## 1 Introduction
The treatment of phosphate rocks gives the following marketed products: phosphoric acid (H3 PO4), single superphosphate (SSP), monoammonium phosphate (MAP), diammonium phosphate (DAP), fertilizer (NPK), and triple superphosphate (TSP). The strategy used by the OCP group for the distribution of phosphate (P2O5) was based on the three sectors, fertilizers (85% by volume of P2O5), animal nutrition (8%) as well as a wide variety of industrial uses (7%), including laundry detergents and food products such as sodas, etc. Another use is that the purified phosphoric acid is used as salts for the food industry such as yeast, cheese, preservation of meat and fish, treatment of drinking water, etc. Other industrial uses include metal processing, textiles, cements etc. Given the complex structures of phosphates and their ubiquitous presence, a fundamental understanding of their structures and properties is a subject of paramount importance. However, such studies are lagging far behind other inorganic materials such as silicates. High-level quantum mechanical calculations always play a role in such cases in providing the information on electronic structure, molecular interaction, and reactivity. They have implications on physical properties including vibrational, optical, and mechanical properties. Such studies on phosphate crystals can facilitate identifying the potential usage of these complex materials. Several such investigations have appeared in the literature in recent years. [PERSON] et al. [PERSON] et al. (2016) investigated the behavior of phosphate species using ab initio molecular dynamics. Application of pyrophosphate for water oxidation catalysts was investigated by [PERSON] et al. [PERSON] et al. (2017) using both experimental and computational methods. Other density functional theory (DFT)-based calculations for different kinds of pyrophosphates has been done by [PERSON] et al. [PERSON] et al. (2018); [PERSON] et al. [PERSON] et al. (2019), and [PERSON] et al. [PERSON] et al. (2019). In this work, we present the results of calculations of five pyrophosphate crystals including the one that was published a year ago on K\({}_{2}\)Mg(H\({}_{2}\)P\({}_{2}\)O)\({}_{7}\)\(\cdot\)2H\({}_{2}\)O [PERSON] et al. (2019). The only difference in the structural components of these five crystals are the alkali metal K or NH\({}_{4}\) and metallic elements such as Mg, Zn, or Cu. They have the same pyrophosphate group H\({}_{2}\)P\({}_{2}\)O\({}_{7}\) and same number of H\({}_{2}\)O molecules. As expected, the electronic structure and bonding in these five crystals are very similar, but to our great surprise, they show some considerable variations. The presence of narrow metallic bands at the top of valence band (VB) in the two Cu-containing pyrophosphates is identified. Also, the mechanical properties with the parameter gauging brittleness and ductility can differ by as much as 50%. Since the mechanical properties of all materials ultimately depends on the strengths of interatomic bonding, what could be the atomistic origin of such unusual behavior for the pyrophosphate crystals? With the detailed and accurate calculations of the electronic structure and mechanical and optical properties, we offer some tangible insights that defies the conventional wisdom. In the next two sections, we briefly describe the crystal structures and computational methods used in the calculation. The main results are presented and discussed in Section 4. The paper ends with a summary and some conclusions.