Hydrogen bonding and structural complexity in the Cu5(PO4)2(OH)4 polymorphs (pseudomalachite,ludjibaite, reichenbachite): combined experimental and theoretical study

Hydrogen bonding in the Cu₅(PO₄)₂(OH)₄ polymorphs pseudomalachite, ludjibaite and reichenbachite has been studied by low-temperature single-crystal X-ray diffraction (XRD; pseudomalachite) and solid-state density functional theory (DFT; pseudomalachite, ludjibaite, reichenbachite) calculations. Pseudomalachite at 100 K is monoclinic, P2₁/c, a = 4.4436(4), b = 5.7320(5), c = 16.9300(15) Å, β = 91.008(8)°, V = 431.15(7) ų and Z = 2. The structure has been refined to R ₁ = 0.025 for 1383 unique observed reflections with |F _o| ≥ 4σ_F. DFT calculations were done with the CRYSTAL14 software package. For pseudomalachite, the difference between the calculated and experimental H sites does not exceed 0.152 Å. Structural configurations around hydroxyl groups in all three polymorphs show many similarities. Each OH5 group is involved in a three-center (bifurcated) hydrogen bond with the H···A distances in the range of 2.141–2.460 Å and the D–H···A angles in the range of 122.41°–139.30°, whereas each OH6 group forms a four-center (trifurcated) bond (H···A = 2.093–2.593 Å; D–H···A = 122.79°–137.71°). The crystal structures of the Cu₅(PO₄)₂(OH)₄ polymorphs are based on three-dimensional frameworks of Cu and P polyhedra. The copper-centered octahedra share edges to form two-dimensional layers parallel to (100) in all three structures. The layers have square voids above and beneath PO₄ tetrahedra that link adjacent layers by sharing O atoms with two CuO₆ octahedra each. From the topological point of view, none of the polymorphs can be obtained from another by a displacive transformation, and therefore pseudomalachite, ludjibaite and reichenbachite can be viewed as combinatorial polymorphs. According to information-based structural complexity considerations, the three phases are very similar in their configurational entropies and preferential crystallization of one phase over another cannot be entropy driven and is probably governed by other mechanisms that may involve such factors as structures of prenucleation clusters, chemical admixtures, etc.