₄ bands shown in panel (a).

The linear absorption spectra of Na₂SO₄ exhibit weak but systematic changes of line shape upon addition of Mg²⁺ ions, as presented in Figure 1b for Mg²⁺ concentrations between 0.2 and 1.5 M (Na₂SO₄ concentration 0.2 M). One observes a decrease in amplitude by about 10% at the maximum of the band (1100 cm^–1) and an increase in absorption around 1150 cm^–1, as manifested in the difference spectra of Figure 1c and very similar to the differential spectrum of MgSO₄ and Na₂SO₄ (dashed line). Such changes are confined to the initial line shape. This behavior is different from Mg²⁺ addition to phosphate groups in aqueous environment,^34,35 where a new blue-shifted absorption band due to CIP formation with the PO₂^– subgroup arises. The population decay time of the ν₃ mode was measured in femtosecond pump–probe experiments discussed in the Supporting Information. For Na₂SO₄, one observes a decay of the v = 1 state with a time constant of 290 ± 20 fs.

In Figure 2, 2D-IR spectra of 0.2 M aqueous solutions of Na₂SO₄ (panels a,b) and MgSO₄ (panels c,d) are presented for different waiting (population) times T. The absorptive 2D signal (cf. Supporting Information) is plotted as a function of the excitation frequency ν₁ (ordinate) and detection frequency ν₃ (abscissa) and shows contributions arising from ground-state bleaching (GSB) and stimulated emission (SE) on the v = 0 → 1 transition (yellow-red contours) and contributions arising from excited-state absorption on the v = 1 → 2 transition (blue contours). At the early waiting time T = 300 fs (Figure 2a,c), the 2D-IR spectra of both samples are characterized by line shapes of the GSB/SE signal stretched along the frequency diagonal ν₁ = ν₃, reflecting a substantial inhomogeneous broadening due to a distribution of local SO₄^2– environments in the liquid.

Figure 2.

2D-IR spectra of Na₂SO₄ and MgSO₄ for waiting times (a,c) T = 300 fs and (b,d) T = 600 and 500 fs (ion concentrations 0.2 M). Absorptive 2D signals are shown as a function of excitation frequency ν₁ and detection frequency ν₃. Contributions arising from GSB/SE on the v = 0 → 1 transition are shown with yellow-red contours, and v = 1 → 2 excited-state absorption contributions are shown in blue. Signal amplitudes are normalized to the maximum GSB/SE signal in each spectrum with a 5% signal change between neighboring contour lines.

The 2D-IR spectrum of Na₂SO₄ recorded at T = 600 fs displays a more circular and upright shape of the GSB/SE signal peak compared to the T = 300 fs spectrum. This reshaping is a manifestation of spectral diffusion which is induced by fluctuating forces from the aqueous environment and randomizes the initial distribution of transition frequencies in the ensemble. The change in line shape results in a spectral narrowing of cuts of the 2D-IR spectra along the ν₁ = ν₃ direction (Figure 3c).

Figure 3.

2D-IR spectra of Na₂SO₄/Mg²⁺ for waiting times of (a) T = 300 fs and (b) T = 600 fs (Na₂SO₄ concentration 0.2 M, Mg²⁺ concentration 1.0 M). (c,d) Frequency cuts of 2D-IR spectra of (c) Na₂SO₄, (d) MgSO₄, and (e) Na₂SO₄/Mg²⁺ along a diagonal line parallel to ν₁ = ν₃ which crosses the maximum of the respective v = 0 → 1 peak. The dotted line in panel (e) shows the T = 300 fs cut for Na₂SO₄ as a reference. (f) Horizontal cuts of 2D-IR spectra along the detection frequency ν₃ at an excitation frequency ν₁ = 1080 cm^–1 (waiting time T = 300 fs).

The 2D-IR spectra of MgSO₄ (Figure 2c,d) show a minor reshaping with increasing waiting time T, essentially retaining an elliptic shape of the GSB/SE peak. This fact is also evident from the nearly identical diagonal cuts for T = 300 and 500 fs (Figure 3d). The very limited change in 2D line shape directly points to a slowing down of spectral diffusion compared to the Na₂SO₄ case and, thus, a modification of the underlying fluctuating forces from the environment in the presence of Mg²⁺ ions.

To explore the impact of Mg²⁺ ions on spectral diffusion more closely, 2D-IR spectra of Na₂SO₄ (c = 0.2 M) with additional Mg²⁺ ions of 1 M concentration were recorded (Figure 3a,b). Most interestingly, the presence of Mg²⁺ ions suppresses the fast reshaping observed in the 2D-IR spectra of the Na₂SO₄ solution (Figure 2a,b). Instead, the 2D-IR spectra for T = 300 and 600 fs and the related diagonal cuts in Figure 3e have a similar shape, exhibiting a persistence of the pronounced inhomogeneous broadening as in the MgSO₄ sample.

Cuts of the 2D-IR spectra along the detection frequency ν₃ of the three samples, Na₂SO₄, MgSO₄, and Na₂SO₄/Mg²⁺, reveal a substantial broadening and plateau-like line shape for low excitation frequencies ν₁ = 1080–1120 cm^–1 compared to excitation frequencies in the range ν₁ = 1130–1150 cm^–1 (Figure 3f). Such anomalous frequency dependence introduces a slightly trigonal line shape of the 2D-IR spectra in Figures 2 and 3a,b that points to a cross peak at (ν₁,ν₃) = (1080,1120) cm^–1 within the 2D envelope and is assigned to a dynamic exchange of subcomponents of the asymmetric SO₄^2– stretching vibration.

The 2D-IR line shapes were analyzed by density matrix simulations of the third-order vibrational response^36,37 with a frequency fluctuation correlation function (FFCF) approximated by a sum of Kubo terms. Results of this treatment are presented in the Supporting Information and discussed below.

Atomistic MD and density functional theory QM/MM instantaneous normal mode simulations were employed to obtain microscopic insight into the structure and fluctuation dynamics of sulfate hydration shells, which are made up of water molecules and Na⁺ or Mg²⁺ ions. MD simulations employ a SO₄^2– force field which has been adapted to reproduce the solvation free energies of single ions and activity coefficients of concentrated solutions (cf. ref (10) and Supporting Information).

The solvation shell of the SO₄^2– ion is made up of on average 11.5 water molecules in the first hydration layer (Figure 4a). Each of the four oxygen atoms is coordinated by about three water molecules in a tetrahedral environment. In MD simulations with SO₄^2– and Mg²⁺ ions, we find an equilibrium of SIP (Figure 4d), SSIP (Figure 4e), and FIP species,¹² characterized by S···Mg²⁺ distances of ≈0.55 nm, 0.7 nm, and >0.8 nm, respectively (Figure 4b). The double peak found in the radial distribution of S···Mg²⁺ distances of SIP around ≈0.55 nm arise from two possible coordination geometries of bridging water molecules between the Mg²⁺ and SO₄^2– ions: either a single water molecule is part of the solvation shell of the Mg ²⁺ and the SO₄^2– ion or two water molecules bridge the Mg²⁺ and SO₄^2– ions in a bidentate coordination (Figure 4d). Each solvation structure is observed with similar probability and interconverts with a mean lifetime of about 10 ps. There is no formation of Mg²⁺/SO₄^2– CIP over the full length of the MD trajectories of 1 μs.

Figure 4.

(a) Coordination number of SO₄^2– ions by water molecules derived from MD simulations. (b) Radial distribution of sulfur-magnesium (S···Mg²⁺) distances. (c) Radial distribution of sulfur-sodium (S···Na⁺) distances. CIP: contact ion pairs, SIP: solvent shared ion pairs, SSIP: solvent separated ion pairs, FIP: free ion pairs; exemplary molecular SIP bridged by a single molecule (left) or two water molecules (right) and SSIP structures of Mg²⁺ and SO₄^2– ions are depicted in panels (d) and (e), respectively. MD simulations were performed with a cubic box (L = 20 Å) of 290 SPC/E water molecules at the respective experimental concentrations of MgSO₄ and Na₂SO₄ of about 0.2 M (see the Supporting Information for details).

In MD simulations of Na₂SO₄, CIP are in equilibrium with SIP, SSIP, and FIP species [S···Na⁺ distances ≈0.35, 0.6, 0.75 and >0.85 nm, Figure 4c]. The weak shoulder in the radial distribution of S···Na⁺ distances around 0.35 nm arises from the coordination of the SO₄^2– ion by Na⁺ ions in the bisector of the O=S=O group (bidentate oxygen coordination). Nevertheless, coordination is observed predominantly via single oxygen atoms of the O=S=O group, characterized by a mean S=O.... Na⁺ angle of about 124° being indicative of the replacement of a water molecule in the first solvation shell of the SO₄^2– ion by a Na⁺ ion. Thus, the predominantly realized CIP coordination geometries resemble the ion pair structures of Na⁺ ions with the phosphate groups.³⁸

Fluctuation amplitudes of the electric field in the solvent and the underlying dynamics of the hydration shell are imprinted on the line shapes of the linear infrared absorption and nonlinear 2D-IR spectra of the asymmetric SO₄^2– stretching mode. A key quantity is the electric field acting on the molecular coordinates of the SO₄^2– ion. Here, we consider the electric field projected on the bisector of a SO₂ subgroup and averaged over the six possible permutations of such units in the ion. To characterize the electric field dynamics, we derived the time-dependent field autocorrelation functions C(t) from the MD simulations. In Figure 5, the results are summarized for Na₂SO₄ (green line) and MgSO₄ (orange line), together with the components of the MgSO₄ function originating from SIP (blue line) and FIP/SSIP (red line).

Figure 5.

Normalized electric field autocorrelation functions C(t) derived from MD simulations for Na₂SO₄ (green line), MgSO₄ (orange line), and components of the MgSO₄ correlation function originating from SIP (blue line) and FIP/SSIP (red line). Note the pronounced changes in the relative amplitude of the initial femtosecond decay of correlation.

The different correlation functions consist of an initial femtosecond decay which mainly reflects the librational dynamics of water molecules and a slower decay extending well into the picosecond time range. This slower component is due to rotational motions of water molecules and hydrogen bond breaking and reformation. The correlation functions C(t) of MgSO₄ and Na₂SO₄ are best represented by bi- and triexponential fits, respectively, with a fast sub-100 fs time constant and an additional, slightly slower 600 fs time constant for Na₂SO₄ (cf. Supporting Information for details). For Na₂SO₄, the relative amplitude of the fast, sub-picosecond decay is on the order of 0.7, while MgSO₄ displays a less prominent fast decay with a relative amplitude of approximately 0.48. This significant decrease in amplitude points to a partial suppression of fast librational water motions in a more rigid solvation environment existing in MgSO₄. Decomposition of the overall correlation function into different ionic species of MgSO₄ shows a much smaller amplitude of the fast decay for SIP, causing the reduced fast decay component in the overall C(t) of MgSO₄. In contrast, the pronounced fast decay components arise for FIP and SSIP geometries (red line), closer to the Na₂SO₄ case (green line). In our simulations of the 2D-IR spectra, we use FFCF with exponential decay components, that is, Kubo terms, mimicking the C(t) functions of Na₂SO₄ and MgSO₄.

Density functional theory QM/MM instantaneous normal mode simulations relying on geometries from MD simulations connect the sampled geometries to the spectroscopic observables, allowing to benchmark the sampled structures and thus giving quantitative insight into the hydration dynamics. The theoretical approach allows for quantitative modeling of the linear infrared absorption spectrum, covering the full 1050–1150 cm^–1 width of the vibrational band (Figure 6a). The large width of the vibrational band arises due to the contributions of three vibrational subcomponents of the asymmetric SO₄^2– stretching vibration. Compared to the gas phase, the degeneracy of asymmetric SO₄^2– stretching modes is broken in the instantaneous solvent field configuration (Figure 6b). Because of the high sensitivity of the SO₄^2– stretching modes to the local environment and the strong coupling to the water librational degrees of freedom, the mode character of the vibrational subcomponents is highly dynamic. On the observation time scale of the 2D-IR experiment set by the vibrational lifetime of some 300 fs, frequency excursions cover the individual subdistributions, and changes of mode character further induce an exchange between the subdistributions, both effects contributing to spectral diffusion.

Figure 6.

(a) Experimental (red) and simulated (blue, pw6b95-D QM/MM level of theory, see the Supporting Information for details) linear absorption spectra of the asymmetric SO₄^2– stretching vibration. (b) Simulated distributions of the subcomponents of the SO₄^2– stretching vibration.

The performance and accuracy of different density functionals in calculating the linear infrared absorption spectrum were analyzed in a systematic way, and the results are presented in the Supporting Information (Figure S9). Moreover, the size of the QM region was systematically varied in order to demonstrate convergence of the highly accurate simulations of the infrared absorption spectrum of the asymmetric SO₄^2– stretching vibration (Figure S10). A faithful agreement of the frequency position in theory and experiment requires to treat the SO₄^2– ion and its first solvation shell on the QM level, in turn electrostatically embedded in the remainder of the aqueous environment. A further increase of the QM region to account for water molecules of the second solvation shell does not improve the agreement with the experiment.

Discussion

Our experiments were performed at Na₂SO₄ and MgSO₄ concentrations of 0.2 M, much lower than in most studies reported in the literature. The moderate concentration, which corresponds to a ratio of sulfate ions and water molecules of 1:280, allows for uncorrelated ion solvation with several water layers in-between solvation sites. More precisely, the first SO₄^2– solvation shell and the first octahedral water shell around a Mg²⁺ ion contains ∼12 and 6 H₂O molecules, respectively. This translates in a concentration of first-shell water of 18 × 0.2 = 3.6 M, which is small compared to the total water concentration of 56 M.

The linear absorption spectra of the asymmetric sulfate stretching vibration (ν₃ mode, Figure 1) exhibit a different line shape for Na₂SO₄ and MgSO₄, the latter with a relative enhancement of absorption around 1150 cm^–1, within the spectral range covered by the broad absorption bands. A similar enhancement is observed upon gradual addition of Mg²⁺ ions to a Na₂SO₄ solution (Figure 1c). It has been shown that the Raman band of the symmetric SO₄^2– vibration (ν₁ mode) of MgSO₄ in water develops a high-frequency shoulder with increasing ion concentration.⁸ Such behavior clearly suggests the impact of a Mg²⁺ ion on the solvation shell of a SO₄^2– ion by their close spatial arrangement. However, a direct interpretation of the spectrally broad time-averaged infrared and Raman bands in terms of an ion pairing geometry is speculative and has led to controversy in the existing literature.

The 2D-IR spectra presented in Figures 2 and 3 give direct insight into spectral diffusion and the underlying fluctuation dynamics of SO₄^2– solvation shells. The Na₂SO₄ spectra in Figure 2a,b show a pronounced reshaping from an initially elliptic v = 0 → 1 band (yellow-red contours) toward a more round shape. Such changes are a hallmark of spectral diffusion. Our simulation results suggest a highly dynamic mode character of the vibrational subcomponents with frequency excursions within the subdistributions and exchange between subdistributions on the ∼600 fs observation time scale of the experiment. The weak cross peak feature in the 2D-IR line shapes supports the picture of a femtosecond mode exchange with a loss of frequency memory. However, the resolved frequency distributions of Figure 6b show that spectral excursions of the three subcomponents on the ultrafast time scale of the 2D-IR experiment are limited to a frequency interval of approximately 50 cm^–1, that is, do not cover the full spectral range of the linear infrared absorption. Otherwise, any frequency resolution within the vibrational lineshape would be diminished, leading to a predominant homogenous broadening mechanism which would not allow to distinguish between Na₂SO₄ and MgSO₄ samples.

The fast spectral diffusion and rapid mode exchange are primarily imposed by fast librational water motions in the first and second hydration layers, which translate into fast fluctuations of the local electric field acting on the sulfate ion and cause the prominent femtosecond decay of the electric field autocorrelation function (Figure 5). Because of the short ∼300 fs lifetime of the ν₃ excitations, the 2D-IR spectra mainly reflect such ultrafast fluctuation kinetics, while the slower, mainly reorientational dynamics of the solvent is not visible.

The presence of Mg²⁺ ions changes this picture substantially. The 2D-IR spectra in Figure 2c,d and 3 exhibit a minor reshaping and maintain an elliptic shape throughout the experimental time window limited by the femtosecond population decay of the SO₄^2– vibration. The slowing down of spectral diffusion is caused by a reduction of fast structural fluctuations of SO₄^2– solvation shells with Mg²⁺ ions nearby. The latter fact is evident from the calculated electric-field autocorrelation functions C(t) in Figure 5 where MgSO₄ shows a significantly reduced amplitude of the femtosecond decay in comparison to Na₂SO₄. The analysis of C(t) for the different solvation geometries demonstrates that the reduction of fast fluctuations occurs mainly in SIP arrangements of SO₄^2– and Mg²⁺.

The numerical simulation of the 2D-IR spectra with FFCF mimicking the different components of C(t) for Na₂SO₄ and MgSO₄ (cf. Supporting Information) reproduces the main features of the experimental spectra and, thus, provides strong support for this picture. Specifically, the simulations for Na₂SO₄ account reasonably well for the reshaping of the 2D-IR envelope during the initial 600 fs waiting time period, induced by the strong femtosecond components of the FFCF, although the narrowing of the diagonal cut with increasing T is less pronounced in the simulation than in the experiment. In contrast, due to the comparable amplitude of the femtosecond and picosecond correlation decays, the envelopes of the 2D-IR spectra of MgSO₄ display negligible changes with waiting time. Because FFCFs are derived from MD simulations that employ a fixed charge force field, the neglect of polarization contributions to spectral diffusion arising from the molecular polarizabilities may be one reason for the remaining discrepancies between simulations and experiment. As an additional caveat, we stress that, as in the case of linear infrared absorption, the 2D-IR spectra represent the average over all ionic arrangements (FIP, SIP, and SSIP) in the sample. As a consequence, any interpretation in terms of ion geometries requires complementary theoretical analysis at molecular length and time scales.

The MD simulation suggests two SIP geometries, one in which a water molecule of the rigid octahedral water shell around Mg²⁺ forms a hydrogen bond with a sulfate oxygen and another one with two bidentate water molecules between the ions (Figure 4d). In both cases, the short water-Mg²⁺ hydrogen bonds restrict fast librational motions and, thus, reduce fast spectral diffusion. The specific slow-down of librations and, on a somewhat longer picosecond time scale, water reorientation are locally restricted to the first solvation shell around the ions, that is, there is no long-range change of water structure. Our results suggest that the nonadditive slow-down of water dynamics for increasing ion concentration^1,12 is associated with the increasing probability of SIP formation, in contrast to the qualitative picture drawn in ref (12).

The radial distributions shown in Figure 4 reveal similar fractions of SIP, SSIP, and FIP geometries, with, however, a stronger relative abundance of SIP in MgSO₄ than in Na₂SO₄. Interconversion of the different species by ion and water rearrangements require a reorganization of the hydrogen bond network which occurs on a time scale of 100 ps and beyond and, thus, has a minor influence on the vibrational line shapes.

The MD simulations give a negligible time-averaged number of CIP in MgSO₄ and not a single CIP formation event during the 1 μs length of the MD trajectories. While a CIP arrangement of Mg²⁺ and SO₄^2– ions is certainly favored by their attractive Coulomb interaction, it would require a hydration shell adapted to the CIP geometry. Here, the rigid octahedral first water shell around Mg²⁺ with short Mg²⁺—water hydrogen bonds represents a steric boundary condition which may suppress the formation of an appropriate hydration layer around the interacting SO₄^2– ion with typically 3 to 4 water molecules per SO unit. In the case of the Na⁺/SO₄^2–, for which a minor fraction of CIP is predicted by the MD simulation, the more flexible water shell around Na⁺ appears to be compatible with CIP formation. It should be noted that CIP formation of Mg²⁺ with sterically less restricting PO₂^– groups has been observed in both model systems and RNA structures.^35,39 A validation of this qualitative discussion requires in-depth structure calculations and experimental work, for example, on clusters, which are beyond the scope of the present study.

In conclusion, our combined experimental and theoretical study reveals a cooperative slow-down of water dynamics around solvent-separated pairs of sulfate and magnesium ions. This slow-down is evident from a significant reduction of spectral diffusion of asymmetric sulfate stretching excitations, which is benchmarked by a direct comparison to the femtosecond spectral diffusion observed in aqueous Na₂SO₄. According to our QM/MM simulations, the slow-down displays a short-range character in space and is due to a restriction of librational water motions in the first and second solvation shells around the ions. As a result, fast fluctuations of the electric field from the more rigid first solvation layers are reduced. Contact pairs between sulfate and magnesium ions are absent, while MD simulations predict a minor fraction of sulfate/sodium contact ions in Na₂SO₄ without, however, a clear spectroscopic signature. In contrast to simplistic pictures of structure-making and −breaking ions, which classify the effect of single ions on the water structure and dynamics,¹ our results demonstrate a particular relevance of individual solvation geometries of specific ion pairs for the dynamics of diluted aqueous systems.

Materials and Methods

Aqueous solutions of anhydrous MgSO₄, Na₂SO₄, and (NH₄)₂SO₄ were prepared with a concentration of 0.2 M in ultrapure water. For experiments with additional Mg²⁺ ions, MgCl₂ with concentrations from 0.1 to 1.5 M was added to the 0.2 M aqueous solution of Na₂SO₄. A Fourier transform infrared spectrometer was used for recording linear infrared absorption spectra with a spectral resolution of 2 cm^–1. The sample thickness was 25 μm. The absorption spectrum of neat water was measured under the same conditions and subtracted from the spectrum of the ionic solutions (cf. Figure 1).

2D-IR spectra were measured in 3-pulse photon-echo experiments with heterodyne detection of the nonlinear signal. Femtosecond infrared pulses with a center frequency of ∼1100 cm^–1, a spectral width of ∼190 cm^–1 (intensity FWHM), and a pulse energy of 5.2 μJ are generated by optical parametric amplification with a 1 kHz repetition rate. Two passively phase-stabilized pulse pairs with wavevectors (k₁, k₂) (mutual delay τ, coherence time) and (k₃, k_LO) are generated by reflection from a diffractive optic element. In a box-CARS beam geometry, three pulses are focused into the sample by an off-axis parabolic mirror to generate a photon echo signal. The third-order signal emitted in the phase-matching direction −k₁ + k₂ + k₃ = k_Sig is overlapped with a local oscillator pulse (k_LO) for spectrally resolved detection by a 64-pixel mercury cadmium telluride detector array (frequency ν₃, spectral resolution 2 cm^–1). Signals measured for different coherence times τ are Fourier-transformed along τ to generate the excitation frequency coordinate ν₁. In Figures 2 and 3 and S2–S4 of the Supporting Information, the absorptive 2D-IR signal, which is given by the real part of the sum of the rephasing and nonrephasing signals, is plotted as a function of ν₁ and ν₃. More details on experimental methods are given in the Supporting Information.

MD simulations were performed with the GROMACS 2018 program^40,41 in a cubic box of 290 equilibrated SPC/E water molecules (L = 20 Å) with periodic boundary conditions in all three directions at the experimental concentration of about 0.2 M of MgSO₄ and Na₂SO₄, respectively. Following equilibration in the NVT and NPT ensembles, production run simulations were performed in the NPT ensemble (1 bar pressure, T = 300 K) with a time step of 2 fs covering a simulation time of 1 μs. During all simulations, the geometry of SPC/E water molecules was restricted with the SHAKE algorithm. Simulations were performed with the SO₄^2– and Mg²⁺ parametrization presented in ref (10). For solutions of Na₂SO₄ and aiming at a balanced description of interaction with the different ions, the recently developed Na⁺ ion parameters⁴² were employed and, as in the case of MgSO₄, a scaling factor λ_σ = 1.65 of modified Lorentz–Berthelot combination rules was used. The employed Na⁺/SO₄^2– force field parameter combination was verified via the concentration-dependent activity coefficient derivative of the Na₂SO₄ solution (Figure S5).

Time-dependent electric field autocorrelation functions C(t) (Figure 5) consider the electric field amplitude E(t) obtained upon projection of the electric field vector on the bisector of the SO₂ subgroup (cf. Figure S7), followed by averaging over the six possible permutations of such units in the SO₄^2– ion. The electric field amplitude E(t) accounts for all partial charges of water molecules and the charges of counter ions Na⁺ and Mg²⁺. Respective field autocorrelation functions C(t) of SIP, SSIP, and FIP hydration species were calculated for consecutive trajectory segments of the individual hydration species with a distance-based criterion for the assignment of hydration species (SIP: S···Mg²⁺ distance r ≤ 0.625 nm; SSIP: 0.625 nm < r ≤ 0.863 nm; FIP: r > 0.863 nm; cf. Figure 4).

QM/MM simulations of vibrational frequencies were performed with NWChem (version 6.3)⁴³ using a 6-311+G* basis set for the sulfur atom and the 6-31G* basis for all other atoms (O, H, Na, and Mg). Production run simulations (Figure 6) employ the pw6b95 density functional together with Grimme’s DFT-D3 dispersion correction⁴⁴ (pw6b95-D) and take into account the first solvation shell around the ions on the QM level of theory. The dependence on the employed density functional is explored in Figure S9, and the influence of the QM region on the frequency position and line shape of the asymmetric stretch vibration of the SO₄^2– tetrahedron (ν₃ mode) is analyzed in Figure S10. Further details on the theoretical methods are provided in the Supporting Information.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsphyschemau.2c00034.

• Experimental methods, experimental results, simulation of 2D-IR spectra, theoretical methods, and theory results (PDF)

Author Present Address

^⊥ Department Chemie, Ludwig-Maximilians-Universität München, München 81377, Germany

Author Contributions

T.E. and B.P.F. initiated, conceived, and supervised the study. A.K. performed the experiments, S.I.M and B.P.F. performed the simulations. All authors contributed to the analysis of the results. B.P.F. and T.E. wrote the manuscript with input from all authors. All authors have given approval to the final version of the manuscript

The authors declare no competing financial interest.