Effects of crystal lattice and counterions on the geometries of metal complexes: Hexaaquomagnesium cation as a case study

Abstract We address how diverse are crystallographic geometries of several compounds of the same metal complex cation, and also how they contrast from those resulting from quantum chemical calculations on isolated molecules. In a crystal, besides the desired molecule or molecular ion of interest, there are usually present co-crystallized molecules and/or counterions, that, together with the crystal lattice, perturb its geometry. In order to examine the nature and intensity of each of these effects, we present a novel methodology to separate and quantify them. Accordingly, we compared the crystallographic geometries of the hexaaquomagnesium cation in 45 different compounds, each one with different counter ions and other co-crystallized molecules. We show that the resulting perturbations of the counterions on the geometry of the complex behave as pseudorandom around a mean, and are subject to suitable probability distributions. Results indicate that the crystal lattice effect seems to compress the hexaaquomagnesium complex cation by a magnitude which we estimate to be 0.047 A in its distances, and 6.6% in its volume. This crystal lattice effect is then superimposed to the effect of the counter ions and other molecules, which provokes a further ±0.035 A variation on the geometries of the compounds. Consequently, perturbations of counterions and the lattice effect, together, amount to a statistical difference of ≈0.05 A for distances, and ≈5° for the angles. As such, only within these boundaries, may quantum chemical calculations on isolated complexes be compared to crystallographic results.