^{1}, B. M. Auer

^{1}and J. L. Skinner

^{1,a)}

### Abstract

We study theoretically the steady-state and ultrafast vibrational spectroscopy, in the OD-stretch region, of dilute HOD in aqueous solutions of sodium bromide. Based on electronic-structure calculations on clusters containing salt ions and water, we develop new spectroscopic maps that enable us to undertake this study. We calculate OD-stretch absorption line shapes as a function of salt concentration, finding good agreement with experiment. We provide molecular-level understandings of the monotonic (as a function of concentration) blueshift, and nonmonotonic line width. We also calculate the frequency time-correlation function, as measured by spectraldiffusion experiments. Here again we obtain good agreement with experiment, finding that at the highest salt concentration spectraldiffusion slows down by a factor of 3 or 4 (compared to pure water). For longer times than can be accessed experimentally, we find that spectraldiffusion is very complicated, with processes occurring on multiple time scales. We argue that from 6 to 40 ps, relaxation involves anionic solvation shell rearrangements. Finally, we consider our findings within the general context of the Hofmeister series, concluding that this series must reflect only local ordering of water molecules.

The authors thank Piotr Pieniazek and Tom Record for helpful discussions. This research was supported by the National Science Foundation, through Grant No. CHE-0750307, and by the Department of Energy, through Grant No. DE-FG02-09ER16110.

I. INTRODUCTION

II. SIMULATION MODELS

III. THEORETICAL SPECTROSCOPY METHODOLOGY

A. OD-stretch “maps”

B. Salt maps: Total field

C. Salt maps: Effective field

IV. VIBRATIONAL SPECTROSCOPY RESULTS

A. Line shapes in NaBr solution

B. Spectraldiffusion

V. DISCUSSION

A. Concentration-dependent line shapes: Non-Condon effects and motional narrowing

B. Concentration-dependent line shapes: Molecular interpretation

C. Spectraldiffusion

VI. HOFMEISTER EFFECTS

VII. CONCLUSION

### Key Topics

- Diffusion
- 44.0
- Blue shift
- 19.0
- Sodium
- 18.0
- Hydrogen bonding
- 17.0
- Molecular spectra
- 17.0

## Figures

Theoretical ( is or ) radial distribution functions.

Theoretical ( is or ) radial distribution functions.

Theoretical (Th) and experimental (Exp) (Ref. 71) second-order orientational time-correlation functions for water molecules in pure water and aqueous NaBr solutions. is the second-order Legendre polynomial; is the unit vector along the OH bond (OD bond of the dilute HOD molecules in experiment).

Theoretical (Th) and experimental (Exp) (Ref. 71) second-order orientational time-correlation functions for water molecules in pure water and aqueous NaBr solutions. is the second-order Legendre polynomial; is the unit vector along the OH bond (OD bond of the dilute HOD molecules in experiment).

Calculated OD-stretch frequencies for clusters and point charges of surrounding molecules, vs the electric field on the D, projected along the OD vector. 99 randomly chosen data points (out of 999) are shown in this figure. The frequency map is the red curve. The rms deviation between the map and data points is .

Calculated OD-stretch frequencies for clusters and point charges of surrounding molecules, vs the electric field on the D, projected along the OD vector. 99 randomly chosen data points (out of 999) are shown in this figure. The frequency map is the red curve. The rms deviation between the map and data points is .

Experimental (Ref. 71) (upper panel) and theoretical (two lower panels) line shapes for the OD stretch of HOD in pure water (in black), concentrated NaCl (in red) and NaBr (in green) solutions. The background-subtracted FTIR spectrum of the OD stretch in concentrated NaCl (5.4 M NaCl in 5% ) was taken by the authors. The experimental for the OD stretch of HOD in pure water is used for the line shape calculations for pure water; the experimental for the concentrated NaBr solution is used in the calculations for both concentrated NaCl and NaBr solutions (Ref. 71). The middle panel shows theoretical curves calculated using , and the lower panel shows theoretical curves calculated using . The theoretical black curves for pure water in the two lower panels are the same.

Experimental (Ref. 71) (upper panel) and theoretical (two lower panels) line shapes for the OD stretch of HOD in pure water (in black), concentrated NaCl (in red) and NaBr (in green) solutions. The background-subtracted FTIR spectrum of the OD stretch in concentrated NaCl (5.4 M NaCl in 5% ) was taken by the authors. The experimental for the OD stretch of HOD in pure water is used for the line shape calculations for pure water; the experimental for the concentrated NaBr solution is used in the calculations for both concentrated NaCl and NaBr solutions (Ref. 71). The middle panel shows theoretical curves calculated using , and the lower panel shows theoretical curves calculated using . The theoretical black curves for pure water in the two lower panels are the same.

Calculated OD-stretch frequencies and dipole derivatives for clusters sampled from a simulation of concentrated NaCl solution, vs effective electric field on the D atom, projected along the OD vector. The red curves are the maps.

Calculated OD-stretch frequencies and dipole derivatives for clusters sampled from a simulation of concentrated NaCl solution, vs effective electric field on the D atom, projected along the OD vector. The red curves are the maps.

Experimental (Ref. 71) and theoretical line shapes for the OD stretch of HOD in pure water and aqueous NaBr solutions. The experimental ’s are used in the line shape calculations (Ref. 71)

Experimental (Ref. 71) and theoretical line shapes for the OD stretch of HOD in pure water and aqueous NaBr solutions. The experimental ’s are used in the line shape calculations (Ref. 71)

Theoretical and experimental (Ref. 71) normalized FTCFs for the OD stretch of HOD in pure water and aqueous NaBr solutions.

Theoretical and experimental (Ref. 71) normalized FTCFs for the OD stretch of HOD in pure water and aqueous NaBr solutions.

Calculated frequency distributions, spectral densities and line shapes for the OD stretch of HOD in pure water and 5.9 M NaBr solution.

Calculated frequency distributions, spectral densities and line shapes for the OD stretch of HOD in pure water and 5.9 M NaBr solution.

Distributions of OD-stretch frequencies (top panel) and spectral densities (bottom panel) for different hydrogen-bonding classes for the OD stretch of HOD in pure water and aqueous NaBr solutions. Dashed lines are for class W, dotted lines for class A, and solid lines for class F. Black is for pure water, red is for 1.8 M, green is for 3.1 M, and blue is for 5.9 M.

Distributions of OD-stretch frequencies (top panel) and spectral densities (bottom panel) for different hydrogen-bonding classes for the OD stretch of HOD in pure water and aqueous NaBr solutions. Dashed lines are for class W, dotted lines for class A, and solid lines for class F. Black is for pure water, red is for 1.8 M, green is for 3.1 M, and blue is for 5.9 M.

Theoretical normalized TCFs for pure water and aqueous NaBr solutions, up to 10 ps. Solid lines are the frequency TCFs, and dashed lines are the NTCFs (see text). Black is for pure water, red is for 1.8 M, green is for 3.1 M, and blue is for 5.9 M.

Theoretical normalized TCFs for pure water and aqueous NaBr solutions, up to 10 ps. Solid lines are the frequency TCFs, and dashed lines are the NTCFs (see text). Black is for pure water, red is for 1.8 M, green is for 3.1 M, and blue is for 5.9 M.

Theoretical normalized TCFs for pure water and aqueous NaBr solutions, up to 40 ps. Solid lines are the FTCFs (black is pure water, red is for 1.8 M, green is for 3.1 M, and blue is for 5.9 M). The dashed, dot-dash, and dotted red lines, are for the D, , and NTCFs, respectively, for the 1.8 M solution.

Theoretical normalized TCFs for pure water and aqueous NaBr solutions, up to 40 ps. Solid lines are the FTCFs (black is pure water, red is for 1.8 M, green is for 3.1 M, and blue is for 5.9 M). The dashed, dot-dash, and dotted red lines, are for the D, , and NTCFs, respectively, for the 1.8 M solution.

Theoretical spectral densities for different solvation shells, normalized to peak height.

Theoretical spectral densities for different solvation shells, normalized to peak height.

Relaxation to equilibrium of the average OD-stretch frequencies for different subensembles of water molecules, based on ionic solvation shells.

Relaxation to equilibrium of the average OD-stretch frequencies for different subensembles of water molecules, based on ionic solvation shells.

Theoretical rotational anisotropy TCFs for different solvation shells.

Theoretical rotational anisotropy TCFs for different solvation shells.

## Tables

Overview of the MD simulations. and are the number of water molecules and ion pairs, respectively. Box size is calculated using the experimental densities.^{120,121}

Overview of the MD simulations. and are the number of water molecules and ion pairs, respectively. Box size is calculated using the experimental densities.^{120,121}

Potential parameters used in the MD simulations. The Lorentz–Berthelot combination rules are used to determine the intermolecular Lennard-Jones interactions between different atom types.^{122}

Potential parameters used in the MD simulations. The Lorentz–Berthelot combination rules are used to determine the intermolecular Lennard-Jones interactions between different atom types.^{122}

Relationships for the transition frequency (in ), dipole derivative (normalized by the gas-phase value ), and 1–0 matrix element of the OD-stretching coordinate (in Å). is the electric field (in atomic units) on the D atom projected along the OD bond. The correlation coefficient and rms error of each fit are listed.

Relationships for the transition frequency (in ), dipole derivative (normalized by the gas-phase value ), and 1–0 matrix element of the OD-stretching coordinate (in Å). is the electric field (in atomic units) on the D atom projected along the OD bond. The correlation coefficient and rms error of each fit are listed.

Summary of theoretical (Th), using and approaches, and experimental (Exp) line shapes for pure water, and concentrated aqueous NaCl and NaBr solutions. Peak position, shift in peak position from pure water, and FWHM are all in .

Summary of theoretical (Th), using and approaches, and experimental (Exp) line shapes for pure water, and concentrated aqueous NaCl and NaBr solutions. Peak position, shift in peak position from pure water, and FWHM are all in .

Summary of theoretical (Th) and experimental (Exp) (Ref. 71) line shapes for pure water and aqueous NaBr solutions of various concentrations. Peak position, shift in peak position from pure water, and FWHM are all in .

Summary of theoretical (Th) and experimental (Exp) (Ref. 71) line shapes for pure water and aqueous NaBr solutions of various concentrations. Peak position, shift in peak position from pure water, and FWHM are all in .

Summary of calculated frequency distributions and spectral densities of the OD stretch of HOD in pure water and aqueous NaBr solutions. Both peak position and FWHM are in .

Summary of calculated frequency distributions and spectral densities of the OD stretch of HOD in pure water and aqueous NaBr solutions. Both peak position and FWHM are in .

Summary of the populations, , of the three hydrogen-bonding classes (F, W, A) for the D atom of HOD in pure water and aqueous NaBr solutions.

Summary of the populations, , of the three hydrogen-bonding classes (F, W, A) for the D atom of HOD in pure water and aqueous NaBr solutions.

Article metrics loading...

Full text loading...

Commenting has been disabled for this content