B(OH)₄^- hydration and association in sodium metaborate solutions by X-ray diffraction and empirical potential...

X-ray diffraction is used to study the structure of aqueous sodium metaborate solutions at salt concentrations of 1, 3, and 5 (oversaturated) mol dm^-3. The X-ray structure factors are subjected to empirical potential structure refinement (EPSR) modelling to extract the individual site-site pair correlation functions, the coordination numbers, and the spatial density functions (three-dimensional structure) of ion hydration and association as well as solvent water in the borate solutions. The sodium ion is surrounded on average by (5.4 ± 0.7), (4.6 ± 1.0), and (3.7 ± 1.2) water molecules at 1, 3, and 5 mol dm^-3, respectively, with the Na-O (H₂O) distance of 2.34 Å. The decrease in hydration number of the sodium ion is compensated by direct binding of the oxygen atom of the borate ion, B(OH)₄^-, with the average coordination number of (0.2 ± 0.5), (1.0 ± 0.8), and (2.1 ± 1.3) at the Na-O(B) distance of 2.34 Å to keep the octahedral hydration shell of the sodium ion. The average number of water molecules around the borate ion is (13.9 ± 1.8), (14.2 ± 1.8), and (16.1 ± 2.4) per borate ion with increasing salt concentration with the B-O(H₂O) distance of 3.72 Å. The number of nearest-neighbour water molecules around a central water molecule in a solvent decreases as (4.8 ± 1.2), (3.8 ± 1.1), and (2.8 ± 1.1) with an increase in salt concentration with the O(H₂O)-O(H₂O) distance of 2.79 Å. The Na⁺-B(OH)₄^- ion association is characterized by the Na-O(B) and Na-B pair correlation functions. The Na-B interactions are observed at 3.00 Å as a shoulder and 3.57 Å as a main peak in the site-site pair correlation function, suggesting two occupancy sites of Na⁺ with one for the edge-shared bidentate bonding and the other for the corner-shared monodentate bonding. The total number of Na-B interactions at 3.00 and 3.57 Å is consistent with that of the Na-O(B) interactions. The detailed three-dimensional structure of the ion hydration and association is visualized as a function of salt concentration. The structure and stability of [NaB(OH)₄(H₂O)₆]⁰ clusters are further investigated by DFT calculations, and the most likely structure is proposed and cross-checked.