Hydration of ${\mathrm{NH}}_4^{+}$ in Water: Bifurcated Hydrogen Bonding Structures and Fast Rotational Dynamics

Understanding the hydration and diffusion of ions in water at the molecular level is a topic of widespread importance. The ammonium ion (${\mathrm{NH}}_4^{+}$) is an exemplar system that has received attention for decades because of its complex hydration structure and relevance in industry. Here we report a study of the hydration and the rotational diffusion of ${\mathrm{NH}}_4^{+}$ in water using ab initio molecular dynamics simulations and quantum Monte Carlo calculations. We find that the hydration structure of ${\mathrm{NH}}_4^{+}$ features bifurcated hydrogen bonds, which leads to a rotational mechanism involving the simultaneous switching of a pair of bifurcated hydrogen bonds. The proposed hydration structure and rotational mechanism are supported by existing experimental measurements, and they also help to rationalize the measured fast rotation of ${\mathrm{NH}}_4^{+}$ in water. This study highlights how subtle changes in the electronic structure of hydrogen bonds impacts the hydration structure, which consequently affects the dynamics of ions and molecules in hydrogen bonded systems.

Figure 1

Hydration structures of ${\mathrm{NH}}_4^{+}$ in water obtained from AIMD. (a) The N-O radial distribution function (solid line) and the corresponding running coordination number (dashed line). The running coordination number $n_{\mathrm{NO}}(R)=4\pi \rho {\int }_0^R{G}_{\mathrm{NO}}(r)r^{2}dr$, where $\rho$ is the density. The first minimum ($r_{\min }$) of ${\mathrm{G}}_{\mathrm{NO}}(\mathrm{r})$ is 3.64 Å, 3.38 Å, 3.55 Å for SCAN, PBE, $\mathrm{PBE}+\mathrm{vdW}$, respectively. The coordination number (CN) is $n(r_{\min })$. The convergence of ${\mathrm{G}}_{\mathrm{NO}}(\mathrm{r})$ is shown in Fig. S2(a). (b) The distribution of the coordination number of the first hydration shell. (c) Calculated $H_N\text{−}\mathrm{O}$ radial distribution functions. The first minimum of $G_{{\mathrm{H}}_N\mathrm{O}}(r)$ is 2.40 Å, 2.45 Å, 2.39 Å for SCAN, PBE, $\mathrm{PBE}+\mathrm{vdW}$, respectively. (d) Average number of ${\mathrm{NH}}_4^{+}$-water hydrogen bonds (HBs) predicted by different exchange correlation (XC) functionals. (e) The difference of the joint distribution in the first hydration shell between the SCAN and the PBE results as a function of $r$ and $\beta$ [defined in the inset of (d)]. Red color implies a larger value from SCAN. The joint distributions are shown in Fig. S3. (f) The $N$-water total distribution function $G_N(r)$. The blue solid line is from the neutron diffraction work of Hewish et al. [43]. The grey bars indicate the positions of the second maximum and the second minimum of the experimental $G_N(r)$.

Figure 2

Benchmarks of different DFT functionals against DMC calculations. (a)–(e) Snapshots of the selected configurations. Atoms in bright colors represent the first hydration shell of ${\mathrm{NH}}_4^{+}$ in water (blue: N; red: O; white: H). (f) Relative energies calculated using different methods at different configurations with CN from four to eight. The relative energy is defined as the energy difference to the energy of the configuration with $\mathrm{CN}=6$. (g) Relative energies of gas phase ${\mathrm{NH}}_4^{+}$ clusters calculated using different methods and plotted against the DMC results. The relative energy is defined as the energy difference to the energy of the configuration with the lowest one. The gas phase ${\mathrm{NH}}_4^{+}$ clusters are randomly selected from the AIMD trajectories, which consist of ${\mathrm{NH}}_4^{+}$ and eight neighboring water molecules.

Figure 3

Rotation mechanism of ${\mathrm{NH}}_4^{+}$ in water. (a) Rotation angle $\theta$ (the angle change with respect to $T=17.0$) as a function of time. Calculated $\theta$ is averaged by the vector ${\overrightarrow{\mathrm{NH}}}_2+{\overrightarrow{\mathrm{NH}}}_3$, ${\overrightarrow{\mathrm{NH}}}_2+{\overrightarrow{\mathrm{NH}}}_4$, and ${\overrightarrow{\mathrm{NH}}}_3+{\overrightarrow{\mathrm{NH}}}_4$. (b)–(c) Snapshots of a typical rotational process. The blue sphere is N, red spheres are O, and white spheres are H. ${\mathrm{H}}_1$ to ${\mathrm{H}}_4$ belongs ${\mathrm{NH}}_4^{+}$. Water molecules $W_1$ to $W_6$ represent the first hydration shell at $T=17.0\mathrm{ps}$. Rotation is associated with bifurcated hydrogen bonds formed with ${\mathrm{H}}_3$ and ${\mathrm{H}}_4$.

Figure 4

Diffusion of ${\mathrm{NH}}_4^{+}$ in water. (a) Rotational diffusion constant $D_R$ from experiments and our simulations at different temperatures [11]. The purple dashed line is a linear fit of the experimental rotational diffusion constant as a function of temperature for H, and the green dashed line is a parallel line to the purple dashed line crossing the only available experimental data for $D$ as a guide to the eye. (b) $D_R$ calculated from our simulations at 363 K as a function of the average number of bifurcated hydrogen bonds. The gray line is a linear fit.