Evaluation of Point Group Symmetry in Lanthanide(III) Complexes – a New Implementation of the Continuous Symmetry Measure with Autonomous Assignment of the Principal Axis

Abstract

The structure of molecular systems dictates the physical properties, and symmetry is determining for all electronic properties. This makes group theory a powerful tool in quantum mechanics, when computing molecular properties. For inorganic compounds, the coordination geometry has been estimated as idealized polyhedra of high symmetry, which through ligand field theory provides predictive capabilities. However, real samples rarely have ideal symmetry, and even though continuous symmetry measures can be used to evaluate deviation form ideal symmetry, this often fails for lanthanide(III) complexes with high coordination numbers and no obvious principal axis. In lanthanide complexes, the unique electronic structures and the associated properties are intricately tied to the symmetry around the lanthanide center. Robust methodologies to evaluate and estimate point group symmetry is therefore instrumental for building structure property relationships. Here, we have demonstrated an algorithmic approach that determines the principal axis, and computes a deviation from ideal symmetry. This approach is based on the continuous symmetry measures and evaluates deviations from ideal symmetry for each symmetry operation in all relevant point groups. To demonstrate the methodology we have investigated the structure and symmetry of 8 and 9 coordinated lanthanide(III) aqua complexes, and correlated the luminescence from 3 europium(III) crystals to their actual symmetry. To document the methodology the approach has been tested on 26 molecules with different symmetry. It was concluded that the method is robust and fully autonomous.