The hydration and diffusion of ions and molecules in water is one of the most fundamental processes in nature and in modern technology, having a direct impact on nucleation and crystallization, ion sieving, and aqueous chemical reactions, to name just a few examples. A prototypical example of ion solvation with hydrogen bonding is the ammonium ion (NH₄⁺) in water. This system has a complex and debated hydration structure since 1980s. In simulations the coordination number of NH₄⁺ is around five, whereas experiments indicated that the coordination number is larger. In addition, there is an interesting but unresolved experimental observation that NH₄⁺rotates rapidly in water. In order to correctly simulate the diffusion of ions in water, it is essential to use a theoretical method that is able to reliably describe hydrogen bonds and the energetics involved.

In the study of Guo et al., a new design of simulation is carried out, combining accurate electronic structure described with quantum Monte Carlo (QMC) calculation and ab initio molecular dynamics (AIMD) simulation. QMC benchmarks the interaction of different hydration structure of NH₄⁺ in water, to which density functional theory (DFT) calculations are compared with (Fig. 1). The correct Born-Oppenheimer potential energy surface is selected and AIMD simulations are performed to examine the hydration structure and rotational dynamics. The simulations find NH₄⁺ hydration structure features bifurcated hydrogen bonds, and a linear relation is identified between the number of bifurcated hydrogen bonds and the rotational diffusion constant of NH₄⁺. The theoretical description of the hydration structure and the rotational diffusion constant agree very well with previous experimental measurements (Fig. 2).

Fig. 1 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 NH₄⁺ 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 CN=6. (g) Relative energies of gas phase NH₄⁺ 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 NH₄⁺ clusters are randomly selected from the AIMD trajectories, which consist of and eight neighboring water molecules.

Fig. 2  Comparison of simulations with previous experiments. (a) The N-water total distribution function. The blue solid line is from the neutron diffraction work of Hewish et al. [Chem. Phys. Lett. 84,425 (1981)]. The grey bars indicate the positions of the second maximum and the second minimum of the experimental distribution function. (b) Rotational diffusion constant DR from experiments [JACS 108,1088(1986)] and our simulations at different temperatures. 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.

This study accurately reveals the hydration structure of NH₄⁺ theoretically, rationalizing the measured fast rotation of NH₄⁺ 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. The combined use of QMC and AIMD may help to understand other complex systems in the future. The study “Hydration of NH₄⁺ in Water: Bifurcated Hydrogen Bonding Structures and Fast Rotational Dynamics” is published on Sep. 1, 2020, [Phys. Rev. Lett. 125, 106001 (2020)]. (https://link.aps.org/doi/10.1103/PhysRevLett.125.106001).

PhD student Jianqing Guo of ICQM, School of Physics, Peking University is the first author, and his Supervisors Enge Wang, Limei Xu, and Ji Chen are the corresponding authors. This work is supported by National Key R&D Program of China and the National Science Foundation of China.