Complex interplay of interatomic bonding in a multi-component pyrophosphate crystal: K ₂Mg (H ₂P ₂O ₇) ₂·2H ₂O

Abstract

The electronic structure and interatomic bonding of pyrophosphate crystal K ₂Mg (H ₂P ₂O ₇) ₂·2H ₂O are investigated for the first time showing complex interplay of different types of bindings. The existing structure from single-crystal X-ray diffraction is not sufficiently refined, resulting in unrealistic short O─H bonds which is rectified by high-precision density functional theory (DFT) calculation. K ₂Mg (H ₂P ₂O ₇) ₂·2H ₂O has a direct gap of 5.22 eV and a small electron effective mass of 0.14 m _e. Detailed bond analysis between every pair of atoms reveals the complexity of various covalent, ionic, hydrogen bonding and bridging bonding and their sensitive dependence on structural differences. The K--O bonds are much weaker than Mg--O bonds and contributions from the hydrogen bonds are non-negligible. Quantitative analysis of internal cohesion in terms of total bond order density and partial bond order density divulges the relative importance of different types of bonding. The calculated optical absorptions show multiple peaks and a sharp Plasmon peak at 23 eV and a refractive index of 1.44. The elastic and mechanical properties show features unique to this low-symmetry crystal. Phonon calculation gives vibrational frequencies in agreement with reported Raman spectrum. These results provide new insights indicating that acidic pyrophosphates could have a variety of unrealized applications in advanced technology.