^{1}, A. Semparithi

^{1}and Amalendu Chandra

^{1,a)}

### Abstract

A theoretical study of vibrational spectraldiffusion and hydrogen bonddynamics in aqueous ionic solutions is presented from first principles without employing any empirical potential models. The present calculations are based on *ab initio*molecular dynamics for trajectory generation and wavelet analysis of the simulated trajectories for time dependent frequency calculations. Results are obtained for two different deuterated aqueous solutions: the first one is a relatively dilute solution of a single ion and the second one is a concentrated solution of NaCl dissolved in liquid. It is found that the frequencies of OD bonds in the anion hydration shell, i.e., those which are hydrogen bonded to the chloride ion, have a higher stretch frequency than those in the bulk water. Also, on average, the frequencies of hydration shell OD modes are found to increase with increase in the anion-water hydrogen bond distance. On the dynamical side, when the vibrational spectraldiffusion is calculated exclusively for the hydration shell water molecules in the first solution, the dynamics reveals three time scales: a short-time relaxation corresponding to the dynamics of intact ion-water hydrogen bonds, a slower relaxation corresponding to the lifetimes of chloride ion-water hydrogen bonds, and another longer-time constant corresponding to the escape dynamics of water from the anion hydration shell. Existence of such three time scales for hydration shell water molecules was also reported earlier for water containing a single iodide ion using classical molecular dynamics [B. Nigro *et al.*, J. Phys. Chem. A110, 11237 (2006)]. Hence, the present study confirms the basic results of this earlier work using a different methodology. However, when the vibrational spectraldiffusion is calculated over all the OD modes, only two time scales of and are found without the slowest component of . This is likely because of the very small weight that the hydration shell water molecules carry to the overall spectraldiffusion in the solution containing a single ion. For the concentrated solution also, the slowest component of is not found in the spectraldiffusion of all water molecules because a distinct separation between the hydration shell and bulk water in terms of their stretch frequencies does not hold at this high concentration regime. The present first principles results are compared with those of the available experiments and classical simulations.

Financial supports from the Department of Science and Technology (DST), Department of Atomic Energy (DAE), and Council of Scientific and Industrial Research (CSIR), Government of India, and Alexander von Humboldt Foundation are gratefully acknowledged. We are also thankful to Professor S. Keshavamurthy for many useful discussions and help in the frequency calculations.

I. INTRODUCTION

II. DETAILS OF SIMULATIONS AND FREQUENCY CALCULATIONS

III. VIBRATIONAL FREQUENCIES OF WATER IN AND OUTSIDE THE HYDRATION SHELL OF

IV. DYNAMICS OF -WATER HYDROGEN BONDS AND ESCAPE OF WATER FROM HYDRATION SHELL IN THE SOLUTION CONTAINING A SINGLE ION (SYSTEM 1)

V. VIBRATIONAL SPECTRALDIFFUSION OF HYDRATION SHELL WATER IN THE SOLUTION CONTAINING A SINGLE ION (SYSTEM 1)

VI. SPECTRALDIFFUSION AND HYDROGEN BONDDYNAMICS OF ALL WATER MOLECULES: EFFECTS OF ION CONCENTRATION

VII. SUMMARY AND CONCLUSIONS

### Key Topics

- Hydrogen bonding
- 82.0
- Diffusion
- 67.0
- Solution processes
- 45.0
- Molecular dynamics
- 38.0
- Molecular spectra
- 26.0

## Figures

The time dependence of the fluctuating frequency of an OD bond of a water as it escapes from the solvation shell of to which it was hydrogen bonded initially. The time when the escape occurs, i.e., when distance exceeds , is taken to be and the frequency and distance fluctuations are shown for 5 ps before and after the escape event. (a) The time dependence of the frequency of the OD bond and (b) the corresponding distance. The results of this figure and also of Figs. 2–8 are for the relatively dilute solution (system 1).

The time dependence of the fluctuating frequency of an OD bond of a water as it escapes from the solvation shell of to which it was hydrogen bonded initially. The time when the escape occurs, i.e., when distance exceeds , is taken to be and the frequency and distance fluctuations are shown for 5 ps before and after the escape event. (a) The time dependence of the frequency of the OD bond and (b) the corresponding distance. The results of this figure and also of Figs. 2–8 are for the relatively dilute solution (system 1).

(a) The distribution of OD stretch frequencies averaged over all OD modes (dashed), those in the bulk (dashed-dotted) and those in the hydration shell (solid). The dotted curve shows the corresponding distribution for pure water (Ref. 28). The inset shows the frequency distributions of bulk and hydration shell OD bonds each normalized to the maximum value of 1. (b) The frequency distributions for different values of the hydrogen bond angle . The solid, dashed, dotted, and dashed-dotted curves are for OD groups with hydrogen bond angles of , , , and , respectively. The top dashed curve represents averages over all OD groups.

(a) The distribution of OD stretch frequencies averaged over all OD modes (dashed), those in the bulk (dashed-dotted) and those in the hydration shell (solid). The dotted curve shows the corresponding distribution for pure water (Ref. 28). The inset shows the frequency distributions of bulk and hydration shell OD bonds each normalized to the maximum value of 1. (b) The frequency distributions for different values of the hydrogen bond angle . The solid, dashed, dotted, and dashed-dotted curves are for OD groups with hydrogen bond angles of , , , and , respectively. The top dashed curve represents averages over all OD groups.

(a) The distribution of the distance for fixed values of the OD frequency. The black solid, red dashed-dotted, and blue dashed curves are for OD frequency , , and , respectively, where represents the deviation from the average frequency. (b) Joint probability distribution of OD frequency and distance. The contour levels of different fractions of the maximum value are shown in different color codes. The results are for water molecules in the hydration shell.

(a) The distribution of the distance for fixed values of the OD frequency. The black solid, red dashed-dotted, and blue dashed curves are for OD frequency , , and , respectively, where represents the deviation from the average frequency. (b) Joint probability distribution of OD frequency and distance. The contour levels of different fractions of the maximum value are shown in different color codes. The results are for water molecules in the hydration shell.

The power spectra of the velocity time correlation of deuterium atoms of heavy water in the hydration shell (dashed) and in the bulk region (solid) of system 1.

The power spectra of the velocity time correlation of deuterium atoms of heavy water in the hydration shell (dashed) and in the bulk region (solid) of system 1.

(a) The time dependence of the continuous (solid) and intermittent (dashed) correlation functions of -water hydrogen bonds. (b) The escape dynamics of water molecules from the hydration shell of . The solid and dashed curves are for the continuous (with an allowance time of 2 ps) and intermittent residence time correlation functions of water molecules in the solvation shell.

(a) The time dependence of the continuous (solid) and intermittent (dashed) correlation functions of -water hydrogen bonds. (b) The escape dynamics of water molecules from the hydration shell of . The solid and dashed curves are for the continuous (with an allowance time of 2 ps) and intermittent residence time correlation functions of water molecules in the solvation shell.

The time variation in the (a) average frequency shifts of the hole modes after excitations in blue (solid curve) and in red (dashed curve) of the hydration shell OD modes. The corresponding results for the blue excitation after normalization by the initial frequency shift are shown in (b). The smooth gray solid curve in (b) represents the fit by a function of Eq. (13). See the text in Sec. V for definitions of the blue and red excitations that are used in the current work.

The time variation in the (a) average frequency shifts of the hole modes after excitations in blue (solid curve) and in red (dashed curve) of the hydration shell OD modes. The corresponding results for the blue excitation after normalization by the initial frequency shift are shown in (b). The smooth gray solid curve in (b) represents the fit by a function of Eq. (13). See the text in Sec. V for definitions of the blue and red excitations that are used in the current work.

The time variation in the (a) average frequency shifts of the remaining modes after excitations in blue (solid curve) and in red (dashed curve) of the hydration shell OD modes. The corresponding results for the red excitation after normalization by the initial frequency shift are shown in (b). As in the previous figure, the smooth gray solid curve in (b) represents the fit by a function of Eq. (13). The definitions of the blue and red excitations used in the current work are described in Sec. V.

The time variation in the (a) average frequency shifts of the remaining modes after excitations in blue (solid curve) and in red (dashed curve) of the hydration shell OD modes. The corresponding results for the red excitation after normalization by the initial frequency shift are shown in (b). As in the previous figure, the smooth gray solid curve in (b) represents the fit by a function of Eq. (13). The definitions of the blue and red excitations used in the current work are described in Sec. V.

The time variation in the (a) average frequency shifts of the hole modes when all OD modes are considered in the calculations. The corresponding results after normalization by the initial frequency shifts are shown in (b). As before, the solid and dashed curves correspond to excitations in blue and red, respectively. The smooth gray solid curves in (b) represent the fits by a function of Eq. (13). The results of this figure and also of all the previous figures are for system 1 and the definitions of the blue and red excitations in the context of the present work are described in Sec. V.

The time variation in the (a) average frequency shifts of the hole modes when all OD modes are considered in the calculations. The corresponding results after normalization by the initial frequency shifts are shown in (b). As before, the solid and dashed curves correspond to excitations in blue and red, respectively. The smooth gray solid curves in (b) represent the fits by a function of Eq. (13). The results of this figure and also of all the previous figures are for system 1 and the definitions of the blue and red excitations in the context of the present work are described in Sec. V.

The time correlation functions of OD fluctuating frequencies averaged over all the water molecules of the relatively dilute (system 1) and concentrated (system 2) solutions. The lower and upper dashed curves correspond to the simulation results for systems 1 and 2, respectively. The gray solid curves represent the fits by a function as given by Eq. (13).

The time correlation functions of OD fluctuating frequencies averaged over all the water molecules of the relatively dilute (system 1) and concentrated (system 2) solutions. The lower and upper dashed curves correspond to the simulation results for systems 1 and 2, respectively. The gray solid curves represent the fits by a function as given by Eq. (13).

The time dependence of the continuous and intermittent hydrogen bond correlation functions for systems 1 (solid) and 2 (dashed). The results of (a) are for only -water hydrogen bonds and those of (b) are for all the hydrogen bonds present in systems 1 and 2.

The time dependence of the continuous and intermittent hydrogen bond correlation functions for systems 1 (solid) and 2 (dashed). The results of (a) are for only -water hydrogen bonds and those of (b) are for all the hydrogen bonds present in systems 1 and 2.

The time dependence of the fluctuating frequency of an OD bond of a water as it escapes from the solvation shell of a ion of the concentrated solution (system 2). The time when the escape occurs, i.e., when distance exceeds , is taken to be and the frequency and distance fluctuations are shown for 8 ps before and after the escape event. (a) The time dependence of the frequency of the OD bond and (b) the corresponding distance.

The time dependence of the fluctuating frequency of an OD bond of a water as it escapes from the solvation shell of a ion of the concentrated solution (system 2). The time when the escape occurs, i.e., when distance exceeds , is taken to be and the frequency and distance fluctuations are shown for 8 ps before and after the escape event. (a) The time dependence of the frequency of the OD bond and (b) the corresponding distance.

## Tables

The average lifetimes of chloride ion-water and all hydrogen bonds (HBs) of the relatively dilute (system 1) and concentrated (system 2) solutions. Results are also included for the residence times of water in the ion hydration shell. All time constants are expressed in picoseconds.

The average lifetimes of chloride ion-water and all hydrogen bonds (HBs) of the relatively dilute (system 1) and concentrated (system 2) solutions. Results are also included for the residence times of water in the ion hydration shell. All time constants are expressed in picoseconds.

Spectral diffusion data for the hydration shell OD modes of the dilute solution (system 1). The time constants (ps), frequency , and weights of time dependent frequency shifts of hole and remaining modes for blue and red excitations of OD bonds in the hydration shell.

Spectral diffusion data for the hydration shell OD modes of the dilute solution (system 1). The time constants (ps), frequency , and weights of time dependent frequency shifts of hole and remaining modes for blue and red excitations of OD bonds in the hydration shell.

Spectral diffusion data for all OD modes of the relatively dilute (system 1) and concentrated (system 2) solutions. The units of different quantities are as in Table II.

Spectral diffusion data for all OD modes of the relatively dilute (system 1) and concentrated (system 2) solutions. The units of different quantities are as in Table II.

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