Golden ratio and bond-valence parameters of hydrogen bonds of hydrated borates

A quantitative understanding of microscopic characteristics of hydrogen bonds in various compounds is quite important for the deep study of structure-property relationships of functional crystals. The present work skillfully applies the well-known Golden ratio in the quantitative analysis of bond lengths of O–H⋯O hydrogen bonds. On the basis of the bond valence sum model, the bond-valence parameters d0 of the stronger O–H and weaker H⋯O bonds are respectively calculated from the bond length data of hydrogen bonds in hydrated borates, which are available in the Inorganic Crystal Structure Database (2004). Two linear functions directly relating d0 value to the respective bond length are recommended here, which provide us a powerful tool to structurally design new types of hydrated borate crystals by employing hydrogen bonds in the crystallographic frame.