Understanding metal-ligand interactions in coordination polymers using Hirshfeld surface analysis

Properties related to the size and shape of Hirshfeld surfaces provide insight into the nature and strength of interactions among the building blocks of molecular crystals. In this work, we demonstrate that functions derived from the curvatures of the surface at a point, namely, shape index (S) and curvedness (C), as well as the distances from the surface to the nearest external (d_e) and internal (d_i) nuclei, can be used to help understand metal-ligand interactions in coordination polymers. The crystal structure of catena-poly[[[(1,10-phenanthroline-κ²N,N')copper(II)]-μ-4-nitrophthalato-κ²O¹:O²] trihydrate], {[Cu(C₈H₃NO₆)(C₁₂H₈N₂)]·3H₂O}_n, described here for the first time, was used as a prototypical system for our analysis. Decomposition of the coordination polymer into its metal centre and ligand molecules followed by joint analysis of the Hirshfeld surfaces generated for each part unveil qualitative and semi-quantitative information that cannot be easily obtained either from conventional crystal packing analysis or from Hirshfeld surface analysis of the entire polymeric units. The shape index function S is particularly sensitive to the coordination details and its mapping on the surface of the metallic centre is highly dependent on the nature of the ligand and the coordination bond distance. Correlations are established between the shape of the Hirshfeld surface of the metal and the geometry of the metal-ligand contacts in the crystals. This could be applied not only to estimate limiting coordination distances in metal-organic compounds, but also to help establish structure-property relationships potentially useful for the crystal engineering of such materials.