Heterogeneous Occupancy and Vibrational Dynamics of Spatially

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B: Liquids, Chemical and Dynamical Processes in Solution, Spectroscopy in Solution

Heterogeneous Occupancy and Vibrational Dynamics of Spatially Patterned Water Molecules Sohag Biswas, and Bhabani S. Mallik J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.9b00271 • Publication Date (Web): 24 Apr 2019 Downloaded from http://pubs.acs.org on April 29, 2019

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The Journal of Physical Chemistry

Heterogeneous Occupancy and Vibrational Dynamics of Spatially Patterned Water Molecules ∗

Sohag Biswas†, ‡ and Bhabani S. Mallik†,

†

Department of Chemistry, Indian Institute of Technology Hyderabad, Kandi, Sangareddy - 502285, Telangana, India.

E-mail: [email protected]

Phone: +91 40 2301 7051

ACS Paragon Plus Environment

1

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract We performed first principles molecular dynamics simulations of relatively dilute aqueous solutions of sulfate and thiosulfate dianions to analyze the structure, dynamics and vibrational spectral properties of water molecules around the solute, especially the spatially patterned solvent molecules in the first solvation layer and the extended layers. This study also involves the investigation of dynamics of dangling OH groups in these layers and their role in patterning the water molecules around the dianions. Structural evaluation of the systems is carried out by radial distribution functions (RDFs), number integrals (NIs) and spatial distribution functions (SDFs). The lifetime of dangling OH groups inside the solvation shell is more compared to that of the bulk. By constructing the O–H groups in three ensembles (S1, S2, and S3) around the anion, we show that frequency distribution of OH modes in the S1 ensemble show red-shifting for both sulfate and thiosulfate. The O–H groups in S2 ensemble of sulfate-water system show red-shifting by 10 cm-1 while in case of thiosulfate-water, these O–H groups show blue-shifting by 8 cm-1. The water molecules in S1 and S2 sub ensembles have slower dynamics compared to the bulk (S3). The dynamics of various kinds of hydrogen bonds were characterized by hydrogen bond population correlation functions. The spectral diffusion of solvation shell O–H modes was performed through a frequency-time correlation function. We find a significant amount of orientational retardation of water molecules in the S1 layer and moderate retardation in the S2 layer as compared to the bulk, S3 layer. All these findings, the redshift of OH stretching frequency in S1 and S2 layer, slowing down the orientational dynamics of OH vectors in S1 and S2 layers and less diffusivity of water in S1 and S2 layer, show the long-range kosmotropic effect of multivalent sulfate and thiosulfate oxyanions. Due to long-range effect, heterogeneous occupancy of water molecules is observed, and the water molecules are found to be in a patterned manner in the vicinity of anions with varied local density.


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Introduction The structural, dynamical and spectral signature of water molecules surrounding multiply charged anions are significant in chemistry, biology, and astronomy.1–6 The properties of water molecules in the vicinity of highly charged anions differ from those bulk water molecules due to the sensitivity of the local environment. When ions are added into pure water, the ions can affect the properties of surrounding water molecules.2,5,6 In fact, most of the properties of water molecules are primarily governed by the intermolecular three-dimensional hydrogen bonding network and the perturbing factors on it. The strength of anion-water hydrogen bond depends on the size of the particular anions and most importantly on the anion charge density and cooperativity.2,7,8 The dissolved ions in aqueous solutions change the macroscopic properties of water molecules close to their solvation shell, even beyond, and hence affect the structure and dynamics of water molecules.6 Several experimental methods such as ultrafast infrared spectroscopy,9 X-ray diffraction,2,10 neutron diffraction,11–13 NMR,2,14 Raman,15,16 and dielectric relaxation17,18 suggested structural changes of water regarding breaking and making of hydrogen bonds beyond the first solvation shell of the ions. The choice upon a combination of cation and anion also dramatically influences the hydration structure of ions7,17,19; for example, in the aqueous solutions of MgSO4 and Na2SO4, water molecules form rigid hydration layers around the anion than the other salts such as CsF, CsCl, CsI, LiCl, MgCl2, Mg(ClO4)2. The rigid hydration structure arises due to the cooperative effects, in which cations and anions fix the dipole vectors and direction of O–H vectors of water molecules, respectively.7,17 At lower salt concentrations, ion pairing also plays a vital role to form rigid hydration structure.20 The long-range effect by the ions on bulk water has been reported by the molecular dynamics simulations.21–24 Moreover, the extension of the hydration effect by the ions beyond the first solvation shell is one of the debated issues, which has been gaining much attention for a few years. ACS Paragon Plus Environment


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In aqueous solutions, the oxyanions in the Hofmeister series are categorized by either structure maker (kosmotropes) or structure breaker (chaotropes).25–28 In the present study, we consider aqueous solutions of doubly charged sulfur oxydianions, SO42- (sulfate) and S2O32-(thiosulfate). By the ability to folding, crystallization and stability of proteins, enzymatic activity, and molecular charge density, SO42- and S2O32- ions occupy extremely left positions in the Hofmeister series after CO32-.29,30 Therefore, these anions are known as the strong kosmotropes. Out of these anions, SO42-, the second highest abundant chemical component as Mg2SO4 in the sea water, plays a significant role in atmospheric aerosol,31 climate change,32 absorption phenomenon,33–36 mineralization and oil formation37–39 and surfactants as alkyl derivatives.40 Also, the hydrated cluster of this anion is believed to be a significant source of water in the MARS41–43 and EUROPA.43–45 On the other hand, thiosulfate is used in paper industry and photography to eliminate the chlorine and AgBr, respectively,46–48 and as fertilizer in agriculture as a source of sulfur.49 Due to the wide range of applications of sulfoxy anions, these two anions were studied extensively using both experimental and theoretical methods. Caminiti et al. investigated the SO42--H2O interactions in aqueous solutions of (NH4)2SO450 and In2(SO4)3

51,52

in the presence of sulphuric

acid, nickel and magnesium cations.53 Due to the presence of a double negative charge, this anion is highly unstable in the gas phase. Performing photoelectron spectroscopy, Wang and co-worker54 showed that minimum three water molecules were required to stabilize the sulfate di-anion through anion-water hydrogen bonding. When five water molecules were added to the cluster, then only waterwater hydrogen bond was possible. Cannon et al. first investigated the thermophysical and dynamical properties of water molecules using molecular mechanics simulations;55 they reported the first solvation shell coordination number of SO42- as 13.2. From the ab initio QMCF MD simulations study of aqueous sulfate solution, the coordination number of sulfate anion was found to be ~11.56 A Car-Parrinello Molecular Dynamics (CPMD) study of the small hydrated ACS Paragon Plus Environment

cluster

of

(SO4(H2O)n2-,

n=13)57,58

provided

the

coordination

number

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approximately 8 in the first solvation shell. A considerable amount of efforts have also been devoted to spectral and dynamical properties of water in SO42-(H2O)n clusters. Infrared photodissociation (IRPD) spectroscopy of gas phase sulfatewater clusters revealed the size-dependent appearance of dangling OH stretching frequency.59,60 It was found that, for SO42-(H2O)n, n > 43, a new band appeared at ~3710 cm-1 due to the free OH groups, and the peak intensity of this band grew with an increase in some water molecules. The IRPD spectra also identified dangling OH peaks in the second or third solvation shell of SO42- ion in nanodroplets containing ~250 water molecules. A theoretical investigation based on ab initio calculations could able to reproduce dangling OH peaks in a sulfatewater cluster with 14 and 17 numbers of water molecules.61 A low-temperature photoelectron spectroscopic study was performed for small SO42-(H2O)n (n=4-7) cluster to understand the structure and dynamics of these solvated systems.62 Bush et al.63 and Zhou et al.64 also performed IR spectroscopy experiments to understand the symmetric nature of small sulfate-water clusters. Theoretical calculations suggested that sulfate ion had a significant effect on the surrounding water structure, even beyond the second solvation shell.61 SO42- ion also has a substantial impact on rotational anisotropy of water molecules. Moreover, a study based on classical molecular dynamics simulations reported substantial slow down of rotational motion of water molecules near SO42- ion. On the other hand, S2O32- is believed to be less interacting with surrounding water molecules due to the presence of less electronegative element S in compare to oxygen. SO42- is more kosmotropic30 than S2O32- in Hofmeister series. The X-ray diffraction experiments were carried out for aqueous salts of thiosulfate to study the structural features and hydrogen bonding interactions of S2O32- with water molecules.65–67 Eleman et al.67 studied the hydrogen bonding interaction in S2O32.6H2O cluster with neutron diffraction study. They reported that Ow–Hw…O hydrogen bond distance was relatively shorter compared to Ow–Hw…S hydrogen bond distance. So, S…Hw hydrogen bond is relatively weaker compared O…Hw ACS Paragon Plus Environment


hydrogen bond in S2O32—(H2O)n clusters. Here, the atoms corresponding to water molecules are designated by a subscript ‘w’. Recently, Eklund et al.68 have concluded the similar observations with the help of QMCF MD simulations and Low-Angle X-ray Spectroscopy (LAXS) experiment; in aqueous thiosulfate solution oxygen atoms of S2O32- unit behaves as strong water structure maker while S atom acts as a weak water structure breaker. The hydration structures and dynamical properties of aqueous thiosulfate solution were studied recently by QMCF MD simulations.69 The special attention was given to the solvation shell structure of terminal S atom of S2O32-. These simulations revealed that 8.9 water molecules were required to complete the first solvation shell of thiosulfate,69 and 3.5 water molecules were present around terminal S atom. The ab initio study of S2O32(H2O)n (n=0-16) cluster highlighted70 the presence of 15 water molecules in the first solvation shell of thiosulfate. However, the ultrasonic velocity data of an aqueous solution of thiosulfate predicted the appearance of 13 water molecules in the first solvation shell of thiosulfate ion.71 Therefore, an ambiguity was observed in the determination of proper solvation shell and the coordinating water molecules. So, understanding the solvation behavior regarding structure, dynamics, patterned solvation shells and vibrational spectral features of solvation shell water molecules of sulfoxy divalent ions are essential to fill the gap in our understanding. In this work, we investigate relatively dilute aqueous solutions of SO42- and S2O32- anions through first principles molecular dynamics simulations to show the role of highly charged sulfoxy dianions on properties of water molecules present in the first solvation shell, and spatial extension of this effect on other water molecules. We have explored the possibility of layering of water molecules around these anions by calculating various structural, dynamical and vibrational spectral properties and correlated our calculated data with experimental and other theoretically obtained results wherever possible.


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Computational Methodology We performed first principles molecular dynamics simulations of aqueous solutions of SO42- and S2O32- anions with 100 water molecules; each aqueous system contained a single anion, and Na+ ions were added to neutralize the systems. The initial trajectories for FPMD simulations were obtained from wellequilibrated classical molecular dynamics simulations using OPLS72 and SPC/E73 models for ions and water, respectively using the experimental density of pure water. The FPMD simulations were performed with the CP2K software package.74,75 In CP2K, the electronic structure is calculated by using the QUICKSTEP76 method which uses the hybrid Gaussian and plane waves (GPW) schemes for calculating forces and energies. We have used Becke-Lee-Yang-Parr (BLYP)77,78 for the exchange-correlation function together with the van der Waals correction of the Grimme’s D3 method.79 The van der Waals corrections are crucial for reproducing the correct water density and dynamics.80–82 The basis set TZV2P was used for Gaussian wave functions. For the Na+ ion, we used DZVP basis set. The density cut-off was set to 600 Ry for the auxiliary plane waves, and the core electrons were treated by Goedecker-Teter-Hutter pseudopotentials.83 The periodic boundary conditions were employed in all XYZ directions. We performed the simulations at NpT ensemble at ambient conditions for 15 ps to obtain the correct box length corresponding to equilibrated density for the adopted electronic parameters. The temperature of each system was maintained by applying NoseHoover thermostat84 and the time step was set to 0.5 fs. The pressure was controlled by the thermostat suggested by Mundy and coworkers.85 We obtained 1.0 g cm-3 for both the systems. After getting the appropriate box length, we performed 50 ps of simulation within NVT ensemble. To calculate the structural and dynamical and spectral properties, we Environment performed another 50 ps simulation at ACS Paragon Plus NVE ensemble. The average temperatures of the sulfate and thiosulfate systems


were 303 and 301 K, respectively. The trajectories of NVE simulations were used to calculate various properties reported here. The frequencies of the OH stretching modes were calculated from the time-dependent trajectories by using the wavelet analysis of the time series method.86,87 The details of the wavelet analysis calculation for OH stretching frequencies from ab initio molecular dynamics are available from earlier published articles.86–90

Results and Discussion A. Structure, hydrogen bond dynamics and vibrational spectral diffusion of solvation shell water molecules In this study, the primary goal is to explore the ability of sulfate and thiosulfate anions to facilitate the patterning of surrounding water molecules through the hydrogen bond network. Moreover, some of the hydrogen atoms of water molecules in these patterned layers do not participate in the hydrogen bond network. These hydrogen atoms of the hydroxyl groups prefer to stay as free or dangling. Appropriate structure of the first solvation shell and no of water molecules inside it are few of the things, which have been much debated in earlier studies. Therefore, before going to discuss the water patterns around these anions, we present here the structure, dynamics and spectral feature of water molecules inside the first solvation shell. Solvation shell structure: The structure of solvation shells of SO42- and S2O32is studied by calculating radial distribution functions (RDFs). The possible RDF pairs of SO42--H2O and S2O32--H2O are shown in Figure 1 (a) and (b). The maxima of first peaks of O–Ow, and O–Hw RDFs of sulfate-water appear at 2.78 and 1.78 Å, respectively. The positions of first maxima for O–Ow, and O–Hw RDFs of thiosulfate-water appear at 2.88 and 1.88 Å, respectively. The maxima of first ACS Paragon Plus Environment

peaks of O–Hw RDFs at 1.78 and 1.88 Å are due to the strong anion-water

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hydrogen bonding. The values of depth of the minima of the O–Hw RDFs pair of sulfate-water and thiosulfate-water indicate that sulfate-water hydrogen bond is stronger than thiosulfate-water. The hydrogen bond number from the number integral (NI) value for the O–Hw RDF pair for sulfate-water is found to be 9.6; each oxygen atom of SO42- unit can make approximately 2.4 hydrogen bonds with surrounding water molecules. The hydrogen bond number of thiosulfate-water is found to be 6.75. Each oxygen atom of S2O32- moiety can participate in 2.25 hydrogen bonds with water molecules. This number is less compared to hydrogen bond number of sulfate-water system. The O–Ow RDFs of both sulfate-water and thiosulfate-water show the extended solvation shell up to ~4.5 Å. The positions of maxima for second peaks of the O–Ow RDFs for sulfate and thiosulfate are found to be at 4.98 and 5.10 Å, respectively. The shifting of peak positions corresponding to O–Ow, and O–Hw RDFs of sulfate-water towards lower distance implies more kosmotropic (structure maker) effect on water than thiosulfate. The first peak position of S–Ow RDF of sulfate-water is situated at 3.77 followed by a minimum at 4.50 Å. The corresponding NI value up to this minimum is 10.89. Our calculated coordination number of S–Ow solvation shell of SO42- is overestimated as compared to that of X-ray and infrared (IR) spectroscopy studies; the coordination numbers are found to be between 6.4 to 8.1 for X-ray studies50–53 and this value is 8.0 for IR study.91 However, according to the LAXS study, the coordination number for sulfate-water is 12.56 The molecular dynamics simulations studies predicted the coordination number values of around 12.892 and 13.25.55 Our data is relatively close to LAXS and MD simulations data. The Car-Parrinello molecular dynamics simulation predicted the coordination number value of 8 for the small sulfate-water cluster.58 Furthermore, our calculated coordination number is excellent agreement with coordination number 11.10 obtained from QMCF MD simulations.56 The maximum of the first peak of S–Ow RDF of thiosulfate-water is found to be at 3.90 followed by a minimum at 4.65 Å. The solvation shell of thiosulfate contains approximately 12 water molecules. Rohman et al. estimated ACS Paragon Plus Environment

the

primary

coordination

number

value

of

13

for

thiosulfate

anion


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experimentally.71 Trinapakul et al.69 also predicted the same coordination number from QMCF MD simulations. Thus, our calculated coordination number is well agreement with earlier reported values. We also calculated terminal S–Ow and S– Hw RDFs of S2O32--H2O system and the results are shown in Figure 1(c). The terminal S–Hw and S–Ow RDFs show the maxima at 2.33 and 3.33 Å followed by minima at 2.80 and 3.78 Å, respectively. We observe a weak hydrogen bonding interaction between the terminal sulfur atom and water hydrogen as compared to oxygen atoms of the anions. The NI value of terminal S–Hw RDF up to the first minimum (3.08) indicates the weak hydrogen bonding ability of sulfur atom with water molecules. Therefore, from the peak positions of O–Hw, and S–Hw RDFs of thiosulfate-water, it is observed that oxygen atoms behave as structure maker while sulfur atom acts as a weak structure breaker for surrounding water molecules. Hydrogen bond and residence dynamics: After analyzing the structure of anion-water hydrogen bonds, it is interesting to know the dynamics of those hydrogen bonds concerning time-dependent forming and breaking phenomena. The hydrogen bond dynamics was analyzed by following the population correlation function approach.93–102 Here, we consider three kinds of hydrogen-bonding environments: Ow…Hw, O…Hw and S…Hw hydrogen bonded pairs. We define continuous hydrogen bond correlation function that describes the probability that initially hydrogen-bonded pair remains bonded all times up to t for these various kinds of hydrogen bonds. The distance criterion for these hydrogen bonds has been adapted from the first minimum of the corresponding atom-atom pair correlation function. We define the population correlation function variable ℎ(𝑡) that is unity, when a particular type of atom-atom pair is hydrogen bonded at time t, and zero otherwise. The other variable 𝐻 𝑡 = 1, if a hydrogen bond continuously exists from time=0 to t, or otherwise zero. The time dependent continuous hydrogen bond auto correlation function 𝑆!" (𝑡) is defined as ACS Paragon Plus Environment

𝑆!" 𝑡 =

! ! !(!) !(!)!

,

(1)

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where ⋯ denotes an average overall hydrogen bond for a particular type of pair. Assuming that the correlation function 𝑆!" (𝑡) decays bi-exponentially, the long time scale correlates to the associated integrated relaxation time, 𝜏!" . The relaxation time, 𝜏!" , gives the average lifetime of a hydrogen bond. To see the effect of sulfate and thiosulfate anion on hydrogen bond lifetime of water, we calculated hydrogen bond auto correlation function over all OH modes present in the systems. In the second attempt, we calculated water-water hydrogen bond auto correlation function outside the solvation shell of sulfate and thiosulfate anions. The calculated water-water hydrogen bond autocorrelation functions are shown in Figure SI 1 for both sulfate-water and thiosulfate-water systems. The average lifetimes of all OH modes of sulfate-water and thiosulfate-water are found to be 1.21 and 1.29 ps, respectively. These values are more than that of pure water, but average lifetimes of hydrogen bonded OH modes outside the solvation shells of both the ions are in very good agreement with the bulk water:103 1.16 (sulfatewater) and 1.24 ps (thiosulfate-water). The hydrogen bond lifetime of all OH modes is higher compared to the water molecules outside the solvation shell of sulfate and thiosulfate anions. The lower value of hydrogen bond lifetime outside the solvation shell indicates the strong structuring effect of sulfate and thiosulfate anions. This effect is more prominent in the sulfate-water system compared to the thiosulfate-water system.

We also calculated the intermolecular O…Hw and

terminal S…Hw hydrogen bond autocorrelation functions. The O…Hw lifetime of sulfate-water (2.37 ps) is more than thiosulfate-water (2.27 ps). The O…Hw hydrogen bond correlation functions are shown in Figure 2(a) for sulfate and thiosulfate anions. The S…Hw hydrogen bond autocorrelation function is also shown in the same figure. The S…Hw hydrogen bond lifetime is found to be 0.81 ps. Therefore, from the analysis of hydrogen bond auto correlation functions, we observe that oxygen atoms of sulfate and thiosulfate anions behave as structure makers while the terminal sulfur atom of thiosulfate behaves as weak structure breaker. An IR study showed that the SO42- anion is weak “structure maker” which ACS Paragon Plus Environment

mean sulfate-water hydrogen bonds should be slightly stronger than the water-


water hydrogen bonds.104,105 Moreover, we observe from our calculation that O…Hw hydrogen bonds of sulfate-water and thiosulfate-water are much stronger than Ow…Hw. Therefore, our hydrogen bonding analysis of sulfate-water and thiosulfate-water solutions completely agree qualitatively with the previous experimental reports. The residence dynamics analysis was performed to calculate the escape time scale of a water molecule from the first solvation shell of sulfate and thiosulfate anions. The time correlation of residence dynamics of water molecules is defined as follows 𝐶 𝑡 = The time average ⋯

! ! !(!) !(!)!

(2)

is performed over all water molecules within the first

solvation shell of sulfate and thiosulfate anions. We define population variable 𝑏(𝑡) which is unity when water molecules remain inside the first solvation shell at time t and zero otherwise. The variable 𝐵 𝑡 = 1, if a water molecule remains continuously in the first solvation shell from time t =0 to t, or it is zero otherwise. Thus 𝐶(𝑡) represents the conditional probability that water molecule which was initially in the first solvation shell remains in the first solvation shell at time t without ever leaving the first solvation shell. The obtained long time scale from fitting gives the associated relaxation time, 𝜏! , is known as escape dynamics or residence dynamics of water molecules. The results of residence dynamics for sulfate-water and thiosulfate-water molecules are shown in Figure SI 2. The residence time of water molecules inside the first solvation of sulfate ion is 16.95 ps while in case of the thiosulfate-water system, this value is found to be 14.03 ps. From the molecular mechanics simulations, the residence dynamics of water molecules was reported to be 23 ps for thiosulfate solvation shell.55 The higher time scale for escape dynamics of sulfate anion also contributes towards greater structure making effect on the water molecules than thiosulfate. Vibrational spectral diffusion: The vibrational spectral diffusion through timeACS Paragon Plus Environment

dependent infrared spectroscopy plays a crucial role in exploring the time scales of

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the hydrogen bond fluctuations in liquids. The correlation between the stretching frequency of a hydroxyl group and the distance of the associated hydrogen bond facilitates the interpretation of the spectral results of experiments. With the progress of time, the process of continuous hydrogen bond making and breaking phenomenon takes place. Moreover, a fluctuation in the strength of the hydrogen bond leads to a change in the stretching frequency of the corresponding covalent bond. As a result, the dynamics of frequency fluctuations that captures the timedependent variations of the hydrogen bonds in the liquid and escape dynamics related to residence dynamics in case of solvation shell modes change. These frequency fluctuations can be studied from the time series analysis of molecular dynamics trajectories by constructing a suitable correlation function. In this study, the vibrational spectral diffusion of all and water molecules inside the ion solvation shell was studied by frequency-frequency time correlation function. The frequencytime correlation function is defined as 𝐶! 𝑡 =

!"(!)!"(!) !"(!)!

,

(3)

where 𝛿𝜔(𝑡) is fluctuation from the average frequency at time t. In the aqueous solvation shell of sulfate and thiosulfate, the water molecules make strong hydrogen bonds with these anions, which are evident from hydrogen bond autocorrelation function. The calculated frequency-frequency time correlation functions of water molecules are shown in Figure 2 (b) and (c) for both the systems. The calculated correlation functions were fitted with the tri exponential function as follows 𝑦 = 𝑎! exp

!! !!

+ 𝑎! 𝑒𝑥𝑝

!! !!

+ 1 − 𝑎! − 𝑎! 𝑒𝑥𝑝

!! !!

(4)

The relaxation time and weights are included in Table 1 for solvation shell and bulk OH modes. Three timescales are observed for the solvation shell OH modes. The longer time scales obtained for sulfate-water (19.01 ps) and thiosulfate-water (18.91 ps) systems representACS theParagon escape dynamics of water molecules from first Plus Environment solvation shell. These time scales are along with the timescales obtained from


residence dynamics calculations, which captures the escape dynamics of water molecules from the solvation shell of the anion. The shorter time scales of 1.81 (sulfate-water) and 1.63 ps (thiosulfate-water) indicate the intermolecular O…Hw hydrogen bonding and the very short time scales are for underdamped intact ionwater interaction. When we consider all OH modes frequency correlation functions, the longer time scales corresponding to escape dynamics of water from the solvation shell are missing; the obtained longer timescales 1.31, and 1.29 ps are mainly due to the intermolecular water-water hydrogen bonding. The shorter time scales in the range between 0.06 to 0.26 ps are due to intact water-water interactions. The hydrogen binding time scales obtained from these correlation functions correlate to the hydrogen bond lifetime calculated from the continuous hydrogen bond correlation time.

B. Spatially patterning of water molecules around anions It is believed that ions can have a tremendous structuring effect on water molecules of the first hydration layer. However, ion-induced long-range structural effects beyond this layer can be seen for particular anions rather than all ions in general. Till now, we focus on results based on solvation shell and bulk water molecules. As the anions considered here are doubly charged, they are known to facilitate the patterning of water molecules beyond the first solvation shell due to the strong long-range structural effect. Therefore, our next aim is to study the long-range effects of the sulfate and thiosulfate anions on neighboring water molecules. The patterned water molecules promote the formation of a spatially extended network of water molecules varied with more than one local density. Due to the difference in densities, the water molecules arrange themselves in a patterned manner around the dianions, which essentially hints towards multiple local density states of water molecules106–108 and heterogenous occupancy of water molecules around ions. Williams and co-workers59 reported the long-range patterning effects of SO42- by performing Infrared photodissociation (IRPD) ACS Paragon Plus Environment

spectroscopy of gas-phase SO42-(H2O)n clusters with up to 80 water molecules at

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low temperature, and found that the free-OH band of spectra, more structurally informative than the bonded-OH modes, was sensitive to the change in patterning of water molecules around the anion. A similar study in the condensed phase is not available primarily due to difficulty in experimental setup and analysis of obtained spectral data. The three-dimensional spatial structure around the anions can be obtained from the simulation trajectories obtained from the present FPMD simulations. First, to analyze the three-dimensional arrangement of water molecules around anions, we calculated the spatial distribution functions of water molecules around sulfate and thiosulfate anions. The calculated results of the spatial map containing oxygen atoms of water molecules around these two anions are shown in Figure SI 3. The patterning of water molecules into layers around the anions is evident from the figure. The first layer corresponds to distance within 4.50 Å of S–Ow RDF, and second layer belongs to distance within the range of 4.50 to 6.50 Å. The first layer of oxygen cloud is highly dense around these two anions compare to the second layer. Keeping this type of patterning behavior of water molecules in mind, we categorized the OH groups geometrically into different layers based on the O–Ow radial distribution functions of SO42--H2O and S2O32--H2O systems for further detailed analysis. We separated the O–H groups in three ensembles namely S1, S2, and S3. The S1 ensemble contains the O–H groups, which are present in the first solvation shell of O–Ow RDFs(less than 4.1 Å). In this ensemble, approximately nine intermolecular hydrogen-bonded O–H chromophores are present for the sulfate-water system. For the thiosulfate-water system, this number is 6.9 which are directly hydrogen bonded to oxygen atoms of S2O32- and ~3 OH chromophores which are weakly hydrogen bonded to terminal S atom of S2O32- anion. The S2 ensemble contains those O–H groups which are exclusively present in the second solvation shell that extends from 4.10 to 6.10 (minimum of the second peak of O– Ow RDF) Å. The ensemble, S3, contains rest of the O–H groups present in both the systems which are beyond the distance of 6.10 Å. A representative snapshot from ACS Paragon Plus Environment


the simulation having S1, S2 and S3 layers are shown in Figure 3 for sulfate-water and thiosulfate-water system with different representations of water molecules. Vibrational spectral properties of patterned water molecules: The frequencies of stretching vibrations of hydroxyl groups of water molecules are particularly sensitive to hydrogen bonding environment. The vibrational density of state was calculated to obtain the peak position of vibrational stretching frequency of dangling OH modes which can be related to observed experimentally in SO42(H2O)n=43 gas phase cluster.59 We calculated the vibrational density of states(VDOS) from Fourier transform of velocity autocorrelation function in different regions (S1, S2, and S3 ensembles) for both the systems. The VDOS was calculated using the following equation 𝑉𝐷𝑂𝑆 𝜔 =

! !

𝑣!" (𝑡) ∙ 𝑣!" (0) 𝑒 !!"# 𝑑𝑡 … … … (5),

where 𝑣!" (𝑡) represents the velocity of H atoms present in the respective regions for both sulfate-water and thiosulfate-water systems. The calculated results of the VDOS are shown in Figure 4. The distribution of S1 region is narrow as compared to the other two regions due to polarizing effects of anions. In the S1 ensemble region, the shoulder at ~3578 cm-1 is due to free OH groups which are originated through the hydrogen bonding interaction between anion-water in different topological manner. The peak positions, which are less than the average value of 3500 cm-1, are due to water-water and anion-water hydrogen bonds in the first solvation shell. On progressing from S1 to S3 layer, the bump of the shoulder in the range of 3550-3700 cm-1 is missing, and most of the hydroxyl groups of water molecules are involved in hydrogen bonding with neighboring water molecules like bulk water configuration. For both the systems, the average frequencies for the last layer are very close. The dangling OH peak intensity is slightly more pronounced for the thiosulfate-water system due to weak interaction between water and terminal S atom. The features of dangling OH frequency peaks in vibrational density of state plot for both the correlate to our earlier discussed lifetimes ACS systems Paragon Plus Environment of those modes.

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We also calculated the distribution and average stretching frequencies O–H chromophores in S1, S2 and S3 ensembles from FPMD trajectories by following earlier discussed wavelet method. The frequency distribution plots are shown in Figure 5. The average frequency of S1 and S2 ensemble for sulfate-water are 3415 and 3448 cm-1, respectively. The average frequency of S1 ensemble is well satisfied with vibrational stretching frequency of hydrogen-bonded OH of the sulfate-water system, which is obtained from the IRPD spectrum of sulfate-water clusters.59 The average frequency of the bulk (S3) O–H modes is found to be 3458 cm-1. Therefore, OH modes in the S1 and S2 ensembles show a redshift of 43 and 10 cm-1, respectively compared to the bulk. The redshift in S1 ensemble frequency is due to the strong intermolecular hydrogen bonding. From the combined Raman spectroscopy and multivariate curve resolution study of the aqueous solutions of various ions in the Hofmeister series, the average OH frequency of water in sulfate-water solution was found to be 3441 cm-1.109 Our calculated result of bulk (S3) OH frequency is in good agreement with this experimental finding. For thiosulfate-water, the O–H stretching frequency in the S1 region also shows red shifting by 31 cm-1 compared to S3 region. The corresponding average frequency of S1 and S3 region are 3424 and 3455 cm-1, respectively. In the S2 region, the average O–H stretching frequency, higher than that of the S3 region, is 3464 cm-1, which is blue shifted by 9 cm-1 compared to the bulk. Thus, the effect of S2O32- ion on the second solvation is minimal compared to SO42- ion. Dynamics of dangling bonds: We performed free or dangling OH bond autocorrelation analysis to determine the persistence time of free OH groups of water molecules inside and outside the solvation shell of sulfate and thiosulfate anions. The time correlation function of dangling OH correlation is defined as follows 𝑆!" 𝑡 =

! ! !(!) !(!)!

(6)



The 𝑆!" (𝑡) gives the probability that initially non-hydrogen bonded OH group remains dangling at all times up to t. In the above equation 𝑆!" 𝑡 = 1 when a particular OH group is identified as free while 𝑆!" 𝑡 = 0 when a particular OH group is identified as hydrogen bonded. Thus, the time average ⋯ was performed over several free OH groups. We analyzed three types of dangling OH groups: The first one belongs to average over bulk OH, the second one corresponds to the group inside the S–Ow solvation shell of sulfate (within 4.50 Å of S–Ow RDF) and thiosulfate (within 4.65 Å of S–Ow RDF) ions and the last category is the groups within the range of 6.50 Å from central S atom. The results of 𝑆!" (𝑡) are shown in Figure 6. The persistence time of free OH group inside the solvation shell is more compared to the bulk values. For the sulfate-water system, the solvation shell free OH lifetime is 0.27 ps (0.26 ps for thiosulfate), and outside the solvation shell or bulk, this value is 0.10 ps (0.08 ps for thiosulfate). Further increasing this S–Ow distance up to 6.50 Å, the dangling lifetime slightly decreases. The long time scale inside the solvation shell indicates survival of long-lived free OH groups, which arise due to strong hydrogen bond formation between SO42- and water molecules in various topological manners. The strength of the ion-water hydrogen bonds prevents free OH groups to change their dangling states. This observation is in well agreement with the results of experimental findings of dangling OH IRPD spectra59 of SO42-(H2O)n for n > 43 which revealed the existence of these free OH groups mostly in the outer shell of the sulfate anion. Moreover, an ab initio study also reported the existence of semi-dangling OH groups in SO42-(H2O)n=14,17 clusters.61 Translational dynamics: We analyze the diffusive motion of water molecules in different solvation layers (S1, S2, and S3) to understand the long-range effect of these two anions through calculation of mean squared displacement (MSD) (Figure 7). The MSD can lead one to obtain the corresponding diffusion coefficient, however, the obtained trajectories from our FPMD simulations are not long Paragon PlusWe Environment enough to estimate diffusion ACS coefficients. compare the slopes of MSD of water

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molecules in three layers, which mainly provide the effect of ions on the translational dynamics of the solvent molecules. Overall, water molecules around S2O3-2 diffuse relatively faster than another anion irrespective of layers. Due to the presence of ions, the water molecules in S2 layer experience the resistive retarding force as compared to the next layer, S2, a factor more than two. However, the water molecules in the S3 layer do not experience that much resisting force from the ions; in fact, the translational dynamics is close to that of bulk water molecules. So, The corresponding diffusion coefficients of the S3 layer water molecules will be much faster compared to the S1 and S2 layers. Thus, both sulfate and thiosulfate anions have strong structure maker property, and the former has more kosmotropic effect on water molecules over later anion. Moreover, the concept of water patterns around these anions may be feasible as far as the translational motions are concerned. We have to analyze more properties of these layers to establish the observed patterning of water molecules. To fill the gap of our understanding, we examine kosmotropic nature as well as orientational profiles of the patterned water molecules in the next section. Long-range effects and Kosmotropic nature of ions: The ranking of kosmotropic nature of ions is primarily derived based on their influence on enzymatic activity and physical behavior in aqueous environments. On the dynamical perspectives, kosmotropic ions are known to strengthen intermolecular hydrogen bonding in bulk water, and this effect is more pronounced in case of anion than the cation.30 However, femtosecond pump-probe spectroscopic studies of an aqueous solution of ions by Bakker and coworkers110–113 revealed the minimal effect of ions on hydrogen bonding network. Saykally et al.114 also studied that aqueous solution of salts with Raman spectroscopy. From the spectroscopic point of view, they also suggested no effect of ions on OH vibrations of water molecules in bulk structure. In the present simulation study, we address these kosmotropic and long-range effects of SO42- and S2O32- ions based on several parameters. In Figure 8, we show the closest ACS intermolecular Ow–Ow distance distribution of S1, S2, Paragon Plus Environment


and S3 layers. The distribution of oxygen-oxygen distance in S1 and S2 layers is different from the S3 layer. The overall oxygen-oxygen distribution in the S1 and S2 layers is slightly towards lower distance than the bulk water layer (S3) although the maxima of peaks appear at similar positions. The average values of distances are shown in Table 2. The average values for the S1 layer of SO42- and S2O32- are found to be 3.18 and 3.20 Å. We also analyze the orientational dynamic of water molecules in three mentioned layers to explore the effects of anions. In aqueous ionic solutions, water molecules possess multiple time scales anisotropically and show nonuniformity in structure and dynamics. The experimental technique, such as dielectric relaxation studies identified slower retardation of anisotropy decay of specific part of water molecules while other parts of water molecules behaved as bulk like water.18,20,115– 117

Optical Kerr-effect spectroscopy,118 X-ray diffraction,13,119 X-ray absorption

spectroscopy,120 Raman spectroscopy,114 dielectric relaxation studies and timeresolved infrared (fs-IR) vibrational spectroscopy110,121,122 revealed that the effect of ion in aqueous solution limited only up to the first solvation shell. The simulations based results also reported that in anionic hydration shell only a fraction of the water molecules is unaffected by the ions.22,23 Tielrooij et al.8,17 performed the dielectric relaxation, and fs-IR spectroscopic measurements of an aqueous solution of SO42- unit having different counterions such as Mg2+, Cs+, Na+ and reported that significant retardation of anisotropic decay of water molecules inside the anionic hydration shell. They also explained that this retardation was caused by the strong hydration of sulfate ion governed by the hydrogen bonding formation. The multivalent ions produced higher local electric field than the monovalent anions, which in turn strengthen the hydrogen bond, and affect the reorientation dynamics of water molecules. The counter ions also played a vital role in forming a rigid hydration structure around the anions via cooperative effects. The authors also suggested that there is a slight discrepancy in measurement techniques between dielectric relaxation and fs-IR methods, as Environment these two methods produced different ACS Paragon Plus

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results. Here, we investigate layer-wise effects of sulfate and thiosulfate ions on the reorientation dynamics of water molecules by constructing the orientational time correlation function as below !

𝐶! 𝑡 = ! 𝑃!

!!" ! .!!" (!) !!" (!)∥!!" (!)

(7)

In the above equation, P2 represents the second order Legendre polynomial in the form of 𝑃! 𝑥 = 1 2 3𝑥 ! − 1 . 𝑟!" (𝑡) and 𝑟!" (0) represent the unit vector of OH bonds at time = t and 0, respectively. Therefore, equation 7 represents the second order orientational time correlation function of water OH bonds. The physical significance of calculating rotational time correlation is that it can be directly related to the anistropic decay of water OH from the dielectric relaxation and fs-IR experiments.123 The calculated results of the rotational time correlation function of different layers of OH unit vectors of water molecules for sulfate-water and thiosulfate-water systems are shown in Figure 9. The presence of multiple time constants can be observed from the decay of orientational correlation functions. The significant orientation retardation is observed for S1 layer water molecules for both the systems followed by the molecules in S2 and S3 layers; the retardation is not so significant for S2 compared to S3. Our simulated results are very much in line with experimental results performed by the Tielrooji and co-workers7 with the fact that rigid hydration structure of sulfate and thiosulfate dianions govern the relatively strong hydrogen bond formation than the bulk. Here, we construct different layers based on the O–Ow RDFs, and calculated hydrogen bond autocorrelation suggest stronger O…Hw hydrogen bonds than the Ow…Hw pairs. Oxygen atoms in SO42- anion form more than 9 hydrogen bonds while oxygens of S2O32- make ~7 hydrogen bonds. Therefore, our results directly support the rigid S1 hydration shell with accordance to the experimental fact of the rigid hydration shell structure of SO42-. The time constants associated with these decays are shown in Table 2. We assume that these correlation function decays bi-exponentially, and hence we fit the decays with the bi-exponential function ACSfollowing Paragon Plus Environment


𝐶! 𝑡 = 𝑎! 𝑒𝑥𝑝

!! !!

+ 1 − 𝑎! 𝑒𝑥𝑝

!! !!

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(8)

The short time scale, 𝜏! , represents the fast inertial relaxation involving librational motion of water molecules having short-time contribution. The relaxation time, 𝜏! , of the long-time decay of 𝐶! 𝑡

represents the second order rotational time

constant. The rotational time constant for water molecules in the S1 layer of S2O32shows a lower value than that of SO42-, which is expected due to short of one oxygen atom and presence of weak structure breaker terminal S atom. A moderate retardation is found for water molecules in the S2 layer for both the systems. The water molecules belonging to the S1 layer are strongly affected by these two Hofmeister series anions and the orientational dynamics of water molecules are well affected beyond the first solvation shell. The obtained results hold good for an agreement of kosmotropicity and long range effects by these two sulfoxy dianions with the fact that we observe the slow down of the translational and rotational dynamics of water molecules inside S1 and S2 layers compared to the bulk. Here, we observe a slower diffusivity of S1 and S2 layer water molecules. The red shifting of ~43 and ~10 cm-1 of average OH frequency of S1 and S2 layers, respectively, of sulfate anion compared to the S3 layer. However, for thiosulfate anion, we observe ~31 cm-1 red shifting of S1 OH groups and ~9 cm-1 blue shifting of S2 OH groups. Therefore, the overall strength of hydrogen bonds made by water molecules in the S2 layer can be thought to be stronger than the bulk water. We also find the retardation of orientational dynamics of water molecules in S1 and S2 layer, which are mainly caused by strong hydrogen bond formation. Thus, the shorter oxygenoxygen distance distribution, stronger intermolecular ion-water, and water-water hydrogen bonds, slower water diffusivity in S1 and S2 layers, red shifting of OH vibrational stretching frequencies and significant amount of orientational retardation of OH vectors in S1 and S2 layers make the SO42- and S2O32- molecules ideal kosmotropes having long range effects. ACS Paragon Plus Environment

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Conclusions The ab initio molecular dynamics simulations were performed for sulfate-water and thiosulfate-water systems to study the effect of anion on neighboring water molecules in the first solvation shell and beyond. We observed the long-range effects of the sulfate and thiosulfate anions on neighboring water molecules. The extended solvation shell structure was found for both sulfate and thiosulfate anions due to patterned water molecules, which promote the formation of this extended network. Within this network water molecules are found to have more than one local density. Due to the difference in densities, the water molecules arrange themselves in a patterned manner around the dianions, which essentially hints towards multiple local density states of water molecules and heterogenous occupancy of water molecules around ions. The O…Hw hydrogen bond lifetimes of sulfate-water and thiosulfate-water pairs are found to be almost two folds greater than Ow…Hw, which indicates the strong structure maker property of these two anions. The lower value of S…Hw hydrogen bond lifetime compared to Ow…Hw implies the weak structure breaker behavior of the terminal sulfur atom of thiosulfate. The persistence time of dangling O-H groups inside the solvation shell is more compare to bulk. The long-range effect of sulfate and thiosulfate anions on water molecules were further studied by categorizing O–H groups in different ensembles based on their distance form anion. The O–H groups in the S1 ensemble show the red shifting of 43 and 31 cm-1 compare to that of S3 due to O…Hw hydrogen bonding in sulfate-water and thiosulfate-water solutions. The O–H groups in the S2 layer of sulfate-water shows the red shifting of 10 cm-1 while similar O–H groups of thiosulfate-water shows the blue shifting of 9 cm-1 compared to S3 layer. The diffusion of the S1 and S2 water molecules are also found to be very low compared to the S3. The position corresponding to dangling O–H peak is found to be around at 3578 cm-1 from VDOS calculation, which is slightly underestimated compared to the experimental results. The strong ACS Paragon Plus Environment

reorientational retardation is observed in S1 OH groups while moderate


retardation is found for S2 OH groups. Overall, the sulfate and thiosulfate anions have strong and long-range kosmotropic effects on the water molecules; moreover, the earlier one has a stronger structure making ability than the later.


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AUTHOR INFORMATION Corresponding Author: *E-mail: [email protected] ; Tel: +91 40 2301 7051; Fax: +91 40 23016032 ‡

Present address: Charles University, Faculty of Mathematics and Physics, Ke Karlovu 3, 121 16 Prague 2, Czech Republic

Notes The authors declare no competing financial interest. ACKNOWLEDGEMENTS The authors acknowledge financial support from Department of Science and Technology (DST), India (EMR/2016/004965) for this work.



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Table 1. Spectral diffusion data for solvation shell O–H modes and all O–H modes of sulfatewater and thiosulfate-water systems. The relaxation times (τ) are expressed in ps.

Systems

Region

𝜏!

𝜏!

𝜏!

𝑎!

𝑎!

SO42- -

Solv

0.10

1.81

19.01

0.76

0.10

Solv

0.07

1.63

18.91

0.63

0.17

All

0.06

0.26

1.29

0.65

0.20

All

0.07

0.24

1.31

0.62

0.26

H2O S2O32- H2O SO42- H2O S2O32- H2O

Table 2. Rotational time constants (𝜏 in ps) and average oxygen-oxygen distance (Ro-o in Å) of S1, S2 and S3 ensemble water molecules of sulfate-water and thiosulfate-water solutions

Systems

Quantity

S1

S2

S3

SO42- -H2O

𝜏

19.18

2.18

1.67

S2O32- -H2O

𝜏

14.52

3.02

1.77

SO42- -H2O

Ro-o

3.18

3.25

3.26

S2O32- -H2O

Ro-o

3.20

3.23

3.24


33


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Figure 1. Panels (a) and (b): Radial distribution functions of different pairs of sulfate-water and thiosulfate-water systems. O(S) and O(T) represent the oxygen atoms of SO42- and S2O32- units. The S(S) and S(T) denote the S atoms of SO42- and S2O32- unit. Panel (c): The radial distribution functions of terminal S–Ow and S–Hw pairs for S2O32- -H2O. The solid lines represent the radial distribution functions while the dashed lines represent the corresponding number integrals.


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Figure 2. (a) The continuous hydrogen bond autocorrelation function between sulfate-water and thiosulfate-water. The black solid line represents between oxygen atoms of sulfate and hydrogens of water molecules, the red dashed line represents oxygen atoms of thiosulfate and water hydrogens, and green dotted-dashed represents terminal S atom of thiosulfate and water hydrogens, respectively. (b) and (c): The decay of the time correlation function of OH fluctuating frequencies of water molecules in the bulk and solvation shell regions. The grey dashed lines represent the fits by a triexponential function.


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Figure 3. Snapshot from the NVE simulation represents different layers of water molecules based on the O–Ow RDFs. Panel (a) for sulfate-water and panel (b) represents thiosulfate-water systems. Sulfate and thiosulfate are shown in VDW model. Layer S1 water molecules are shown in CPK model. Layer S2 water molecules are shown in licorice orange color, and rest of the water molecules (S3) are shown in licorice green color.


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Figure 4. The power spectrum of OH bonds of S1, S2, and S3 ensembles. The left panel represents the sulfate-water system, and the right panel depicts the thiosulfate-water systems.


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Figure 5. The average frequency distribution of O–H bonds which are present in the S1 (red dashed line), S2 (blue dotted-dashed line) and S3 (solid black) ensembles. The upper panel (a) represents the O–H frequency distribution in the sulfate-water system and the lower panel (b) represents the O–H frequency distribution in the thiosulfate-water system.


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Figure 6. The continuous relaxation dangling correlation function of OH bonds in sulfate-water (upper panel) and thiosulfate-water (lower panel). Black color represents the dangling OH for bulk water; red represents dangling OH groups within the S-Ow distance of 4.50 Å and blue represents dangling OH groups within the S-Ow distance of 6.5 Å.


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Figure 7. The time dependence of the mean-square displacement of S1, S2 and S3 regions of water molecules. The upper panel (a) represents the sulfate-water system, and the lower panel (b) represents the thiosulfate-water system.


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Figure 8. The nearest oxygen-oxygen distance distribution of water molecules inside S1 (red dashed), S2 (blue dotted-dashed) and S3 (black) ensembles. Panel (a) is for sulfate-water and panel (b) is for thiosulfate-water systems.


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Figure 9. Second order orientational dynamics of OH bonds of water present in S1 (red diamond), S2 (blue triangle) and S3 (black star) ensembles, respectively. Panel (a) and (b) represent sulfate-water and thiosulfate-water systems., respectively.


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TOC Graphics


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Heterogeneous Occupancy and Vibrational Dynamics of Spatially

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