We Are Never Ever Getting (back to) Ideal Symmetry: Structure and Luminescence in a Ten-Coordinated Europium(III) Sulfate Crystal

Our theoretical treatment of electronic structure in coordination complexes often rests on assumptions of symmetry. Experiments rarely provide fully symmetric systems to study. In solution, fluctuation in solvation, variations in conformation, and even changes in constitution occur and complicates the picture. In crystals, lattice distortion, energy transfer, and phonon quenching is in play, but we are able to have distinct symmetries. Yet the question remains: How is the real symmetry in a crystal compared to ideal symmetries? Moreover, at what level of detail do we need to study a system to determine, if the electronic structure behaves as if it has ideal symmetry? Here, we have revisited the Continues Shape Measurement (CShM) approach developed by Ruiz-Martínez and Alvarez to evaluate the structure of ten-coordinated europium(III) ions in a K5Na[Eu2(SO4)6] structure. By comparing the result of the symmetry deviation analysis to luminescence data, we are able to show the effect of small deviations from ideal symmetry. We suggest using a symmetry deviation value, σideal, determined by using our updated approach to Continues Shape Measurements, where we also align the structure via our AlignIt code. AlignIt includes normalization and relative orientation in the symmetry comparison, and by combining the calculated values with the experimentally determined energy level splitting, we were able create the first point on a scale that can show how close to ideal an experimental structure actually is.