*4.1. Verification of the Validity of the 4.75-Hydrate Crystal Structure*

The published crystal structures of pentahydrate, 4.75H, and tetrahydrate have very similar lattice constants but different water contents. Moreover, the space group of 4.75H is *P*21, whereas those of the pentahydrate and tetrahydrate forms are both *P*21/*m* [33,35]. The crystal structure of DIC-Na 4.75H contains a pseudo-mirror plane between two corresponding DIC anions. However, the shape of the cluster of Na<sup>+</sup> ions and water molecules is greatly distorted from the mirror symmetry, so it is not suitable to set the mirror plane on this cluster. The published pentahydrate structure was solved in the *P*21/*m* space group by employing a disordered model at the position of Na<sup>+</sup> ions [33]. However, this assignment of the occupancy of disordered water may have been incorrect. The present study revealed that, in one unit cell, four DIC-Na molecules are associated with not 20 but 19 water molecules (4.75 water molecules for one DIC anion) in the hydrated solid state. Notably, the 4.75H structure model reported by Llinàs et al. was validated by a low *R* factor in their structural refinement [34].

Figure 13 shows the Na–O coordination network observed in the crystal structure of DIC-Na 4.75H. Three 6-coordinated sodium ions (Na1, Na2, and Na3) form a waving [Na– O–Na–O] chain structure, while a 5-coordinated sodium ion (Na4, orange) is connected to the chain via water. The lower panel in Figure 13 displays the chain seen from the direction parallel to the pseudo-mirror plane. Although most atoms have a corresponding atom across the pseudo-mirror plane, one water molecule (red) does not. A different Fourier map exhibited a 0.36 eÅ−<sup>3</sup> residual electron peak at the corresponding position, which might indicate a water oxygen. However, refining such a model was difficult because the occupancy factor decreased to less than 8%, and the position was unstable. Thus, we concluded that the residual error is not significant, and the phase contains 4.75 water molecules.

**Figure 13.** Na–O chain observed in the crystal structure of 4.75H. Three 6-coordinated sodium ions (Na1, Na2, and Na3) form a waving [Na–O–Na–O] chain structure. Red water molecules do not have an associated atom across the pseudo-mirror plane (non-paired water molecule). Figures were drawn with crystallographic a, b, c-axis marks.
