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The aqueous sodium-ion battery is a promising alternative to the well-known lithium-ion battery owing to the large abundance of sodium ion resources. Although it is safer than the lithium-ion battery, the voltage window of the sodium-ion battery is narrower than that of the lithium-ion battery, thus limiting its practical implementation. Therefore, a highly concentrated electrolyte is required to address this issue. In the present work, the effect of the salt concentration on the transport properties of water molecules is investigated via theoretical analyses at the quantum mechanical level. A molecular dynamics simulation at the quantum mechanical level revealed that as the salt concentration increases, the ion-water interactions became stronger, leading to a lower diffusivity and a lower electronic band gap. These imply that the superconcentrated aqueous-based electrolytes have high potentials for the sodium-ion battery applications.

The density-functional tight-binding (DFTB) method is one of the useful quantum chemical methods, which provides a good balance between accuracy and computational efficiency. In this account, we reviewed the basis of the DFTB method, the linear-scaling divide-and-conquer (DC) technique, as well as the parameterization process. We also provide some refinement, modifications, and extension of the existing parameters that can be applicable for lithium-ion battery systems. The diffusion constants of common electrolyte molecules and LiTFSA salt in solution have been estimated using DC-DFTB molecular dynamics simulation with our new parameters. The resulting diffusion constants have good agreement to the experimental diffusion constants.

The diffusion of the hydroxide ion in bulk water was examined by linear-scaling divide-and-conquer density-functional tight-binding molecular dynamics (DC-DFTB-MD) simulations using three different-sized unit cells that contained 522, 1050, and 4999 water molecules as well as one hydroxide ion. The repulsive potential for the oxygen-oxygen pair was improved by iterative Boltzmann inversion, which adjusted the radial distribution function of DFTB-MD simulations to that of the reference density functional theory-MD one. The calculated diffusion coefficients and the Arrhenius diffusion barrier were in good agreement with experimental results. The results of the hydroxide ion coordination number distribution and potential of mean force analyses supported a dynamical hypercoordination diffusion mechanism.

The process of proton diffusion in liquid water was investigated using molecular dynamics (MD) simulations, and the total energy and atomic forces were evaluated by the divide-and-conquer-type density-functional tight-binding (DC-DFTB) method. The effectiveness of this approach was confirmed by comparing the computational time of water clusters with conventional treatments. The unit cell employed herein, which contained 523 water molecules and 1 excess proton, was moderately large in comparison with those used in previous studies. The reasonable accuracy obtained by using this unit cell was confirmed by examining the temperature fluctuation. The diffusion coefficients for the vehicular and Grotthuss processes were accurately reproduced by the DC-DFTB-MD simulations with the unit cell containing 523 water molecules. Furthermore, the energy barriers were evaluated from the temperature dependence of the diffusion coefficient for each process. The calculated barrier for Grotthuss diffusion was in good agreement with the experimental value.