# Solvation Structure and Ion–Solvent Hydrogen Bonding of Hydrated Fluoride, Chloride and Bromide—A Comparative QM/MM MD Simulation Study

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Ion–Water Interaction Potentials

#### 2.2. QM/MM MD Simulation Protocol

#### 2.3. Analysis

## 3. Results

## 4. Conclusions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Overview of the 42 ion–oxygen Lennard–Jones parameter combinations employed to identify suitable interaction potentials for the description of aqueous F${}^{-}$, Cl${}^{-}$ and Br${}^{-}$. (

**b**) Maxima of the first shell peak in the ion–oxygen RDF determined for a hydrated ion with charge −1.0e in combination with the 42 Lennard–Jones parameters. The RDFs obtained for F${}^{-}$ (black), Cl${}^{-}$ (red) and Br${}^{-}$ (green) have been selected by comparing the resulting ion–oxygen RDFs and the the coordination number in the first hydration shell to data provided in the literature. The respective parameter sets are highlighted via the black circles and are listed in Table 1. In the case of Cl${}^{-}$ an additional simulation employing an $\epsilon $-value of 1.2552 kJ mol${}^{-1}$ proved necessary.

**Figure 2.**Ion–oxygen (red) and ion–hydrogen (black) radial distribution functions (left column) for aqueous F${}^{-}$ (top row), Cl${}^{-}$ (center row) and Br${}^{-}$ (bottom row) determined from the QM/MM (solid line) and classical (dashed line) MD simulations along with the associated coordination number distributions based on a radial $g\left(r\right)$-cutoff criterion (center column) and the RAD analysis (right column) as obtained from the QM/MM (black) and classical (red) simulation trajectory.

**Figure 3.**First shell ion–oxygen–oxygen three-body correlation function g${}^{3}$ (left) and the associated O–ion–O cosine distribution functions (right) obtained for aqueous F${}^{-}$ (top), Cl${}^{-}$ (center) and Br${}^{-}$ (bottom) from the QM/MM (black) and classical (red) MD simulations. The absolute values for the O–ion–O angles follow a non-linear trend and are shown on the secondary x-axis.

**Figure 4.**Oxygen-hydrogen radial distribution function of water molecules in the first solvation shell of aqueous F${}^{-}$ (black), Cl${}^{-}$ (red) and Br${}^{-}$ (green) separated into contributions of the H-atoms in proximal (H${}_{1}$, top left) and distal (H${}_{2}$, bottom left) position with respect to the solute along with the associated ion⋯H${}_{1}$–O cosine distribution function (bottom right). The screenshot of aqueous F${}^{-}$ displays the assignment of H${}_{1}$ and H${}_{2}$ for an exemplary first shell water molecule, that is re-evaluated in every simulation step.

**Figure 5.**Two-dimensional histogram correlating the ion⋯H${}_{1}$–O and ion⋯H${}_{2}$–O angles registered for each first shell ligand of Br${}^{-}$ obtained from the QM/MM MD simulation.

**Table 1.**Lennard–Jones potential parameters $\epsilon ({\mathrm{X}}^{-}$–$\mathrm{O})$ in kJ mol${}^{-1}$ and $\sigma ({\mathrm{X}}^{-}$–$\mathrm{O})$ in Å of the ion–oxygen potential describing the interaction between the QM solute and water molecules in the MM zone. The respective minimum distance ${r}_{\mathrm{m}}({\mathrm{X}}^{-}$–$\mathrm{O})$ in Å is listed as well (see also Figure 1).

$\mathit{\epsilon}({\mathbf{X}}^{-}$–$\mathbf{O})$ | $\mathit{\sigma}({\mathbf{X}}^{-}$–$\mathbf{O})$ | ${\mathit{r}}_{\mathbf{m}}({\mathbf{X}}^{-}$–$\mathbf{O})$ | |
---|---|---|---|

F${}^{-}$ | 0.6276 | 3.1181 | 3.5 |

Cl${}^{-}$ | 1.2552 | 3.5636 | 4.0 |

Br${}^{-}$ | 1.8828 | 3.5636 | 4.0 |

**Table 2.**Maximum, avarage and minimum distances ${r}_{\mathrm{M}}^{1}$, $\langle {r}_{\mathrm{M}}^{1}\rangle $ and ${r}_{\mathrm{m}}^{1}$ of the first solvation shell in the ion–O RDF in Å, average first shell coordination number determined via a g(r)-based cutoff CN${}_{\mathrm{GC}}^{1}$ as well as the relative angular distance approach CN${}_{\mathrm{RAD}}^{1}$, first shell mean ligand residence time ${\tau}_{1}$ in ps, number of registered ligand exchange events ${N}_{0.5}^{1}$ (${t}^{*}\ge 0.5$ ps) and associated rate coefficient R${}_{\mathrm{ex}}^{1}$ obtained for aqueous F${}^{-}$, Cl${}^{-}$ and Br${}^{-}$ via classical (MM) and RIMP2-based QM/MM MD simulations in comparison to data reported in the literature.

${\mathit{r}}_{\mathbf{M}}^{1}$ | $\langle {\mathit{r}}_{\mathbf{M}}^{1}\rangle $ | ${\mathit{r}}_{\mathbf{m}}^{1}$ | CN${}_{\mathbf{GC}}^{1}$ | CN${}_{\mathbf{RAD}}^{1}$ | ${\mathit{\tau}}_{1}$ | ${\mathit{N}}_{0.5}^{1}$ | R${}_{\mathbf{ex}}^{1}$ | |||
---|---|---|---|---|---|---|---|---|---|---|

F${}^{-}$ | MM MD | 2.59 | 2.63 | 3.25 | 6.2 | 6.3 | 15.4 | 10 | 5.4 | this work |

RIMP2/MM MD | 2.46 | 2.68 | 3.36 | 4.9 | 5.2 | 1.1 | 115 | 5.2 | this work | |

MM MD | 2.53 | 5.8 ± 0.1 | Ref. [73] | |||||||

HF/MM MD | 2.68 | 4.6 ± 0.2 | Ref. [73] | |||||||

BLYP CPMD | 2.66 | 5.1 | Ref. [75] | |||||||

BLYP CPMD | 2.7 | 3.4 | Ref. [77] | |||||||

NDIS KF/D${}_{2}$0 1.2:100 | 2.54 | 3.27 | 6.9 | Ref. [81] | ||||||

Cl${}^{-}$ | MM MD | 3.26 | 3.35 | 3.93 | 7.6 | 7.8 | 4.2 | 46 | 6.7 | this work |

RIMP2/MM MD | 3.23 | 3.48 | 4.16 | 8.1 | 7.5 | 1.6 | 178 | 4.5 | this work | |

MM MD | 3.15 | 5.9 ± 0.1 | Ref. [73] | |||||||

HF/MM MD | 3.24 | 5.9 ± 0.1 | Ref. [73] | |||||||

HF/MM MD | 3.25 | 3.9 | 6.8 | 2.0 | 4.6 | Ref. [74] | ||||

PBE-D3 CPMD | 3.14 | 3.78 | 6.0 | Ref. [79] | ||||||

PBE0-D3 CPMD | 3.17 | 3.85 | 6.1 | Ref. [79] | ||||||

SCAN CPMD | 3.17 | 3.85 | 6.7 | Ref. [79] | ||||||

PBE CPMD | 3.11 | 3.64 | 5.5 ± 0.2 | Ref. [78] | ||||||

PBE+TS-vdW CPMD | 3.14 | 3.78 | 6.3 ± 0.9 | Ref. [78] | ||||||

PBE0 CPMD | 3.14 | 3.72 | 5.8 ± 0.7 | Ref. [78] | ||||||

PBE0+TS-vdW CPMD | 3.16 | 3.73 | 6.3 ± 0.8 | Ref. [78] | ||||||

EXAFS NaCl 40 mM | 2.91/3.11 | 4+3 | Ref. [82] | |||||||

NDIS KCl/D${}_{2}$O 1.2:100 | 3.14 | 3.78 | 7.1 | Ref. [81] | ||||||

Br${}^{-}$ | MM MD | 3.33 | 3.45 | 4.05 | 8.1 | 8.1 | 3.0 | 313 | 4.7 | this work |

RIMP2/MM MD | 3.31 | 3.68 | 4.30 | 9.1 | 7.4 | 0.9 | 390 | 2.9 | this work | |

MM MD | 3.27 | 3.9 | 7.6 ± 0.5 | 2.6 | Ref. [76] | |||||

BLYP CPMD | 3.33 | 3.9 | 6.5 ± 0.3 | 5.7 | Ref. [76] | |||||

XAFS/MM MC YBr${}_{3}$ 0.3M | 3.44 ± 0.07 | 6 ± 0.5 | Ref. [80] | |||||||

XAFS RbBr 0.2M | 3.35 | 7.1 ± 1.5 | Ref. [83] | |||||||

XAFS RbBr 1.5M | 3.36 | 7.2 ± 0.4 | Ref. [83] | |||||||

XAFS RbCl 0.5 mM | 3.26 | 10 | Ref. [82] | |||||||

NDIS KBr/D${}_{2}$O 1.2/100 | 3.32 | 3.90 | 6.7 | Ref. [81] |

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**MDPI and ACS Style**

Hofer, T.S.
Solvation Structure and Ion–Solvent Hydrogen Bonding of Hydrated Fluoride, Chloride and Bromide—A Comparative QM/MM MD Simulation Study. *Liquids* **2022**, *2*, 445-464.
https://doi.org/10.3390/liquids2040026

**AMA Style**

Hofer TS.
Solvation Structure and Ion–Solvent Hydrogen Bonding of Hydrated Fluoride, Chloride and Bromide—A Comparative QM/MM MD Simulation Study. *Liquids*. 2022; 2(4):445-464.
https://doi.org/10.3390/liquids2040026

**Chicago/Turabian Style**

Hofer, Thomas S.
2022. "Solvation Structure and Ion–Solvent Hydrogen Bonding of Hydrated Fluoride, Chloride and Bromide—A Comparative QM/MM MD Simulation Study" *Liquids* 2, no. 4: 445-464.
https://doi.org/10.3390/liquids2040026